Content check — Prealgebra, Chapter 9: Math Models and Geometry

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 9: Math Models and Geometry

397 problems · 79 figures

Be Prepared 9.1 §9.1 source ↗

Translate

“6

less than twice

x ”

into an algebraic expression.
If you missed this problem, review Example 2.25.

Example 2.25 in the book ↗

Answer

2 x - 6

Be Prepared 9.2 §9.1 source ↗

Solve:

\frac{2}{3} x = 24 .

If you missed this problem, review Example 8.16.

Example 8.16 in the book ↗

Answer

36

Be Prepared 9.3 §9.1 source ↗

Solve:

3 x + 8 = 14 .

If you missed this problem, review Example 8.20.

Example 8.20 in the book ↗

Answer

2

Try It 9.1 §9.1 source ↗

Joaquin bought a bookcase on sale for

$120,

which was two-thirds the original price. What was the original price of the bookcase?

Answer

$180

Try It 9.2 §9.1 source ↗

Two-fifths of the people in the senior center dining room are men. If there are

16

men, what is the total number of people in the dining room?

Answer

Try It 9.3 §9.1 source ↗

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was

3

more than the number of notebooks. He bought

5

textbooks. How many notebooks did he buy?

Answer

Try It 9.4 §9.1 source ↗

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed

14

Sudoku puzzles. How many crossword puzzles did he complete?

Answer

Try It 9.5 §9.1 source ↗

Pilar's rent increased by

4% .

The increase was

$38 .

What was the original amount of Pilar's rent?

Answer

$950

Try It 9.6 §9.1 source ↗

Steve saves

12%

of his paycheck each month. If he saved

$504

last month, how much was his paycheck?

Answer

$4,200

Try It 9.7 §9.1 source ↗

The difference of a number and eight is

17 .

Find the number.

Answer

Try It 9.8 §9.1 source ↗

The difference of a number and eleven is

−7 .

Find the number.

Answer

Try It 9.9 §9.1 source ↗

The sum of four times a number and two is

14 .

Find the number.

Answer

Try It 9.10 §9.1 source ↗

The sum of three times a number and seven is

25 .

Find the number.

Answer

Try It 9.11 §9.1 source ↗

One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.

Answer

9, 15

Try It 9.12 §9.1 source ↗

The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.

Answer

27, 31

Try It 9.13 §9.1 source ↗

The sum of two numbers is negative twenty-three. One number is

7

less than the other. Find the numbers.

Answer

−8, −15

Try It 9.14 §9.1 source ↗

The sum of two numbers is negative eighteen. One number is

40

more than the other. Find the numbers.

Answer

−29, 11

Try It 9.15 §9.1 source ↗

One number is eight more than twice another. Their sum is negative four. Find the numbers.

Answer

−4, 0

Try It 9.16 §9.1 source ↗

One number is three more than three times another. Their sum is negative five. Find the numbers.

Answer

−2, −3

Try It 9.17 §9.1 source ↗

The sum of two consecutive integers is

95 .

Find the numbers.

Answer

47, 48

Try It 9.18 §9.1 source ↗

The sum of two consecutive integers is

−31 .

Find the numbers.

Answer

−15, −16

Try It 9.19 §9.1 source ↗

Find three consecutive integers whose sum is

96 .

Answer

31, 32, 33

Try It 9.20 §9.1 source ↗

Find three consecutive integers whose sum is

−36 .

Answer

−11, −12, −13

9.1-1 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Two-thirds of the children in the fourth-grade class are girls. If there are $20$ girls, what is the total number of children in the class?

Answer

There are 30 children in the class.

9.1-3 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Zachary has $25$ country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

Answer

Zachary has 125 CDs.

9.1-5 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

There are $16$ girls in a school club. The number of girls is $4$ more than twice the number of boys. Find the number of boys in the club.

Answer

There are 6 boys in the club.

9.1-7 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Lee is emptying dishes and glasses from the dishwasher. The number of dishes is $8$ less than the number of glasses. If there are $9$ dishes, what is the number of glasses?

Answer

There are 17 glasses.

9.1-9 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

After $3$ months on a diet, Lisa had lost $12%$ of her original weight. She lost $21$ pounds. What was Lisa's original weight?

Answer

Lisa's original weight was 175 pounds.

9.1-11 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Tim left a $$9$ tip for a $$50$ restaurant bill. What percent tip did he leave?

Answer

18%

9.1-13 §9.1 source ↗

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Yuki bought a dress on sale for $$72 .$ The sale price was $60%$ of the original price. What was the original price of the dress?

Answer

The original price was $120.

9.1-15 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of a number and eight is $12 .$ Find the number.

Answer

9.1-17 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The difference of a number and twelve is $3 .$ Find the number.

Answer

9.1-19 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of three times a number and eight is $23 .$ Find the number.

Answer

9.1-21 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The difference of twice a number and seven is $17 .$ Find the number.

Answer

9.1-23 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Three times the sum of a number and nine is $12 .$ Find the number.

Answer

−5

9.1-25 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

One number is six more than the other. Their sum is forty-two. Find the numbers.

Answer

18, 24

9.1-27 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two numbers is twenty. One number is four less than the other. Find the numbers.

Answer

8, 12

9.1-29 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

A number is one more than twice another number. Their sum is negative five. Find the numbers.

Answer

−2, −3

9.1-31 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two numbers is fourteen. One number is two less than three times the other. Find the numbers.

Answer

4, 10

9.1-33 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

One number is fourteen less than another. If their sum is increased by seven, the result is $85 .$ Find the numbers.

Answer

32, 46

9.1-35 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two consecutive integers is $77 .$ Find the integers.

Answer

38, 39

9.1-37 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two consecutive integers is $−23 .$ Find the integers.

Answer

−11, −12

9.1-39 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of three consecutive integers is $78 .$ Find the integers.

Answer

25, 26, 27

9.1-41 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive integers whose sum is $−36 .$

Answer

−11, −12, −13

9.1-43 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Shopping Patty paid $$35$ for a purse on sale for $$10$ off the original price. What was the original price of the purse?

Answer

The original price was $45.

9.1-45 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Shopping Minh spent $$6.25$ on $5$ sticker books to give his nephews. Find the cost of each sticker book.

Answer

Each sticker book cost $1.25.

9.1-47 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Shopping Tom paid $$1,166.40$ for a new refrigerator, including $$86.40$ tax. What was the price of the refrigerator before tax?

Answer

The price of the refrigerator before tax was $1,080.

9.1-49 §9.1 source ↗

Solve Number Problems

In the following exercises, solve each number word problem.

Write a few sentences about your thoughts and opinions of word problems. Are these thoughts positive, negative, or neutral? If they are negative, how might you change your way of thinking in order to do better?

Answer

Answers will vary.

Be Prepared 9.4 §9.2 source ↗

Multiply:

14 (0.25) .

If you missed this problem, review Example 5.15.

Example 5.15 in the book ↗

Answer

3.5

Be Prepared 9.5 §9.2 source ↗

Simplify:

100 (0.2 + 0.05 n) .

If you missed this problem, review Example 7.22.

Example 7.22 in the book ↗

Answer

20 + 5 n

Be Prepared 9.6 §9.2 source ↗

Solve:

0.25 x +

0.10 (x + 4) =

2.5

If you missed this problem, review Example 8.44.

Example 8.44 in the book ↗

Answer

6

Try It 9.21 §9.2 source ↗

Michaela has

$2.05

in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?

Answer

9 nickels, 16 dimes

Try It 9.22 §9.2 source ↗

Liliana has

$2.10

in nickels and quarters in her backpack. She has

12

more nickels than quarters. How many coins of each type does she have?

Answer

17 nickels, 5 quarters

Try It 9.23 §9.2 source ↗

Sumanta has

$4.20

in nickels and dimes in her desk drawer. She has twice as many nickels as dimes. How many coins of each type does she have?

Answer

42 nickels, 21 dimes

Try It 9.24 §9.2 source ↗

Alison has three times as many dimes as quarters in her purse. She has

$9.35

altogether. How many coins of each type does she have?

Answer

51 dimes, 17 quarters

Try It 9.25 §9.2 source ↗

Jesse has

$6.55

worth of quarters and nickels in his pocket. The number of nickels is five more than two times the number of quarters. How many nickels and how many quarters does Jesse have?

Answer

41 nickels, 18 quarters

Try It 9.26 §9.2 source ↗

Elaine has

$7.00

in dimes and nickels in her coin jar. The number of dimes that Elaine has is seven less than three times the number of nickels. How many of each coin does Elaine have?

Answer

22 nickels, 59 dimes

Try It 9.27 §9.2 source ↗

The first day of a water polo tournament, the total value of tickets sold was

$17,610 .

One-day passes sold for

$20

and tournament passes sold for

$30 .

The number of tournament passes sold was

37

more than the number of day passes sold. How many day passes and how many tournament passes were sold?

Answer

330 day passes, 367 tournament passes

Try It 9.28 §9.2 source ↗

At the movie theater, the total value of tickets sold was

$2,612.50 .

Adult tickets sold for

$10

each and senior/child tickets sold for

$7.50

each. The number of senior/child tickets sold was

25

less than twice the number of adult tickets sold. How many senior/child tickets and how many adult tickets were sold?

Answer

112 adult tickets, 199 senior/child tickets

Try It 9.29 §9.2 source ↗

Eric paid

$16.64

for stamps so he could mail thank you notes for his wedding gifts. The number of

49-cent

stamps was eight more than twice the number of

8-cent

stamps. How many

49-cent

stamps and how many

8-cent

stamps did Eric buy?

Answer

32 at 49 cents, 12 at 8 cents

Try It 9.30 §9.2 source ↗

Kailee paid

$14.84

for stamps. The number of

49-cent

stamps was four less than three times the number of

21-cent

stamps. How many

49-cent

stamps and how many

21-cent

stamps did Kailee buy?

Answer

26 at 49 cents, 10 at 21 cents

9.2-51 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

Jaime has $$2.60$ in dimes and nickels. The number of dimes is $14$ more than the number of nickels. How many of each coin does he have?

Answer

8 nickels, 22 dimes

9.2-53 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

Ngo has a collection of dimes and quarters with a total value of $$3.50 .$ The number of dimes is $7$ more than the number of quarters. How many of each coin does he have?

Answer

15 dimes, 8 quarters

9.2-55 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

Carolyn has $$2.55$ in her purse in nickels and dimes. The number of nickels is $9$ less than three times the number of dimes. Find the number of each type of coin.

Answer

12 dimes and 27 nickels

9.2-57 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

Chi has $$11.30$ in dimes and quarters. The number of dimes is $3$ more than three times the number of quarters. How many dimes and nickels does Chi have?

Answer

63 dimes, 20 quarters

9.2-59 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

A cash box of $$1$ and $$5$ bills is worth $$45 .$ The number of $$1$ bills is $3$ more than the number of $$5$ bills. How many of each bill does it contain?

Answer

10 of the $1 bills, 7 of the $5 bills

9.2-61 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

In a cash drawer there is $$125$ in $$5$ and $$10$ bills. The number of $$10$ bills is twice the number of $$5$ bills. How many of each are in the drawer?

Answer

10 of the $10 bills, 5 of the $5 bills

9.2-63 §9.2 source ↗

Solve Coin Word Problems

In the following exercises, solve the coin word problems.

Mukul has $$3.75$ in quarters, dimes and nickels in his pocket. He has five more dimes than quarters and nine more nickels than quarters. How many of each coin are in his pocket?

Answer

16 nickels, 12 dimes, 7 quarters

9.2-65 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

The play took in $$550$ one night. The number of $8 adult tickets was $10$ less than twice the number of $$5$ child tickets. How many of each ticket were sold?

Answer

30 child tickets, 50 adult tickets

9.2-67 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

The movie theater took in $$1,220$ one Monday night. The number of $$7$ child tickets was ten more than twice the number of $$9$ adult tickets. How many of each were sold?

Answer

110 child tickets, 50 adult tickets

9.2-69 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

Julie went to the post office and bought both $$0.49$ stamps and $$0.34$ postcards for her office's bills She spent $$62.60 .$ The number of stamps was $20$ more than twice the number of postcards. How many of each did she buy?

Answer

40 postcards, 100 stamps

9.2-71 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

Maria spent $$16.80$ at the post office. She bought three times as many $$0.49$ stamps as $$0.21$ stamps. How many of each did she buy?

Answer

30 at 49 cents, 10 at 21 cents

9.2-73 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

Hilda has $$210$ worth of $$10$ and $$12$ stock shares. The numbers of $$10$ shares is $5$ more than twice the number of $$12$ shares. How many of each does she have?

Answer

15 at $10 shares, 5 at $12 shares

9.2-75 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

Parent Volunteer As the treasurer of her daughter's Girl Scout troop, Laney collected money for some girls and adults to go to a $3-day$ camp. Each girl paid $$75$ and each adult paid $$30 .$ The total amount of money collected for camp was $$765 .$ If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?

Answer

9 girls, 3 adults

9.2-77 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

Suppose you have $6$ quarters, $9$ dimes, and $4$ pennies. Explain how you find the total value of all the coins.

Answer

Answers will vary.

9.2-79 §9.2 source ↗

Solve Ticket and Stamp Word Problems

In the following exercises, solve the ticket and stamp word problems.

In the table used to solve coin problems, one column is labeled “number” and another column is labeled ‘“value.” What is the difference between the number and the value?

Answer

Answers will vary.

Be Prepared 9.7 §9.3 source ↗

Solve:

x + 3 + 6 = 11 .

If you missed this problem, review Example 8.6.

Example 8.6 in the book ↗

Answer

x = 2

Be Prepared 9.8 §9.3 source ↗

Solve:

\frac{a}{45} = \frac{4}{3} .

If you missed this problem, review Example 6.42.

Example 6.42 in the book ↗

Answer

60

Be Prepared 9.9 §9.3 source ↗

Simplify:

\sqrt{36 + 64} .

If you missed this problem, review Example 5.72.

Example 5.72 in the book ↗

Answer

10

Try It 9.31 §9.3 source ↗

An angle measures

25° .

Find its: ⓐ supplement ⓑ complement.

Answer

ⓐ 155°

ⓑ 65°

Try It 9.32 §9.3 source ↗

An angle measures

77° .

Find its: ⓐ supplement ⓑ complement.

Answer

ⓐ 103°

ⓑ 13°

Try It 9.33 §9.3 source ↗

Two angles are supplementary. The larger angle is

100°

more than the smaller angle. Find the measures of both angles.

Answer

40°, 140°

Try It 9.34 §9.3 source ↗

Two angles are complementary. The larger angle is

40°

more than the smaller angle. Find the measures of both angles.

Answer

25°, 65°

Try It 9.35 §9.3 source ↗

The measures of two angles of a triangle are

31°

and

128° .

Find the measure of the third angle.

Answer

21°

Try It 9.36 §9.3 source ↗

A triangle has angles of

49°

and

75° .

Find the measure of the third angle.

Answer

56°

Try It 9.37 §9.3 source ↗

One angle of a right triangle measures

56° .

What is the measure of the other angle?

Answer

34°

Try It 9.38 §9.3 source ↗

One angle of a right triangle measures

45° .

What is the measure of the other angle?

Answer

45°

Try It 9.39 §9.3 source ↗

The measure of one angle of a right triangle is

50°

more than the measure of the smallest angle. Find the measures of all three angles.

Answer

20°, 70°, 90°

Try It 9.40 §9.3 source ↗

The measure of one angle of a right triangle is

30°

more than the measure of the smallest angle. Find the measures of all three angles.

Answer

30°, 60°, 90°

Try It 9.41 §9.3 source ↗

$Δ A B C$ is similar to $Δ X Y Z .$ Find $a .$

Two triangles are shown. They appear to be the same shape, but the triangle on the right is larger The vertices of the triangle on the left are labeled A, B, and C. The side across from A is labeled a, the side across from B is labeled 15, and the side across from C is labeled 17. The vertices of the triangle on the right are labeled X, Y, and Z. The side across from X is labeled 12, the side across from Y is labeled y, and the side across from Z is labeled 25.5.

Answer

Try It 9.42 §9.3 source ↗

$Δ A B C$ is similar to $Δ X Y Z .$ Find $y .$

Answer

22.5

Try It 9.43 §9.3 source ↗

Use the Pythagorean Theorem to find the length of the hypotenuse.

Answer

Try It 9.44 §9.3 source ↗

Use the Pythagorean Theorem to find the length of the hypotenuse.

Answer

Try It 9.45 §9.3 source ↗

Use the Pythagorean Theorem to find the length of the leg.

Answer

Try It 9.46 §9.3 source ↗

Use the Pythagorean Theorem to find the length of the leg.

A right triangle is shown. The right angle is marked with a box. The side across from the right angle is labeled as 15. One of the sides touching the right angle is labeled as 9, the other is labeled “b”.

Answer

Try It 9.47 §9.3 source ↗

John puts the base of a $13-ft$ ladder $5$ feet from the wall of his house. How far up the wall does the ladder reach?

A picture of a house is shown. There is a ladder leaning against the side of the house. The ladder is labeled 13 feet. The horizontal distance from the ladder's base to the house is labeled 5 feet.

Answer

12 feet

Try It 9.48 §9.3 source ↗

Randy wants to attach a $17-ft$ string of lights to the top of the $15-ft$ mast of his sailboat. How far from the base of the mast should he attach the end of the light string?

A picture of a boat is shown. The height of the center pole is labeled 15 feet. The string of lights is at a diagonal from the top of the pole and is labeled 17 feet.

Answer

8 feet

9.3-81 §9.3 source ↗

Use the Properties of Angles

In the following exercises, find ⓐ the supplement and ⓑ the complement of the given angle.

$53°$

Answer

ⓐ 127°

ⓑ 37°

9.3-83 §9.3 source ↗

Use the Properties of Angles

In the following exercises, find ⓐ the supplement and ⓑ the complement of the given angle.

$29°$

Answer

ⓐ 151°

ⓑ 61°

9.3-85 §9.3 source ↗

In the following exercises, use the properties of angles to solve.

Find the supplement of a $135°$ angle.

Answer

45°

9.3-87 §9.3 source ↗

In the following exercises, use the properties of angles to solve.

Find the complement of a $27.5°$ angle.

Answer

62.5°

9.3-89 §9.3 source ↗

In the following exercises, use the properties of angles to solve.

Two angles are supplementary. The larger angle is $56°$ more than the smaller angle. Find the measures of both angles.

Answer

62°, 118°

9.3-91 §9.3 source ↗

In the following exercises, use the properties of angles to solve.

Two angles are complementary. The smaller angle is $34°$ less than the larger angle. Find the measures of both angles.

Answer

62°, 28°

9.3-93 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

The measures of two angles of a triangle are $26°$ and $98° .$ Find the measure of the third angle.

Answer

56°

9.3-95 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

The measures of two angles of a triangle are $105°$ and $31° .$ Find the measure of the third angle.

Answer

44°

9.3-97 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

One angle of a right triangle measures $33° .$ What is the measure of the other angle?

Answer

57°

9.3-99 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

One angle of a right triangle measures $22.5 ° .$ What is the measure of the other angle?

Answer

67.5°

9.3-101 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.

Answer

45°, 45°, 90°

9.3-103 §9.3 source ↗

Use the Properties of Triangles

In the following exercises, solve using properties of triangles.

The angles in a triangle are such that the measure of one angle is twice the measure of the smallest angle, while the measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.

Answer

30°, 60°, 90°

9.3-105 §9.3 source ↗

Find the Length of the Missing Side

In the following exercises, $Δ A B C$ is similar to $Δ X Y Z .$ Find the length of the indicated side.

side $b$

Answer

9.3-107 §9.3 source ↗

On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. The actual distance from Los Angeles to Las Vegas is $270$ miles.

A triangle is shown. The vertices are labeled San Francisco, Las Vegas, and Los Angeles. The side across from San Francisco is labeled 1 inch, the side across from Las Vegas is labeled 1.3 inches, and the side across from Los Angeles is labeled 2.1 inches.

Find the distance from Los Angeles to San Francisco.

Answer

351 miles

9.3-109 §9.3 source ↗

Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

Answer

9.3-111 §9.3 source ↗

Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

A right triangle is shown. The right angle is marked with a box. One of the sides touching the right angle is labeled as 15, the other as 20.

Answer

9.3-113 §9.3 source ↗

Find the Length of the Missing Side

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

9.3-115 §9.3 source ↗

Find the Length of the Missing Side

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

9.3-117 §9.3 source ↗

Find the Length of the Missing Side

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

10.2

9.3-119 §9.3 source ↗

Find the Length of the Missing Side

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

16.2

9.3-121 §9.3 source ↗

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

A $13-foot$ string of lights will be attached to the top of a $12-foot$ pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?

Answer

5 feet

9.3-123 §9.3 source ↗

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of $10$ feet. What will the length of the path be?

A square garden is shown. One side is labeled as 10 feet. There is a diagonal path of blue circular stones going from the lower left corner to the upper right corner.

Answer

14.1 feet

9.3-125 §9.3 source ↗

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

Building a scale model Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is $30$ feet wide and $35$ feet tall at the highest point of the roof. If the dollhouse will be $2.5$ feet wide, how tall will its highest point be?

Answer

2.9 feet

9.3-127 §9.3 source ↗

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

Write three of the properties of triangles from this section and then explain each in your own words.

Answer

Answers will vary.

Be Prepared 9.10 §9.4 source ↗

The length of a rectangle is

3

less than the width. Let

w

represent the width. Write an expression for the length of the rectangle.
If you missed this problem, review Example 2.26.

Example 2.26 in the book ↗

Answer

w - 3

Be Prepared 9.11 §9.4 source ↗

Simplify:

\frac{1}{2} (6 h) .

If you missed this problem, review Example 7.7.

Example 7.7 in the book ↗

Answer

3 h

Be Prepared 9.12 §9.4 source ↗

Simplify:

\frac{5}{2} (10.3 - 7.9) .

If you missed this problem, review Example 5.36.

Example 5.36 in the book ↗

Answer

6

Try It 9.49 §9.4 source ↗

Determine whether you would use linear, square, or cubic measure for each item.

ⓐ amount of paint in a can ⓑ height of a tree ⓒ floor of your bedroom ⓓ diameter of bike wheel ⓔ size of a piece of sod ⓕ amount of water in a swimming pool

Answer

ⓐ cubic

ⓑ linear

ⓓ linear

ⓔ square

ⓕ cubic

Try It 9.50 §9.4 source ↗

Determine whether you would use linear, square, or cubic measure for each item.

ⓐ volume of a packing box ⓑ size of patio ⓒ amount of medicine in a syringe ⓓ length of a piece of yarn ⓔ size of housing lot ⓕ height of a flagpole

Answer

ⓐ cubic

ⓑ square

ⓓ linear

ⓔ square

ⓕ linear

Try It 9.51 §9.4 source ↗

Each box in the figure below is 1 square inch. Find the ⓐ perimeter and ⓑ area of the figure:

A rectangle is shown comprised of 3 squares.

Answer

ⓐ 8 inches

ⓑ 3 sq. inches

Try It 9.52 §9.4 source ↗

Each box in the figure below is 1 square inch. Find the ⓐ perimeter and ⓑ area of the figure:

A square is shown comprised of 4 smaller squares.

Answer

ⓐ 8 centimeters

ⓑ 4 sq. centimeters

Try It 9.53 §9.4 source ↗

The length of a rectangle is

120

yards and the width is

50

yards. Find ⓐ the perimeter and ⓑ the area.

Answer

ⓐ 340 yd

ⓑ 6000 sq. yd

Try It 9.54 §9.4 source ↗

The length of a rectangle is

62

feet and the width is

48

feet. Find ⓐ the perimeter and ⓑ the area.

Answer

ⓐ 220 ft

ⓑ 2976 sq. ft

Try It 9.55 §9.4 source ↗

Find the length of a rectangle with a perimeter of

80

inches and width of

25

inches.

Answer

15 in.

Try It 9.56 §9.4 source ↗

Find the length of a rectangle with a perimeter of

30

yards and width of

6

yards.

Answer

9 yd

Try It 9.57 §9.4 source ↗

The width of a rectangle is seven meters less than the length. The perimeter is

58

meters. Find the length and width.

Answer

18 m, 11 m

Try It 9.58 §9.4 source ↗

The length of a rectangle is eight feet more than the width. The perimeter is

60

feet. Find the length and width.

Answer

11 ft , 19 ft

Try It 9.59 §9.4 source ↗

The length of a rectangle is eight more than twice the width. The perimeter is

64

feet. Find the length and width.

Answer

8 ft, 24 ft

Try It 9.60 §9.4 source ↗

The width of a rectangle is six less than twice the length. The perimeter is

18

centimeters. Find the length and width.

Answer

5 cm, 4 cm

Try It 9.61 §9.4 source ↗

The area of a rectangle is

598

square feet. The length is

23

feet. What is the width?

Answer

26 ft

Try It 9.62 §9.4 source ↗

The width of a rectangle is

21

meters. The area is

609

square meters. What is the length?

Answer

29 m

Try It 9.63 §9.4 source ↗

The perimeter of a rectangular swimming pool is

200

feet. The length is

40

feet more than the width. Find the length and width.

Answer

30 ft, 70 ft

Try It 9.64 §9.4 source ↗

The length of a rectangular garden is

30

yards more than the width. The perimeter is

300

yards. Find the length and width.

Answer

60 yd, 90 yd

Try It 9.65 §9.4 source ↗

Find the area of a triangle with base

13

inches and height

2

inches.

Answer

13 sq. in.

Try It 9.66 §9.4 source ↗

Find the area of a triangle with base

14

inches and height

7

inches.

Answer

49 sq. in.

Try It 9.67 §9.4 source ↗

The perimeter of a triangular garden is

48

feet. The lengths of two sides are

18

feet and

22

feet. How long is the third side?

Answer

8 ft

Try It 9.68 §9.4 source ↗

The lengths of two sides of a triangular window are

7

feet and

5

feet. The perimeter is

18

feet. How long is the third side?

Answer

6 ft

Try It 9.69 §9.4 source ↗

The area of a triangular painting is

126

square inches. The base is

18

inches. What is the height?

Answer

14 in.

Try It 9.70 §9.4 source ↗

A triangular tent door has an area of

15

square feet. The height is

5

feet. What is the base?

Answer

6 ft

Try It 9.71 §9.4 source ↗

Find the length of each side of an equilateral triangle with perimeter

39

inches.

Answer

13 in.

Try It 9.72 §9.4 source ↗

Find the length of each side of an equilateral triangle with perimeter

51

centimeters.

Answer

17 cm

Try It 9.73 §9.4 source ↗

A backyard deck is in the shape of an isosceles triangle with a base of

20

feet. The perimeter of the deck is

48

feet. How long is each of the equal sides of the deck?

Answer

14 ft

Try It 9.74 §9.4 source ↗

A boat’s sail is an isosceles triangle with base of

8

meters. The perimeter is

22

meters. How long is each of the equal sides of the sail?

Answer

7 m

Try It 9.75 §9.4 source ↗

The height of a trapezoid is

14

yards and the bases are

7

and

16

yards. What is the area?

Answer

161 sq. yd

Try It 9.76 §9.4 source ↗

The height of a trapezoid is

18

centimeters and the bases are

17

and

8

centimeters. What is the area?

Answer

225 sq. cm

Try It 9.77 §9.4 source ↗

The height of a trapezoid is

7

centimeters and the bases are

4.6

and

7.4

centimeters. What is the area?

Answer

42 sq. cm

Try It 9.78 §9.4 source ↗

The height of a trapezoid is

9

meters and the bases are

6.2

and

7.8

meters. What is the area?

Answer

63 sq. m

Try It 9.79 §9.4 source ↗

Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are

10.8

yards and

6.7

yards, and the height is

4.6

yards. How many square yards of sod does he need?

Answer

40.25 sq. yd

Try It 9.80 §9.4 source ↗

Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are

18

feet and

14

feet and whose height is

15

feet, how many square feet of pavers will he need?

Answer

240 sq. ft

9.4-129 §9.4 source ↗

Understand Linear, Square, and Cubic Measure

In the following exercises, determine whether you would measure each item using linear, square, or cubic units.

amount of water in a fish tank

Answer

cubic

9.4-131 §9.4 source ↗

Understand Linear, Square, and Cubic Measure

In the following exercises, determine whether you would measure each item using linear, square, or cubic units.

living area of an apartment

Answer

square

9.4-133 §9.4 source ↗

Understand Linear, Square, and Cubic Measure

In the following exercises, determine whether you would measure each item using linear, square, or cubic units.

height of a doorway

Answer

linear

9.4-135 §9.4 source ↗

In the following exercises, find the ⓐ perimeter and ⓑ area of each figure. Assume each side of the square is $1$ cm.

Answer

ⓐ 10 cm

ⓑ 4 sq. cm

9.4-137 §9.4 source ↗

In the following exercises, find the ⓐ perimeter and ⓑ area of each figure. Assume each side of the square is $1$ cm.

Answer

ⓐ 8 cm

ⓑ 3 sq. cm

9.4-139 §9.4 source ↗

In the following exercises, find the ⓐ perimeter and ⓑ area of each figure. Assume each side of the square is $1$ cm.

Answer

ⓐ 10 cm

ⓑ 5 sq. cm

9.4-141 §9.4 source ↗

Use the Properties of Rectangles

In the following exercises, find the ⓐ perimeter and ⓑ area of each rectangle.

The length of a rectangle is $85$ feet and the width is $45$ feet.

Answer

ⓐ 260 ft

ⓑ 3825 sq. ft

9.4-143 §9.4 source ↗

Use the Properties of Rectangles

In the following exercises, find the ⓐ perimeter and ⓑ area of each rectangle.

A rectangular room is $15$ feet wide by $14$ feet long.

Answer

ⓐ 58 ft

ⓑ 210 sq. ft

9.4-145 §9.4 source ↗

In the following exercises, solve.

Find the length of a rectangle with perimeter $124$ inches and width $38$ inches.

Answer

24 inches

9.4-147 §9.4 source ↗

In the following exercises, solve.

Find the width of a rectangle with perimeter $92$ meters and length $19$ meters.

Answer

27 meters

9.4-149 §9.4 source ↗

In the following exercises, solve.

The area of a rectangle is $414$ square meters. The length is $18$ meters. What is the width?

Answer

23 m

9.4-151 §9.4 source ↗

In the following exercises, solve.

The length of a rectangle is $9$ inches more than the width. The perimeter is $46$ inches. Find the length and the width.

Answer

7 in., 16 in.

9.4-153 §9.4 source ↗

In the following exercises, solve.

The perimeter of a rectangle is $58$ meters. The width of the rectangle is $5$ meters less than the length. Find the length and the width of the rectangle.

Answer

17 m, 12 m

9.4-155 §9.4 source ↗

In the following exercises, solve.

The width of the rectangle is $0.7$ meters less than the length. The perimeter of a rectangle is $52.6$ meters. Find the dimensions of the rectangle.

Answer

13.5 m, 12.8 m

9.4-157 §9.4 source ↗

In the following exercises, solve.

The perimeter of a rectangle of $150$ feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.

Answer

25 ft, 50 ft

9.4-159 §9.4 source ↗

In the following exercises, solve.

The length of a rectangle is $3$ meters less than twice the width. The perimeter is $36$ meters. Find the length and width.

Answer

l = 11 m, w = 7 m

9.4-161 §9.4 source ↗

In the following exercises, solve.

The width of a rectangular window is $24$ inches. The area is $624$ square inches. What is the length?

Answer

26 in.

9.4-163 §9.4 source ↗

In the following exercises, solve.

The area of a rectangular roof is $2310$ square meters. The length is $42$ meters. What is the width?

Answer

55 m

9.4-165 §9.4 source ↗

In the following exercises, solve.

The perimeter of a rectangular courtyard is $160$ feet. The length is $10$ feet more than the width. Find the length and the width.

Answer

35 ft, 45 ft

9.4-167 §9.4 source ↗

In the following exercises, solve.

The width of a rectangular window is $40$ inches less than the height. The perimeter of the doorway is $224$ inches. Find the length and the width.

Answer

76 in., 36 in.

9.4-169 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

Find the area of a triangle with base $12$ inches and height $5$ inches.

Answer

30 sq. in.

9.4-171 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

Find the area of a triangle with base $8.3$ meters and height $6.1$ meters.

Answer

25.315 sq. m

9.4-173 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

A triangular flag has base of $1$ foot and height of $1.5$ feet. What is its area?

Answer

0.75 sq. ft

9.4-175 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

If a triangle has sides of $6$ feet and $9$ feet and the perimeter is $23$ feet, how long is the third side?

Answer

8 ft

9.4-177 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

What is the base of a triangle with an area of $207$ square inches and height of $18$ inches?

Answer

23 in.

9.4-179 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

The perimeter of a triangular reflecting pool is $36$ yards. The lengths of two sides are $10$ yards and $15$ yards. How long is the third side?

Answer

11 yd

9.4-181 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

An isosceles triangle has a base of $20$ centimeters. If the perimeter is $76$ centimeters, find the length of each of the other sides.

Answer

28 cm

9.4-183 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

Find the length of each side of an equilateral triangle with a perimeter of $51$ yards.

Answer

17 yd

9.4-185 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

The perimeter of an equilateral triangle is $18$ meters. Find the length of each side.

Answer

6 m

9.4-187 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

The perimeter of an isosceles triangle is $42$ feet. The length of the shortest side is $12$ feet. Find the length of the other two sides.

Answer

15 ft

9.4-189 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

A dish is in the shape of an equilateral triangle. Each side is $8$ inches long. Find the perimeter.

Answer

24 in.

9.4-191 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

A road sign in the shape of an isosceles triangle has a base of $36$ inches. If the perimeter is $91$ inches, find the length of each of the other sides.

Answer

27.5 in.

9.4-193 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

The perimeter of a triangle is $39$ feet. One side of the triangle is $1$ foot longer than the second side. The third side is $2$ feet longer than the second side. Find the length of each side.

Answer

12 ft, 13 ft, 14 ft

9.4-195 §9.4 source ↗

Use the Properties of Triangles

In the following exercises, solve using the properties of triangles.

One side of a triangle is twice the smallest side. The third side is $5$ feet more than the shortest side. The perimeter is $17$ feet. Find the lengths of all three sides.

Answer

3 ft, 6 ft, 8 ft

9.4-197 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

The height of a trapezoid is $12$ feet and the bases are $9$ and $15$ feet. What is the area?

Answer

144 sq. ft

9.4-199 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Find the area of a trapezoid with a height of $51$ meters and bases of $43$ and $67$ meters.

Answer

2805 sq. m

9.4-201 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

The height of a trapezoid is $15$ centimeters and the bases are $12.5$ and $18.3$ centimeters. What is the area?

Answer

231 sq. cm

9.4-203 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Find the area of a trapezoid with a height of $4.2$ meters and bases of $8.1$ and $5.5$ meters.

Answer

28.56 sq. m

9.4-205 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Laurel is making a banner shaped like a trapezoid. The height of the banner is $3$ feet and the bases are $4$ and $5$ feet. What is the area of the banner?

Answer

13.5 sq. ft

9.4-207 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width $18.5$ inches and lengths $62$ and $50$ inches. What is the area of the counter?

Answer

1036 sq. in.

9.4-209 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Fence Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a $50$ foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be $10$ feet. How long can he make the other side if he wants to use the entire roll of fence?

Answer

15 ft

9.4-211 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Fence Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are $6$ feet, $8$ feet, and $10$ feet. The fence costs $$10$ per foot. How much will it cost for Christa to fence in her flowerbed?

Answer

$240

9.4-213 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.

Answer

Answers will vary.

9.4-215 §9.4 source ↗

Use the Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Look at the two figures.

ⓐ Which figure looks like it has the larger area? Which looks like it has the larger perimeter?

ⓑ Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?

Answer

Answers will vary.

Be Prepared 9.13 §9.5 source ↗

Evaluate

x^{2}

when

x = 5 .

If you missed this problem, review Example 2.15.

Example 2.15 in the book ↗

Answer

25

Be Prepared 9.14 §9.5 source ↗

Using

3.14

for

π,

approximate the (a) circumference and (b) the area of a circle with radius

8

inches.
If you missed this problem, review Example 5.39.

Example 5.39 in the book ↗

Answer

(a)

50.24 in .

; (b)

200.96 sq . in

Be Prepared 9.15 §9.5 source ↗

Simplify

\frac{22}{7} {(0.25)}^{2}

and round to the nearest thousandth.
If you missed this problem, review Example 5.36.

Example 5.36 in the book ↗

Answer

0 .196

Try It 9.81 §9.5 source ↗

A circular mirror has radius of

5

inches. Find the ⓐ circumference and ⓑ area of the mirror.

Answer

ⓐ 31.4 in.

ⓑ 78.5 sq. in.

Try It 9.82 §9.5 source ↗

A circular spa has radius of

4.5

feet. Find the ⓐ circumference and ⓑ area of the spa.

Answer

ⓐ 28.26 ft

ⓑ 63.585 sq. ft

Try It 9.83 §9.5 source ↗

Find the circumference of a circular fire pit whose diameter is

5.5

feet.

Answer

17.27 ft

Try It 9.84 §9.5 source ↗

If the diameter of a circular trampoline is

12

feet, what is its circumference?

Answer

37.68 ft

Try It 9.85 §9.5 source ↗

Find the diameter of a circle with circumference of

94.2

centimeters.

Answer

30 cm

Try It 9.86 §9.5 source ↗

Find the diameter of a circle with circumference of

345.4

feet.

Answer

110 ft

Try It 9.87 §9.5 source ↗

Find the area of each shaded region:

Answer

28 sq. units

Try It 9.88 §9.5 source ↗

Find the area of each shaded region:

Answer

110 sq. units

Try It 9.89 §9.5 source ↗

Find the area of each shaded region.

Answer

36.5 sq. units

Try It 9.90 §9.5 source ↗

Find the area of each shaded region.

A blue geometric shape is shown. It looks like a rectangle with an equilateral triangle attached to the top. The base of the rectangle is labeled 12, each side is labeled 5. The base of the triangle is split into two pieces, each labeled 2.5.

Answer

70 sq. units

Try It 9.91 §9.5 source ↗

Find the area:

Answer

103.2 sq. units

Try It 9.92 §9.5 source ↗

Find the area:

Answer

38.24 sq. units

9.5-217 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

The lid of a paint bucket is a circle with radius $7$ inches. Find the ⓐ circumference and ⓑ area of the lid.

Answer

ⓐ 43.96 in.

ⓑ 153.86 sq. in.

9.5-219 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A farm sprinkler spreads water in a circle with radius of $8.5$ feet. Find the ⓐ circumference and ⓑ area of the watered circle.

Answer

ⓐ 53.38 ft

ⓑ 226.865 sq. ft

9.5-221 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A reflecting pool is in the shape of a circle with diameter of $20$ feet. What is the circumference of the pool?

Answer

62.8 ft

9.5-223 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A circular saw has a diameter of $12$ inches. What is the circumference of the saw?

Answer

37.68 in.

9.5-225 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A barbecue grill is a circle with a diameter of $2.2$ feet. What is the circumference of the grill?

Answer

6.908 ft

9.5-227 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A circle has a circumference of $163.28$ inches. Find the diameter.

Answer

52 in.

9.5-229 §9.5 source ↗

Use the Properties of Circles

In the following exercises, solve using the properties of circles.

A circle has a circumference of $17.27$ meters. Find the diameter.

Answer

5.5 m

9.5-231 §9.5 source ↗

In the following exercises, find the radius of the circle with given circumference.

A circle has a circumference of $150.72$ feet.

Answer

24 ft

9.5-233 §9.5 source ↗

In the following exercises, find the radius of the circle with given circumference.

A circle has a circumference of $40.82$ miles.

Answer

6.5 mi

9.5-235 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

Answer

16 sq. units

9.5-237 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

Answer

30 sq. units

9.5-239 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.

Answer

57.5 sq. units

9.5-241 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

Answer

12 sq. units

9.5-243 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.

Answer

67.5 sq. units

9.5-245 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.

Answer

89 sq. units

9.5-247 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

Answer

44.81 sq. units

9.5-249 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diameter of the circle are 8.

Answer

41.12 sq. units

9.5-251 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

Answer

35.13 sq. units

9.5-253 §9.5 source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.

A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diameter of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.

Answer

95.625 sq. units

9.5-255 §9.5 source ↗

In the following exercises, solve.

A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides $250$ feet long, and the triangles are isosceles right triangles. Find the area of the park.

A square is shown with four triangles coming off each side.

Answer

187,500 sq. ft

9.5-257 §9.5 source ↗

In the following exercises, solve.

Perry needs to put in a new lawn. His lot is a rectangle with a length of $120$ feet and a width of $100$ feet. The house is rectangular and measures $50$ feet by $40$ feet. His driveway is rectangular and measures $20$ feet by $30$ feet, as shown. Find the area of Perry’s lawn.

A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.

Answer

9400 sq. ft

9.5-259 §9.5 source ↗

In the following exercises, solve.

Area of a Tabletop Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a $1-ft$ by $3-ft$ rectangle with a semicircle at each end, as shown. ⓐ Find the area of the table with one leaf up. ⓑ Find the area of the table with both leaves up.

An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.

Answer

ⓐ 6.5325 sq. ft

ⓑ 10.065 sq. ft

9.5-261 §9.5 source ↗

In the following exercises, solve.

Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.

A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.

Answer

Answers will vary.

Be Prepared 9.16 §9.6 source ↗

Evaluate

x^{3}

when

x = 5 .

If you missed this problem, review Example 2.15.

Example 2.15 in the book ↗

Answer

125

Be Prepared 9.17 §9.6 source ↗

Evaluate

2^{x}

when

x = 5 .

If you missed this problem, review Example 2.16.

Example 2.16 in the book ↗

Answer

32

Be Prepared 9.18 §9.6 source ↗

Find the area of a circle with radius

\frac{7}{2} .

If you missed this problem, review Example 5.39.

Example 5.39 in the book ↗

Answer

\frac{77}{2}

Try It 9.93 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of rectangular solid with the: length

8

feet, width

9

feet, and height

11

feet.

Answer

ⓐ 792 cu. ft

ⓑ 518 sq. ft

Try It 9.94 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of rectangular solid with the: length

15

feet, width

12

feet, and height

8

feet.

Answer

ⓐ 1,440 cu. ft

ⓑ 792 sq. ft

Try It 9.95 §9.6 source ↗

A rectangular box has length

9

feet, width

4

feet, and height

6

feet. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 216 cu. ft

ⓑ 228 sq. ft

Try It 9.96 §9.6 source ↗

A rectangular suitcase has length

22

inches, width

14

inches, and height

9

inches. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 2,772 cu. in.

ⓑ 1,264 sq. in.

Try It 9.97 §9.6 source ↗

For a cube with side 4.5 meters, find the ⓐ volume and ⓑ surface area of the cube.

Answer

ⓐ 91.125 cu. m

ⓑ 121.5 sq. m

Try It 9.98 §9.6 source ↗

For a cube with side 7.3 yards, find the ⓐ volume and ⓑ surface area of the cube.

Answer

ⓐ 389.017 cu. yd.

ⓑ 319.74 sq. yd.

Try It 9.99 §9.6 source ↗

A packing box is a cube measuring

4

feet on each side. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 64 cu. ft

ⓑ 96 sq. ft

Try It 9.100 §9.6 source ↗

A wall is made up of cube-shaped bricks. Each cube is

16

inches on each side. Find the ⓐ volume and ⓑ surface area of each cube.

Answer

ⓐ 4,096 cu. in.

ⓑ 1536 sq. in.

Try It 9.101 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of a sphere with radius 3 centimeters.

Answer

ⓐ 113.04 cu. cm

ⓑ 113.04 sq. cm

Try It 9.102 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of each sphere with a radius of

1

foot

Answer

ⓐ 4.19 cu. ft

ⓑ 12.56 sq. ft

Try It 9.103 §9.6 source ↗

A beach ball is in the shape of a sphere with radius of

9

inches. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 3052.08 cu. in.

ⓑ 1017.36 sq. in.

Try It 9.104 §9.6 source ↗

A Roman statue depicts Atlas holding a globe with radius of

1.5

feet. Find the ⓐ volume and ⓑ surface area of the globe.

Answer

ⓐ 14.13 cu. ft

ⓑ 28.26 sq. ft

Try It 9.105 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of the cylinder with radius 4 cm and height 7cm.

Answer

ⓐ 351.68 cu. cm

ⓑ 276.32 sq. cm

Try It 9.106 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of the cylinder with given radius 2 ft and height 8 ft.

Answer

ⓐ 100.48 cu. ft

ⓑ 125.6 sq. ft

Try It 9.107 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of a can of paint with radius 8 centimeters and height 19 centimeters. Assume the can is shaped exactly like a cylinder.

Answer

ⓐ 3,818.24 cu. cm

ⓑ 1,356.48 sq. cm

Try It 9.108 §9.6 source ↗

Find the ⓐ volume and ⓑ surface area of a cylindrical drum with radius 2.7 feet and height 4 feet. Assume the drum is shaped exactly like a cylinder.

Answer

ⓐ 91.5624 cu. ft

ⓑ 113.6052 sq. ft

Try It 9.109 §9.6 source ↗

Find the volume of a cone with height

7

inches and radius

3

inches

Answer

65.94 cu. in.

Try It 9.110 §9.6 source ↗

Find the volume of a cone with height

9

centimeters and radius

5

centimeters

Answer

235.5 cu. cm

Try It 9.111 §9.6 source ↗

How many cubic inches of candy will fit in a cone-shaped piñata that is

18

inches long and

12

inches across its base? Round the answer to the nearest hundredth.

Answer

678.24 cu. in.

Try It 9.112 §9.6 source ↗

What is the volume of a cone-shaped party hat that is

10

inches tall and

7

inches across at the base? Round the answer to the nearest hundredth.

Answer

128.2 cu. in.

9.6-263 §9.6 source ↗

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find ⓐ the volume and ⓑ the surface area of the rectangular solid with the given dimensions.

length $2$ meters, width $1.5$ meters, height $3$ meters

Answer

ⓐ 9 cu. m

ⓑ 27 sq. m

9.6-265 §9.6 source ↗

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find ⓐ the volume and ⓑ the surface area of the rectangular solid with the given dimensions.

length $3.5$ yards, width $2.1$ yards, height $2.4$ yards

Answer

ⓐ 17.64 cu. yd.

ⓑ 41.58 sq. yd.

9.6-267 §9.6 source ↗

In the following exercises, solve.

Moving van A rectangular moving van has length $16$ feet, width $8$ feet, and height $8$ feet. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 1,024 cu. ft

ⓑ 640 sq. ft

9.6-269 §9.6 source ↗

In the following exercises, solve.

Carton A rectangular carton has length $21.3$ cm, width $24.2$ cm, and height $6.5$ cm. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 3,350.49 cu. cm

ⓑ 1,622.42 sq. cm

9.6-271 §9.6 source ↗

In the following exercises, find ⓐ the volume and ⓑ the surface area of the cube with the given side length.

$5$ centimeters

Answer

ⓐ 125 cu. cm

ⓑ 150 sq. cm

9.6-273 §9.6 source ↗

In the following exercises, find ⓐ the volume and ⓑ the surface area of the cube with the given side length.

$10.4$ feet

Answer

ⓐ 1124.864 cu. ft.

ⓑ 648.96 sq. ft

9.6-275 §9.6 source ↗

In the following exercises, solve.

Science center Each side of the cube at the Discovery Science Center in Santa Ana is $64$ feet long. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 262,144 cu. ft

ⓑ 24,576 sq. ft

9.6-277 §9.6 source ↗

In the following exercises, solve.

Base of statue The base of a statue is a cube with sides $2.8$ meters long. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 21.952 cu. m

ⓑ 47.04 sq. m

9.6-279 §9.6 source ↗

Find the Volume and Surface Area of Spheres

In the following exercises, find ⓐ the volume and ⓑ the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

$3$ centimeters

Answer

ⓐ 113.04 cu. cm

ⓑ 113.04 sq. cm

9.6-281 §9.6 source ↗

Find the Volume and Surface Area of Spheres

In the following exercises, find ⓐ the volume and ⓑ the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

$7.5$ feet

Answer

ⓐ 1,766.25 cu. ft

ⓑ 706.5 sq. ft

9.6-283 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Exercise ball An exercise ball has a radius of $15$ inches. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 14,130 cu. in.

ⓑ 2,826 sq. in.

9.6-285 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Golf ball A golf ball has a radius of $4.5$ centimeters. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 381.51 cu. cm

ⓑ 254.34 sq. cm

9.6-287 §9.6 source ↗

Find the Volume and Surface Area of a Cylinder

In the following exercises, find ⓐ the volume and ⓑ the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.

radius $3$ feet, height $9$ feet

Answer

ⓐ 254.34 cu. ft

ⓑ 226.08 sq. ft

9.6-289 §9.6 source ↗

Find the Volume and Surface Area of a Cylinder

In the following exercises, find ⓐ the volume and ⓑ the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.

radius $1.5$ meters, height $4.2$ meters

Answer

ⓐ 29.673 cu. m

ⓑ 53.694 sq. m

9.6-291 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Coffee can A can of coffee has a radius of $5$ cm and a height of $13$ cm. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 1,020.5 cu. cm

ⓑ 565.2 sq. cm

9.6-293 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Barber shop pole A cylindrical barber shop pole has a diameter of $6$ inches and height of $24$ inches. Find its ⓐ volume and ⓑ surface area.

Answer

ⓐ 678.24 cu. in.

ⓑ 508.68 sq. in.

9.6-295 §9.6 source ↗

Find the Volume of Cones

In the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.

height $9$ feet and radius $2$ feet

Answer

37.68 cu. ft

9.6-297 §9.6 source ↗

Find the Volume of Cones

In the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.

height $12.4$ centimeters and radius $5$ cm

Answer

324.47 cu. cm

9.6-299 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Teepee What is the volume of a cone-shaped teepee tent that is $10$ feet tall and $10$ feet across at the base?

Answer

261.67 cu. ft

9.6-301 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Silo What is the volume of a cone-shaped silo that is $50$ feet tall and $70$ feet across at the base?

Answer

64,108.33 cu. ft

9.6-303 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

Street light post The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is $30$ feet tall with base radius $1$ foot. The smaller cone is $10$ feet tall with base radius of $0.5$ feet. To the nearest tenth,

ⓐ find the volume of the large cone.

ⓑ find the volume of the small cone.

Answer

ⓐ 31.4 cu. ft

ⓑ 2.6 cu. ft

9.6-305 §9.6 source ↗

In the following exercises, solve. Round answers to the nearest hundredth.

The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.

Answer

Answers will vary.

Be Prepared 9.19 §9.7 source ↗

Write

35

miles per gallon as a unit rate.
If you missed this problem, review Example 5.65.

Example 5.65 in the book ↗

Answer

\frac{35 miles}{1 gallon}

Be Prepared 9.20 §9.7 source ↗

Solve

6 x + 24 = 96 .

If you missed this problem, review Example 8.20.

Example 8.20 in the book ↗

Answer

12

Be Prepared 9.21 §9.7 source ↗

Find the simple interest earned after

5

years on

$1,000

at an interest rate of

4% .

If you missed this problem, review Example 6.33.

Example 6.33 in the book ↗

Answer

$200

Try It 9.113 §9.7 source ↗

Lindsay drove for

5 \frac{1}{2}

hours at

60

miles per hour. How much distance did she travel?

Answer

330 mi

Try It 9.114 §9.7 source ↗

Trinh walked for

2 \frac{1}{3}

hours at

3

miles per hour. How far did she walk?

Answer

7 mi

Try It 9.115 §9.7 source ↗

Lee wants to drive from Phoenix to his brother’s apartment in San Francisco, a distance of

770

miles. If he drives at a steady rate of

70

miles per hour, how many hours will the trip take?

Answer

11 hours

Try It 9.116 §9.7 source ↗

Yesenia is

168

miles from Chicago. If she needs to be in Chicago in

3

hours, at what rate does she need to drive?

Answer

56 mph

Try It 9.117 §9.7 source ↗

Solve the formula $d = r t$ for $r :$

ⓐ when $d = 180$ and $t = 4$

ⓐ in general

Answer

ⓐ $r = 45$

ⓑ $r = \frac{d}{t}$

Try It 9.118 §9.7 source ↗

Solve the formula $d = r t$ for $r :$

ⓐ when $d = 780$ and $t = 12$

ⓑ in general

Answer

ⓐ $r = 65$

ⓑ $r = \frac{d}{t}$

Try It 9.119 §9.7 source ↗

Use the formula $A = \frac{1}{2} b h$ to solve for $h:$

ⓐ when $A = 170$ and $b = 17$

ⓑ in general

Answer

ⓐ

h = 20

ⓑ

h = \frac{2 A}{b}

Try It 9.120 §9.7 source ↗

Use the formula $A = \frac{1}{2} b h$ to solve for $b :$

ⓐ when $A = 62$ and $h = 31$

ⓑ in general

Answer

ⓐ $b = 4$

ⓑ $b = \frac{2 A}{h}$

Try It 9.121 §9.7 source ↗

Use the formula $I = P r t .$

Find $t :$ ⓐ when $I =$ $$2,160,$ $r =$ $6%,$ $P =$ $$12,000;$ ⓑ in general

Answer

ⓐ $t = 3 years$

ⓑ $t = \frac{I}{P r}$

Try It 9.122 §9.7 source ↗

Use the formula $I = P r t .$

Find $r :$ ⓐ when $I =$ $$5,400,$ $P =$ $$9,000,$ $t =$ $5 years$ ⓑ in general

Answer

ⓐ $r = 0.12 = 12%$

ⓑ $r = \frac{I}{P t}$

Try It 9.123 §9.7 source ↗

Solve the formula $3 x + 4 y = 10$ for $y :$

ⓐ when $x = 2$

ⓑ in general

Answer

ⓐ $y = 1$

ⓑ $y = \frac{10 - 3 x}{4}$

Try It 9.124 §9.7 source ↗

Solve the formula $5 x + 2 y = 18$ for $y :$

ⓐ when $x = 4$

ⓑ in general

Answer

ⓐ $y = −1$

ⓑ $y = \frac{18 - 5 x}{2}$

Try It 9.125 §9.7 source ↗

Solve the formula

P = a + b + c

for

b .

Answer

b = P − a − c

Try It 9.126 §9.7 source ↗

Solve the formula

P = a + b + c

for

c .

Answer

c = P − a − b

Try It 9.127 §9.7 source ↗

Solve the formula

7 x + y = 11

for

y .

Answer

y = 11 − 7x

Try It 9.128 §9.7 source ↗

Solve the formula

11 x + y = 8

for

y .

Answer

y = 8 − 11x

Try It 9.129 §9.7 source ↗

Solve the formula

4 x + 7 y = 9

for

y .

Answer

y = \frac{9 - 4 x}{7}

Try It 9.130 §9.7 source ↗

Solve the formula

5 x + 8 y = 1

for

y .

Answer

y = \frac{1 - 5 x}{8}

9.7-307 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Steve drove for $8 \frac{1}{2}$ hours at $72$ miles per hour. How much distance did he travel?

Answer

612 mi

9.7-309 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Yuki walked for $1 \frac{3}{4}$ hours at $4$ miles per hour. How far did she walk?

Answer

7 mi

9.7-311 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Connor wants to drive from Tucson to the Grand Canyon, a distance of $338$ miles. If he drives at a steady rate of $52$ miles per hour, how many hours will the trip take?

Answer

6.5 hours

9.7-313 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Aurelia is driving from Miami to Orlando at a rate of $65$ miles per hour. The distance is $235$ miles. To the nearest tenth of an hour, how long will the trip take?

Answer

3.6 hours

9.7-315 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Javier is driving to Bangor, Maine, which is $240$ miles away from his current location. If he needs to be in Bangor in $4$ hours, at what rate does he need to drive?

Answer

60 mph

9.7-317 §9.7 source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Aisha took the train from Spokane to Seattle. The distance is $280$ miles, and the trip took $3.5$ hours. What was the speed of the train?

Answer

80 mph

9.7-319 §9.7 source ↗

Solve a Formula for a Specific Variable

In the following exercises, use the formula. $d = r t .$

Solve for $t :$

ⓐ when $d = 350$ and $r = 70$

ⓑ in general

Answer

ⓐ $t = 5$

ⓑ $t = \frac{d}{r}$

9.7-321 §9.7 source ↗

Solve a Formula for a Specific Variable

In the following exercises, use the formula. $d = r t .$

Solve for $t :$

ⓐ when $d = 510$ and $r = 60$

ⓑ in general

Answer

ⓐ $t = 8.5$

ⓑ $t = \frac{d}{r}$

9.7-323 §9.7 source ↗

Solve a Formula for a Specific Variable

In the following exercises, use the formula. $d = r t .$

Solve for $r :$

ⓐ when $d = 204$ and $t = 3$

ⓑ in general

Answer

ⓐ $r = 68$

ⓑ $r = \frac{d}{t}$

9.7-325 §9.7 source ↗

Solve a Formula for a Specific Variable

In the following exercises, use the formula. $d = r t .$

Solve for $r :$

ⓐ when $d = 160$ and $t = 2.5$

ⓑ in general

Answer

ⓐ $r = 64$

ⓑ $r = \frac{d}{t}$

9.7-327 §9.7 source ↗

In the following exercises, use the formula $A = \frac{1}{2} b h .$

Solve for $b :$

ⓐ when $A = 126$ and $h = 18$

ⓑ in general

Answer

ⓐ $b = 14$

ⓑ $b = \frac{2 A}{h}$

9.7-329 §9.7 source ↗

In the following exercises, use the formula $A = \frac{1}{2} b h .$

Solve for $h :$

ⓐ when $A = 375$ and $b = 25$

ⓑ in general

Answer

ⓐ $h = 30$

ⓑ $h = \frac{2 A}{b}$

9.7-331 §9.7 source ↗

In the following exercises, use the formula $I = P r t .$

Solve for the principal, $P$ for:

ⓐ $I = $5,480$ , $r = 4%$ , $t = 7 years$

ⓑ in general

Answer

ⓐ $P =$ $$19,571.43$

ⓑ $P = \frac{I}{r t}$

9.7-333 §9.7 source ↗

In the following exercises, use the formula $I = P r t .$

Solve for the time, $t$ for:

ⓐ $I = $2,376$ , $P = $9,000$ , $r = 4.4 %$

ⓑ in general

Answer

ⓐ $t = 6 years$

ⓑ $t = \frac{I}{P r}$

9.7-335 §9.7 source ↗

In the following exercises, solve.

Solve the formula $2 x + 3 y = 12$ for $y :$

ⓐ when $x = 3$

ⓑ in general

Answer

ⓐ $y = 2$

ⓑ $y = \frac{12 - 2 x}{3}$

9.7-337 §9.7 source ↗

In the following exercises, solve.

Solve the formula $3 x + y = 7$ for $y :$

ⓐ when $x = −2$

ⓑ in general

Answer

ⓐ y = 13

ⓑ y = 7 − 3x

9.7-339 §9.7 source ↗

In the following exercises, solve.

Solve $a + b = 90$ for $b .$

Answer

ⓐ b = 90 − a

9.7-341 §9.7 source ↗

In the following exercises, solve.

Solve $180 = a + b + c$ for $a .$

Answer

a = 180 − b − c

9.7-343 §9.7 source ↗

In the following exercises, solve.

Solve the formula $8 x + y = 15$ for $y .$

Answer

y = 15 − 8x

9.7-345 §9.7 source ↗

In the following exercises, solve.

Solve the formula $- 4 x + y = −6$ for $y .$

Answer

y = −6 + 4x

9.7-347 §9.7 source ↗

In the following exercises, solve.

Solve the formula $4 x + 3 y = 7$ for $y .$

Answer

y = \frac{7 - 4 x}{3}

9.7-349 §9.7 source ↗

In the following exercises, solve.

Solve the formula $x - y = −4$ for $y .$

Answer

y = 4 + x

9.7-351 §9.7 source ↗

In the following exercises, solve.

Solve the formula $P = 2 L + 2 W$ for $L .$

Answer

L = \frac{P - 2 W}{2}

9.7-353 §9.7 source ↗

In the following exercises, solve.

Solve the formula $C = π d$ for $d .$

Answer

d = \frac{C}{π}

9.7-355 §9.7 source ↗

In the following exercises, solve.

Solve the formula $V = L W H$ for $L .$

Answer

L = \frac{V}{W H}

9.7-357 §9.7 source ↗

In the following exercises, solve.

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was $40°$ Celsius. Solve for $F$ in the formula $C = \frac{5}{9} (F - 32)$ to find the temperature in Fahrenheit.

Answer

104° F

9.7-359 §9.7 source ↗

In the following exercises, solve.

Solve the equation $2 x + 3 y = 6$ for $y :$

ⓐ when $x = −3$

ⓑ in general

Answer

Answers will vary

9.R-361 §9.R source ↗

Approach Word Problems with a Positive Attitude

In the following exercises, solve.

How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.

Answer

Answers will vary.

9.R-363 §9.R source ↗

Use a Problem Solving Strategy for Word Problems

In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Three-fourths of the people at a concert are children. If there are $87$ children, what is the total number of people at the concert?

Answer

There are 116 people at the concert.

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Use a Problem Solving Strategy for Word Problems

In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Reza was very sick and lost $15%$ of his original weight. He lost $27$ pounds. What was his original weight?

Answer

His original weight was 180 pounds.

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Solve Number Problems

In the following exercises, solve each number word problem.

The sum of a number and three is forty-one. Find the number.

Answer

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Solve Number Problems

In the following exercises, solve each number word problem.

One number is nine less than another. Their sum is twenty-seven. Find the numbers.

Answer

18, 9

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Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Francie has $$4.35$ in dimes and quarters. The number of dimes is $5$ more than the number of quarters. How many of each coin does she have?

Answer

16 dimes, 11 quarters

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Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Paulette has $$140$ in $$5$ and $$10$ bills. The number of $$10$ bills is one less than twice the number of $$5$ bills. How many of each does she have?

Answer

6 of $5 bills, 11 of $10 bills

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Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

A church luncheon made $$842 .$ Adult tickets cost $$10$ each and children’s tickets cost $$6$ each. The number of children was $12$ more than twice the number of adults. How many of each ticket were sold?

Answer

35 adults, 82 children

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Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

Ana spent $$4.06$ buying stamps. The number of $$0.41$ stamps she bought was $5$ more than the number of $$0.26$ stamps. How many of each did she buy?

Answer

3 of 26 -cent stamps, 8 of 41 -cent stamps

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Use Properties of Angles

In the following exercises, solve using properties of angles.

What is the supplement of a $48°$ angle?

Answer

132°

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Use Properties of Angles

In the following exercises, solve using properties of angles.

Two angles are complementary. The smaller angle is $24°$ less than the larger angle. Find the measures of both angles.

Answer

33°, 57°

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Use Properties of Triangles

In the following exercises, solve using properties of triangles.

The measures of two angles of a triangle are $22$ and $85$ degrees. Find the measure of the third angle.

Answer

73°

9.R-385 §9.R source ↗

Use Properties of Triangles

In the following exercises, solve using properties of triangles.

One angle of a triangle is $30°$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

Answer

30°, 60°, 90°

9.R-387 §9.R source ↗

In the following exercises, $Δ A B C$ is similar to $Δ X Y Z .$ Find the length of the indicated side.

side $x$

Answer

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Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

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Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

9.R-393 §9.R source ↗

Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

8.1

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In the following exercises, solve. Approximate to the nearest tenth, if necessary.

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $8$ feet tall and Sergio has $10$ feet of wire. How far from the base of the antenna can he attach the wire?

An image of a house is shown. A 10-foot wire is going from the roof of the house to the ground. The wire hits the house at a height of 8 feet.

Answer

6 feet

9.R-397 §9.R source ↗

Understand Linear, Square, Cubic Measure

In the following exercises, would you measure each item using linear, square, or cubic measure?

amount of sand in a sandbag

Answer

cubic

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Understand Linear, Square, Cubic Measure

In the following exercises, would you measure each item using linear, square, or cubic measure?

size of a patio

Answer

square

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In the following exercises, find

Three squares are shown, in a sideways L shape.

Answer

ⓐ 8 units

ⓑ 3 sq. units

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Use Properties of Rectangles

In the following exercises, find the ⓐ perimeter ⓑ area of each rectangle

The length of a rectangle is $42$ meters and the width is $28$ meters.

Answer

ⓐ 140 m

ⓑ 1176 sq. m

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Use Properties of Rectangles

In the following exercises, find the ⓐ perimeter ⓑ area of each rectangle

A sidewalk in front of Kathy’s house is in the shape of a rectangle $4$ feet wide by $45$ feet long.

Answer

ⓐ 98 ft.

ⓑ 180 sq. ft.

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In the following exercises, solve.

Find the length of a rectangle with perimeter of $220$ centimeters and width of $85$ centimeters.

Answer

25 cm

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In the following exercises, solve.

The area of a rectangle is $2356$ square meters. The length is $38$ meters. What is the width?

Answer

62 m

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In the following exercises, solve.

The length of a rectangle is $12$ centimeters more than the width. The perimeter is $74$ centimeters. Find the length and the width.

Answer

24.5 cm., 12.5 cm.

9.R-413 §9.R source ↗

Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

Find the area of a triangle with base $18$ inches and height $15$ inches.

Answer

135 sq. in.

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Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

A triangular road sign has base $30$ inches and height $40$ inches. What is its area?

Answer

600 sq. in.

9.R-417 §9.R source ↗

Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

A tile in the shape of an isosceles triangle has a base of $6$ inches. If the perimeter is $20$ inches, find the length of each of the other sides.

Answer

7 in., 7 in.

9.R-419 §9.R source ↗

Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

The perimeter of a triangle is $59$ feet. One side of the triangle is $3$ feet longer than the shortest side. The third side is $5$ feet longer than the shortest side. Find the length of each side.

Answer

17 ft., 20 ft., 22 ft.

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Use Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

The height of a trapezoid is $8$ feet and the bases are $11$ and $14$ feet. What is the area?

Answer

100 sq. ft.

9.R-423 §9.R source ↗

Use Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

Find the area of the trapezoid with height $25$ meters and bases $32.5$ and $21.5$ meters.

Answer

675 sq. m

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Use Properties of Circles

In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

A circular mosaic has radius $3$ meters. Find the

ⓐ circumference

ⓑ area of the mosaic

Answer

ⓐ 18.84 m

ⓑ 28.26 sq. m

9.R-427 §9.R source ↗

Use Properties of Circles

In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

Find the diameter of a circle with circumference $150.72$ inches.

Answer

48 in.

9.R-429 §9.R source ↗

Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

A geometric shape is shown, formed by two rectangles. The top is labeled 8. The width of the top rectangle is labeled 3. The right side of the figure is labeled 5. The width of the bottom rectangle is labeled 3.

Answer

30 sq. units

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Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

A geometric shape is shown. It is formed by two triangles. The shared base of the two triangles is labeled 20. The height of each triangle is labeled 15.

Answer

300 sq. units

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Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

Answer

199.25 sq. units

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Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the

a rectangular solid with length $14$ centimeters, width $4.5$ centimeters, and height $10$ centimeters

Answer

ⓐ 630 cu. cm

ⓑ 496 sq. cm

9.R-437 §9.R source ↗

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the

a cube of tofu with sides $2.5$ inches

Answer

ⓐ 15.625 cu. in.

ⓑ 37.5 sq. in.

9.R-439 §9.R source ↗

Find Volume and Surface Area of Spheres

In the following exercises, find the

a sphere with radius $4$ yards

Answer

ⓐ 267.95 cu. yd.

ⓑ 200.96 sq. yd.

9.R-441 §9.R source ↗

Find Volume and Surface Area of Spheres

In the following exercises, find the

a baseball with radius $1.45$ inches

Answer

ⓐ 12.76 cu. in.

ⓑ 26.41 sq. in.

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Find Volume and Surface Area of Cylinders

In the following exercises, find the

a cylinder with radius $2$ yards and height $6$ yards

Answer

ⓐ 75.36 cu. yd.

ⓑ 100.48 sq. yd.

9.R-445 §9.R source ↗

Find Volume and Surface Area of Cylinders

In the following exercises, find the

a juice can with diameter $8$ centimeters and height $15$ centimeters

Answer

ⓐ 753.6 cu. cm

ⓑ 477.28 sq. cm

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Find Volume of Cones

In the following exercises, find the volume of the cone.

a cone with height $5$ meters and radius $1$ meter

Answer

5.233 cu. m

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Find Volume of Cones

In the following exercises, find the volume of the cone.

a cone-shaped water cup with diameter $2.6$ inches and height $2.6$ inches

Answer

4.599 cu. in.

9.R-451 §9.R source ↗

Use the Distance, Rate, and Time Formula

In the following exercises, solve using the formula for distance, rate, and time.

A plane flew $4$ hours at $380$ miles per hour. What distance was covered?

Answer

1520 miles

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Use the Distance, Rate, and Time Formula

In the following exercises, solve using the formula for distance, rate, and time.

Jack is driving from Bangor to Portland at a rate of $68$ miles per hour. The distance is $107$ miles. To the nearest tenth of an hour, how long will the trip take?

Answer

1.6 hours

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Solve a Formula for a Specific Variable

In the following exercises, use the formula $d = r t .$

Solve for $t :$

ⓐ when $d = 403$ and $r = 65$

ⓑ in general

Answer

ⓐ $t = 6.2$

ⓑ $t = \frac{d}{r}$

9.R-457 §9.R source ↗

In the following exercises, use the formula $A = \frac{1}{2} b h .$

Solve for $b :$

ⓐ when $A = 416$ and $h = 32$

ⓑ in general

Answer

ⓐ $b = 26$

ⓑ $b = \frac{2 A}{h}$

9.R-459 §9.R source ↗

In the following exercises, use the formula $I = P r t .$

Solve for the principal, $P,$ for:

ⓐ $I = $720$ , $r = 4%$ , $t = 3 years$

ⓑ in general

Answer

ⓐ $P = $6000$

ⓑ $P = \frac{I}{(r \cdot t)}$

9.R-461 §9.R source ↗

In the following exercises, solve.

Solve the formula $6 x + 5 y = 20$ for $y :$

ⓐ when $x = 0$

ⓑ in general

Answer

ⓐ $y = 4$

ⓑ $y = \frac{20 - 6 x}{5}$

9.R-463 §9.R source ↗

In the following exercises, solve.

Solve $a + b = 90$ for $a .$

Answer

a = 90 − b

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In the following exercises, solve.

Solve the formula $4 x + y = 17$ for $y .$

Answer

y = 17 − 4x

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In the following exercises, solve.

Solve the formula $P = 2 L + 2 W$ for $W .$

Answer

W = \frac{P - 2 L}{2}

9.T-471 §9.T source ↗

The sum of

13

and twice a number is

- 19 .

Find the number.

Answer

−16

9.T-473 §9.T source ↗

Bonita has

$2.95

in dimes and quarters in her pocket. If she has

5

more dimes than quarters, how many of each coin does she have?

Answer

7 quarters, 12 dimes

9.T-475 §9.T source ↗

Find the complement of a

52°

angle.

Answer

38°

9.T-477 §9.T source ↗

The perimeter of an equilateral triangle is

145

feet. Find the length of each side.

Answer

48.3

9.T-479 §9.T source ↗

Find the length of the missing side. Round to the nearest tenth, if necessary.

Answer

9.T-481 §9.T source ↗

A baseball diamond is shaped like a square with sides $90$ feet long. How far is it from home plate to second base, as shown?

A baseball diamond is shown. It is in the shape of a sideways square. The bottom corner is labeled Home and there is a dotted line to the top corner, labeled 2nd base. The right corner is labeled 1st base and the left corner is labeled 3rd base.

Answer

127.3 ft

9.T-483 §9.T source ↗

A triangular poster has base

80

centimeters and height

55

centimeters. Find the area of the poster.

Answer

2200 square centimeters

9.T-485 §9.T source ↗

A circular pool has diameter

90

inches. What is its circumference? Round to the nearest tenth.

Answer

282.6 inches

9.T-487 §9.T source ↗

Find the volume of a rectangular room with width

12

feet, length

15

feet, and height

8

feet.

Answer

1440

9.T-489 §9.T source ↗

A traffic cone has height

75

centimeters. The radius of the base is

20

centimeters. Find the volume of the cone. Round to the nearest tenth.

Answer

31,400 cubic inches

9.T-491 §9.T source ↗

The Catalina Express takes

1 \frac{1}{2}

hours to travel from Long Beach to Catalina Island, a distance of

22

miles. To the nearest tenth, what is the speed of the boat?

Answer

14.7 miles per hour

9.T-493 §9.T source ↗

Solve the formula $A = \frac{1}{2} b h$ for $h :$

ⓐ when $A = 1716$ and $b = 66$

ⓑ in general

Answer

ⓐ $height = 52$

ⓑ $h = \frac{2 A}{b}$

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Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.