What lf I Have frouble with Word Problems? - Hackensack ...

M@MtuThe Student Handbook is the additional skill and reference material found at theend of the text. This Handbook can help you answer these questions.

llllhat lf I ileed Problem-Solving Practice?You have probably used several differentproblem-solving strategies in previous mathcourses. The Problem-Solving Handbooksection provides example and problems forrefreshing your skills at using various strategies.

What lf I ]{eed More Practke?You, or your teacheLnay decide that workingthrough some additional problems would behelpful. The Extra Practice section provides theseproblems for each lesson so you have ampleopportunity to practice new skills.

What lf I Have frouble with Word Problems?The Mixed Problem Solving portion of the bookprovides additional word problems that use theskills presented in each lesson. These problemsgive you real-world sifuations where math canbe applied.

What if I Forget What I Learned last Year?Use the Concepts and Skills Bank section torefresh your memory about things you havelearned in other math classes. Here's a list of thetopics covered in your book.

l. Converting Units of MeasureFactors and MultiplesPrime FactorizationMeasuring AnglesVenn DiagramsMisleading Graphs

What lf I Need to Review a Contept?The Key Concepts section lists all of theimportant concepts that were highlighted in yourtext along with the pages where they appear.

What lI I Need to Check a Homework Answer?The answers to odd-numbered problems areincluded in Selected Answers and Solutions.Check your answers to make sure youunderstand how to solve all of the assignedproblems.

What lf I forget a Uotabulary Word?

The English-Spanish Glossary provides a list ofimportant or difficult words used throughout thetextbook. It provides a definition in English andSpanish as well as the page number(s) where theword canbe found.

What lf I Need to Find Something Quickly?The Index alphabetically lists the subjectscovered throughout the entire textbook and thepages on which each subject can be found.

What if I Forget a tormula?Inside the back cover of your math book is a listof Formulas and Symbols that are used in thebook.

2.

t.4.

5.

6.

Problem-solving Strategy: Look for a PatternThere are many problem-solving strategies in mathematics. One of the mostcommon is to look for a pattern. To use this strategy, analyze the first few numbersor figures in a pattern and identify a rule that relates the first number or figure inthe pattern to the second, and then to the third, and so on. Then use the rule toextend the pattern and find a solution.

Refer to the graph. Describe the pattern in thecoordinates and predict the next point in thepattern in the positive direction.Step I List the coordinates of the points shown

on the graph.

(-3, -5), (-2, -3), (-1, -1), (0,1), (1,,3),and (2,5)

Step Z Identify the pattern in the x-coordinatesand the y-coordinates.

As the x-coordinates increase by 1, the y-coordinates increase by 2 each time. So inthe positive direction, the next point is (2 + 1,5 + 2) or (3,7).

Solve each problem by looking for a pattern.

I. The graph of a function passes through the pointsshown.

a. Describe the pattern in the coordinates, andpredict the next point in the pattern in thepositive direction.

b. Predict the next point in the pattern in thenegative direction.

2. List the first five common multiples of 3,4, and 6. Write an expression to describeall common multiples of 3, 4, and 6.

5. \tVhat is the perimeter of the twelfth figure?

4. The football parent booster group sold hotchocolate at the game on Friday night. Thetable shows the total amount of moneyraised based on the number of cups of hotchocolate sold. Use this data table todetermine how much money would beraised selling 75 cups of hot chocolate.

CFigure 1

Perimeter - 6

Figure 2

Perimeter - 8

CFigure 3

Perimeter - 10

o

i

804 Problem-Solving Handbook

Problem-solving Strategy: Create a Table

One strategy for solving problems is to create a table. A table allows you to organizeinformation in an understandable way.

A fruit machine accepts dollars, and each piece of fruit costs 65 cents. If themachine gives only nickels, dimes, and quarters, what combinations of thosecoins are possible as change for a dollar?

The machine will give back $1.00 - $0.65 or35 cents in change in a combination of nickels,dimes, and quarters.

Make a table showing different combinationsof nickels, dimes, and quarters that total35 cents. Organize the table by starting with thecombinations that include the most quarters.

Solve each problem by creating a table.

l. How many ways can you make change for a half-dollar using only nickels,dimes, and quarters?

2. A penny, a nickel, a dime, and a quarter are in a purse. How many amounts ofmoney are possible if you grab two coins at random?

5. How many ways can you receive change for a quarter if at least one coin is a dime?

4. |ohanna had a bag of four marbles. One marble is blue. TWo marbles are green.

One marble is orange. How many different ways are there to draw the marblesout of the bag one at a time?

5. At Midas High School, students are selling popcorn at a football game. Eachsmall bag of popcorn is $1.25. Each large bag of popcorn is$2.25. Create a table toshow the purchase price of up to five bags of each size of popcorn.

6. Make a table to show the ordered pairs that satisfy the equationf(x) :3x3 - 4.

Use the domain of integers between 3 and 10.

7. The equation of a line is y : |x - 2. Create a table to show five ordered pairs

with x-coordinates belonging to the set l-2, -1.,0,1.,21.8. Aria asked her friends whether they

used wrapping paper, gift bags,recycled paper, or no wrapping towrap birthday presents. Create a

table to show how many studentspreferred each method of the24 students she asked. Then predicthow many would choose eachmethod if 120 students were asked.

paperrecycled12.50/o

wrapprng paper50"/"

gift bag -./25o/" /'

Problem-Solving Handbook

Problem-solving Strategy: Make a ChartData presented in a problem can be organized by making a chart. Thisproblem-solving strategy allows you to see patterns and relationshipsamong data.

It takes an average driver 1.5 seconds to begin braking after they see anobstruction. The driver can safely decelerate a car or light truck with goodtires on a dry street surface at the rate of about 15 feet per second (fps).The distance vehicle will travel while braking can be found bymultiplying the initial velocity by the deceleration time and dividingby 2. Find the stopping distance for a car traveling at 45,55,55 and75 miles per hour.

Step I Make a chart that includes the given information and the informationto be found. Before setting up your chart, think about how speed,distance, and time are related.

Since the distance is listed in feet, find the rate of speed it takes tostop in feet per second. To convert from miles per hour to feet per

second, multiply by a conversion factor * ffi. Then find the

Step 2 To find the distance traveled before braking, multiply the initial velocity bythe reaction time, 1.5 seconds. Then find the distance traveled whilebraking. Add to find the total stopping distance.

deceleration time by dividing the initial velocity by 15 fps.


12 cm3cm

nSolve each problem by making a chart.

L As the length of a square doubles,the area increases by a scale factor.Using the squares in the diagram,make a chart of each length and eacharea. Then find the scale factor.

2. Given the functionsf(x) :2x + 3 and

8(r) : -x - 3, use a table to find.f(x) - g(r) for all positive integers less

than or equal to 6.

The chart shows at whichpoint drivers determinewhen they are going to fillthe gas tank. Make a chart toshow how many people of200 surveyed would beexpected to have eachresPonse.

4. The following table shows the official state reptile in each state. Make a tallychart that shows how many states have turtles (tortoise, terrapin), snakes,

alligators, lizards, toads, or none. Find the ratio of states with alligators tostates with no official state reptile.

At_ red-bellied turtle tA American alligator OH black racer (snake)

AK none ME n0ne OK collared lizard

A7 ridge-nosed rattlesnake MD diamondback terrapin OR n0ne

AR none MA garter snake PA none

CA desert tortoise MI painted turtle RI n0ne

co n0ne MN Blanding's turtle sc loggerhead turtle

CT n0ne MS American alligator SD n0ne

DE none MO three-toed turtle TN eastern box turtle

Ft American alligator MT none TX Texas horned lizard

GA gopher tortoise NE none UT n0ne

HI n0ne NV desert tortoise w n0ne

ID none NH none VA n0ne

It painted turtle N' none WA n0ne

IN none NM whiptail lizard WV n0ne

IA none NY snapping turtle WI n0ne

KS ornate box turtle NC eastern box tuftle WY horned toad

KY none ND none

Sowce: Bruskin/Goldring for Exxon

Problem-Solving Handbook 807

I!!lrlETtl.E,rl,t-.'r{A(lr{-eii!Ft,d

CLET3€r

Problem-solving Strateg;y: Guess-and-CheckTo solve some problems, you can make a reasonable guess and then check it in theproblem. You can then use the results to improve your guess until you find thesolution.' This strategy is called guess-and-check.

The product of two even consecutive integers is at least 1000.

Make a guess. Let's try 24 and,26. +24 x 26 = 624 @Adjust the guess upward.Try 30 and32. 30x32=960Adjust the guess upward again.Try 34 and 36. x 36 = 1224

Try between 30 and 34.Try 32 and 34. 32x34 = 1088

The integers are 32 and 34.

Solve each problem by using the guess-and-check strategy.

I. The product of two consecutive odd integers is 783. What are the integers?

2. Brianne is three times as old as Camila. Four years from now she will be just twotimes as old as Camila. How old are Brianne and Camila now?

5. Rafael is burning a CD for Selma. The CD will hold 35 minutes of music. \Atrhichsongs should he select from the list to record the maximum time on the CDwithout going over?

Each hand in the human body has 27 bones. There are 6 more bones in the fingersthan in the wrist. There are 3 fewer bones in the palm than in the wrist. Howmany bones are in each part of the hand?

The Science Club sold candy bars and soft pretzels to raise money for an animalshelter. They raised a total of $62.75. They made 25C. profit on each candy bar and30C profit on each pretzel sold. How many of each did they sell?

The product of two consecutive even integers is 4224. Find the integers.

Odell has the same number of quarters, dimes, and nickels. In all he has $4 inchange. How many of each coin does he have?

Anita sold tickets to the school musical. She had 3 types of bills worth $75 for thetickets she sold. If all the money that the club collected was in $5 bills, $10 bills,and $20 bills, how many of each bill did Anita have?

TWo angles of a triangle are shown. Find the thirdangle if the three angles have a sum of 180o.

5.

6.

7.


Problem-solving Stratega: Work Backward

On most problems, a set of conditions or facts is given and an end result must be

found. However some problems start with the result and ask for something thathappened earlier. The strategy of working backward can be used to solve problemslike this. To use this strategy, start with the end result and undo each step.

Kendrick spent half of the money he had this morning on lunch. After lunch,he loaned his friend a dollar. Now he has $L.50. How much money didKendrick start with?

Start with end result, $1.50, and work backward to find the amount Kendrickstarted with.

Kendrick now has $1.50. $1.50+ 1.00Undo the $1 he loaned to his friend.

Undo the half he spent for lunch.

-

$5'00

The amount Kendrick started with was $5.00.

CHECK Kendrick started with $5.00. If he spent half of that, or$2.50, on lunch and loaned his friend $1.00, he wouldhave $1-.50 teft. This matches the amount stated in theproblem, so the solution is correct.

$2.50x2

Add S1.00 to undo

eivine his friend S1.00.

Multiply by 2 to undo

spending half the

original amount.

I

I

I

Solve each problem by working backwatd.

l. A certain number is multipliedby 3, and then 5 is added to the result. The finalanswer is 41. What is the number?

2. A certain bacteria doubles its population twice each day. After 3 full days, thereare 1600 bacteria in a culture. How many bacteria were there at the beginning ofthe first day?

3. To catch a 7:30 e.tr. bus, Don needs 30 minutes to get dressed, 30 minutes forbreakfast, and 5 minutes to walk to the bus stop. \Mhat time should he wake up?

4. Find the length of the side of the quadrilateral ifthe perimeter is 83 meters.

5. Trov lives ll miles from his school. If he has"-E

walked f mile to-meet a friend and then they 15 m

walked another I mile to meet another friend,

6.

7.

how far do they still need to walk to get to school?

If alizard in its cage weighs 23 pounds, find the weight of the lizard if the cageweighs 19 pounds and the sand weighs 2 pounds.

Mattie spent $125.50 on three items at the mall. She bought one pair of socks for$1.20, one pair of shoes for $48.95. How much money did she spend on the jacketshe purchased?


Problem-solving Strategy: Solve a Simpler ProblemOne of the strategies you can use to solve a problem is to solve a simpler problem.To use this strategy, first solve a simpler or more familiar case of the problem. Thenuse the same concept and relationships to solve the original problem.

Find the sum of the number l through 500.

Consider a simpler problem. Find the sum of the numbers 1 through 10.Notice that you can group the addends into partial sums as shown below.

1. + 2+ 3 + 4+5 + 6 + 7 + I +9 + 10 = 55

The number of sums is 5, orhalf the number of addends.

The sum is 5 x 11 or 55.

Use the same concepts to find the sum of the numbers 1 through 500.

ufj11

1. + 2 + 3 + ... + 499 + 500 = 250 x 501:125,250 Multiply half the number of addends, 250, by

the sum of the first and last numbert 50t.

Solve each problem by solving a simpler problem.

l. Find the number of squares of any size in the gameboard shown at the right.

2. Find the sum of the numbers ihrough 1000.

5. How many links are needed to join 30 pieces of chain intoone long chain?

4. Three people can pick six baskets of apples in one hour.How many baskets of apples can 2 people pick in one-half hour?

5. A shirt shop has 112 orders for T-shirt designs. Three designers can make 2 shirtsin 2 hours. How many designers are needed to complete the orders in 8 hours?

Find the area of the figure at the right.

To add $ and {r,no* could you solve a simpler

problem that leads to the answer?

If one fourth of the l-36 freshmen at Bayridge 6 cm

High School packed their lunches, explain howto use a simpler problem to find the number ofstudents.

Explain how to find the greatest common factorof 35 and 49 using a simpler problem.

Problem-Solving Handbook

6.

7.

8.

9.

810

Each paftial sum is I l, thesum of the first and last

numbers.

Problem-solving Strategy: Draw a DiagramAnother strategy for solving problems is to draw a diagram. There will be timeswhen a sketch or diagram will give you a better picture of how to tackle a

mathematics problem. Adding details like units,labels, and numbers to the drawingor sketch can help you make decisions on how to solve the problem.

Imani is trying to determine the number of 9-inch tiles needed to cover herpatio. The rectangular patio measures 8-feet by 1O-feet. What is the minimumnumber of f-inch tiles Imani should purchase?

First, draw a diagram of the situation. Express the measurement of the patio ininches.

If each tile is 9 inches square, theminimum number of tiles for the widthof the patio is 96 + 9 = \0.7 or 11 tiles.

The minimum number of tiles for the lengthof the patio is L20 + 9 = L3.3 or L4 tiles.

So the minimum number of tiles Imani needsto cover the patio is 1L x 14 or154 tiles.

Solve each problem by drawing a diagram.

l. The area of a rectangular flower bed is 24 square feet. If the sides are wholenumber dimensions, how many combinations of lengths and widths are possiblefor the flower bed? List them.

2. Kevin was hired to paint a mural on a wall that measures 5 feet by 20 feet.Starting from the center of the wall, he will paint a square that measures 3 feet.The dimensions of the next square will be 0.5 times greater than and centered onthe previous square. How many squares can Kevin paint on the wall?

5. It takes 42 minutes to cut a 2-inch by 4-inch piece of wood rntoT equally sizedpieces. How long will it take to cut a similar 2-inch by 4-inch piece into 4 equallysized pieces?

4. Find the number of line segments that can be drawnbetween any two vertices of an octagon.

5. How many different teams of 3 players can be chosenfrom 8 players?

6. A right triangle has measures of 1L, 60, and61 millimeters. Find the area of the triangle. 11

7. Nitarren is trying to decide how many 9 inchdiameter pies will fit on her dessert table thatmeasures 4 feetby 2 feet. How many pies couldNitarren fit on the table?

8ft=96in.

10ft=100in.


Problem-solving Stratq;y: Use EstimationWhen you need to make a decision on the basis of inexact information, a commonstrategy is to use estimation. Often estimation is used when an exact answer is notrequired or when mental math is used rather than a calculator or paper and pencil.You should use estimation to determine if your answer is reasonable.

In a recent year,5't million internationalvisitors came to the United States. Giventhe information in the table, estimate whatpercentage of the visitors were from fapan.

Step I Determine about how manyinternational visitors came to theUnited States.

51 million or 51,000,000 would be aneasier number to work with if it wasrounded to only one digit in the tenmillions place, so round 51,000,000 to50,000,000.

Step 2 Determine from the chart the number of visitors who were from Japan.

According to the chart,5,000,000 visitors to the United States were from]apan.

Step 5 To determine the percentage, divide.

number of visitors from ]apantotrl ra"r"Der ot

"rs'rtoas

5,000,000

or 10/"

About 1,0% of the visitors to the United States in 2000 were from Japan,

Solve each problem by using estimation.

l. Use the table at the right to find the total areaof the Great Lakes.

2. The length of Fun Center's go-kart track is843 feet. If Nadia circled the track 9 times, abouthow many feet did she travel?

5. The Student Council is making pizzas to sell atthe football game on Friday. Eachpizza requires

Zj cupsof cheese. If Student Council membersmhke 25 pizzas, how many cups ofcheese will they need?

4. In Florida, National Parks, State Parks, andState Forests have acreage shown in the table.If the total land and water area is 65,754.59square miles, about what percentage of thetotal area is parks and forests? Use 1 squaremile = 640 acres.


50,000,000

Source: Travel lndustry Association

National Park 2,571,164.45

State Parks 890,000

State Forests 723,000

Source: BAND Florida

Problem-solving Strategy: Eliminate Unnecessary lnformationA useful problem-solving strategy is to learn how to eliminate unnecessaryinformation. If there is a diagram, it is important to determine if all or some of theinformation is necessary to find a solution.

Twila is making a quilt that shows ahouse repeating on each block of thequilt. Which information is unnecessaryto find the area of the white door of thehouse?

The dimensions needed to find the area

of the door are the length and width of

the door. So, the dimensions of 2] inches1

by 5; inches are needed. The other

dimensions, such as the width of thewindow or the size of the square, are unnecessary.

.+r

,;+

-

Solve each problem by eliminating unnecessary information.

t. Which information is notnecessary to find thetemperature differencebetween the record lowsin Alaska and Maine?

The Gemini North telescopewas placed in Mauna Kea,Hawaii, in the year 2000.The Gemini South telescopewas placed in Cerro Pachon,Chili, in the year 2001. Eachof the twin telescopes are 8.1 meters in diameter. What information is notnecessary to find the circumference of the base of the telescopes?

Which information is not necessary to find the difference in height between thetallest building and the 4th tallest building?

Taipei l0l, Taipei, Taiwan 2004 l0l 508 1,667

2. Petronas Tower l, Kuala Lumpur, Malaysia I 998 88 452 t,485

3. Petronas Tower 2. Kuala Lumpur, Malaysia I 998 88 452 1,483

4. Sears Tower, Chicago 1974 lr0 442 1,451

5. Jin Mao Building, Shanghai r 999 88 421 r,381

Source: Council 0n Tall Buildinq and Urban Habitat

Source: National 0ceanic and Atmospheric Administration


EttC,',trE:{t,t-ir I j.,ll.lEI:.--tr-q{.!F

,6lEaEF,oe-

Problem-solving Strategy: Write an EquationA natural outcome of recognizing mathematical patterns and organizing data is towrite an equation. Look at a set of data or read a word problem to determine whichvalues are constants and which values vary. Figure out the dependent andindependent variables in order to write an equation to reflect the given situation.

For every $10 gift card sold the theater department at Wallace High Schoolearns $L.25. Write an equation to represent the amount raised based on thenumber of cards sold.

Step I Make a table of data to represent thenumber of cards sold and the amountof money raised.

Step 2 Find the value that varies.The valuethat varies is the number of cardssold and the amount raised basedon the number of cards sold.

Step f Find the value that is constant for each card sold. The value that is constantfor each card sold is the amount of money raised per card, $1.25. This is theslope of the line.

Step + Write the equation that shows how the total amount changes based on thenumber of cards sold.

The equationis y :1.25v.

Solve each problem by writing an equation.

l. Write an equation that can be usedto find the number of Korean WarVeterans.

2, The land area of Alaska is 571,95Lsquare miles. Montana's land area is1,45,552 square miles. Write anequation to find how much largerAlaska's land area is compared toMontana.

Increasingly, Internet users are using broadbandInternet in their homes. Write an equation for theslope of this data in the five years shown.

Iceland spent approximately 8.8% of its grossdomestic product (GDP) on public health

t.

June 2000 I s

May 2005 I 66

expenditures in 2006, the highest percentage of all source: Pew lnternet Project

countries. If Iceland had a GDP of $11,380,000,000ln2006, write an equation to show how much money was spent on public healthexpenditures.


Source: U.S. Census Bureau

Variables and Expressions (pp. s-g)

Write an algebraic expression for each verbal expression.

l. the sum of b and2l

5. the sum of 4 and 6 times a number z

5. one-half the cube of a number x

Write a verbal expression for each algebraic expression.

7. 2n

lO. xy

lr. 17 - 4m5

2. the product of x andT

4. the sum of 8 and -2 times n

6. four-fifths the square of rn

9. m5

12. 9a3 + 1.

15. 3x2 -2x

8. 107

tt. 5n2 - 6t a-214.?

Evaluate each expression if a = 2, b : 5, x = 4,and n = L0.

Evaluate each expression.

r.3+8+2-54. 9 -327.3(12+3)-5.e

ro. z(s3 + g2)

15. 24

16. 203

19. 106

22.8a+b

25. bx + an

28. nz + 3(a + 4)

,t. (3b2)3 + 2x

used in each step.

r |ls + (12-2)l

4.23+B+37+127. 22.5 + 17.6 + 44.5

r0. 6.8.5.315. 90 .12. 0.5

Order of Operations (pp. ro-rs)

2. 4+7.2+B5. (8 - 1).3

8.53+63-52tL##A. 102

fl. 36

20. 35

,.5(e +3)-3.46. 4(5 - 3)2

9. 16+2.5.3 + 6

t2. 25 - ]tra + ol

E. 73

t8. 45

2t.153

2a. a(6 - 3n)

27.3b*16a-9n50. la + 8(b - 2))z + +

15. lx * 2n(3a + 4)l - aa

5. [(18 + 3) .0] .10

6. 10.25 + 2.5 + 3.75

e. s$+rc++|+zs12. 0.25 .7 . B

E. 4!. rc.126

21. 48 + ab

26. x2 - 4n

29. (2x)2 't an - 5b

52. b2 * 3n3 - 4(x - g1z

' iln'(+'')]Use the properties of numbers to evaluate each expression.

s. 19 + 46 +81. +54

,.r++6+zl++rr. 18 .5 .2.5u. s+.4.6

Properties of Numbers (pp. r6-22)

Evaluate each expression using the properties of numbers. Name the property

Extra Practice 815

The Distributive Property (pp.2r-2e)

Use the Distributive Property to rewrite each expression. Then evaluate.

2. B(10 + 20)

5. 32(r - +)

Simplify each expression. If not possible, write simylified.

t. 5(2 + e)

a. 9@n + 5)

7. 13a + 5a

lO. 4m - 4n

8. 2Lx - 1.0x

tt. 3(5am - 4)

14. 11.a2 - 11.a2 + 12a2

17. 8x + 4y +9x

6(y + 4)

c(7 - d)

9. 8(3x + 7)

12. 15x2 +7x2

15.6a+7a+12b+8b

18.3a+5b+2c+8b

5.

6.

t.

6.

2.

5.

9.

12.

8.

I t.

t!.9y2 +13y2 +316.5a+6b+7a

Equations (pp. ir-57)

y = ll, 3, 5,7, 9|.

l. x-4=44. 5y - 4:11.

Solve each equation..t t_27+9

2

s(4\ - 610. -#:z

22+i

25-y=t$u:ff +z

78-7 _,,13-2-v72+9(2+1)

-_

?

2(10) - 1 -'

3x + 1. :25ao=;-3

6(s) + 3"- 2(4)+3

33+52n---- 2(3-1J

Find the solution of each equation if the replacement sets are x = 10,2, 4, 6,8) and

(pp.38-44)

Describe what is happening in each graph.

l. The graph shows the averagemonthly high temperatures for a

city over a one-year period.

2. The graph shows the speed ofa roller coaster car during a

two-minute ride.

=lEA rhExpress the relation shown in each table, mapping or graph as a set of orderedpairs. Then describe the domain and range.

5.

1-

-2<-6-

+5,>4>1

815 Extra Practice

Functions gp.4s-s2)

termine whether each relation is a function. Explain.De

t. 2.xY

4, x2 +A:11 5'Y=2 6. {(-2,4), (1,3), (5,2), (1., 4)l

lf fkl :2x * 5 and g(r) = 3x2 -'l.,fiind. each value.

7.f(-4) 8. s(2) e. /(3) - s 10. g(a) + 1

Identify the hypothesis and conclusion of each statement.

l. If an animal is a dog, then it barks.

2. If a figure is a pentagon, then it has five sides.

3. If3x-1-8,thenx:3.4. If 0.5 is the reciprocal of 2, then 0.5 . 2 : 1.

Identify the hypotheses and conclusion of each statement. Then writethe statement in if-then form.

5. A square has four congruent sides. 6. 6a + 10 = 34 when a = 4.

7. The video store is open every night. 8. The band will not practice on Thursday.

Find a counterexample for each conditional statement.

ffiffi

9. If the season is spring, then it doesnot snow.

ll. It2y * 4:10,then y <3.

10. If you live in Portland, then you live inOregon.

12. lf a2 > 0, then a > O.

-2<3=-4-2

0

2

logical Reasoning and CounterexamPles (pp. s4-ss)

Writing Equations @p. 7s-80)

Translate each sentence into a formula.

l. Anumber z times 2 minus 6 is the same as z divided by 3.

2. The cube of a decreased by the square of b is equal to c.

5. TWenty-nine decreased by the product of x and y is the same as z.

4. The perimeter P of an isosceles triangle is the sum of twice the length of leg a and thelength of the base b.

5. Thirty increased by the quotient of r and / is equal to z.r.

6. The area A of a rhombus is half the product of lengths of the diagonals a andb.

Tlanslate each equation into a sentence.

7.0.5x*3:-10lO. n2 = 1.6

8. -!=:2n * 7-b

ll. 2x2 *3:219. 18 - 5h=13h

12.#*4:12

Extra Practice 817

Solving One-Step Equations 0p. Bi-Be)

Solve each equation. Check your solution.

l. -2* g:74. m+6=27. a- (-6):-5

t0. b - (-201:41

13. 7p =i$16. 62y: -2356

tt.h-r:l22. xt8=+zs. -|r =rl

,. -4*y=-96. a-7:-49. d+(-44)=-61

12. -63-f =-8215. 2y: -318. 1= -7-59il. -4*:r-(-ro$)24. u3 =d*(-r*),r. g =tf,l

2. 9 + s = -55. f +(-4)=108. -2-x=-8ll.p-47=2214. -3x: -2417. J= = -2-620.f-(-+) =*25. 1*+s=2zo. zli=s!6'5

Solving Multi-Step Equations (pp. er-s6)


l.2x-5=34. 47: -Bg +77.5s*4s=-72

10. -W +7.569:24.069

rt.[+6:-2o+3

t6. t-=4rc.4-9=n

2. 4t + 5:375. -3c -9 = -248. 3x -7 :2tt. 7 -9.1f :137.585

A14. O-8:-5

t4 _,717. -!Z:- = 1

zo. if :a

!,7a*6=-366.5k-7=-529. 8 + 3x:5

12. 6-5 :2.4m - 4.9

tt.-#y-7:65f+1

18. t- = -3

21.4.8a -3+L.2a=9

Solving Equations with the Variable on Each Side (pp. s7-to2)


l.5x*1.=3x-35. -32 * 5 = 2z -15

1_15. ;a - 4:3 - lna

7. -28*P=7(p-10)9. -4x * 6:0.5(x + 30)

ll. 1.9s *6= 3.1 -s15. 2.9m * 1.7 :3.5 + 2.3m

15.;-+:t-+,r.+=|t-ste.3u-!=1,-53-

21. -0.2(1. - x) = 2(4 + 0.1x)

818 Extra Practice

2.6-8n:5n+19t. ln+s:-4-+hs. 6(A - 5) : 18 -Zya. lfa-e)=b+g

to. 4(2y - 1) : -8(0.5 - y)

12.2.85y-7-12.85y-214.3(x +1)-5:3x-216. @u2:a

18. 0.4(x - 12):1,2@ - a)

,0.tr{_4_r*Lr.22. 3.2(y + 1) : zQ.ay - 3)

Solving Equations lnvolving Absolute Value (pp. roi-r0e)

Evaluate each expression when a:7,b = 5, and, c = -2.

Solve each open sentence.

l. lc-51=44. l10-kl:87. l6-3wl=8

10. la - bl

t5. -l cl+lbl

t.t:hn. 1=*, n _n*4,. 3- 7

,0.#:#*,t.+:ryrc.%f =+

,t. 1,+

,r.z,H

3. 14-81=06.12r-61=109. l4z-t 6l:12

12. l?n + cl

15. l4b - cl

2. le + 3l:75. 14 + 4l:tz8. 17 + 2xl -- t4

tt. lb - al

14. -lbl+la+cl

Ratios and Proportions (pp. rrr-ra)

n b -3,. $-7

- t-5 3r' 4 -2

,.ry=?n

,r.+:1,n. fun3:y#fl. r-!- =?r+l 5

,0.+,+,,, I,H

,.

6.

9.

12.

15.

t8.

21.

24.

y354x 0.2493

1_3y-r y-56p -2 5p +7:-78w-5 w*3:-434n+5 2n+7

57

Determine whether each pair of ratios are equivalent ratios. Write yes or no.I 17.60'1c'B133',1

Solve each proportion. If necessary, round to the nearest hundredth.

Percent of change (pp. lle-125)

State whether each percent of change is a percent ol increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.

l. original: $100new: $67

4. original: 78 penniesnew:36 pennies

Find the final price of each item.

7. television:fi299discount:20%

10. boots: $49.99discount:15%sales tax:3.5%

original: 62 acresnew: 98 acres

original: $212new: $230

book: $15.95sales tax:7o/o

jacket: $65discount 30%sales tax:4%

5. original:322peoplenew:289 people

6. original:35 mphnew:65 mph

software: $36.90sales tax: 6.25%

backpack:$28.95discount: L0%sales tax: 57o

2.

9.8.

I l. 12.

Extra Practice 819

literal Equations and Dimensional Analysis (pp.126-15r)

Solve each equation or formula for x.

l. x+r=q4. ,*ory=a7. d(x - 3) :5to.y:|t*-zzl

2. ax + 4:7x+u,. -;=o

8. nx-a=bx*dtt. A=|n1x +y)

u. g(h + 8): -j,forh9x-u17.;i:12,forx20. -18k*m:22k,fork

2bx-b=-Sax+l

2-3x-r:r(-3+x)A:2rr2 * Ztrrx

11.n + o=8,fotP

2k-3:5.forkm+p39k + 3j : -6m, for j

Solve each equation or formula for the variable indicated.

,.

6.

9.

12.

15.

I8.

21.

15.

16.

19.

S : 2b(a + c) + Zac, for bu-10a

- 7.t), IOt U

14h+j=2h,forh

t.

2.

3.

4.

5.

* Averages (PP' I52-l3s)

ADVERTISING An advertisement for grape drink claims that the drink contains 10%grape juice. How much pure grape juice would have to be added to 5 quarts ofthe drink to obtain a mixture containing 40"/o grapejuice?

GRADES In Ms. Pham's social studies class, a test is worth four times as much ashomework. If a student has an average of 85"/" on tests and 95% on homework,what is the student's average?

ENTERTAINMENT At the Golden Oldies Theater, tickets for adults cost $5.50 andtickets for children cost $3.50. How many of each kind of ticket were purchased if21 tickets were bought for $83.50?

FOOD Wes is mixing peanuts and chocolate pieces. Peanuts sell for $4.50 a poundand the chocolate sells for $6.50 a pound. How many pounds of chocolate mixeswith 5 pounds of peanuts to obtain a mixture that sells for $5.25 a pound?

TRAVET Missoula and Bozeman are 210 miles apart. Sheila leavesMissoula for Bozeman and averages 55 miles per hour. At the same time, Caseyleaves Bozeman and averages 65 miles per hour as he drives to Missoula. Whenwill they meet? How far will theybe from Bozeman?

Graphing Linear Equations (pp. 153-160)

Determine whether each equation is a linear equation. Write yes ot no.lf yes, write the equation in standard form.

l.3x:44. 5x -7y:2x -7

2.2x-3:a25.2x*5x=7y+2

l. 4x=2y +8o.**|:-+

Graph each equation by using the x- and y-intercepts or by making a table.

7.3x+y=4 8.y=3x+1 9.3r-2y=72ll.2x-3y:8 12.y:-Z 15.y-5x-715. .r + Lg =z 15. 5x -2y =B 17. 4.5x *2.5y =)

820 Extra Practice

10.2x-A:614. x:4,r. Lrt * 3y :12

Solve each equation.

l, -x*6=04. -2x * 5:5

7.6x-4=B+6x

Solving Linear Equations by Gtaphing (pp. r6r-r66)

2.8x+2:0

5.3=4x-L

8' +:3x - 4

5. 4x +3 = -2+ 4x

,.i**5:-19.7:-x-4

Rate of Change and Slope (pp, r70-r78)

Find the slope of the line that passes through each pair of points.

lc x

,. (-2,2), (3, -3)7. (1.8, -4), (6, -1.0)

4. (-2, -8), (1,4) 5. (3,4), (4,6)

8. (-4, -6), (-4, -8) 9. (0, 0), (-1, 3)

Find the value of r so the line that passes through each pair of points has thegiven slope.

I l. (-1, r), (1., -4), m = -5 12. (r, -Z), (-7, -7), m :

6.

t0.

(-5,4), (-1, 11)

(-8,1), (2,1)

_14

Direct Variation (pp. rBo-rBE)

Name the constant of variation for each equation. Then find the slope of the linethat passes through each pair of points.

l. Yl(3, 2)

I--A\_U :1, i

Graph each equation.

4'Y=5* 5' Y: -6*

Suppose y varies directly as x. Write a direct variation equation thatrelates r and y. Then solve.

7. If y:45 when x:9,findy when x =7.

8. If y: -7 when x : -1, find r when U : -84.

I itri

$-'fm+of

:ii-,

1u = -2,

4Y: -5x

Extra Practice

Arithmetic Sequences as Linear Functions (pp. rs7-re3)

Determine whether each sequence is an arithmetic sequence. Write yes ot no.Explain.

l. -2, -1.,0,1., ...

4. -21., -16, -11., -6, ...

2. 3,5,8,12,.._

5. 0, 0.25, 0.5, 0.75, ...

l. 2,4,8,16,...^ 111 1-' 3'g' 27' gl'"'

Find the next three terms of each arithmetic sequence.

7. 3,13,23,33, ._. g. -4, -6, -8, -10, ... g. -2, -L.4, -0.8, -0.2, ...

10. 5, 13, 21.,29, ... tr. t,I,r,z, ... tr. -+,-2,-+,-+,Write an equation for the rth term of the arithmetic sequence. Then graph thefirst five terms in the sequence.

15. -3,1,5,9,... 14. 25,40,55,70,... 15. -9, -3,3,9, ... 16. -3.5, -2, -0.5,

The table shows the number of cups of flourused to make batches of brownies.

5a. Write an equation for the data given.

5b. Graph the equation.

5c. Find the number of cups of flour needed for 6 batches of brownies.

Write an equation in function notation for each relation.

Graphing Equations in Slope-lntercept Form (pp.214-221)

Write an equation, in slope-intercept form, of the line with the given slope andy-intercept.

Graph each equation.

l0.y:5x-L822 Extra Practice

I

(0, -3)(-2, -2)I

7.

l. m:5, y-intercept: -L5 2. m:

+. m: -f,y-intercept: N 5. m:

Write an equation in slope-intercept form

-6, y-intercept:3

-1, A-rntercept:2

for each graph shown.

5. m: 0.3, y-intercept: -2.6,7

6.m: i, y-intercept: -2

vl-+-t 1 l_(0,3)

\1,,,i -

8.

ll.y--2x+3 12. 3x-!:6

Writing Equations in Slope-lntercept Form (pp. 224-230)

Write an equation of the line that passes through the given point and has thegiven slope.

t. (0,0); m: -Z5. (0,5);m=-1.

5. (1, -5); *:?

7. (-1,7), (8, -2)9. (8, -1), (7, -1)il. (0, 0), (-4,3)

2.(-3,2);m=44. (-2,3);m:-l

'' (+,f,),*=a

8. (4,0), (0,5)

to. (-2,3), (1,3)

".(-+,1),(tn,l)

Write an equation of the line that passes through each pair of points.

A:-5x!=5x-1.8

Writing Equations in Point-Slope Form @p.231-236)

Write an equation in point-slope form for the line that passes through each pointwith the given slope. Then graph the equation.

l. (5, -2), m = 3

5. (-3,1),m:0

Write each equation in standard form.

s.y+3=2(x-4)7. y-+:-l{x-s)9.y-1:1.5(x+3)

Write each equation in slope-intercept form.

ll.y-1:-2(x*5)15.y-6:-4(x-2)

ts.y-z:-|{x-z)

2. (0,6),m = -24. (-2, -4), m = |

6.y+z=-|@+6)B.y+z:f{x-o)

10. y+6=-3.8(x-2)

12.

t4.

t6.

y+3=a@-\y+1:ftr+s)

v ++:tr? *l)

Paralleland Perpendicular lines Op. 257-24s)

Write the slope-intercept form of an equation for the line that passes through thegiven point and is parallel to the graph of each equation. Then write an equationin slope-intercept form for the line that passes through the given point and isperpendicular to the graph of each equation.

l. (1,6),a:4x-2t. (-g,O),y =Zt *,5. (0,4),3x + By : 4

2. (4,6),!:2x-74. (5, -2), A : -Zx - 7

6. (2,3), x - 5y :7

Determine whether the graphs of each pair of equations are parallel,p erp endicul ar, or neithen

7. Y=-2x+11'y+2x=23

8. 3y :2x + 1.4

2x-3y:2Extra Practice 823

Scatter Plots and Lines of Fit tpp. 245-251)

Determine whether each graph shous a positive correlatiory a negative correlatioryor no correlation. If there is a corelation, ilescribe its meaning in the situation.

9r'8zo-E rs

ol0G5

123 4 5

Age of Car (years)

a

t a a

o.o*.eu9o6.oo$rd$^u$r$n$

Year

Regression and Median-Fit lines (pp.25i-260)

l. COMPUTERS The media center is keeping track of student computer use todetermine if they need to purchase more computers. There are 6 computers inthe center. The results of the 10-day tracking period are recorded in the table.Write an equation for the regression line for the data. Then find the correlationcoefficient.

STOCKS For a class project the students were asked to keep track of a stock pricefor a company of local interest. They were to record the closing price of the stockat the end of each Friday for 8 weeks. Marcus was out of town one week andmissed the price for week 4. Find the equation for the data, and approximate theprice for week 4.

2.

Special Functions (pp. 26r-268)

Graph each function.

t. f(x) = -gflrn

+. f(x) : lx + 2l

2. g(x) = [4x]

s.g(r):l3x-11

t. h(x): 2[rn - 3

6. f(x):tT{;,'!,7. PARKING Short-term parking at the airport

is $2 for the first half-hour and $1 for eachhalf-hour after that. Draw a graph thatrepresents this information.

824 Extra Practice

Solving lnequalities by Addition and Subtraction (pp.28i-2so)

Solve each inequality. Check your solution, and then graph it on a number line.

l. c+9<35. -11 >d-49. 1,4p>5+13p

15.9x<8x-2

t. 7b > -49

5. -8f < 48

9. 4c> -6ll. -1,5a < -28

2. d- (-3)<136. 2x> x -3

10. -7 <1.6-z14. -2 * 9n <10n

2. -5j < -60

6. -0.25t > -10

lO. 6 < O.Bn

u. -+x < 42

t, -r,*.n?= -r,0.375y < 32

t)4. ;.88. -4.3x < -2.58

12. -25 > -0.05a

16. -7y > 91.

t. z-4>20 4. h-(-7)>-27.2x-3>x 8.16+w<-20tt. 1,.1a - 1,> 2.1,a - 3 n. |t * i.-it - ?15. a-2.3> -7.8 16.52-6>42

Define a variable, write an inequality, and solve each problem. Check your solution.

17. The sum of a number and negative six is greater than 9.

18. Negative five times a number is less than the sum of negative six times the number and 12.

Solving lnequalities by Multiplication and Division (pp.2e0-2es)

Solve each inequality. Check your solution.

t.

7.

il.

15.

Define a variable, write an inequality, and solve each problem. Then check yoursolution.

17. Negative one times a number is greater than -7.18. Three fifths of a number is at least negative L0.

19. Seventy-five percent of a number is at most 100.

Solving Multi-Step lnequalities (pp. 2s6-30r)

Solve each inequality. Check your solution.

l. 3y - 4> -37!. -5q+9>245. -2k+12<307. 1,5t - 4> ltt - 16

e.5q+7<3(q+1)

tl. -4t-5>2t+1.3tt.ft+7>-515.8c-(c-5)>c+1717.9m+7 <2(4m-l)19. 5x < 10(3r + 4)

2.7s-12<134. -6a -3>-336. -2x + 1 < 1,6 - x

8. 13 - y <29 +2!to. 2(w + 4) > 7(zo - 1)

rz. {zf} < -o14.t3r-11>7r+37

t6. -5(k + 4) > 3(k - 4)

18. 3(3y + 1) < 13y -8zo. t(a+l)>,-t

Extra Practice 825

Solve each compound inequality. Then graph the solution set.

ng Compound lnequalities (pp. 304-i0e)

1.2+x<-50r2+x>55.3<29+7and2g+7<1.55. 3b - 4 < 7b * 12 and 8b - 7 < 25

7. 5m- 8 > 10 - m or 5m * L1. < -99.2h-2<3h<4h-1.ll. 2r + 8 > 1.6 - 2r andTr + 2l< r - 9

t!. 2(q - 4) <3(q + 2) or q - 8. 4 - q

15. n - (6 - n) > 10 or -3n - 1 > 20

17. WND SPEED The Fujita Scale (F-scale) is the officialclassification system for tomado damage. One factorused to classify a tornado is wind speed. Use theinformation in the table to write an inequality for therange of wind speeds of an F3 tornado.

lnequalities lnvolving Absolute Value (pp.3ro-314)

2. -4+f >-5or-4+t<74.2a-2<3aand4a-1.>3o6. -9 <22*7 <10

8. 12c - 4 <5c + L0 or -4c- 1 < c + 24

10. 3p + 6 < 8 - p and 5p + 8 > p + 6

t2. -E +3 <j +22andj - 3 < 2j -15ru. lta+5> w+2=fu*,16. -(2x+5)<r+5<2x-9

l. lx+41<10n.l\31=n7. l\a + 21< 4

ro. lffl>s

2. ly - 3l= 3

s.lu/1,_zg.lw-81=14

rr. l$1.+

t. lZx+51>2,14#l.-,e. l3x+21>8

rz. lz;el> s

73-l l2 mph

t t s-t sz mph

261-518 mph

Solve each inequality. Then graph the solution set.

Graphing lnequalities in Two Variables (pp. ir5-520)

Determine which ordered pairs are part of the solution set for each inequality.

l. x * y > 0, {(0, 0), (1, -3), (2,2), (3, -g)l2. 2x + y

=8, {(0,0), (-L, -l), (3, -2), (8,0)}

Graph each inequality.

5. y. -26. 3y -2x <2

4. x<47. y>4x-1.

5. x+y<-28.3x+y>1

9. DELIVERIES A delivery truck with a 4000-pound weight limit is transportingtelevisions that weigh 77 powrds each and microwaves that weigh 55 poundseach.

a. Define variables and write an inequality for this situation.

b. Will the truck be able to deliver 35 televisions and 25 microwaves at once?

Explain.

426 Extra Practice

Graphing Systems of Equations (pp. iii-3ie)

Graph each system of equations. Then determine whether the system has nosolution, one solutioru or infinitely many solutions. If the system has onesolutiory name it.

l, y:3*4x +2y =39

4. x+y:6*-Y=2

7. 2x +y:8*-Y=4

10. r+2y:-9*-y:6

12.I t.

X: -4x+y-1.x+Y:63x+3y=!lr-o:9

5

3x-5y=$, +ty:eA:3x-4

Y=x+43x + 2y :18

U: -3x4x+y=2x+2Y:0

!*3=-xzt*lr='4x+3y:t2

Substitution Op. s4z-347)

Use substitution to solve each system of equations. If the system does not haveexactly one solution, state whether it has no solutions or infinitely manysolutions.

l. y=,5x :12y

4. 3x + y:6!*2:x

7. x-f2y=10-x+y-2

rc.fu*Lry:1x-Y:to

l!. 2x *3y:54x-9Y:)

U =7 - x2x-y=gx-3y=!2x+9y=112x=3-A2y=12-xx*6y=l3x-10y:Jlx=4-8y3x +2U =12

Elimination Using Addition and Subtraction 0p.548-3s4)

2.2x-A=322x+y=69x=a-72x-5y=-)x*!=$2x-y:63x+0.2y=73x=0.4y+4ax-ty:s5x+ty:e

12.

I5.

t l.

14.

x=5-A3y=3x+13x=-1.8+2yx*3y={6y-x=-36A: -3x3x-2y=123^f-Y=c3x-2y=-J25x + 10y =215

-!*x=6!'lx=53x * 5y: -1.63x-2y=-22s-3t=-4s=7-3t9x + 2y :261..5x-4=132x-y:3.,

zx - A: -t

l. x+y=7*-Y=9

4. s * 2t:63s-2t:2

7. x-y:3x+y-3

10. -6x * 1,6y : -g6x-42=16y

15. x: y

x*Y=/

12.I t.

Use elimination to solve each system of equations.

14. 15.

Extra Practice 827

Elimination Using Multiplication 0p. 35s-i60)

Use elimination to solve each system of equations.

l. -3x *2y =19-2x-A=-51

4. t-V:-llr-Zo:-t55"

7. x +8y:34x-2y=7

10. r*fu=302x-Y:-6

ll. 2x -7y =9-3x * 4U :6

2.2x+5y=13

12.

15.

It.

14.

4x-3y=-133x-5y:$4x-7y=tQ

4x-y-4x *2Y:J3x-2y=g4x+U=52x-6y=-1.65x+7y=-18

5x+3y:4-4x*5y=-18x - 0.5Y :10.4x*U=-2

3y-8x=9y-x=29x-3y=5x+Y:16x-3y=-9-8x*2y=4

Applying Systems of linear Equations (pp. i62-i67)

Determine the best method to solve each system of equations.Then solve the system.

l. Y:2x+1'U:-3x+1

4.2x-Zy:5A: -6x

7. -7x *3y: -42x+3y=5

10. -1,3r * 8y : -63x-4Y:2

15. 12x - 3y:7x:2 * 13y

A=5x-8A=3xx: -1.a =B4x-y:11x*2Y:$-x -l7Y : )-4x*6y=-86x:59y-2x:7

x+2y=-6y:y*34x+y:5-4x - 2Y :92y-x=-7x*3y=$2x+5y=75x-2y:ti17x + By -- -4-8y-2x--9

12.

15.

I t.

Organizing Data Using Matrices (pp. i6e-57s)

wite impossible.

,l_);l .[-3 _i]

5. l4s 36 18.l _ f4s -2 361

163 29 51 118 9 101

' '[: -i)-,1? -l].nl-'n -")

Use matrices A, B, C, D, and. E to find the following.

o : [ ?],, : [-l _?], . = [_3

-Z]," =l-Z

2.[0 -1 3] +

4. 4[-8 2 e) - 3[2 -7 6l

5

-,)-3

, tsl_i;il. ^,1_3:|]

- ,,1-ll]

7. A+Btt.D-C

828 Extra Practice

8. C+D12. E+24

-21,, :l-:, -i]

9. A_Btr. D-28

10. 48

14.2A+3E

Perform the indicated matrix operations. If the matrix does not exist,

_D

l.5a+3b=62a-b=9

4. 4c - 3d: -1,5c-2d=39

Using Matrices to Solve Systems of Equations (pp.376-581)

2.3x*4U=-82x-3y=6

5. x*2y-z=6-2x*3y+z:1x+y+32:8

Solve each matrix equation or system of equations.

'.[-]-:l3lll. 3m I t:4 12.

2m + 2t:315. x + A: -3 16.

3x-10y:{J

9.

6c+5d:73c-1.0d=-42m - 3p:J-4m I9p = -8

m*3P:l4* - p: -222a-3b-c:44a+b*c:15a-b-c=-2

[r ol -zg1Lo 1l sz)

l5. 3a - 5b :1.a*3b:5

17. x+y=12x-2Y:-12

,.P 4l33lL2 -s l-1.1

I0.5x-A:78x+2y:4

14.2r-7t=24-r+8t:-21

Write an augmented matrix equation for each system of equations.

l. x<5y>-3

5. x+y<2u-x<4J_

9. txt>2lvl<5

x+y<5x<2

1_V<*x+5-J

y>2x+1.u<xy<-x+4y>-1

y+x<2y>xy+x>1u-x>-1.y<-13x-2u>6

J_

Solve each system of inequalities.

Systems of lnequalities (pp. 582-387)

2.y <3a-x>-1y<x+4y-x>Lx<2a<3v>-?+3

Multiplying Monomials (pp. 40r-407)

12.

7.

il.t0.

reasoning.

t. n2-3 2.53

Simplify each expression.

s. as@)(a7)

8. (bc3)(b4ca)

tt. (snst2)(-4n3t2)

u. -1r(ozyer+\4

, ga2b3

o. (r3ta)(rata)

s. (-zmp2)(s*'p')tz. x3(xay3)

s. (|*)2(o*4)'z

4. 15 - x2y

t. (x3ya)(xy3)

ro. [{a3)2]2

tt. (rryztx+)3

re. [{-23)3]2

GEOMETRY

17-

Express the volume of each solid as a monomial.

Determine whether each expression is a monomial. Write yes or zo. Explain your

4k3

t8.x2y

Extra Practice 829

Monomials (pp. 408-4rs)

Simplifu. Assume that no denominator is equal to zero.

- 6tol.-

6/

- 12ab5l' no+6s

g. o56on-7

(-r)sstt.+r-"s--

"(#)

(-a)Ebs

a4b7

-9h2k418hsj3k4

wY(jztesm)a

(jkn)-'

I sn-'*2\o\r";-t)

(-*)3y3

*'yuI zo2b+\2

\ffi)ffit'wl(gabzc)-3

@

- b6c52.- ,.b3ct

- 24xs5.+ 7.-BxzI -e a\2

lO. \-:u "a"! u.(u3a)-"

14. 28a_4bo 15.

1.4arb'1

,r. ( zo.3u =z \-1 19.

\2_ta_5b3 I

12.

r6.

l. 1.,400,322

4. 0.004500

Scientific Notation Op. 416-422)

2. 134,490,000

5. 12,000,000

8. 5.4 x L03

ll. 5.22 x 104

3. 0.00009

6. 0.0000233

g. 3.934 x 10-e

12. 7.256 x 10-1

Express each number in standard form.

7. 2.23 x L0-2

lO. 4.7 x 10-6

Evaluate. Express the results in both scientific notation and standard form.

t5. (2.3 x 10-2X2.55 x t03)

,U. fiaa x 70!4.2 x 10-'

14. (5.23 x 10-7X8.2 x 10s)

,r. 2.644 x lO _5

3.2 x 1.0-'

Express each number in scientific notation.

Polynomial s gp. 424-42s)

State whether each expression is a polynomial. If so, identify it as a monomial,abinomial, or a trinomial.

l. 5x2y -l3xy - 7 2. 0

Find the degree of each polynomial.

6. L4abcd - 6d3

,0.+-t*iArrange the terms of each polynomial so that the powers of r are inascending order.

t f; -tczY

,.+tr. -6

4. 3a2x - 5a

8. 10

12. a2b3 - a3bZ

5. a+5c

9. -4h5

descending order.

19.5x2-gx3+7+2x22. 21p2x + 3px3 + pa

830 Extra Practice

15. 2x2 - 3r * 4x3 - xs

16. -5bx3 - 2bx + 4x2 - b3

Arrange the terms of each polynomial so that the powers of x are in

14.x3-x2+x-l17. xB *2x2 - x6 +1

15. 2a + 3ax2 - 4ax

18, cdx2-c2d2x+d3

20. -6x+ xs + 4x3 -20 21. 5b +bsxz +lbx2t. zaxz -6a2x3 +7as -8x 24, +2f *n +-Zusax2

Adding and Subtracting Polynomials (pp. 43i-4i8)

Find each sum or difference.

t. (3a2 + 5) + (4a2 - 1)

5. (62+2)-(92+3)5. e7* + 4ts - 6s2) + e5* - 12ts + 3s2)

7. (4a2 - 1ob2 + 7c2) * (-5a2 + 2c2 + 2b)

e. (4d-t 3e - 8fl - (-3d-t 10e - 5f + 6)

tt. (9x2 - llxy - 3y') - (*2 - 1.6xy + 12y2)

13. (6 -7y + 3y') + (3 - 5y - 2y') + (-L2 - 8y + y')

14. (-7c2 - 2c -5) + (9c - 6) + (16c2 + 3) + (-9c2 - 7c + 7)

2. (5x - 3) + (-2x + r)

a. (-4n + 7) - (-7n - 8)

6. (6a2 - 7ab - 4b\ - (2n2 + Sab + 6b2)

8. (22 -t 6z - 8) - (422 - 7z - 5)

10. (7g + th -e) + (-g - 3h - 6k)

12. (-3m * 9mn - 5n) + (1'4m - Smn - 2n)

Multiplying a Polynomial by a Monomial (pp,43e-444)

Find each product.

l. -3(8r + 5)1

+. y$x - 6)

7. -ab(3bz + 4ab - 6a2)


10. -3a(2a - 12) + 5a

t!. 11.(n - 3) + 2(n2 + 22n)

Solve each equation.

16. -6(11 - 2x) - 7(-2 - 2x)

18. a(a - 6) + 2a:3 + a(a - 2)

20. w(w + 12) = w(w i 14) + 12

22. -3(x+ 5) + x(x - 1) : x(x t 2) - 3

2. 3b(5b + 8)

s. 7xy(5x2 - y2)

B. 4m2(gtn2n + mn - 5n2)

5. 1.La(2a + 7)

6. 5y(y2 - 3y + 6)

s. 4st2(-4s2t3 + 7s5 - 3st3)

tt. 6(12b2 -2b) +7(-2- 3b) 12. x(x - 6) + x(x -2) +2x

14. -2x(x + 3) + 3(x + 3) 15. 4m(n - 1) - Sn(n + 1)

17. 11(n - 3) + 5:2n + 44

te. q(zq + 3) + 20 :2q(q - 3)

21. x(x - 3) + 4x - 3:8x * x(3 + x)

25. n(n - 5) + n(n + 2) = Zn(n - 1) + 1.5

Multiplying Polynomials (pp.447-4s2)

Find each product.

t. (d +2)(d +5)4. (a +2)(a - 19)

7. (2x - 5Xx + 6)

10. (7a + 3)(a + 4)

tt. (4a + 3)(2a - 1)

16. (12r - 4s)(5r + 8s)

Ie. (x -2)(x2 +2x + 4)

22. (5x - 2)(-5x2 + 2x + 7)

25. (x2+x+1)(x2-x-1)

2. (z -r 7)Q - a)

5. (c + 1s)(c - 3)

8. (7a - a)Qa - 5)

tt. (7s - 8)(3s - 2)

ta. (7y - 1)(2y - 3)

17. (-a + 1)(-3a - 2)

20. (3x + 5)(2x2 - 5x + 11)

25. (-n+2)(-2n2+n-L)26. (a2 + 2a + 5)(a2 - 3a - 7)

5. (m - 8)(m - 5)

6. (x + y)(x - 2v)

e. (4x + y)(2x - 3y)

D. @g + 3h)(29 - 5h)

15. (2x + 3fi$x + 2y)

18. (2n - 4G3n - 2)

21. (4s + 5)(3s2 + 8s - 9)

24. (x2 - 7x * 4)(2x2 - 3x -6)27. (Sxa - 2x2 + 1)(x2 - 5x + 3)

Extra Practice 831

Special Products (pp.a5r-a58)

Find each product.

t. (t + 7)2

4. (10x + 11.y)(10x - 11y)

7. (a + 2b)2

10. (3m - 7d1z

15. (5x - 9y)2

,r. (+.- ro)(ry + ro)

re. (x +2)(x-2)(2x+5)22. (a + 1)(a + 1)(a - 1) (a - 1)

24. (2c + 3)(2c + 3)(2c - 3) (2c - 3)

(w-rT)(w+12)

$p + 3)2

(3x + y)2

(5b-6)(5b+6)

(8a-2b)(8a+2b)

(+"-*)(+"+*)(ax-\(4x+1)@-a)

5. @-afi26. (2b - 4d)(2b + 4d)

9. (6m *2n)2

12. (1, + x)2

s. (Ls + +)'

18. (a - 1)(a - 1)(a - 1)

21. (x - 5)(x + 5)(x + \@ - a)

2.

5.

8.

t l.

14.

17.

20.

21. (n - 1)(n + 1)(n - 1)

2s. (4d + 59(4d + s8)(4d - 59ed - sg)

Monomials and Factoring {pp.471-474)

Factor each monomial completely.

l. 240mn Z. -64a3b

4. -231.xy22 5. 44rs2tg

Find the GCF of each set of monomials.

g. 45,80

tt. 128,245

17. 1.6pq2,12p2q,4pq

21. 26jk4,1.6jk3,8j2

-26*y2

-756m2n2

10.29,58

t+. 7y2,14y2

lg. 5,15,10

5. 27a2b +9b3

6. 1.4mn2 * 2mn

9. 2ax + 6xc + ba + 3bc

12. a2-2ab+a-2b15. x2-xy-xy+y2

18. z(z - 2.5) = g

21. (a - 1)(a * 1):924. 1.4d2 * 49d:021. 32x2 :1.6x

5.

6.

7.16,60

il. 55,305

15. 4xy, -6x

g. 15,50

12. 126,252

16. 35P,7t

19. 12mn, 10mn, 1.5mn 20. L4xy, 12y, 20x

l. 1Oa2 + 4Oa

4. Llx * 44x2y

7. 25a2b2 -l30ab3

lO. 6mx - 4m -l3rx - 2r

It. \ac - 2ad + 4bc - bd

2. 15wx - 35wx2

5. 16y2 + 8y

8. 2m3n2 - 1.6mn2 * *mn

ll. 3ax - 6bx *8b - 4a

14. 2e2g +zfg + +e2h + +fh

17. d(d * L1) :620. (4n - 7)(3n -t 2) : g

25, 8b2 -12b:026. 33x2 = -22x

Solve each equation. Check your solutions.

16. a(a - 9):0te. (2y + 6)(y - 1) :022. 1.0x2 - 2Ox:0

25. L5az:60a

832 Extra Practice

Using the Distributive Propefi @p.a76-as2)

Use the Distributive Property to factor each polynomial.

Quadratic Equations: x2 + hx * c= 0 (pp.48s-4sl)

2. a2-9a-365. b2+22b+21

8. n2-8n+7u. s2 - tSst - 30*

14. x2+5x-617. rf + 24o - 52


Factor each trinomial.

l. x2 -9x + L4

4. n2-8n+157. x2-5x-24

10. z2 + LSz + 36

lr. 12+3r-4016. 12 +16r + 63

19. a2*3a-4=O22. y2 +y - 42:O

25. n2 -9n: -182S. 10 -l a2 : -7a

integers, write prime.

l. 4n2 -t 4a - 63

4. 222 - 112 + 15

7. 6n2 *7n -310. 5a2 - 3a + 15

15, 10x2 - 20xy + l0y2

5, x2+2x-156. c2+2c-3g. m2 - 1.om - 39

12. y2 +2y -35


rc.BP+32t+24=o19.9x2 * L8x -27 =O

22. 12x2-x- 35:025. 14b2 +7b - 42=0

20. x2 -8x -20:023. k2+2k-24:026. 2z + z2 =3529. z2 - 57 :1.62

2. 3x2 -7x - 6

5. 3a2 -2a -218. 5x2 - 17x + 14

ll. 1,8a2 + 24t: + 12

14. 12c2 - L1.cd - 5d2

17. 6y2 +72y *192:020.4x2-4x-4=425. LBx2 * 36x - 1,4 = 0

26. 1312 + 21.r - 10 = 0

21.

24.

27.

50.

Quadratic Equations: Differences of Squares (pp. 4ee-s04)

write prime.

l. x2-97. a2 - 4b2

z. a2-64 5. 4x2 -gy28. 7512 - 48 g. x2 - 36y2 lo.

15. 5a2 - 48 14. 1.69 - 16P tS. 8r2 - 4 16.

Solve each equation by factoring. Check your solutions.

17. 4x2 : 16 18, 2x2 :50 19. 9n2 - 4 - 0 20.

25.20-5g':o 24.16-+r':0 25. ir'-$:o 26.

| - 922 5. 1.6a2 - 9b2

ga2 - t6 tt. 9x2 - looy2

-45m2 + 5

o'-H:o ,r.+-b2:o2q3 -2q:O 27. 3r3 = 48r

Equations: ox2 + bx + c= 0 (pp.4e3-4es)

Factor each trinomial, if possible. If the trinomial cannot be factored using

15. x2 - 4xy - 5y2

18. k2 - 27kj - 9oj2

b2 + Ilb *24:012-lgr-48:o

-20x -l 19 = -x2x2=-1.4x-33

t.4r2-25r+66.4y2+fly+69. 2n2 - lln -113

12. 4k2 +2k-1215. 30n2 - mn - m2

18. 5x2 *3x -2:021.12n2-L6n-3=024. 1,5a2+a-2:027. 35y2 - 60y -20 =O

6. 8x2 - 12y2

12. 49 - a2bz

22. t8_Lfr=O28. 100d - 4d3:0

Extra Practice 833

Factor each polynomial, if possible. If the polynomial cannot be factore4

Quadratic Equations: Perfect Squares (pp. s05-5r2)

Determine whether each trinomial is a perfect square trinomial. Write yes or no.If so, factor it.

l. x2+12x+36

4. x2 - 1or - 1oo

Factor each polynomial, if possible. If the polynomial cannot be factored, writeprime.


15. x2 * 22x * 1.21.:0

18.c2+10c+36=11

2. n2-13n+365. 2n2 +17n +21

8. 4p2 + 12pr +9r2 9. 6a2 +72

12. 1. - 1.Oz + 2522 lt. 28 - 63b2

16. 343d2 =719. 1.6s2 * 81. :72s

!. a2+4a+46. 4a2 -2Oa +25

10. s2 + 30s +225

14.4c2+2c-7

17. (n - 7)2:520. 9p2 - 42p *20 = -29

l. 3x2 -75ll.24x2 +24x+9

Graphing Quadratic Functions (pp. s2s-si6)

Use a table of values to graph each function. State the domain and range.

l- y:x2+6x+8 2. y:-x2+3x

Find the vertex/ the equation of the axis of symmetry, and the y-intercept.

4. Y:-x2+2x-37. y:5x2-2Ox+37l0.y:x2-6x+5

5. y:3x2 +24x +80 6.

Consider each equation.

a. Determine whether the function has maximum or minimum value.b. State the maximum or minimum value.

c. What are the domain and range of the function?

8. y=3x2+6x+3ll. y:x2+6x+9

3. y: --*'

a=x2-4x-4U :2x2 * 72x

!/:-x2*16x-1.59.

12.

It. y:4x2-716.y:-x2-1

14. y: -2x2 - 2x + 4 15. y :6x2 - 12x - 4

17. y:-x2+x+7 18. y:--5x2-3x+2

Solve each equation by graphing. If integral roots cannot be found, estimate theroots to the nearest tenth.

7. x2+2x-3:010.2r2-8r+5:0B. 3P * 2:0

834 Extra Practice

Solving Quadratic Equations by GraphinS (pp.537-s+2)

Solve each equation by graphing.

l. n2-25:o 2. n2-8n:o4.b2-18b+81:0 5. x2+3x+27:0

8. -x2+6x-5:0ll. -3x2*6x-9:O14. -b2 * 5b * 2:0

5. d2 +,36 : 0

6. -y'-3y+ L0:0

9. -a2 - 2a + 3:012. c2 * c:015. 3x2 I 7x :1.

Transformations of Quadratic Functions (pp. s44-54e)

Describe how the graph of each function is related to the graph ol f(x) = x2.

l.g(r):x2-54. g(x) = x2 +97. g(x):?fz + +

List the functions in order from the most stretched vertically to the leaststretched vertically graph.

2. h(x) =lf'5. g(r) : -3x2S. h(x) = 1..2x2 - 7.5

z. *-6t+9=1.65. x2 +2x +L:81

8. x2 +lOx + c

ll. p2 - 1,4p + c

14. c2*6=-5c17. t2+3t=4020. P+12t+32=02t. 222 - 5z - 4:0

t. h(x): -x2 + 5

6. h(x): -x2 - 6

9. g(r) = -7 - Lr*'

ll. g(r) =5x2,h(O:L;szt5. g(x) - -6x2,h(x) = zx2,f1x1 = 0.4x2

lo. g(x) - -2.3x2,h1x1:1z12. g(x) = -x2, h(x) = 9{',, f(r) : -2.5x2

tenth if necessary.

l. x2-4x+4:94. a2-22a+121.=3

Solving Quadratic Equations by Completing the Square (pp.5s2-s57)

Find the value of c that makes each trinomial a perfect square.

!. b2 + 1.0b + 25:11.

6. *-36t+324:85

g. t2+12t+c12. b2 +13b + c

15. p2 - 8p + 5:018. x2 *8x-9=021. 2x - 3x2 = -824.8P-12t-1.=0

7. a2+20a+c

10.y2-9y+c

Solve each equation by completing the square. Round to the nearest tenth ifnecessary.

It. a2-8a-84=orc.2y2*7y-4=019. y2 +5y - 84:022. 2y2 -y -9:O

Solve each equation by taking the square root of each side. Round to the nearest

Solving Quadratic Equations by Using the Quadratic Formula (pp. ss8-s64)

Solve each equation by using the Quadratic Formula. Round to the nearest tenthif necessary.

l. x2-8x-4:04. y'-7y-8:o7. m2+4m+2:0

lO. t2 + 1.6 :015. 8* * 10f + 3:016. n2 - 3n + 1:0

$. 3f -t 2f :622. 4r2 -12r +9 =O

2. x2+7x-8--05. m2-2m:358.2t2 -f -15:0ll. -4x2 -l8x : -314. zxz-Et-|:o17.222*52-1.=0

20. 2x2 :0.7x + 0.3

2t. x2 - 5x: -9

3. x2-5x+6:06. 4n2 -20n:Og. 5*:125

12, 3k2 *2: -8k15. -5b2*3b-L=018. 3h2 =27

21.3w2-2zl+B:O24. 25* * 30t = -9

State the value of the discriminant for each equation. Then determine the numberof real solutions of the equation.

Extra Practice

Exponential Functions @p. 567-s72)

Graph each function. State the y-intercept, and state the domain and range. Thenuse the graph to determine the approximate value of the given expression. Use acalculator to confirm the value.

l. Y =7x'71"5''

(*)', (*)"

Graph each function. State the y-intercept.

4. y=3x+'1 5, y=2x-5,.y:(?). ,.v:5(?)

12. y=2(5)x +1 t5.y=(+)'.'

Determine whether the data in each table display exponential behavior. Explainwhy or why not.

t6.

3.v=(3)',(3)*'

6' Y:z'*l 7'

10. y=$(ix1 tt.

14.y=(*) 15.

U:3x+1U = 4(5)'

, =(1). -,

I 2 3 4

25 125 62s 3125

Grorrth and Decay Op.s75-s77)

FARMING Mr. Rogers purchased a combine for $175,000 for his farming operation.It is expected to depreciate at a rate of 18% per year. What will be the value of thecombine in 3 years?

REAI ESTATE The Jacksons bought a house for $65,000 n1992. Houses in theneighborhood have appreciated at the rate of 4.5"h ayear. How much is thehouse worth in 2003?

POPUTATION In 1950, the population of a city was 50,000. Since then, thepopulation has increased by 2.25% per year. If it continues to grow at this rate,what will the population be in 2005?

BEARS In a particular state, the population of black bears has been decreasing atthe rate of 0.75% per year. 1n1990, it was estimated that there were 400 blackbears in the state. If the population continues to decline at the same rate, whatwill the population be in 2010?

INVESTMENTS Determine the amount of an investment if $500 is invested at aninterest rate of 5.75% compounded monthly for 25 years.

MONEY Marco deposited $8500 in a 4-year certificate of deposit earning 7.25%compounded monthly. Write an equation for the amount of money Marco willhave at the end of the four years. Then find the amount.

TRANSPORTATION Elise is buying a new car for $21,500. The rate of depreciationon this type of car is B% per year. Write an equation for the value of the car in5 years. Then find the value of the car in 5 years.

POPUTATION In 2000, the town of Belgrade had a population of 3422. For each ofthe next B years, the population increasedby 49% per year. Find the projectedpopulation of Belgrade in 2008.

Extra Practice

17.

2.

t.

4.

5.

-l 0 I 2

-5 -l 3 7

Geometric Sequences as Exponential Functions (pp. s78-s8i)

836

Graph each set or ordered pairs. Determine whether the ordered pairs represent a

linear function, a quadratic function, or an exponential function.

l. (-2,1), (-1, -2), (0, -3), (1, -2), (2, L)

2. (-4, -5), (-2, -4), (0, -3), (2, -2), (4,0)

3. (-3,1), (-2,2), (-1, 4), (0,8), (L, 1.6)

Determine which model best describes the data. Then write an equation for thefunction that models the data.

COMPUTER GAME Kylie started a game of compute! "Tag, You're It"'She tagged two friends and so there are three players after round1. Each of them tagged three friends, and so on. The table showsthe number of players after the first few rounds. Determine whichfunction best models the number of players and then write a functionthat models the data.

ROCKET The table shows the height of a rocket that is launchedfrom ground level after a period of 4 consecutive seconds.

Determine which model best represents the height of therocket with respect to time. Then write a function that modelsthe data.

7.

Square Root Functiols (pp. 605-610)

Graph each function.

l. Y=lx-44. y:12l-+57' Y = -3\/T

10. y:5\/x + 1

Determine the domain and range of the function.

2.y:1lx+Z-t5' Y: -tE8. y=t/i+Stt. y:1f,i-z

t.

6.

9.

12.

y:L;/-x +z

U = 2t/x

,:tfzx-tU=6-\Ei

Simplifying Radical Expressions Op. Gr2-617)

Simplify.

r. \6d_ \/5). ----=

V5

' 'l{''lT15. Vm- .\/n

n {+*\u $. l tztf

\hoo

t?\l 32

/to-tlest/o . zt/s

tl r?Sr^b'

WYT

4.

8.

12.

t6.

20.

lt6zlBt'll12.

Vso

6\/, .\/3

t.

7.

It.

t5.

2. \/2oo

,.4tlo

*'G''1,14, \/7 . \/5

32cs

9d299x3y754

g221.

18.

Extra Practice

Simptify.

r.3\m+6\E -z\n4. s\E- q\/' + 3\D7. 2\E - 4\E

rc. z\re - 6\/N + 8\6tr. 5\/7 - 3\/N16. 4\/6 +s\/, -z\/ilT r=rs. toy'f - t/+s - rrl;Find each product.

zz. t/s(\E +z)z+, (t/z +s)'zo. (A + V-gXV5 +t/-z)

l. t/Sx :5+. {gb t2:o7. 2+3li =tsto. 14 -4=815.7+tl5c=9tO. +tfv-5:15p. tf zo, -.t++ =,zz. r/UltOaza =Sa

Operations with Radical Expressions (pp. 6le-623)

2. 6\re +7\E5. 3V5 - 5V5

s. 8\E + 4\Fdt. L4lst + s\Etr+. ztE - Vi8t7. -3lzo + 2\E - \/7t;zo. Vrs - lt

3. 2\E + sVd

6. 4\/s - 316

s. \/4s +6\/nt2.7\/6x -12\R15. 7'\/98 + s\E - z\Et8. 4\B + 6\E,r. zl!-r'l#*\@

t. t/T -5:o6.5-l3x:lg. t/a -2:0tz.1fSya4=7ts. 't/u = z\/p

n. |-to*-5:g*zt. tf2; - 12:,z+.1f3-2c13:2c

zt. 'tr(li + 3VF)

zs. (s - 'fr)(s + t/-z)

zt. (+tfr + '/r)({i - gv-s)

Radical Equations @p.624-628)

2. 4\/7 : \FmS. 1/V - 3:6a. lfzg - o

il.5+lv=914. Af 5t : to

17.4-\,lE-:920. \,fty+1=y-3zl. tfmazam:+


ffi Prhagorean Theorem tnp. G5o-635)

If c is the measure of the hypotenuse of a right triangle, find each missingmeasure. If necessary round to the nearest hundredth.

l. b=20,c=29,a=?4, b = 10, c: tf 2OO, a: ?

2. a=7,b=24,c=?5. a=3,c:3r/-2,b:?

5.

6.

9.

12.

a:2,b:6,c:?a:6,c:14rb:?o:{-6,b=Z,c=?a=9,c:15,b:?

7. a:t/i,r-1@,6-7 B. a=.t/tg,b:6,c=?lo. b=t/75,c:lo,a:? ll, b=g,c=\M,a:?

Determine whether each set of measures can be sides of a right triangle.Then determine whether they form a Pythagorean Tiiple.

15. (1.4,48,50)

17. (15,39,36)

838 Extra Practice

14. (20,30,40) 15. (21.,72,75)

lg. (2,3, 4)

16. (5, D,\M)ts. (10, 12,\D) 20. (\/V,8,\F1,)

The Distance and Midpoint Formulas (pp.656-64r)

Find the distance between each pair of points with the given coordinates.

t. (4,2),(-2,L0)

5. (3,1), (-2, -1)

2. (-5,1), (7, 6)

6. (-2,4), (7, -8)

5. (4, -2), (1.,2)

7. (-5,0),(-9,6)

t t. (3, 6), (5, -5)

4. (-2,4), (4, -2)8. (5, -1), (5, 13)

12. (-4,2), (5, 4)s. Ga,n,$\/-2,9) to. (6,3),(10,0)

Find the possible values of a if. the points with the given coordinates are theindicated distance apart.

15. (0, 0), (a,3); d = 5 14. (2, -1), (-6, a); d = 10 15' (1, 0), (a,6); d -- \/61

'W'NA

x

,,\,,

t_\z 15

For each set of measures given, find the measuresof the missing sides if AABC - LDEE.

4. a:5,d=10,b:8,c:75. a:2,b = 3, c:4, d:36. a = 6, d : 4.5, e :7,f = 7.5

7. a:15, c = 20,b = 1,8,f :198. f = 17.5, d - 8.5, e = 11, a -- 1..7

Use a calculator to find the values of each trigonometric ratio to the nearestten-thousandth.

5. tan42o

Similar Triangles @p. 642-647)

Determine whether each pair of triangles is similar. ]ustify your answer.

Find the values of the three trigonometric ratios for angle X.

4. sin 19" 5. cos 78"

Extra Practice

lnverse Variation gp. 66s-676)

Assume that y varies inversely as r. Write an inverse variation equation thatrelates x and y. Then graph the equation.

l. y= l0whenx=7.5

4. y= lwhenr:-0.52- y: -5whenx:35. y= -2.5whenr=3

!. y: -6whenx=-26. y = -2 when x: -L

Solve. Assume that y varies inversely as x.

7. If y: 54 when x = 4, find x when U :27.8. If y : 18 when x : 6,find x when A = 12.

9, If y =12whenx=24,findxwheny=!.10. If y : 8 when x = -8, findywhen x : -1.6.

ll. If y = 3 when x: -B,fndy when x = 4.

12. If y:27 when*:t,fndywhen * =1.ll. If y = -3 when x = -8,fndy when x:2.la. If y = -3 when x: -3, find r when U = 4.

15. If y: -7.5 when x:2.5,tndy when x: -2.5.16. If y : -1.4when x = -3.2,find x when ! : -0.2.

Rational Functions @p. 677-6Bt)

Identify the asymptotes of each rational function.

r.f(x)=#+. f(x): #s

7.f(x):#to.a-=-z ^" -7X-3

z.f(r)=#s.f(x):#

t. f(x) = V+,6. fk\--]-r, x-6

A:-]:" x-5.1

Y - x+2

State the excluded value for each function.

s. y =*tt. y: 2x*7 12.

iitying Rational Expressions (pp. 684-6er)

State the excluded values for each rational expression.

L--I_x+ I

- 13a5.-39az

8. 1+ba/ -b2^2tt. " -!a- I

u.H840 Extra Practice

- 38x2o' 42xv

a+49. _+_

y'-16

n t+4x" - 1,6

6a3 - lza215._::.----:_

l2u2 - 1.8

- b2-5b+6L-" b2-Bb+15

p+52(p + 5)

c2-4c2+4c+4r3-12r-1.

5x2+1,0x+53x2+6x+3

2.+ . -,,ct-4

Simplify each expression. State the excluded values of the variables.

7.

t0.

15.

16.

Multiplying and Dividing Rational Expressions 0p. oe2-6e8)

Find each product.-a2bc'' u+'a- 70n3 l2n2x4+. .--. --------:--;

6x" 25nzxz

Find each quotient.

1.5*'! . 3oma

l2a' 78ap

xLv 2azta. iu +;x,

,r. t2-.2t=15 *t*3t-5 t+5

6a2n 12n8"'?' %Smsc 4a2m

--;. -------:_

70at 9cJ

t0.

25g7h _,_

Sgshz

28f 42s2t3

p2 .2r?'l,4tr3 7t

+#+@+2)

l0x2+29x+21.5x+7

27c2-24c+89c-2

2a2d 9b2cgbc' 16rn,5n-5 9

3 'n-lx+2

6.

7.(a - 5)(a + 1) (a + 7)(a - 6)

(, + t)@ + n' (a + 8)G_51

az 3a -3b,-b' a

x-1,(x +2)(x -3) (r - 3)(r - 1)

2a+4b 255 '-oa + sb

u. @ff+ 3a +2b

I6.

t9.

12.

15.

t8.

H+Q5d2-F)3d9

2d2-3d ' 2d-3

I0.

15.

I.

t.

5.

7.

9.

12.

(2x2-llx-20)+(2x+3)(*2+4m-5)+(m+5)(c2+6c-27)+(c+9)

Q*-L4t-24)+(3r+4)12n2+36n+15

6n+32n3+9a2+5a-72

a+3

2.

4.

6.

8.

(a2+lOa+2I)+(a+3)(x2-2x-35)+ (x-7)(y2-6y-25)+(y+7)(2r2-3r-35)+(2r+7)

4t3+17t2-II I.

14.

4t+l4bs+7bz-2b+4

b+2

Dividing Polynomials (pp. 700-70s)

Find each quotient.

Adding and Subtracting Rational Expressiotls (pp. 706-7ri)

Find each sum./- a,t.;+;

- k.2k'' 5+Tg.3t+2 + t=*2

3t-2 tz-4

Find each difference.

_? _A10. " + -=---:-a-5 az-5a

ua2'2

4a3I-

2a+6' a+3

8

m-2 m-2P _r*3t

24. x2+2x+1,x2-2x-3

4.

8.

t.

7.

-a2a'' tz+ i

R_2b. =--|--/_a 6a

5-7-I-2t' 2t67-t-------;5x 70x'

12.

r6.

il.

I5.

5x _3x24 24

y _2yb+6 b+6

7p 8p

JJ

q+2 _a+36

8k _3k5m 5m

3z _227w2 w

y+5 _ 2y

Y -5 y2 -25ts. -J-a'-4 20. ffia+2

r8.17.

21.

6

5m

Find the LCM for each pair of polynomials.

22. 27a2bc,36ab2c2 21. 3m - 1,,6m - 2

Extra Practice 841

Mixed Expressions and Complex Fractions

Write each mixed expression as a rational expression..)

1.4+1;t

- L)4. 3z +' !'

a


_q6+;2t

----------= -f ua-1

3b ++:3rz ', --!-

x-3vr1

r0. +x-

v'.2a+.-,

t4. --+ l-i

" a-2

fe.+t'

,P

7

u8. +,!

7

^1

7.+4iq\

:1:

il.3'I'> t5-ry

11xtlJ

t2' T;y-T

+1,2^

15. =' -otz+5t+6

Solve each equation. State any extraneous solutions., k,2k_ 5'' 6-T--,4' 5, + 2*:1- 2b-3 b b+3

7 2- 14

Io. 5x- + 1:5x+l x

lr. 2x = - =4r :72

x-J 3-X

16. 3,T10 + ff6 = 2

2x,27 4x7 ' 1o- i2a-3 2a L

6 -3'2LUa

y-4 5-r-_) .)-

r*2 r+9 "1.416

b-6- 2' b-82a-3 ^ 72a-3 ^- a+2

183b b+33x+2 x+3a , _h

x ' x -r2t3

tt1tL-ITJ L

m 5 -1m+l' m-7

O^^4a + 1,5

z+3 z+1- 1 a-'a- I L-J

12.

15.

t8.

I t.

17.

Identify each sample, suggest a population from which it was selected, and statewhether it is unbiased. (random) or biased.If unbiased, classify the sample assimple, stratified, or systematic. If biased, classify as conoenience or aoluntaryresponse.

l. The sheriff has heard that many dogs in the county do not have licenses.He checks the licenses of the first ten dogs he encounters.

2. Every fifth car is selected from the assembly line. The cars are also identified bythe day of the week during which they were produced.

5. A table is set up outside of a large department store. All people entering the storeare given a survey about their preference of brand for blue jeans. As people leavethe store, they can return the survey.

4. A community is considering building a new swimming pool. Every twentiethperson on a list of residents is contacted for their opinion.

5. A group of custom chopper builders are interested in finding the type of art workpeople prefer on their bikes. They line up a group of each of their choppers at ashow to see which designs people appear to prefer.

842 Extra Practice

Analyzing Survey Results Op.746-7s5)

Which measure of central tendency best represents the data? ]ustify your answenThen find the measure.

l. COMPUTER USAGE To determine if they need to add more computers for internetaccess at the Grandview Lrbrary, the staff kept track of the number of patronswho used the computers each evening between 5PM and 8PM during a two-week perio d. 132, 12, 45, 38, 26, 29, 3L, 22, 40, 20, 24, 271

2. CHOCOLATE MlLK The preschool cafeteria staff wanted to decide if they shouldcontinue to order chocolate milk for the children. For two weeks they kept acount of the number of half-pints of chocolate milk requested by the children.

{21, 17, 17, 2L, 18, 18, 21,, 1,8, 19, 20l.

Given the following portion of a survey report, evaluate the validity of theinformation and conclusion.

5. ONLINE SURVEYS An online survey was conducted by an advertising firm todetermine how many potential customers they might reach. The firm sent out10,000 surveys and receivedz,3}} online resPonses. Question: How many hoursper week, outside of work time, do you spend on your computer? Results: 0-2,4o/";34,20o/o;7-t2,32'/.;1,3-20,20"/";21'10,12"/"; rnore than 30, l'2%. Conclusion:One-third of all adults spend between 7 andl2hours each week on their homecomputers.

Statistics and Parameters (pp. 7s6-762)

Identify the sample and the population for each situation. Then describe thesample statistic and the population parameter.

l. As part of their quality control program, the Venice PizzaParlor called L25 of.

its delivery customers to see if they were satisfied with the delivery service.

The percentage of those responding YES is calculated.

2. A random stratified sample of.1,,200 high school band members from across thecountry is surveyed about how many hours they spend practicing each weekduring football season.

Find the mean, variance, and standard deviation of each set of data.

!. {7,10,22,1,5,11,1 4. 111.,1.6,20,17ll 5, 145,40,54,67,44)

Permutations and Combinations (pp. 764-770)

Determine whether each situation involves a permutation or combination.Explain your reasoning.

l. three topping flavors for a sundae from ten topping choices

2. selection and placement of four runners on a relay team from 8 runners

5. five rides to ride at an amusement park with twelve rides

4, hrst, second, and third place winners for a 10K race

Evaluate each expression.

8. c(6,5)

Extra Practice

5. P(5,2) 6. P(7,7) 7. c(10,2)

Probability of Compound Events @p.771-778)

SIBIINGS Perry took a survey of his classmates to seehow many siblings each had. The results are in the table.

a. Find the probability that a randomly chosenclassmate will have 4 siblings.

b. Find the probability that a randomly chosenclassmate will have less than 3 siblings.

CARS A customer visiting a new car lot was looking for aconvertible. The Buyers Co. lot had 8 black,6 wh7te, 4silver,5 red and 7 green convertibles to consider.

Find the probability that a randomly chosen car willbe silver.

Find the probability that a randomly chosen car willbe red or black.

b.

Probability Distributions (pp. 77e-786)

Use the table that shows the results ofa survey about household occupancy.

I. Find the experimental probability distribution for thenumber of households of each size.

2. Based on the survey, what is the probability that aperson chosen at random lives in a household withfive or more people?

5. Based on the survey, what is the probability that aperson chosen at random lives in a household with1 or 2 people?

Toss 4 coins, one at a time, 50 times and record your results.

l. Based on your results, what is the probability that any two coins show tails?

2. Based on your results, what is the probability that the first and fourth coinsshow heads?

5. \zVhat is the theoretical probability that all four coins show heads?

Determine whether the events are independent or dependent. Then find theprobability.

4. Abag of colored candies contains 12red,5 brown, 7 orange,6 blue,4 green and6 purple candies. Alex reaches in the bag and pulls out one piece of candy andthen a second piece without replacement. What is the probability that the firsttwo choices are blue?

5. Cretchen and her friends are having a sleepover and movie marathon. They haverented four movies: a comedy, a horror movie, a mystery and a romance. What isthe probability that they will watch a mystery and then a romance?

6. For a special gamq the sides on a number cube are colored red for the oddnumbers, L,3, and 5, and green for the even numbets,Z,4 and 6. What is theprobability on two rolls of the cube of getting a green side, followedby a 4?

844 Extra Practice

Probability Simulations Op. 787-7s2)

Expressions, Equations, and Functions (pp. 2-71)

2.

l. GEOMETRY The area of a rectangle is theproduct of the length I and the width zl.(Lesson t-t)

a. Write an expression for the area of arectangle.

b. Write an expression in terms of I for thearea of a rectangie that is twice as wide as itis long. ,ffi

t.

SIGNS A restaurant has a cylindrical shapedsign made to look like a bucket of their friedchicken. The volume of a cylinder can befound by the product of the radius squared,the height of the cylinder and zr.

a. Write an expression for the volume of acylinder.

b. Evaluate the volume of the sign if the radiusis 3 feet and the height is 6 feet.

c. For a bill board on the freeway, thedimensions of the sign were changed to a9 foot diameter and a height of 9 feet. Findthe volume of the bucket on the billboard.(Lesson I -2)

TRAVEL Ticket prices for an amusement parkare shown in the table below. There are twoadults and three children in the Careen family.The children's ages are L1, 8, and 4. (Lesson t-3)

a. Write an expression for the cost c of the dayat the amusement park for the family.

b. Find the cost of the day at the amusementpark.

What is the cost per day of the vacation ifthe family stayed three days?

What is the cost per day of the vacation ifthe family stayed seven days?

,.

d.

4. FOOD The cafeteria has the following menu.

Charlie gets lunch for himself and two friends.Charlie wants pizza and a drink. His friendseach have a sandwich, fries, and a drink. (Lesson

1-4)

a. Write and evaluate an expression to find thetotal cost.

b. How much would it cost if Charlie boughtthe same thing as his friends?

DISTANCE In a given amount of time, ]enadrove twice as far as Rita. Altogether theydrove 120 miles. Find the number of milesdriven by Jena. (Lesson l-s)

GRAPH Describe what is happening in thegraph. The graph represents Nikki's trip to thestore. (Lesson 1-6)

IDistance/l

Time

7. Is the following relation a function?Explain. (Lesson 1-7)

Domain Range

Find a counterexample for the followingstatement. lf you read music, you sing in achoir. (Lessont-l)

Identify the hypothesis and conclusion of thefollowing statement. Then write the statementin if-then form. Mei and lanel znill go to the mallafter school. (Lesson l-7)

5.

6.

8.

9.

-3-1

0

1

I

=6

Mixed Problem Solving 845

linear Equations (pp. 72*r4e)

l. BABY-SIfiING As a part-time job, Andreababysits. She charges $4 per hour and $5 forgas money. Write an equation that could beused to find how much she will make if shebabysits for 4 hours. (Lesson 2-l)

2. WORTD RECORD AtlO7inches, Robert PershingWadlow was the tallestman to ever live. If theaverage 1S-year-old male is68 inches tall, write andsolve an equation to findthe number of inches tallerMr. Wadlow was than theaverage 15-year-oldmale. (Lesson 2-l)

Three fifths of Marcus's classmates havebrown eyes. There are 18 students who havebrown eyes. Determine how many studentsare in the class. (Lesson 2-2)

TOCKER NUMBERS A.dy, Kayla, and Samanthahave 3lockers in a row. The lockers arenumbered consecutively and the sum of thelocker numbers is756. Write and solve anequation to find all three locker numbers.(Lesson 2-5)

BEAD WORK Sarah said, "I counted my beads,and I have three more than 4 times a certainmystery number." |asmine had the sameamount of beads as Sarah, but said she had 9less than 5 times the mystery number. Theychallenged their art teacher to discover themystery number. (Lesson 2-4)

a. \A/hat equation could the art teacher use tofind the number?

b. \Mhat is the mystery number?

c. How many beads does each girl have?

DRMNG A car has an average fuel economy of23 miles per gallon. The car gets 4 miles pergallon fewer in city driving and 4 miles pergallon more in highway driving. Write andsolve an absolute value equation to find thefuel economy of the car in city and highwaydriving. (Lesson 2-5)

**

5.

4.

5.

6.

846 Mixed Problem Solving

8.

IAWN CARE Jos6's mom tells him she will payhim $20 if he mows the lawn in an hour, plusor minus 15 minutes. If it takes los673 minutesto mow the lawn, will his mom pay him?Explain your reasoning. (Lesson 2-5)

ARCHTTECTURE Isaac drew the following floorplan of his room. Write and solve a proportionto find the actual length of his room if theactual width is 12 meters. (Lesson 2-5)

CARS Daniel's father purchased a vintage carwhen it was new. He paid $3334. Last year, hesold it for $28,250. (Lesson 2-7)

a. Determine the percent of change to thenearest percent.

b. Is this a percent of increase or decrease?

Explain.

WEATHER Emily went to Canada for vacation.Listening to the weather report she heard thatthe high for the day was going to be 23"C. Sheremembered that the formula for changingFahrenheit to Celsius was C = ftf - 32).(Lesson 2-8)

a. Solve the formula for F.

b. Use the new formula to find that day's hightemperature in degrees Fahrenheit.

c. If the low temperature for the day was 16oC,find the day's low in oF.

TRANSPORTATION Hector rode his bike toMatthew's house. It took him 10 minutes toride the 3-mile trip. When it was time to leave,he saw that his tire had gone flat and he wouldneed to walk home.It took him 45 minutes towalk home. What was his average speed forthe round trip? Express your answer in milesper hour rounded to the nearest tenth.(Lesson 2-9)

9.

10.

I t.

2.

l. MOVIES Tickets for the movies cost $5 forstudents and $8 for adults. The equation5x + 8y: 80 represents the number ofstudents x and adults y who can attend a

movie for $80. (Lesson 5'1)

a. Use the x- and y-intercepts to graph theequation.

b. Describe what these values mean in thecontext of this situation.

FUNDRAISING Shawn's class is selling candy toraise money for a class trip. They paid $55 forthe candy, and they are selling each candy barfor $1.75. The functionA :1.75x - 55

represents their profit y for selling x candybars. (Lesson 5-z)

a. Find the zero of the function.

b. Describe what the zero means in the contextof this situation.

c. Graph the function.

PHOTOS The average cost of using an onlinephoto finisher decreased from $0.50 per printto $0.27 per print between 2002 and 2005. Findthe average rate of change in the cost. Explainwhat the rate of change means. (Lesson l-3)

WAGES The weekly salary Enrique earns zu

varies directly as the hours h that heworks. (Lesson 5-4)

a. Write this situation as an equation.

b. Graph the equation if Enrique makes $11.50an hour.

c. How many hours does Enrique have towork to earn $690?

5. MONEY The table represents Tiffany'sincome. (Lesson 5-5)

Write an equation for this sequence.

Use the equation to find Tiffany's income ifshe works 20 hours.

,.

a.

b.

7.

SAVINGS Payat has $680 in a savings account.He makes a deposit after he receives eachpaycheck. After one month he has $758 in theaccount. The next month the balance is $836.The balance after the third month is

$914. (Lesson 3's)

a. Write a function to represent the arithmeticsequence.

b. Graph the function.

c. How much will Payat have in his savingsaccount at the end of six months?

SALES Percy sells cell phones in the mall. Inaddition to his salary, he receives a bonus foreach cell phone that he sells. The table showsthe number of phones he sells and the amountof his bonus. (Lesson 5-6)

a. Graph the data.

b. Write an equation to describe thisrelationship.

c. Determine the amount of his bonus if Percy

sells 10 phones.

STRAWBERRIES The table below shows the cost

of picking your own strawberries at a localfarm. (Lesson 5-6)

Graph the data.

Write an equation in function notation todescribe this relationship.

How much would 6 pounds of strawberriescost if you picked them yourself?

How much would 9.5 pounds ofstrawberries cost if you picked themyourself?

8.

a.

b.

d.


Linear Functions and Relations (pp. zlo-2ls)

l. FINANCES Brandon is saving money topurchase a new video game system. He has$94 and plans to save $7 each week for the nextseveral weeks. (Lesson 4-l)

a. Write an equation for the total amount S

that he has saved after w weeks.

b. Graph the equation.

c. Find out how much Brandon will havesaved after B weeks.

2. PHOTOGRAPHY An online photo processingcompany produces printed and bound photoalbums. The standard price for an albumincludes up to 20 pages. There is a fee forevery two additional pages. To make a 30-pagebook, you pay $29.94. To make a 2-pagebook,you pay $41.88. (Lesson 4-2)

a. What is the cost for each additional 2 pages?

b. What is the cost of a2}-page book?

5. FITNESS The graph shows the cost of amembership to the local gym. Write anequation in point-slope form to find the totalprice y for any number of months x. (Lesson 4-3)

Number of Months

MAPS The map below shows InterstateHighways 80 and 70 through a portion ofWyoming and Colorado. (Lesson a-+)

a. Find the slope of the lines that approximatethe path of each highway.

b. Are the highways parallel?

a,a)

a

4.

900

800

700

600

500

4003002001 00.

2 4 6 8 1012141618x


5.

5. PTANETS The table shows the distancebetween selected planets and the Sun and thediameters of the planets. Draw a scatter plotand determine what relationship exists, if any,in the data. (Lesson 4-5)

ATTENDANCE Rodeo Houston is an eventthat features rodeo events, a Bar-B-Quecompetition, concerts by top performers, artauction and contributes scholarships toyouth organizations. The attendance forthe rodeo championships are listed in thetable below.

a. Find an equation for the median-fit line.

b. According to the equation, how manyattended the rodeo's championshipin2009?

7. PARKING Mika was visiting the state library.The fees for parking are shown in thetable. (Lesson 4-7)

Draw a graph that shows the parking feey for the time spent parked x.

If Mika visited the state library for three anda half hours, how much did she pay forparking?

b.

2002 2004 2006 2008

68,256 70,668 72,867 71,165

I5 minutes or less

each addtional hour

or partial hour

Linear lnequalities 0p. 2so-32e)

l. SHOPPING Jeff is buying a new car but owes

$3000 on his old one. Jeff can spend no morethan $18,000 to pay off his old car and buy anew one. (Lesson 5-l)

a. Write an inequality to show how much Jeffcan spend on his new car.

b. Solve the inequality.

2. TOMATOES There are more than 10,000

varieties of tomatoes. One seed comPanyproduces seed packages for 200 varieties oftomatoes. For how many varieties do they notprovide seeds? (Lesson 5-l)

3. SURVEYS Of the students at Davidson HighSchool, fewer than92 students said they likestrawberry ice cream. This is about one sixthof those surveyed. (Lesson 5-2)

a. Write an inequality to represent thissituation.

b. How many students were surveyed?

4. ARCHITECTURE The dimensions of Lisle's roomare shown below. If the area of the room is atleast 96 square feet, what is the least width theroom could have? (Lesson 5-2)

a. Define a variable.

b. Write an inequality.

c. Solve the problem.

SAVINGS Ramone is raking yards for $22peryard to earn money for a car. So far he has

$2150 saved. The car that Ramone wants tobuy costs at least $8290. (Lesson s-3)

a. Write an inequality to show how manymore yards Ramone still needs to rake toearn enough money to buy the car.

b. Solve the inequality.

CHARITY Avery High School holds a walk-a-thon each fall to raise money for charity. Thisyear they want to raise at least $375. Eachstudent earns $0.75 for every half mile walked.How many miles will the students need towalk? (Lesson 5-5)

121,1r-.ltl

5.

6.

7. SATES A school buys 500 T-shirts. In additionto the price per shirt, there is a $45 set-up fee.

The school can afford to spend no more than$2295. (Lesson s-5)

a. Write an inequality to shor,v the relationship.

b. What must the price be for the school toafford the shirts?

S. FISH TANK The temperature in a fish tank mustbe at least 77"F and at most 83oF. (Lesson 5-+)

a. Write a compound inequality that describesacceptable temperatures for a fish tank.

b. Graph the inequality.

9. MOVIES A recent survey showed that73% ofyoung adults had seen a movie recently' Themargin of sampling error was within 5percentage points. Find the range of youngadults who saw a movie recently. (Lesson 5-5)

t0. SNOW When the temperature in the clouds is

7'F plus or minus 3oF, star-shaped crystals ofsnow form. At 14'F plus or minus 4"F, plate-shaped crystals are formed. (Lesson s-5)

a. Find the range of temperature that producesstar-shaped crystals.

b. Find the range of temperature that producesplate-shaped crystals.

I l. ,OBS It takes a librarian L minute to renew a

library card and 3 minutes to make a new card.Together, she can spend no more than 30

minutes renewing and making cards. Write aninequality to represent this situation, if r is thenumber of cards she renews and y is thenumber of new cards she makes. (Lesson 5-6)

t2. MOVING A moving comPany charges $95 anhour and $0.08 per mile. If Brianna has only$500 for moving exPenses, can she afford tohire this moving company if it will take5 hours and the houses are75 miles apart?(Lesson 5-6)

t3. DELIVERIES A delivery truck is transporting theitems shown. (Lesson 5-6)

If the delivery truck has a 2500-poundweight limit, will the truck be able to deliver30 televisions and 45 computers? Explain.


Systems of Linear Equations and lnequalities (pp. 330-5s7)

t. FUNDRAISERS The French Club is sellingheart-shaped lollipops to raise money for a tripto Quebec. They paid $20 for the candy mold,and the ingredients for each lollipop cost 90.50.They plan to sell the lollipops for 91.00.(Lesson 5-l )

a. Write an equation for the cost of supplies yfor the number of lollipops sold x, and anequation for the income y for the number oflollipops sold x.

b. Graph each equation.

c. How many lollipops do they need to sellbefore they begin to make a profit?

2. COMPUTER REPAIR An in-home computerrepair provider charges $40 per hour forinstallations and $60 per hour fortroubleshooting and repair. Last week thebusiest employee worked 40 hours andbrought in $2100. How many hours did theemployee spend doing each type ofservice? (Lesson 6-2)

5. TOURS The Snider family and the Rollinsfamily are traveling together on a trip to visit acandy factory. The number of people in eachfamily and the total cost are shown in the tablebelow. Find the adult admission price and thechildren's admission price. (Lesson 6-J)

4. GEOGRAPHY In 2004, the state capital with thesmallest population was Montpelieq, Vermont.The state capital with the largest populationwas Phoenix, Arizona. The difference betweenthe two populations was 1,410,006. Thepopulation of Phoenix was 3,881 more than176 times as large as the population ofMontpelier. Find the population of eachcity. (Lesson 6-4)

5. CANOEING A canoe travels 10 miles upstreamin 2.5 hours. The return trip takes the canoe2 hours. Find the rate of the boat in still waterand the rate of the current. (Lesson E-4)


7.

6. FAIR At a county fair, the cost for 4 slices ofpizza and 2 orders of French fries is 921.00.The cost of2 slices ofpizza and 3 orders ofFrench fries is $16.50. To find out how much asingle slice of pizza and an order of Frenchfries costs, determine the best method to solvethe system of equations. Then solve thesystem. (Lesson 5-5)

OFFICE SUPPIIES At a sale, Ricardo bought24reams of paper and 4 inkjet cartridges for $320.Britney bought 2 reams of paper and 1 inkjetcartridge for $50. The reams of paper were allthe same price and the inkjet cartridges wereall the same price. A system of equations canbe used to represent this situation. Determinethe best method to solve the system ofequations. Then solve the system. (Lesson 6-5)

EIEVATIONS The highest and lowest elevationsfor several states are shown in the tablebelow. (Lesson 6-6)

a. Write a matrix to organize the given data.

b. \tVhat are the dimensions of the matrix?

c. Which state has the highest elevation? thelowest elevation?

KENNEDY SPACE CENTER Admission to theKennedy Space Center for 2 adults and 3children costs $150. Admission for 5 adults and2 children is $246. (Lesson 6-7)

0. Write a system of linear equations to modelthe situation. Let a represent adultadmission, and let c represent childadmission.

b. Write the augmented matrix.

c. What is the price for adult and childadmissions?

9.

Polynomials (pp. ie8-467)

l. POOTS Find the area of the swimming poolbelow. (Lesson 7-l)

GARDENING Felipe is planting a flower gardenthat is shaped like a trapezoid. Use the formula

A = +hp, + br) to find the area of Felipe's

garden. (Lesson z-t)

GEOMETRY The area of a rectangle is 36man6

square meters. The length of the rectangle is6m3n3 meters. \Atrhat is the width of therectangle? (LessonT-2)

ASTRONOMY The order of magnitude of themass of Earth is about 1024. The order ofmagnitude of the mass of the Moon is about1022. How many orders of magnitude as big isthe Earth as the Moon? (Lesson 7-2)

MAMMATS A blue whale has been caught thatwas 4.2 x 105 pounds. The smallest mammal isa bumblebee bat, which is about 0.0044pound. (Lesson 7-3)

a. Write the whale's weight in standard form.

b. Write the bat's weight in scientific notation.

c. How many orders of magnitude as big is ablue whale as a bumblebee bat?

GARDENS Megan had a square garden. She

expanded this garden by 3 feet in one directionand 5 feet in the other. (Lesson z-+)

a. Write a polynomial to describe the area ofthe new garden if the old garden was x feetwide.

b. If the original width was 12 feet, find thearea of the new garden.

c, Find the area of the new garden if theoriginal width was 16.

5xy

2.

5.

4.

5.

6.

8.

7. GEOMEIRY Write a polynomial that representsthe area of the figure. (Lesson 7-5)

GEOMETRY Find the perimeter and area of therectangle shown below. (Lesson 7-5)

4x+3

SHOPPING Nicole bought r shirts for $15.00each, y pairs of pants for $25.72 each, and zbelts for $12.53 each. Sales tax on these itemswasTo/o. Write an expression to find the totalcost of Nicole's purchases. (Lesson 7-6)

MANUFACIURING AcomPany is designing abox for dry pasta in the shape of a rectangularprism. The length is 2 inches more than twicethe width, and the height is 3 inches more thanthe length. Write an expression for the volumeof the box. (Lesson 7-7)

GEOMETRY Write an expression for the area ofthe trapezoid shown. (Lesson 7-l I)

CARPENTRY Miguel's room is x feet on eachside. He adds book shelves that are 2 feet deepto two adjacent walls. (Lesson 7-8)

a. Show how the new area of the floor space

can be modeled by the square of a binomial.

b. Find the square of this binomial.

TOYS A flying disk shaped like a circle has aradius of x - 4 centimeters. (Lesson 7-8)

a. Write an expression representing the area ofthe flying disk.

b. If x is 15, what is the area of the flying disk?

5x2 +2x-2ffi9.

t0.

lt.

12.

3x+ 5

2x-3

t5.


Factoring and Quadratic Equations (pp. 46s-s2r)

t. CANDY Sada was packing candy into gift bags.She has 42 chocolate truffles, 96 pieces of taffy,and 108 jelly beans. Sada wants to package thesame number of candies in each bag, and eachbag should have every type of candy. ftesson B-t)

a. If she puts the greatest possible number ofcandies in each bag, how many bags can shemake?

b. How many pieces of each type of candy willbe in each bag?

2. VOLUNTEERING Catalina's class collected soap,washcloths, and toothbrushes to give toseveral homeless shelters in the area. Thenumber of each item collected is shown in thetable below. (Lesson B-l)

If she puts the greatest possible number ofitems in each box, how many boxes can shemake?

How many of each item will be in each box?

SOCCER Jorge is kicking a soccer ball straightup into the air. The height of the ball isdescribed by the equation h : -1612 + 20t,where h is the height of the ball and f is thetime in seconds. How long will it take the ballto hit the ground? (Leson a-z)

PHOTOGRAPHY Kelsey has a 4-inch by 6-inchphotograph she wants to frame with a mat.The area of the picture and mat is twice aslarge as the area of the picture itself. If shewants the mat to be the same width on allsides, what are the outside dimensions of themat? (Lesson 8-3)

b.

,,

4.


6.

5. BALTET Aballet dancer is practicing a leapfrom the stage to an upper deck. If her initialvelocity as she leaps is 18 feet per second, howlong is she in the air before she lands on theupper deck,5 feet above the lowerdeck? (Lesson 8-4)

GRAPHICS A computer cartoonist uses theequations A : x2 - 4 and A = 4 - 12 as thebasis for his drawing of a fish. The graphs ofthe two equations intersect at the roots of theequations. Find the roots. (Lesson g-s)

STORAGE Chase is building a box for theshelves in his father's garage. In order to fit theshelves as neatly as possible, the box needs tobe 1 inch taller and 5 inches longer than it iswide. ftesson 8-6)

0. Let ra represent the width of the box. Writean expression for each remaining dimensionin terms of zo.

b. If the volume of the box is 2112 cubic feet,what are the dimensions of the box?

RECREATION Danille and Pete make a slingshotto shoot water balloons. If a water balloonshoots up with an initial velocity of 64 feet persecond, how long is it until it hits theground? (Lesson 8-6)

7.

L

Quadratic and Exponential Functions (pp. 522-6ot)

5.

PHYSICAL SCIENCE A model rocket is launchedwith a velocity of 64feet per second. Theequation h : -16t2 * 64f gives the height ofthe rocket f seconds after it is launched.(Lesson 9-l )

a. Graph the function.

b. What is the maximum height that the rocketreaches?

c. How many seconds is the rocket in the air?

FIREWORKS Some fireworks are fired verticallyinto the air from the ground at an initialvelocity of B0 feet per second. The equationh(t) = -1.6* * BOf models the height h, in feet,of the fireworks after t seconds. Find thehighest point reached by the projectile just as itexplodes. (Lesson 9-l)

BASEBATL The International Space Agency haslanded a robotic explorer on a planet. Therobot launches a baseball directly upward at147 ft/ s. The equation for the path of thebaseball is h : -49t2 + 1.47t, where fu is theheight of the baseball in feet and f is time inseconds. Assuming no wind, how long will ittake for the ball to land on the surface?(Lesson 9-2)

4. DESIGN For a design competition, Maggiedropped a device from the bleachers. Theequation of the dsvice's height in feet h aftet tseionds ish : -1.6P t 20. Compare the graphof this function with its parent graph.(Lesson 9-3)

5. PHYSICS An object is launched at 17.2 m/ sfrom a 25-meter tall platform. The equation forthe object's height h at time f seconds afterlaunch is h(t) = -4.9t2 + 17.2t + 25, where h isin meters. (Lesson 9-4)

a. Graph this equation.

b. When does the object strike the ground?

6. GEOMETRY The area of a square can be tripledby increasing its length by 6 centimeters andincreasing its width by 3 centimeters.

'[,.rF".lx+6

What is the length of the side of the square?(Lesson 9-4)

7. FENCE Jackie and Ken are building a fencearound a rectangular field. They want toenclose an area of 75 square feet. The widthshould be 3 feet longer than the length of thefield. What are the dimensions of the field?Round to the nearest tenth, if necessary.(Lesson 9-5)

S. VOttEYBAtt A volleyball is thrown straight up.The equation that describes its motion ish(t) :-1,6* + 48t + 4, where /z represents the heightin feet and f represents time in seconds. Howlong will it take for the ball to hit the ground?Round to the nearest hundredth, ifnecessary. (Lesson9-5)

9. BIOIOGY The functionf(t) = 50(1.07)' modelsthe growth of a fly population, where f(t) isthe number of flies and f is time in days. Afterthree weeks, approximately how many fliesare in this population? (Lesson 9'6)

10. INVESTMENT Nicholas invested $2000 witha5.75% interest rate compounded monthly.How much money will Nicholas have after5 years? (Lesson 9-7)

I l. RESTAURANTS The total restaurant sales in theUnited States increased at an annual rate ofabout 5.2"/" betw een 1996 and 2004. In 1996,total sales were $310 billion. (Lesson 9-7)

a. Write an equation for the average sales peryear t years after 1996.

b. Predict the total restaurant sales in 2012.

12. TENNIS Each year a local country clubsponsors a tennis tournament. Play starts with256 participants. During each round, half ofthe players are eliminated. How many playersremain after 6 rounds? (Lessong-8)

15. CAR CLUB The table shows the number ofcar club members for four consecutive yearsafter it began. (Lesson 9-9)

Determine which model best representsthe data.

Write a function that models the data.

Predict the number of car club membersafter 6 years.

b.

c.


Radica! Functions and Geometry (pp.602-66s)

l. PENDUTUMS The period of a pendulum is thetime in seconds it takes to swing from one sideto the other and back. If the length of thependulum I is given in meters, the period T is

given by T : Zn ll*,where g is thegravitational condt8nt,9.8 meters per secondsquared. The Foucault Pendulum at thePantheon in Paris, France, has a length of 67meters. Find the period of the FoucaultPendulum. (Lesson l0-l)

KINETIC ENERGY The speed a of aballin metersper second can be determined by the equation

I nt.a : ! ff ,where k is the kinetic energy in

Joules and m is the mass of the ball inkilograms. (Lesson I0-2)

a. Simplify the formula if the mass of the ballis 2 kilograms.

b. If the ball is traveling 10 meters per second,what is the kinetic energy of the ball inJoules?

WALLPAPER Ruby is designing a wallpaperborder using a pattern of two triangles. If themeasurements given are in inches, find theexact length of the segment shown. Then findthe length to the nearest quarter inch.(Lesson ! 0-5)

SOUND The speed of sound V in meters persecond near Earth's surface is given byV = 20 rf t + ZfZ, where f is the surfacetemperature in degrees Celsius. (Lesson l0-J)

a. What is the speed of sound near Earth'ssurface at -1oC and at 6'C in simplestform?

b. Approximately how much faster is thespeed of sound at 6oC than at -1"C?

SKYDMNG The approximate time f in secondsthat it takes an object to fall a distance of d feet

fris given by t :

V #. t"Orose a parachutist

falls 13 seconds before the parachute opens.How far does the parachutist fall during thistime period? (Lesson l0-4)

2.

3.

4.


7.

8.

6. DELIVERY Ben and Amado are delivering afreezer. The bank in front of the house is thesame height as the back of the truck. They setup their ramp as shown. What is the length ofthe slanted part of the ramp to the nearestfoot? (Lesson lO-s)

TADDER An 18-foot ladder is leaning againsta building. For stability, the base of the laddermust be 3 feet away from the wall. How far upthe wall does the ladder reach? (Lesson I0-5)

SNOWMOBITES Tai went snowmobiling withfriends. His starting and ending points areshown on the graph. Use the Distance Formulato find how far he has to ride if he can ridestraight home. (Lesson t o-o)

FLAGS Sarah needs to determine the height ofthe flag pole in her yard. On a sunnyafternoon, Sarah's shadow is2feet 6 incheslong. She is 5 feet 3 inches tall. The shadow ofthe flag pole is 6 feet long. How tall is the flagpole to the nearest tenth of a foot? (Lesson l0-7)

SCHOOL For a class project, Hailey needs tomeasure the height of her school. Hailey placesa mirror 75 feet from the base of the school andbacks 10 feet away from the mirror. If Hailey is5 feet tall, how tall is the school? (Lesson to-z)

I I. TIGHTHOUSE

(Lesson I 0-8)

9.

t0.

How tall is the lighthouse?

#B'

ntl& \,-zg'

@E*25ft

3.5 ft

Rational Functions and Equations (pp. 666-73s)

t. GEOMETRY The length of a rectangle with aconstant area is inversely proportional to itswidth. A rectangle has a length of 10 inchesand a width of 6 inches. Another rectangle, hasthe same area as the first rectangle, but itswidth is 3 inches. Find the length of the secondrectangle. (Lesson lt-l)

2. PHYSICS Given a constant force, theacceleration of an object varies inversely withits mass. A shot putter uses a constant force toput a mass of 8 pounds with an acceleration of10 feet per second squared. If the shot putteruses the same force on a 16-pound mass, whatwould be the acceleration? (Lesson t 1-t)

PHYSICS A rectangle has an area of 36 square

feet. The function [ = #shows therelationship between the length and width ofthe rectangle. Graph the function. (Lesson I t-2)

RUNNING A runner runs 12 miles eachmorning. Her average speed y is given by

1ay : +, where x is the time it takes her to run12 miles. (Lesson I l-2)

a. Graph the function.

b. Describe the asymptotes.

PAINTING The area of each wall in Isabel'sroom can be expresse d as 2x2 + 5r + 3 squarefeet. A gallon of paint will cover an area thatcan be expressed as x2 - 3x - 4 square feet.Write an expression that gives the number ofgallons of paint that Isabel will need to buy topaint her room. (Lesson t t-l)

TORTOISE A giant tortoise can travel 0.17 mileper hour. What is this speed in feet perminute? (Lesson I l-4)

EXCHANGE RATE A pair of shoes bought inFrance cost 125 euros. The exchange rate at thetime was 1 U. S. dollar : 0.68 euro. How muchdid the shoes cost in U. S. dollars? (Lesson !l'4)

GAS A motorcycle travels 225 kilometers with5 liters of gas. How many liters of gas areneeded to travel 135 kilometers? (Lesson t t-+)

5.

3.

4.

6.

7.

8.

9. HOUSING The total cost per month for a dormis $2250 split equally among 15 students. If 10

more students join the dorm and each pays thesame rate as each of the original 15 students,what will be the monthly expenditure?(Lesson t t-+)

10. GEOMETRY The area of a rectangle is3x2 - 6x - 24squarc units. What is thelength? (Lesson t 1-5)

I t.

x-A

GARDENING Trey planted a triangular garden.Write an expression for the perimeter of thetriangle. (Lesson ll-6)

TRACK Trina walked 7 times around the trackat a rate of / laps per hour. She ran around thetrack 10 times at a rate of 4t laps per hour.Write and simplify an expression for the totaltime it took her to go around the track 17times. (Lesson I l-6)

PIAY A total of 1374 people attended threeplays. Letpbe the number of people whoattended the third play. There were twice asmany people at the second play than the thirdand three times as many people at the firstplay than the third. Write an expression torepresent the fraction of people who attendedthe first and second plays. (Lesson 1l-5)

READING Garcia reads 11] pages of a book in8 minutes. What is his av6rage reading rate inpages per minute? (Lesson t t-z)

RA.CING A drag racer drove f, mile in about11f, seconds. What is the speed in miles perhotrr? (Lesson ll-7)

CAR REPAIR Jack and Ivan are working onIvan's car. Jack can complete the job in 6 hours,but Ivan will take B hours. They work togetherfor two hours and Jack has to go. How longwill it take Ivan to finish his car? (Lesson I l-8)

6aa+1

12.

15.

I4.

15.

3a+1a+1

16.


Probability and Statistics (pp. 7r6-s0r)

CANDY Alicia asked every fourth student thatcame in the classroom to choose their favoritefrom three types of candy. (Lesson l2-l)

a. Identify the sample, and suggest apopulation from which it was selected.

b. Classify the type of data collection used.

c. Identify the sample as biased or unbiased.Explain your reasoning.

d. Classify the sample as simple, stratified, orsystematic. Explain your reasoning.

HOUSING A listing was made of the rents paidfor apartments in a particular neighborhood:{$450, $590, $650, $520, $480, $800, $720, $1600,$600). \A/hich measure of central tendency bestrepresents the data? Justify your selection, andthen find the measure. (Lesson l2-2)

CTUBS Given the following portion of a surveyteport, evaluate the validity of the informationand conclusion. (Lesson 12-2)

Question: Should the media club meetbefore or after school?

Sample: Students were randomly given aninvitation to vote while waiting inthe school commons for school tostart.

Results: 6S"hbefore school, 24o/o afterschool, 8% no preference

Conclusion: The media club should meetbefore school.

GRADES Lynette took 5 tests in life science thisgrading period. Find the mean, variance, andstandard deviation of the grades she earned:

176, 88, 82, 91, 78). (Lesson t2-l)

FOOTBATL The following table showsinformation about the number of carries arunning back had over a number of years. Findthe mean absolute deviation of the number ofcarries. (Lesson I2-5)

2.

t.

4.

5.


10.

i

:

6. BAND In a high school band, six girls and fourboys play trumpets. Before auditions at thebeginning of the year, the new band directorrandomly assigns chairs to the students. (Lesson

t2-4)

a. How many ways can the band directorassign first chair, second chair, and thirdchair?

b. \A/hat is the probability that the first threechairs will be assigned to boys?

CARDS If you have drawn and kept the 8 ofspades and the 7 of hearts from a standarddeck of cards, what is the chance you willdraw another 7 or a spade next? (Lesson '12-5)

COOKING Nate has a shelf with 3 cans of greenbeans, 2 cans of corn, and 5 cans of peas and ashelf of 1 package each of egg noodles, riceand zlti.In the freezer, he has 2 pounds ofchicken and 3 pounds of beef. If he randomlygrabs one item from each area to put in acasserole, what is the probability that he makesa chicken-corn-ziti casserole? (Lesson l2-5)

COAIS The table shows the probabilitydistribution of the number of each type of coatthat was sold in a particular week at a sportsstore. (Lesson l2-6)

a. Show that the distribution is valid.

b. What is the probabitity that a randomlychosen coat has fewer than 4 pockets?

c. Make probability graph of the data.

BASKETBATT Liam plays basketball. Lastyear,he made 80% of his attempted free throws.\Mhat objects can be used to model the possibleoutcomes of his next free throw?Explain. (Lesson l2-7)

7.

8.

9.

Q Converting Units of MeasureThere are three types of measurement: length, capacity, and mass.There are two measuring systems that we use: customary and metric.

The general rule when converting between units of measurement is:

. to convert from larger units to smaller units, multiply;

. to convert from smaller units to larger units, divide.

The diagram below shows the relationship between metric units of length

xl0 xl0 xl0 xlo xlo xlo,,^ ,'^, ,,n,,'-,kilo hector deca METER deci centi milli\_/v\/ \_/\/\/

+10 +r0 +10 +t0 +10 +10

Units of Lengh

Complete each sentence.

lA.5m- ? c-5(100) : 5005m:500cm

lB. 63 rn: ? k*63+1000:0.06363m:0.063km

To convert from meters to centimeters, multiply by 100.

To convert from meters to kilometers, divide by 1000.

fl(l6.D!tFTIAar-CLIttr

l,|IEqr

I kilometer (km) : lggg meters (m)

t meter (m) = 100 centimeters (cm)

I centimeter (cm) : 16 millimeters (mm)

I foot (ft) : l2 inches (in.)

t yard (yd) : 5 feet

I mile(mi) = 1760 yards or 5280 feet

I millimeter (mm) = 0.04 inch (in.)

I centimeter (cm) = 0.4 inch (in.)

I meter (m) = l.l yards or 5.5 feet (ft)

I kilometer (km) = 0.6 mile (mi)

height of a comma

half the width of a penny

width of a doonvay

lengh of a city block

I cup (c) = B fluid ounces (fl oz)

I pint (pt) = 2 cups (c)

I quart (qt) : 2 pints (pt)

I gallon (gal) : 4 quarts

I liter (L) : tooo milliliters (mL)

Concepts and Skills Bank 857

I pound (b) : 16 ounces (oz)

I ton G) = 2000 pounds (lb)

I kilogram (kg) : 1000 Srams (8)

t gram (g) = 1000 milliSrams (mg)

Units of Mass


2A.8gal- ? quarts

8(4) = 32

Sgal:32qt

2C. r6pt- ? gal

1.6+2=8qt8 + 4:2gal16 pt:2 gal

Units of Capacrty

larger + smaller, multiply.

Convert from pt to qt.

Convert from qt to gal

Larger -+ smaller, muhiply.

Convert from T to Ib.

Convert from Ib to kg.

28. 24fl oz: ? c

24 + 8:324flo2=3c

58.L.6o,= ? g

1..6+0.04=40

1..6 oz = 40 g

Smaller + larger, divide.


5A. 6.8 kg = j- tb

6.8(2.2) ='J.4.96

6.8 kg = L4.961b

5c. 1T- ? kg

1(2000) = 2000Ib

2000+2.2=909.1.kg

1T = 909 kg


l.5km- ? m

4.37c: ? pt

7. l8cm: ? in.

tO. 210 mm = ? "*

15. 52.9 kg = ? lb

Concepts and Skills Bank

2.3.5"*= ? *5. O.2mi: ? ftg.O.7Sy= ? qt

ll.65g= ? kg

t4.800flo2= ? mL

Smaller + larger, divide.

t. 6L= ? mL

6.400Yd: ? ft

9.93.5b: ? kg

12. 20mL: ? Y

15. 9.05 yd = ? m

QFactorc and MultiplesTWo or more numbers that are multiplied to form a product are called factors.

For example, because 6(7) = 42,6 andT are factors of 42.

Determine whether 138 has a factor o12,3,5,6,9, or 10.

So, 138 has factors of2,3, and 6.

You can also use the factor rules to find all of the factors of a

to find the other factor in each factor pair.

List all of the factors of72.

So, the factors of 72 are L,2,3,

[You can stop finding factors when the'[

numUers start repeating.

4, 6, 8,9,12, 18,24,36, and72.

number. Use division

any whole number. So,64 is aA multiple is the product of a specific number andmultiple of 4 because 4(1.6) = $4.

4 is divisible by 2.2 if the ones digit is divisible by 2.

3 il the sum of the digits is divisible by 3. I + 2 + 5 = 6, and o is divisible byl.

5 if the ones digit is 0 or 5. The ones digit is a 0.

6 if the number is divisible by 2 and 3. 48 is divisible by 2 and 5.

I + I + 9 : 18, and 18 is divisible by 9.9 if the sum of the digits is divisible by 9.

The ones digit is o.l0 if the ones digit is 0.

8 is divisible by 2.

I + 5 + 8 = 12, and 12 is divisible by 5.

The ones digit is not 0 or 5.

138 has a factor of 2 and 5.

| + 5 + 8 : 12, and 12 is not divisible by 9.

The ones digit is not 0.


Determine whether 375 is a multiple of 15.

We can use the factor rules to help determine multiples. Since 15 = 3(5), check 3 and 5.

Since 375 * 15 = 25 with no remainder,375 is a multiple of 15.

t. 39

4. 18

7. 22

r0. 250

tt. 995

16. 1052

2. 46

s.M8. 66

r r. 118

r4. 510

17. 32,460

5. 35

6. 23

9. 212

12. 378

15. 5010

18. 3039

17. 63,3

40.102,4

45. 364,9

46.234,6

49. 3585,65

List all of the factors of each number.

19. 28

25. 8L

27. 60

,1. 102

Determine whether the

35. 49,3

!9.60,6

41.121.,11.

44. 536,3

47.282,31

first number is a multiple of the second.

,6. 64,9

59. 135,5

42. 905,12

45. 657,7

48. 3612,12

20. 75

24. 52

28. 90

t2. L35

21. 74

25. 42

29. 114

55. 365

22. 57

26. 63

50. 124

54. 225

50. MUSIC Seventy-two members of the marching band will march in theHomecoming Parade. They will need to march in rows with the samenumber of students in each row.

a. Can the band be arranged in rows of 7? Explain.

b. How many different ways could the marching band members be arranged?Describe the arrangements.

51. CATENDARS Years that are multiples of 4, called leap years, are 366 days long.Use the rule given below to determine whether 201,0,2015,201.6,2022, and2032 arc leap years.

If the last two digits form a number diaisible by 4, then the number is dioisible by 4.

860 Concepts and Skills Bank

Yes, 575 is a multiple of s.

Yes, 375 is a multiple of 5.

Yes, 575 is a multiple of 15.

Determine whether each number has a factor of 2,3,5, 6,9, or 10.

Q;Prime FactorizationA prime number is a whole number greater than 1., for which the only factors are1 and itself. A whole number greater than 1 that has more than two factors is acomposite number. The numbers 0 and 1 are neither prime nor composite. Noticethat 0 has an endless number of factors and t has only one factor, itself.

ldentify Numbers as Prime or Composite

number is prime or composite.Determine whether each

a. 27

The numbersL,3, and 9 divide into 27 evenTy.5o,27 is a composite number.

A whole number expressed as the product of prime factors is called the primefactorization. The prime factors can be written in any order usually from the leastprime factor to the greatest prime factor. Disregarding order, there is only one wayto write the prime factorization of a whole number.

Prime Factorization of a Whole Number

Write the prime factorization of 120.

Method I Find the least prime factors.

The Ieast prime factor of 120 is 2.

The least prime factor of 50 is z.

The least prime factor o, I0 is 2.

The least prime factor of 15 is x.

Method 2 Use a factor tree.

120

10 12

€fboA--tr

b. 41.

The only numbers that divide evenly into 41

are 1 and 41.. So, 41 is a prime number.

120:2.60=2.2.30:2.2,2.15:2.2.2.3.5

Determine whether each

r. 48 2.29

Write the prime factorization of each

7. 20

r0. 120

15. 144

16. 275

19. 351

Choose any two factors of 120 to begin.

Keep linding factors until each branch ends in a prime factor.

The prime factorization is complete because 2,3, and 5 are primenumbers. Thus, the prime factorization of 120 is2.2.2.3.5 or2' .3 .5.

number is prime or composite.

5. 63 4.75 5. 71. 6. 43

number. Use exponents for repeated factors.

8. 28 9. 64

il. 140

14. 22L

t7. 210

20. 900

r2. 85

r5. 84

18. 441

2r. 1350

Concepts and Skills Bank 861

@ Measuring AnglesThe most commonto measute angles

Use a protractor to measure IABC.

Step I Place the center point of the protractor'sbase on vertex B. Align the straight sidewith the side AB so that the marker for 0o

is on the side.

measure of angles is the degree ("). You can use a protractorin degrees.

The measure of IABC is 120o. Use the symbols wIABC : 720o.

If the sides of the angle are too small to reach the scale on the protractor,you can extend the sides until they are long enough.

Notice that there are measurements going in two directions on the protractor.One is on the outside of the other. You may use either scale for measuring,but you must use the one where one of your sides lines up with 0'to get thecorrect measurement.

Acute angles have measures less than 90o.

Right angles have measures equal to 90o.

Obtuse angles have measures between 90'and 180'.

Straight angles have measures equal to 180'.

So we can classify IABC as an obtuse angle.

to draw an angle of a certain measure.

Draw lD with a measure of 85'.

Step t Draw a ray with an endpoint D. Make sure thatthe ray is long enough so that it crosses the edgeof the protractor.

Step 2 Place the center point of the protractor on D.A1ign the mark labeled 0 with the ray you drew.

Step 5 Use the scale that begins with 0. Locate the marklabeled 85. Then draw the other side of the angle.

We can classify this angle as an acute angle.

Step 2 Use the scale that begins with 0o at AB.Read where the other side of the angle,BC, crosses this scale.

A protractor can also be used

-g


I l. Does lFLlhave the same measure as IELH? Explain.

t2. Which angle, if any, has the same measure as IELH? Explain.

Use a protractor to measure each angle. Then classify each angle as acute, right,obtuse, or straight.

Use the protractor to find the measure of each angle.Then classify each angle as acute,right, obtuse, orstraight.

t. tlLK,. IELK

5. IFLI7. IGLF

9. IILK

Use a protractor to draw

21. 40"

24. 85"

27. 155"

50. 180"

22. 700

25. 95"

28. 1.40"

tt. 20'

"N t+.

/

'"---l

"Yt.\ 20.\

2. IELF

4. tGLI

6. tlLF8. ltLC

IO. ICLK

an angle with each measurement. Then classify each angle.

2r. 65"

26. 1"10'

29. 35'

52. 1.65"

It


@;Venn DiagramsA Venn diagram shows the relationships among sets of numbersor objects by using overlapping circles in a rectangle.

The Venn diagram at the right shows the factors of 72 and20.The common factors are in both circles.

COILEGE Members of a senior class were polled and asked whattype of federal financial aid they are receiving for college.

0. How many students are only receiving grants?

The number only in the grant circle is 36. So,36 seniors arereceiving only grants.

How many students are receiving both loans and grants?

The value in both circles is 61. So, 61 seniors are receiving bothloans and grants.

How many students are not receiving any grants or loans?

The value outside of the circles is 15. So, 15 seniors are notreceiving any grants or loans.

Refer to the Venn diagram at the right.

a. What are the factors in all three circles?

The factors in all three circles are 7,3, and 9.

b. What is the greatest common factor of all three numbers?

The greatest common factor of all three numbers is 9.

What factors are shared only by 54 and 36?

The factors 2,6,18 are shared only by 54 and 36.

What is the greatest common factor of 54 and 36?

The greatest common factor between 54 and 36 is 18.

What factors are shared only by 54 and,45?

There are no factors shared by only 54 and 45.The factors that they have in common are sharedby all three numbers.

What is the greatest common factor of 54 and 45?

The greatest common factor between 54 and 45 is 9.

b.

Factors of 12 Factors of 20

;s:6'.. 12

Grants

!II

!

Factors of 54

Factors of 45

Factors of 16

d.


Refer to the Venn diagram at the right'

l. Which factors are in both circles?

2. What is the greatest common factor of 56 and32?

Refer to the Venn diagram at the right'

5. What are the factors in all three circles?

4. What is the greatest common factor of all three numbers?

5. What factors are shared only by 28 and 42?

6. What is the greatest common factor of 28 and 42?

7. What factors are shared only by 16 and 42?

8. What is the greatest common factor of 1'6 and 42?

TRANSPORTATION Twenty people who have traveled across

the country in the last year were asked if they used,land or air

transportaiion. The results are shown in the Venn diagram'

9. How many people traveled across the country by land?

10. Explain what the 5 in the diagram represents'

SPORTS Ten students were asked which sports they played

in the past month. Use the Venn diagram shown at the rightto answer the following questions.

I t. Which student(s) have played basketball in the last month?

12. Who played only basketball and baseball?

15. Which student(s) have played only soccer in the last month?

14. Who played only soccer and baseball?

15. Which student(s) have played all three sports?

16. Who played at least two of the three sports?

17. What sports did Ted participate in the past month?

MEDTA A hundred teens were polled and asked which ofthree news sources they use daily. The results are shown in the

Venn Diagram at the right.r. o .{.il-z -o-rzq qntrrap?

Factors ol s6 tactors of l2

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Factorn of 28 tactors of ts

!\ 3,6, 21,42 I'!,

$actors of 42

[and

Baseball

1i

! Benitez, Mark ;J\r ,.t'

'1, /"

Basketball

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tautat-

luu"J!,,GraphsThe graphs below show the monthly sales of a local magazine.

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The graphs show the same information. However, while the first graph shows fairlysteady sales, the second graph shows dramatic increases and decrlases in sales. Thegraphs have the same horizontal axis, but notice that the scales are very different onthe vertical axis. By changing the scale on a graph, the visual impression can bechanged so that it is misleading.

The graphs show the number of visitors at a lodge in the smoky Mountainseach year. which graph appears to show the greater increase in the number ofvisitors?

Graph BMonthly Sales

Graph AMonthly Sales

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$14€ r:.s

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8000

7000

6000

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3000

2000

I 000

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8000

7500

E Tooo.E.s 6500

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5500

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The graph on the right appears to show the greater growth. The increments are 500 on the vertical axis,ralhpr fhen 'l OOO lilzo tha firc+ c-o^L' Tl-^ .,^-+i^^I ^-,:^ ^c !L^ --^.^L ^-- rr^ ^ r - r, r- ,

t. TRAFFIC The graphs display the number of cars that went through a tollboothduring the previous hour. Which graph appears to show the greatest increasein the number of vehicles? Explain.

foflbooth Traflit550

325

500

275

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2. Which graph appears to have higher gas prices? Explain.

BUSINESS According to the information in the graph below, there were novisitors to the ski resort n1999. Determine if this statement is accurate.

Justify your responsb.

Ski Resort Visitors

"s"s "$Year

4000

3600

b J2oo,=.g! 2800

2400

2000

Tollbooth Traffit

O S5.oo

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Year

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Year

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Concepts and Skills

&.s,",

Expressions, Equations, andFunctions

Translating Verbal to Algebraic Expressions (p.6)

Addition more than, sum, plus, increased by, added toSubtraction less than, subtracted from, difference, decreased by, minusMultiplication product of, multiplied by, times, ofDivision quotient of, divided by

Order of Operations (p. lo)

Step 1 Evaluate expressions inside grouping symbols.

Step 2 Evaluate all powers.

Step 3 Multiply and/or divide from left to right.

Step 4 Add and/or subtract from left to right.

Reflexive Property (R. 15)

Any quantity is equal to itself.

Symmetric Property (p. 16)

If one quantity equals a second quantity, then the second quantity equalsthe first.

Tiansitive Property (p. 16)

If one quantity equals a second quantity and the second quantity equals a thirdquantity, then the first quantity equals the third quantity.

Substitution Property (R. l6)

A quantity may be substituted for its equal in any expression.

Additive Identity (p. l6)

For any number a, the sum of a and0 is a.

Additive Inverse (p. 16)

A number and its opposite are additive inverses of each other. The sum ofa number and its additive inverse is 0.

Multiplicative Identity (R. l7)

For any number a, the product of a and 1 is a.

Multiplicative Property of Zerc (p. tt)For any number a, the product of a and 0 is 0.

Multiplicative Inverse (p. 17)

Foievery nurnA"i-l,r,in"* a, b + 0, there is exactly one number 4 such that

the oroduct of I and L i, 1,.'ba

Commutative Property (p. l8)

The order in which you add or multiply numbers does not change their sumor product.

Associative Property (R. lB)

The way you group three or more numbers when adding or multiplyingdoes not change their sum or product.

Distributive Property (p. z:)For any numbers a,b, and c, a(b + c) = ab * ac and (b + c)a : ba * ca anda(b - c) : ab - ac and (b - c)a : ba - ca.

Function (p.45)

A function is a relation in which each element of the domain is paired withexactly one element of the range.

Linear Equations

Addition Property of Equality (p. al)If an equation is true and the same number is added to each side ofthe equation, the resulting equivalent equation is also true.

Subtraction Property of Equality (p. a+)

If an equation is true and the same number is subtracted from each side of theequation, the resulting equivalent equation is also true.

Multiplication Property of Equality (p. a+)

If an equation is true and each side is multiplied by the same nonzero numbeq,the resulting equation is equivalent.

Division Property of Equality (p. a+)

If an equation is true and each side is divided by the same number, theresulting equation is true.

Steps for Solving Equations (p. ss)

Step 1. Simplify the expressions on each side. Use the Distributive Property asneeded.

Step 2 Use the Addition and/or Subtraction Properties of Equality to get thevariables on one side and the numbers without variables on the otherside. Simplify.

Step 3 Use the Multiplication or Division Property of Equality to solve.

Absolute Value Equations (p.104)

When solving equations that involve absolute values, there are two casesto consider.

Case L The expression inside the absolute value symbol is positive.

Case 2 The expression inside the absolute value symbol is negative.

Means-Extremes Propefiy of Proportion (p. I l2)In a proportion, the product of the extremes is equal to the product of the means.

Linear Functions

Standard Form of a Linear Equation (p. ls3)The standard form of a linear equation is Ax + By : C,where A > 0,A and B arenot both zero, and A, B, and C are integers with a greatest common factor of 1.

R2 Key Concepts

Parallel and Perpendicular Lines (p.240)

Linear Function (p. 16l)

Alinear function is a function with a graph of a line.

Rate of Change (p.l7o)

If x is the independent variable and y is the dependent variable, thenchange in Yrate of chaneechange in x'

Slope (p. 175)

The slope of a line is the ratio of the rise to the run.

Arithmetic Sequence (p. ls7)

An arithmetic sequence is a numerical pattern that increases or decreases ata constant rate called tlire common dffirence.

nth Term of an Arithmetic Sequence (p.lsa)

The zth term of an arithmetic sequence with first term a, and commondifference d is given by ,n = at + (Tt - 1)d, where n is a positive integer.

Proportional Relationship (p. I95)

A relationship is proportional if its equation is of the form A = kx, k I 0. Thegraph passes through (0, 0).

linear Functions rnd

Slope-Intercept Form (p. 214)

The slope-intercept form of a linear equation is y - mx + b, where la isthe slope and b is the y-intercept.

Point-Slope Form (p. 231)

The linear equation U - At = m(x - x1) is written in point-slope form, where(xt, y) is a given point on a non-vertical line and m is the slope of the line.

Writing Equations (p. 232)

Step I Find the slope.

Step 2 Choose one of the two pointsto use.

Step 5 Follow the steps for writing anequation given the slope andone point.

Step I Substitute the values of m, x,and y into the slope-interceptform and solve for b. Or,use the point-slope form.Substitute the value of m andlet x and y be (xv y).

Step 2 Write the slope-intercept formusing the values of m and b.

Two nonvertical lines are parallel ifthey have the same slope.

Two nonvertical lines are perpendicularif the product of their slopes is -1.

Using a Linear Function to Model Data (p.246)

Step L Make a scatter plot. Determine whether any relationship exists in the data.

Step 2 Draw a line that seems to pass close to most of the data points.

Step 3 Use two points on the line of fit to write an equation for the line.

Step 4 Use the line of fit to make predictions.

Greatest Integer Function (p.251)

The greatest integer function can be described by an equation of the formf(x): [xn.

Absolute Value Function (p.262)

lxifx>Of(x) : I x l, defined as f(x): ]o if x : o

[-xifx<0

Linear lnequalities

Addition Property of Inequalities (p.28J)

If any number is added to each side of a true inequality, the resulting inequalityis also true.

Subtraction Property of Inequalities (p.2e+)

If any number is subtracted from each side of a true inequality, the resultinginequality is also true.

Multiplication Property of Inequalities (p. 2s0)

If a true inequality is multiplied by a positive number, the resulting inequalityis also true. If a true inequality multiplied by a negative number, the directionof the inequality sign is changed to make the resulting inequality also true.

Division Property of Inequalities (p.292)

If a true inequality is divided by a positive number, the resulting inequality isalso true. If a true inequality is divided by a negative number, the direction ofthe inequality sign is changed to make the resulting inequality also true.

Graphing Linear Inequalities (p. 3ls)Step L Graph the boundary. Use a solid line when the inequality contains

( or >. Use a dashed line when the inequality contains < or >.

Step 2 Use a test points to determine which half-plane should be shaded.

Step 3 Shade the half-plane that contains the solution.

Solving by Substitution (p.342)

Step 1. When necessary, solve at least one equation for one variable.

Step 2 Substitute the resulting expression from Step 1 into the other equationto replace the variable. Then solve the equation.

Step 3 Substitute the value from Step 2 into either equation, and solve for theother variable. Write the solution as an ordered pair.

Equations

R4 Key Concepts

Solving by Elimination Using Addition (p.548)

Step 1 Write the system so like terms with the same or opposite coefficientsare aligned.

Step 2 Add or subtract the equations eliminating one variable. Then solvethe equation.

Step 3 Substitute the value from Step 2 into one of the equations and solve forthe other variable. Write the solution as an ordered pair.

Solving by Elimination Using Multiplication (p.lss)

Step 1 Multiply at least one equation by a constant to result in two equationsthat contain opposite terms.

Step 2 Add the equations eliminating one variable. Then solve the equation.

Step 3 Substitute the value from Step 2 into one of the equations and solvefor the other variable. Write the solution as an ordered pair.

Elementary Row Operations (p.377)

The following operations can be performed on an augmented matrix'. Interchange any two rows.. Multiply all entries in a row by anonzero constant.. Replace one row with the sum of that row and a multiple of another row.

Polynomials

Product of Powers (p. ao2)

To multiply two powers that have the same base, add their exponents.

Power of a Power (p.402)

To find the power of a power, multiply the exponents.

Power of a Product (p.403)

To find the power of a product, find the power of each factor and multiply.

Simplify Expressions (p. 404)

To simplify a monomial expression, write an equivalent expression in which:. eachbase appears exactly once,. there are no powers of powers, and. all fractions are in simplest form.

Quotient of Powers (p.408)

To divide two powers with the same base, subtract the exponents.

Power of a Quotient (p.409)

To find the power of a quotient, find the power of the numerator and thepower of the denominator.

Zero Exponent Property (p. +to)

Any nonzero number raised to the zero power is equal to 1.

Negative Exponent Property (p. 4t0)

For any nonzero number a and any integer fi, a-'is the reciprocal of an. AIso,the reciprocal of a-n : an.

Standard Form to Scientific Notation (p.416)

Step L Move the decimal point until it is to the right of the first nonzero digit.The result is a real number a.

Step 2 Note the number of places n and the direction that you moved thedecimal point.

Step 3 If the decimal point is moved left, write the number as a x 1.0'.If the decimal point is moved right, write the number as a x 10-n.

Step 4 Remove the extra zeros.

Scientific Notation to Standard Form (p.4t7)

Step L In a x 10n, note whether n > 0 or n < 0.

Step 2 If n > 0, move the decimal point n places right.If n < 0, move the decimal point -n places left.

Step 3 Insert zeros, decimal point, and commas as needed to indicateplace value

FOIL Method (p. ++s)

To multiply two binomials, find the sum of the products of F the First terms,O the Outer terms, I the lnner terms, L and the Last terms.

Square of a Sum (p.4si)The square of a + b is the square of a plus twice the product of a and b plusthe square of b.

Square of a Difference (p.4s4)

The square of a - b is the square of a minus twice the product ol a and b plusthe square of b.

Product of a Sum and a Difference (p.4ss)

The product of a + b and a - b is the square of a minus the square of b.

Fu.il; '

Equations

Factoring by Grouping O.477)A polynomial can be factored by grouping only if all of the following conditionsexist.. There are four or more terms.. Terms have common factors that can be grouped together.. There are two common factors that are identical or additive inverses of

each other.

Zero Product Property (p.47s)

If the product of two factors is 0, then at least one of the factors must be 0.

Factoring x2 + bx + c (p. 48s)

To factor trinomials in the form x2 + bx + c, find two integers, m and p, wltha sum of b anda product of c. Then wrlte x2 + bx + c as (x + m)(x + p).

Factoring ax2 + bx * c (p.495)

To factor trinomials in the form axT + bx + c, fnd two integers, m and p,with a sum of b and aproduct of ac. Then wite ax2 + bx + c as

axz + mx + px + c, then factor by grouping.

R6 Key Co,ncepts

Difference of Squares (p. +99)

a2 - bz - (a + b)(a - b) or (a - b)(a + b)

Factoring Perfect Square Tiinomials (p. sos)

a2 + Zab + b2 - (a + b)(a + b) : (a + b)2

a2 - Zab * b2 - (a - b)(a - b) = (a - U1z

Square Root Property (p.508)

To solve a quadratic equation in the form x2 : n, take the square root of each side.

Quadratic andfxgon "

Functions

Quadratic Functions (p. s25)

A quadratic function can be described by an equation of the formf(x) = ax2 * bx + c.

Maximum and Minimum Values (p. s28)

The graph of f(x\ = ax2 * bx * c, where n { 0:. opens up and has a minimum value when a > 0, and. opens down and has a maximum value when a < 0.

. The range of a quadratic function is all real numbers greater than or equal tothe minimum, or all real numbers less than or equal to the maximum.

Graph Quadratic Functions (p. s2s)

Step L Find the equation of the axis of symmetry.

Step 2 Find the vertex, and determine whether it is a maximum or minimum.

Step 3 Find the y-intercept.

Step 4 Use symmetry to find additional points on the graph, if necessary.

Step 5 Connect the point with a smooth curve.

Vertical Tianslations (p. s44)

The graph of f(x) = x,2 * c is the graph of f(x): x2 translated vertically.If c j o, the graph of f(x) = x2 is translated lc I units up.If c < 0, the graph of f(x) = x'2 is translated lc I units down'

Dilations (p. s45)

The graph of f(x) = ax2 is the g-raph of f(x): 12 stretched or compressed vertically.If lal> 1, the graph otf(x) = x2 is s^tretched vertically.If 0 < | al < 1, the graph of f(x) = xz is compressed vertically.

Reflections (p. s45)

The graph of the function -f(x) is the reflection of the graph of f(x): x2 across the x-axis.

fhe graph of the function/(-x) is the reflection of the graph of f(x) : xz across the y-axis.

Completing the Square (p.5s2)

To complete the square for any quadratic expression of the formx2 + bx, follow the steps below

Step L Find one half of b, the coefficient of x.

Step 2 Square the result in Step 1.

Step 3 Add the result of Step 2to x2 + bx.

Key Concepts

The Quadratic Formula (p.558)

The solutions of a quadratic equation ax2 + bx* c : 0, where a f 0 arcgiven by the Quadratic Formula.

-b+lYz-ao,L-2a

Exponential Function (p. s67)

An exponential function is a function that can be described by an equationof the formy - nbx, where a +0,b > 0,andb {1,.

General Equation for Exponential Growth (p.5zr)

y=a(l+r)t

General Equation for Compound Interest (p.574)

a: P(l* +)"'

General Equation for Exponential Decay (p. sza)

y:a(l-r)t

zth term of a Geometric Sequence (p. s80)

The nth term an of a geometric sequence with first term a, and common ratior is given by the following formula, where n is any positive integer.

an = alf'- 1

RadicalFunctions,nd--.*''Geometry

Square Root Function (p.605)

A square root function can be described by an equation that contains the squareroot of a variable,

Graphing Square Root Functions of the Form y : a t/x + h+ c (p. 606)

Step L Draw the graph of y : alfi.Ttre graph starts at the origin and passesthrough the point at (1, a).If a > 0, the graph is in quadrant I. If a < 0,the graph is reflected across the x-axis and is in quadrant fV.

Step 2 Tianslate the graph lclunits up if c > 0 and downif c < 0.

Step 3 Translate the graph lhlunits leftlf h > 0 and right if h <0.

Product Property of Square Roots (p.5t2)For any nonnegative real numbers a and b, the square root of ab is equal to thesquare root of a times the square root of b.

Quotient Property of Square Roots (p.6ti)For any real numbers a and b, where a >

,0 andb > O, the square root of ff

isequal to the square root of a divided by the square root of b.

Power Property of Equality (p. G24)

If you square both sides of an equation, the resulting equation is still true.

The Pythagorean Theorem (p.6io)If a triangle is a right triangle, then the square of the length of the hypotenuseis equal to the sum of the squares of the lengths of the legs.

R8 Key Concepts

Converse of the Pythagorean Theorem (p.631)

If a triangle has-side lengths a,b, and c such that c2 : a2 I b2, thenthe triangleis a right triangle. tt c2 { a2 + b2, then the triangle is not a right triangle.

The Distance Formula (p.636)

The distance d between any two points with coordinates (x1, yr) and (xz, yz)

The Midpoint Formula (p.658)

The midpoint M of a line segment with endpoints at (x1, yr) and (xz, yz)lx, + x. u, + y"\

isgivenbyM= |.-, ,=;)

Similar Tiiangles (p.6a7)

If two triangles are similar, then the measures of their corresponding angles are

equal, and the measures of their corresponding sides are proportional.

Trigonometric Ratios (p. 649)

lex opposite lAsine of l-4 = -4--

hypotenuse

cosine of lA =legadjacentto lA

tangent of lA:

hypotenuse

Ieg opposite ZAlegadjacentto lA

lnverse Tiigonometric Functions (p. 651)

If lA is an acute angle and the sine of A is x, then the inverse sine of x is themeasure of lA.If lA is an acute angle and the cosine of A is r, then the inverse cosine of x isthe measure of lA.If lA is an acute angle and the tangent of A is x, then the inverse tangent ofx is the measure of lA.

-::::-ry

Rational Functions andEquations

Inverse Variation (p. 670)

y varies inversely as x lf there is some nonzero constant k such that y -xU:k,whererl0andy+0.

Product Rule for Inverse Variations (p.671)

If (xr, y) and (x2, yr) are solutions of an inverse variation, then the productsx.ryrand x2yzarc equal.

Rational Function (p. 578)

A rational function can be described by an equation of the form y : f,, wherep and q are polynomials and q f 0.

kTor

Key Concepts R9

Asymptotes (p.679)

A rational function

x-value that makesasymptote aty = s.

in the form y : =+ f c has a vertical asymptote at the" x-bthe denominator equal zetot x : b.It has a horizontal

Simplifying Rational Expressions (p. 6Bs)

Let a, b, and c be polynomials with a | 0 and c + 0.

ba b.a bCA- C.A- C

Multiplying Rational Expressions (p. 6e2)

Let a,b, c, and d be polynomials with b * 0 and d + 0.

Dividing Rational Expressions (p. 69J)

Let n, b, c, and d be polynomials with b + 0, c + 0, and d { 0.

a.c a d ad:-.-:-b'd b c bc

Add or Subtract Rational Expressions (p.708)

Use the following steps to add or subtract rational expressions with unlikedenominators.

Step 1 Find the LCD.

Step 2 Write each rational expression as an equivalent expression with the LCDas the denominator.

Step 3 Add or subtract the numerators and write the result over the commondenominator.

Step 4 Simplify if necessary.

Statistics and Probability -* '- "

Data Collection Techniques (p. 740)

survery Data are from responses given by sample of the population.observational study Data are recorded after just observing the sample.experiment Data are recorded after changing the sample.

Random Samples (p.742)

simple random sample A sample that is equally likely to be chosen as anyother sample from the population.stratified random sample The population is first divided in similar,nonoverlapping groups. A sample is then selected from each group.systematic random sample Items in the sample are selected according to aspecified time or item interval.

Measures of Central Tendency (p.746)

mean the sum of the data divided by the number of items in the data setmedian the middle number of the ordered data, or the mean of the middletwo numbersmode the number or numbers that occur most often

acac-.-:-bd bd

RlO Key Concepts

Measures of Variation (p.757)

range the difference between the greatest and least valuesquartile the values that divide the data set into four equal parts

interquartile range the range of the middle half of a data seU the difference

between the upper and lower quartiles

Mean Absolute Deviation (p.7s7)

Step 1 Find the mean.

Step 2 Find the sum of the absolute values of the differences between each

value in the set of data and the mean.

Step 3 Divide the sum by the number of values in the set of data.

Variance and Standard Deviation (p.7s8)

Step L Find the mean/ /-.

Step 2 Find the square of the difference between each value in the set of data

and the mean. Then divide by the number of values in the set of data.

The result is the variance.

Step 3 Thke the square root of the variance.

Factorial (p.764)

The factorial of a positive integer n is the product of the positive integers less thanor equal to n.

Permutation Formula (p. 76s)

The number of permutations of n objects taken r at a time is the quotient of n! and(n - r)1.

Combination Formula (p. 766)

The number of combinations of n objects taken r at a time is the quotient of n! and(n - r)lrt.

Probability of Independent Events (p.771)

If two events, A and B, are independent, then the probability of both events

occurring is the product of the probability of A and the probability of B.

Probability of Dependent Events (p.772)

If two events, A and B, are dependent, then the probability of both events

occurring is the product of the probability of A and ihe probability of B after

A occurs.

Mutually Exclusive Events (p.775)

If two events, A and B, are mutually exclusive, then the probability that eitherA or B occurs is the sum of their probabilities.

Events that are Not Mutually Exclusive (p.774)

If two events, A and B, are not mutually exclusive, then the probability that eitherA or B occurs is the sum of their probabilities decreased by the probability of bothoccurring.

Properties of Probability Distributions (p. 780)

L. The probability of each value of X is greater than or equal to 0 and is less thanor equal to 1.

2. The sum of the probabilities of all values of X is 1'

Key Concepts Rl1

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Rl2 Selected Answers

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