Practice WS

February 23, 2018 | Author: axelramon | Category: Line (Geometry), Equations, Median, Elementary Mathematics, Physics & Mathematics

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Practice Workbook To jump to a location in this book 1. Click a bookmark on the left. To print a part of the book 1. Click the Print button. 2. When the Print window opens, type in a range of pages to print. The page numbers are displayed in the bar at the bottom of the document. In the example below, “1 of 151” means that the current page is page 1 in a file of 151 pages.

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CLASS

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Practice 1.1 Using Differences to Identify Patterns Find the next three terms in each sequence. 1.

14, 21, 28, 35, 42, . . .

2.

1, 2, 4, 8, 16, . . .

3.

13, 15, 17, 19, 21, . . .

4.

26, 39, 52, 65, 78, . . .

5.

1, 6, 11, 16, 21, . . .

6.

1, 7, 3, 9, 5, 11, . . .

7.

25, 36, 49, 64, 81, . . .

8.

2, 2, 4, 6, 10, . . .

9.

7, 22, 43, 70, 103, . . .

10.

9, 36, 81,144, 225, . . .

2, 5, 10, 17, 26, . . .

12.

1000, 729, 512, 343, 216, . . .

11.

Find each sum. Think of a geometric dot pattern, but do not draw a sketch. 13.

1 ⴙ 2 ⴙ . . . ⴙ 80

14.

1 ⴙ 2 ⴙ . . . ⴙ 120

Solve each problem. 15.

The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence?

16.

If the second differences of a sequence are a constant 2, the first of the first differences is 3, and the first term is 12, find the first five terms of the sequence.

17.

Complete the table.

18.

19.

20.

Number

2

4

6

8

Pattern

12

24

36

48

10

12

14

16

6

7

8

12

14

16

Complete the table. Number

1

2

3

4

5

Pattern

2

23

58

107

170

10

Complete the table. Number

2

4

6

8

Pattern

2

6

12

20

There are 6 players in a backgammon tournament. If each player must play every other player, how many games need to be played?

Algebra 1

Practice Workbook

1

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Practice 1.2 Variables, Expressions, and Equations Given the values of the variable, complete each table to find the values of each expression.

1.

x

1

2

3

4

5

6

1

2

3

4

5

6

2

4

6

8

10

12

6x

2.

n 8n ⴚ 6

3.

d 3d ⴙ 21

Use guess-and-check to solve the following equations:

2x ⴙ 3 ⴝ 15

5.

3g ⴚ 4 ⴝ 11

6.

5m ⴚ 7 ⴝ 13

7.

4t ⴙ 2 ⴝ 18

8.

13x ⴚ 13 ⴝ 52

9.

9b ⴙ 14 ⴝ 41

10.

7q ⴚ 8 ⴝ 48

11.

4.

12p ⴙ 9 ⴝ 105

For Exercises 12–15, write an equation and solve by guess-and-check. 12.

If hamburgers cost \$4 each, how many can you buy with \$12?

13.

If tickets for a concert cost \$18 each, how many can you buy with \$54?

14.

Fruit baskets cost \$16 each. How many do you have to sell to raise \$115?

15.

How many \$16 fruit baskets can you buy if you have \$45?

16.

Deluxe fruit baskets cost \$26 each. How many do you have to sell to raise \$190?

2

Practice Workbook

Algebra 1

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Practice 1.3 The Algebraic Order of Operations Evaluate each expression. 1.

16 ⴙ 4 ⴢ 8 ⴙ 2

2.

16 ⴙ 4 ⴢ (8 ⴙ 2)

3.

(16 ⴙ 4) ⴢ (8 ⴙ 2)

4.

(16 ⴙ 4) ⴢ 8 ⴙ 2

5.

0.2(2.5) ⴙ 8

6.

16 ⴢ 37 ⴙ 88 ⴢ 49

7.

16 ⴙ 8 ⴜ 2

8.

4 ⴢ 6 ⴜ 12 ⴙ 10

9.

12 ⴙ 6 4ⴙ2

10.

5ⴙ3ⴢ5 5

11.

12 ⴙ 6 ⴜ 4 ⴙ 2

12.

90 ⴜ 3 ⴙ 5

13.

36 ⴚ 6 ⴢ 3 ⴜ 18 ⴢ 3

14.

9 ⴚ 3 ⴜ 4 ⴙ 2 ⴢ 12 ⴙ 6 ⴜ 2 ⴢ 3

15.

4 ⴙ 1 ⴢ 42 ⴚ 3

16.

6 ⴙ 33 ⴚ 18 ⴜ 6

Place inclusion symbols to make each equation true. 17.

27 ⴙ 5 ⴢ 8 ⴚ 6 ⴝ 37

18.

12 ⴢ 1 ⴙ 5 ⴜ 12 ⴝ 6

19.

44 ⴢ 5 ⴚ 3 ⴙ 2 ⴝ 10

20.

3ⴢ4ⴙ2ⴜ6ⴝ3

Given a ⴝ 3, b ⴝ 6, and c ⴝ 5, evaluate each expression. 21.

bⴚaⴙc

22.

aⴙbⴚc

23.

aⴢbⴙaⴢc

24.

bⴜaⴙaⴢc

25.

a2 ⴙ c 2

26.

b2 ⴚ a2

27.

(a ⴙ b) ⴜ c

28.

a ⴙ b2 ⴚ c

Algebra 1

Practice Workbook

3

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Practice 1.4 Graphing With Coordinates Graph each list of ordered pairs. State whether they lie on a straight line. 1.

(4, 3), (2, 3), (ⴚ2, 3)

2.

(2, ⴚ2), (4, 1), (5, 2)

3.

(5, 5), (1, 2), (ⴚ3, ⴚ1)

4.

(ⴚ4, ⴚ2), (ⴚ2, 0), (0, 2)

5.

(ⴚ3, 4), (0, ⴚ1), (3, ⴚ5)

6.

(5, 6), (2, 3), (ⴚ1, 0)

Make a table for each equation, and find the values for y by substituting 1, 2, 3, 4, and 5 for x. 7.

yⴝxⴙ5

9.

y ⴝ 4x

10.

y ⴝ 3x ⴙ 2

y ⴝ 5x ⴚ 7

12.

y ⴝ ⴚ4x ⴙ 2

11.

4

Practice Workbook

8.

yⴝxⴚ1

Algebra 1

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Practice 1.5 Representing Linear Patterns Find the first differences for each data set, and write an equation to represent the data pattern. 1.

3.

5.

6.

0

1

2

3

4

5

6

13

20

27

34

41

48

55

0

1

2

3

4

5

6

0

4

8

12

16

20

24

2.

0 19

1 24

2 29

3 34

4 39

5 44

6 49

4.

0

1

2

3

4

5

6

4

23

42

61

80

99

118

0

1

2

3

4

5

6

20

120

220

320

420

520

620

0

1

2

3

4

5

6

396

362

328

294

260

226

192

Make a table of values for each question below, using 1, 2, 3, 4, and 5 as values for x. Draw a graph for each equation by plotting points from your data set. 7. 11.

y ⴝ 40x y ⴝ 5x ⴙ 18

8.

y ⴝ 55 ⴙ 5x

9.

12.

y ⴝ 71 ⴚ 6x

13.

y ⴝ 19x ⴙ 14

10.

y ⴝ 424 ⴚ 78x

y ⴝ 175 ⴚ 20x

14.

y ⴝ 2000 ⴚ 250x

Suppose that the cost to order baseball tickets is \$17 per ticket plus \$2.50 handling charge per order (regardless of how many tickets are ordered). 15.

How much does an order of 4 tickets cost?

16.

How much does an order of 6 tickets cost?

17.

Let t represent the number of tickets, and write an equation for the cost, c, of an order of tickets.

Algebra 1

Practice Workbook

5

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Practice 1.6 Scatter Plots and Lines of Best Fit For each scatter plot, describe the correlation as strong positive, strong negative, or little to none. Explain the reason for your answer. 1.

2.

3.

The chart shows the average time that a person can survive in water at a particular temperature Water temperature (°F)

37

45

55

60

Average survival time (in minutes)

7

18

29

60

6

4.

Use the grid at the right to make a scatter plot of water temperature versus average survival time.

5.

Describe the correlation between temperature and survival time. Explain your reasoning.

Practice Workbook

Algebra 1

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Practice 2.1 The Real Numbers and Absolute Value Insert , , or ⴝ to make each statement true.

ⴚ10

1.

5

4.

ⴚ9 3

7.

0

10.

2.

1.40

5.

8.8

ⴚ3

8.

ⴚ18

1 3

11.

98.59

1

5

ⴚ7 32

0.3

1.4

7

3.

19.5

19 10

6.

12.2

12.02

ⴚ18 2

9.

ⴚ2.3

2 10

98.6

12.

0 1

3

2

0.667

Find the opposite of each number. 3

13.

418

14.

ⴚ4.8

15.

0.2

16.

17.

n 4

ⴚ8

18.

76

19.

ⴚ32

20.

1

21.

ⴚ19.5

22.

16 3

23.

ⴚx

24.

1953

2

Find the absolute value of each number. 1

26.

ⴚ100

27.

28.

ⴚ4.12

ⴚ13 2

30.

3 5

29 5

31.

ⴚ22

32.

3.1416

85

34.

ⴚ52

35.

1971

36.

ⴚ 1000

25.

17

29. 33.

1

9

Simplify each expression. 37.

ⴚ(4 ⴜ 2)

ⱍⴚ1.8ⱍ 45. ⱍⴚ3ⱍ ⴙ ⱍ3ⱍ 41.

Algebra 1

38.

ⴚ(0.8 ⴙ 0.095)

42.

ⱍⴚ(ⴚ0.1)ⱍ

46.

ⴚ5

ⱍⱍ 2

39.

43. 47.

ⱍⱍ

ⴚ(ⴚm)

21 7

ⱍⴚ4ⱍ ⴢ ⱍⴚ4ⱍ

40.

( 13

48.

ⱍ8 ⴚ 8ⱍ

3

ⴚ 100 ⴚ 100 44. ⱍ4 ⴚ 4ⱍ

)

7 8

Practice Workbook

7

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Practice 2.2 Adding Real Numbers Use algebra tiles to find each sum. 1.

ⴚ3 ⴙ 2

2.

ⴚ4 ⴙ (ⴚ1)

3.

4 ⴙ (ⴚ5)

4.

ⴚ6 ⴙ 6

5.

ⴚ3 ⴙ (ⴚ7)

6.

9 ⴙ (ⴚ4)

7.

7 ⴙ (ⴚ4)

8.

ⴚ7 ⴙ 9

9.

ⴚ8 ⴙ 3

10.

10 ⴙ (ⴚ9)

11.

ⴚ1 ⴙ (ⴚ9)

12.

(ⴚ6) ⴙ (ⴚ2)

13.

ⴚ4 ⴙ (ⴚ1) ⴙ 3

14.

5 ⴙ (ⴚ1) ⴙ (ⴚ2)

15.

ⴚ3 ⴙ (ⴚ4) ⴙ 2

Find each sum.

ⴚ35 ⴙ 40

17.

15 ⴙ (ⴚ28)

18.

60 ⴙ (ⴚ18)

19.

ⴚ17 ⴙ (ⴚ19)

20.

42 ⴙ (ⴚ56)

21.

ⴚ34 ⴙ 28

22.

59 ⴙ (ⴚ59)

23.

ⴚ86 ⴙ 85

24.

ⴚ45 ⴙ (ⴚ45)

25.

ⴚ68 ⴙ (ⴚ15)

26.

ⴚ3 ⴙ (ⴚ1) ⴙ (ⴚ2)

27.

4 ⴙ (ⴚ7) ⴙ (ⴚ4)

28.

ⴚ54 ⴙ 63 ⴙ (ⴚ20)

29.

ⴚ78 ⴙ (ⴚ78) ⴙ 50

30.

ⴚ6 ⴙ (ⴚ42) ⴙ 24

31.

ⴚ24 ⴙ (ⴚ62) ⴙ (ⴚ11)

32.

ⴚ5 ⴙ ⱍⴚ4ⱍ

33.

ⱍ5ⱍ ⴙ ⱍⴚ4ⱍ

34.

ⱍⴚ5ⱍ ⴙ ⱍⴚ4ⱍ

35.

ⱍⴚ5ⱍ ⴙ ⱍ4ⱍ ⴙ (ⴚ9)

36.

ⴚ48 ⴙ ⱍⴚ64ⱍ ⴙ (ⴚ32)

37.

ⴚ568 ⴙ (ⴚ43) ⴙ ⱍⴚ57ⱍ

16.

Substitute 4 for a, ⴚ6 for b, and 3 for c. Evaluate each expression. 38.

a ⴙ (b ⴙ c)

39.

a ⴙ ⱍb ⴙ cⱍ

40.

(a ⴙ c) ⴙ b

41.

(a ⴙ c) ⴙ ⱍbⱍ

42.

ⱍa ⴙ bⱍ ⴙ c

43.

ⱍa ⴙ cⱍ ⴙ b

44.

ⱍcⱍ ⴙ b ⴙ a

45.

a ⴙ ⱍbⱍ ⴙ ⱍcⱍ

8

Practice Workbook

Algebra 1

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CLASS

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Practice 2.3 Subtracting Real Numbers Use algebra tiles to find each difference. 1.

3ⴚ2

2.

ⴚ3 ⴚ (ⴚ2)

3.

3 ⴚ (ⴚ2)

4.

ⴚ3 ⴚ 2

5.

ⴚ4 ⴚ 3

6.

ⴚ8 ⴚ (ⴚ2)

7.

4ⴚ7

8.

6 ⴚ (ⴚ5)

9.

ⴚ8 ⴚ (ⴚ8)

Evaluate each expression. 10.

56 ⴚ 2

11.

53 ⴚ (ⴚ8)

12.

26 ⴚ (ⴚ26)

13.

ⴚ85 ⴚ (ⴚ34)

14.

ⴚ64 ⴚ 73

15.

ⴚ56 ⴙ (ⴚ42)

16.

58 ⴚ (ⴚ58)

17.

ⴚ49 ⴚ 18

18.

ⴚ24 ⴙ 47 ⴙ (ⴚ24)

19.

ⴚ13 ⴙ 19 ⴚ (ⴚ25)

20.

ⴚ66 ⴚ 66 ⴙ 6

21.

86 ⴚ (ⴚ15) ⴚ 9

22.

45 ⴚ (ⴚ27) ⴚ (ⴚ17)

23.

ⴚ29 ⴚ 16 ⴚ (ⴚ37)

24.

72 ⴚ 56 ⴚ 13

25.

ⴚ99 ⴙ 16 ⴚ (ⴚ24)

Substitute 4 for x, ⴚ4 for y, and ⴚ12 for z. Evaluate each expression. 26.

zⴚy

27.

xⴙz

28.

xⴙyⴚz

29.

(x ⴚ y) ⴙ z

30.

yⴙz

31.

(y ⴙ z) ⴚ x

32.

yⴚz

33.

(x ⴚ z) ⴚ y

34.

zⴚzⴚz

35.

(x ⴙ y) ⴙ (y ⴚ z)

36.

y ⴚ (x ⴚ z)

37.

xⴚxⴚxⴚx

Find the distance between each pair of points on the number line. 38.

6, 10

39.

ⴚ5, 2

40.

ⴚ35, ⴚ38

41.

ⴚ13, 26

42.

ⴚ44, ⴚ29

43.

ⴚ15, 73

Algebra 1

Practice Workbook

9

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Practice 2.4 Multiplying and Dividing Real Numbers Evaluate. 1.

(4)(ⴚ5)

2.

(3)(ⴚ5)

3.

(2)(–5)

4.

(ⴚ1)(ⴚ5)

5.

(ⴚ2)(ⴚ5)

6.

(ⴚ3)(ⴚ5)

7.

(4)(ⴚ3)

8.

(3)(ⴚ3)

9.

(2)(ⴚ3)

10.

(ⴚ1)(ⴚ3)

11.

(ⴚ2)(ⴚ3)

12.

(ⴚ3)(ⴚ3)

13.

(ⴚ11)(ⴚ4)

14.

(ⴚ11) ⴚ (ⴚ4)

15.

(ⴚ7) ⴚ (ⴚ4)

16.

(ⴚ42) ⴜ (ⴚ3)

17.

(ⴚ35)(22)

18.

(ⴚ27)(ⴚ1.3)

19.

(ⴚ240) ⴜ (ⴚ8)

20.

(ⴚ240) ⴙ (ⴚ8)

21.

(ⴚ0.5)(ⴚ12)

22.

(ⴚ2.1) ⴜ (ⴚ7)

23.

(6)(5)(ⴚ7)

24.

(ⴚ3)[(ⴚ1) ⴙ (ⴚ5)]

25.

(ⴚ8) ⴜ [5 ⴙ (ⴚ3)]

26.

(ⴚ2.5) ⴜ (ⴚ4)

27.

(ⴚ7)(ⴚ3)(6)

28.

(ⴚ4488) ⴜ (136)

29.

(ⴚ5)(5)(5) ⴜ (5)

30.

(ⴚ2)[5 ⴙ (ⴚ5)]

31.

(8)(ⴚ1) ⴚ8

32.

(ⴚ2)(ⴚ14) 7

33.

(ⴚ2)(20)(ⴚ40) ⴚ10

Tell whether each statement is true or false.

The product of two negative numbers is positive.

35.

The quotient of two negative numbers is positive.

36.

The average of a set of negative numbers is positive.

37.

The difference of two positive numbers is always positive.

38.

The sum of two positive numbers is positive.

34.

Stephanie opened a savings account with a \$35 deposit. She made a total of 6 additional deposits of \$15 each and withdrawals of \$5, \$10, and \$15. 39.

What is the total amount that Stephanie deposited in her account after her initial deposit?

40.

What is the total amount that Stephanie withdrew from her account after her initial deposit?

41.

What is the total amount currently in Stephanie’s account?

10

Practice Workbook

Algebra 1

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Practice 2.5 Properties and Mental Computation Complete each step, and name the property used. 1.

(24 ⴙ 68) ⴙ 66 ⴝ (68 ⴙ

) ⴙ 66

ⴝ 68 ⴙ (24 ⴙ

)

ⴝ 68 ⴙ ⴝ 2.

35(3 ⴙ 5) ⴝ 35 ⴢ ⴝ

ⴢ5

Property

Use mental math to find each sum or product. Show your work and explain each step. 3.

(46 ⴙ 28) ⴙ 24

4.

(96 ⴢ 4) ⴢ 5

5.

(828 ⴙ 386) ⴙ 412

6.

2 ⴢ (137 ⴢ 5)

Name the property illustrated. Be specific. 7.

46 ⴙ 12 ⴝ 12 ⴙ 46

8.

23 ⴙ (17 ⴙ 34) ⴝ (23 ⴙ 17) ⴙ 34

9.

4(2.3 ⴙ 4.9) ⴝ 4(2.3) ⴙ 4(4.9)

10.

6(3x) ⴝ (6 ⴢ 3)x

11.

5 ⴢ (12 ⴢ 4) ⴝ 5 ⴢ (4 ⴢ 12)

12.

6 ⴢ 300 ⴙ 6 ⴢ 80 ⴝ 6(300 ⴙ 80)

Algebra 1

Practice Workbook

11

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Practice 2.6 Adding and Subtracting Expressions Use the Distributive Property to write equivalent expressions for each expression below. 1.

4(3x ⴙ 7)

2.

5t ⴚ 35

3.

6(2a ⴚ 3)

4.

14f ⴚ 28

5.

9(b ⴙ 11)

6.

18h ⴙ 63

7.

ⴚ12(2x ⴚ 8)

8.

rt ⴙ rk

9.

a(b ⴙ w)

10.

ⴚ25q ⴚ 35

Give the opposite of each expression.

ⴚ10t ⴙ 21

12.

ⴚx ⴙ 2z

13.

4a ⴚ 4b

14.

ⴚ4x ⴙ 3y

15.

ⴚ7a ⴚ 6b ⴚ 4c

16.

m ⴚ 8n ⴚ 4p

17.

ⴚ6x ⴙ (2a ⴙ 5)

18.

9b ⴚ (3 ⴚ 6z)

19.

(c ⴙ d) ⴙ y

20.

5a ⴙ (3c ⴙ 4)

11.

Simplify the following expressions: 21.

2a ⴚ a

22.

6f ⴙ 4f

23.

6r ⴚ 3r

24.

ⴚ2d ⴙ 5d

25.

5a ⴚ (3a ⴙ 1)

26.

mp ⴙ 3mp

27.

(3a ⴙ 2b) ⴙ (ⴚ3a ⴙ b)

28.

(6p ⴚ 3q) ⴚ (ⴚ6p)

29.

(6 ⴚ 2c) ⴚ (2c ⴙ 2)

30.

10 ⴙ r ⴚ 10

31.

(4q ⴙ 2) ⴚ (2q ⴚ 3)

32.

x ⴙ y ⴚ (3t ⴙ y)

33.

3( f ⴙ g) ⴙ 7g

34.

5( f ⴚ h) ⴚ 4f

35.

(3 ⴚ r) ⴙ (4r ⴚ 3s ⴙ 2) ⴚ (1 ⴚ s)

36.

(3x ⴚ 5y) ⴚ (2x ⴚ 3y ⴚ z) ⴙ (y ⴚ z)

12

Practice Workbook

Algebra 1

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Practice 2.7 Multiplying and Dividing Expressions

Simplify the following expressions. Use the Distributive Property if needed. 1.

2 ⴢ 7x

2.

ⴚ4t ⴢ 3

3.

4a ⴢ 3a

4.

ⴚ4(2d ⴚ 3)

5.

ⴚ2.3y ⴢ y

6.

ⴚ12w 2w

7.

7y ⴢ 9y

8.

rt ⴢ rk

9.

ⴚ5(7 ⴚ 4e)

10.

ⴚ36z ⴜ (ⴚ4)

11.

ⴚ15x 3

12.

ⴚ4(6y ⴚ 4)

13.

4g ⴚ 4r 4

14.

ⴚ3(2 ⴚ 7m)

15.

3x ⴚ (2x ⴚ 5)

16.

3 ⴙ 24r 3

17.

10 ⴚ 5x ⴚ5

18.

ⴚ18w ⴙ 12 ⴚ6

19.

ⴚy(c ⴙ d)

20.

32y ⴙ 24y 4y

A computer consultant charges \$50 per hour. How much would the consultant charge for 21.

3 hours?

22.

7.5 hours?

23.

t hours?

A telephone company charges \$40 per hour for repair work, plus a \$25 service charge per job. How much would a customer be charged for a job that takes 24.

2 hours?

25.

3.5 hours?

26.

t hours?

George makes \$8.00 an hour at his part-time job. Find his earnings for each of the following days: 27.

3 hours on Monday

Algebra 1

28.

7 hours on Saturday

Practice Workbook

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Practice 3.1 Solving Equations by Adding and Subtracting Solve each equation. You may use algebra tiles. 1.

xⴙ1ⴝ5

2.

xⴚ7ⴝ1

3.

x ⴙ 3 ⴝ ⴚ2

4.

x ⴚ 4 ⴝ ⴚ1

5.

x ⴙ 1 ⴝ ⴚ8

6.

x ⴚ 3 ⴝ ⴚ1

7.

x ⴙ 5 ⴝ ⴚ2

8.

xⴚ3ⴝ4

9.

x ⴙ 4 ⴝ ⴚ4

State which property you would use to solve each equation. Then solve.

x ⴚ 10 ⴝ 15

11.

x ⴙ 14 ⴝ ⴚ25

12.

45 ⴙ r ⴝ 12

13.

y ⴙ 80 ⴝ ⴚ18

14.

ⴚ44 ⴙ a ⴝ 10

15.

z ⴙ 250 ⴝ ⴚ100

16.

y ⴚ 12 ⴝ 78

17.

r ⴚ 275 ⴝ 180

18.

x ⴙ 6.26 ⴝ 7.26

19.

x ⴚ 3.6 ⴝ 7

20.

8.9 ⴝ a ⴚ 6

21.

r ⴙ 6.5 ⴝ 10.9

22.

yⴚ4 ⴝ8

23.

x ⴙ 5 ⴝ 10

3

1

1

3

10.

Assign a variable and write an equation for the situation below. Then solve the equation. 24.

14

John bought a 60¢ donut and 35¢ cup of coffee. How much did John leave for a tip and taxes if he spent a total of \$1.25?

Practice Workbook

Algebra 1

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CLASS

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Practice 3.2 Solving Equations by Multiplying and Dividing State the property needed to solve each equation. Then solve it. 1.

x 36 ⴝ 6

2.

5.75p ⴝ 46

3.

8 ⴝ ⴚ64y

4.

x 3 ⴝ3

5.

6b ⴝ 54

6.

r ⴚ5 ⴝ 5

7.

ⴚ10y ⴝ 5

8.

ⴚ16n ⴝ ⴚ128

Solve each equation.

658b ⴝ 2632

10.

ⴚ4g ⴝ 36

11.

65x ⴝ 35

12.

x 3 ⴝ ⴚ24

13.

9y ⴝ 153

14.

c 44 ⴝ ⴚ44

15.

x 0.07 ⴝ 5

16.

8t ⴝ ⴚ35

17.

0.66p ⴝ 4.62

18.

ⴚ70g ⴝ 4200

19.

b 20 ⴝ ⴚ20

20.

ⴚ86b ⴝ 43

21.

m ⴚ15 ⴝ 0

22.

x 6 ⴝ ⴚ3

23.

4.4 ⴝ 2.2t

24.

16n ⴝ 320

25.

ⴚ4v ⴝ 68.8

26.

x ⴚ2 ⴝ ⴚ125

27.

ⴚ480 ⴝ ⴚ24z

28.

10d ⴝ 5

29.

0.25q ⴝ 25

30.

w 0.5 ⴝ ⴚ15

31.

ⴚ1 ⴝ ⴚ555

32.

ⴚ495 ⴝ 99y

35.

v ⴝ t for d

9.

3 p

Solve each formula for the variable indicated. 33.

1

A ⴝ 2 bh for b

Algebra 1

34.

z ⴝ wxy for w

d

Practice Workbook

15

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CLASS

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Practice 3.3 Solving Two-Step Equations Solve each equation.

2x ⴙ 1 ⴝ 5

2.

2y ⴚ 4 ⴝ 10

3.

6 ⴙ 3z ⴝ 18

4.

7 ⴚ 5w ⴝ 22

5.

ⴚ15 ⴚ 6c ⴝ 3

6.

9b ⴙ 4 ⴝ ⴚ14

7.

3a ⴚ 7 ⴝ ⴚ28

8.

11 ⴙ 2p ⴝ ⴚ17

9.

21 ⴚ 5q ⴝ ⴚ4

10.

3r ⴙ 3.2 ⴝ 18.2

11.

7m ⴚ 1.2 ⴝ 3

12.

3.1 ⴙ 2n ⴝ 5.3

13.

37 ⴚ 4v ⴝ 57.4

14.

ⴚ8u ⴚ 1.6 ⴝ 8

15.

32 ⴝ 8f ⴙ 16

16.

6 ⴝ 9g ⴚ 12

17.

ⴚ1.6 ⴝ 4 ⴙ 7h

18.

ⴚ2.1 ⴝ 4.5 ⴚ 6i

19.

x 2 ⴙ1ⴝ5

20.

y 2 ⴚ 4 ⴝ 10

21.

3ⴙ3 ⴝ6

22.

28 ⴝ 14 ⴚ 7

23.

10 ⴝ ⴚ30 ⴚ 5

24.

b 9 ⴙ 3 ⴝ ⴚ4

25.

a 5 ⴚ 2 ⴝ ⴚ7

26.

2 ⴙ 2 ⴝ ⴚ9

27.

4 ⴚ 7 ⴝ ⴚ3

28.

r 10 ⴙ 1.1 ⴝ 0.2

29.

m 12 ⴚ 2.1 ⴝ 0.9

30.

ⴚ8 ⴚ 0.8 ⴝ 3.2

31.

13 ⴙ 2 ⴝ 22

32.

ⴚ3 ⴝ ⴚ6 ⴙ 12

33.

g 1 1 ⴝ 4 2 ⴚ8

34.

26 ⴚ 18 ⴝ 3

16

z

c

q

1

v

1

Practice Workbook

1.

w

p

u

f

2

1

h

1

1

Algebra 1

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DATE

Practice 3.4 Solving Multistep Equations

Solve each equation. 1.

4x ⴙ 7 ⴝ 3x ⴙ 18

2.

5y ⴚ 5 ⴝ 7y ⴚ 3

3.

4a ⴚ 6 ⴝ ⴚ2a ⴙ 14

4.

4m ⴚ 5 ⴝ 3m ⴙ 7

5.

5x ⴚ 7 ⴝ 3x ⴙ 2

6.

10y ⴙ 10 ⴝ 4 ⴚ 4y

7.

13 ⴚ 8v ⴝ 5v ⴙ 2

8.

7 ⴚ 5y ⴝ 4y ⴚ 2

9.

2 ⴙ 3y ⴝ 4y ⴚ 1

10.

ⴚ7 ⴚ 3z ⴝ 8 ⴙ 2z

11.

7w ⴚ 19 ⴝ 5w ⴚ 5

12.

28 ⴙ 2a ⴝ 5a ⴙ 7

13.

5x ⴙ 32 ⴝ 8 ⴚ x

14.

m ⴚ 12 ⴝ 3m ⴙ 4

15.

2(x ⴙ 1) ⴝ 3x ⴚ 3

16.

5(3x ⴙ 5) ⴝ 4x ⴚ 8

17.

2r ⴚ 4 ⴝ 2(6 ⴚ 7r)

18.

8y ⴚ 3 ⴝ 5(2y ⴙ 1)

19.

2z ⴚ 5(z ⴙ 2) ⴝ ⴚ8 ⴚ 2z

20.

5t ⴚ 2(5 ⴙ 4t) ⴝ 3 ⴙ t ⴚ 8

21.

15n ⴙ 25 ⴝ 2(n ⴚ 7)

22.

4y ⴙ 2 ⴝ 3(6 ⴚ 4y)

23.

2(3x ⴚ 1) ⴝ 3(x ⴙ 2)

24.

9y ⴚ 8 ⴙ 4y ⴝ 7y ⴙ 16

25.

14d ⴚ 22 ⴙ 5d ⴝ 12d ⴚ 8

26.

23x ⴙ 34 ⴝ 23 ⴚ 12x ⴙ 7x

27.

29 ⴚ 3s ⴝ 23(2s ⴚ 3)

28.

12 ⴚ 5(2w ⴚ 13) ⴝ 3(2w ⴚ 5)

29.

8 ⴙ 5(3q ⴚ 4) ⴝ 7(q ⴚ 12)

30.

2(y ⴙ 2) ⴙ y ⴝ 19 ⴚ (2y ⴙ 3)

31.

0.3w ⴚ 4 ⴝ 0.8 ⴚ 0.2w

32.

2.1z ⴝ 1.2z ⴚ 9

33.

12 ⴙ 2.1w ⴝ 1.3w

34.

3.5( j ⴙ 4) ⴝ 1.4(16 ⴙ j)

35.

4.5 ⴚ 1.9m ⴝ 20.1 ⴚ 2m

36.

x ⴚ 0.09 ⴝ 2.22 ⴚ 0.1x

1 3 2x ⴙ 7 ⴝ 4x ⴚ 4 1 4 39. z ⴝ 3z ⴚ 3 5 1 1 1 41. 2 w ⴙ 3 4 ⴝ 4 ⴙ 3w 37.

(

Algebra 1

)

1 2 4y ⴝ 5y ⴚ 1 a 1 a 1 40. ⴚ ⴝ ⴚ 2 3 3 2 1 1 42. (7 ⴙ 3r) ⴝ ⴚ r 4 8 38.

Practice Workbook

17

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CLASS

DATE

Practice 3.5 Using the Distributive Property Solve each equation.

2(a ⴙ 2) ⴝ 2

2.

3(b ⴚ 3) ⴝ 3

3.

4(c ⴚ 4) ⴝ 4

4.

5(5 ⴚ d) ⴝ ⴚ5

5.

6(6 ⴚ e) ⴝ 6

6.

ⴚ7( f ⴙ 7) ⴝ 7

7.

ⴚ8(8 ⴚ g) ⴝ 8

8.

1 ⴙ 4(2h ⴙ 1) ⴝ ⴚ35

9.

3(5i ⴚ 2) ⴙ 2 ⴝ 26

10.

7(2 ⴚ j) ⴚ 5 ⴝ 30

11.

ⴚ4 ⴚ 6(2 ⴚ k) ⴝ 8

12.

20 ⴚ 3(m ⴚ 1) ⴝ ⴚ4

13.

5(n ⴙ 2) ⴝ 3n

14.

ⴚ2(2p ⴚ 3) ⴝ 2p

15.

8(7 ⴚ 3q) ⴝ ⴚ17q

16.

3r ⴝ 2(7 ⴙ 5r)

17.

s ⴙ 3 ⴝ 3(11 ⴚ 3s)

18.

7t ⴙ 4 ⴝ 2(7t ⴚ 5)

19.

2u ⴚ 4 ⴝ ⴚ4(u ⴚ 5)

20.

2(v ⴙ 1) ⴝ 6v ⴚ 46

21.

2(2w ⴙ 2) ⴝ 3(2w ⴚ 2)

22.

ⴚ4(1 ⴙ x) ⴝ 5(1 ⴚ x)

23.

ⴚ6(y ⴚ 2) ⴝ 7(2 ⴚ y)

24.

9(z ⴙ 1) ⴝ ⴚ3(5 ⴙ z)

25.

1 ⴙ 2(a ⴙ 1) ⴝ 3(a ⴙ 4)

26.

5(b ⴚ 6) ⴝ 3 ⴙ 8(b ⴙ 9)

27.

2c ⴚ (c ⴙ 6) ⴝ 4(c ⴚ 2)

28.

1 ⴙ 2(d ⴙ 1) ⴝ 3 ⴙ 4(d ⴙ 5)

29.

1 ⴚ 2(e ⴚ 1) ⴝ ⴚ3 ⴚ 4(3 ⴚ 5)

30.

3 ⴚ (2 ⴚ f ) ⴙ 1 ⴝ 2(2 ⴚ f )

31.

g ⴙ 5(g ⴙ 1) ⴝ 4(2g ⴚ 2) ⴙ 11g

32.

2(3h ⴚ 1) ⴙ 4h ⴝ 10(2 ⴚ 3h) ⴙ 38h

33.

h ⴙ 1 ⴙ 2(h ⴙ 1) ⴝ 3(h ⴙ 2) ⴚ h ⴙ 2

34.

3(i ⴚ 3) ⴚ 7(i ⴙ 3) ⴝ 4(2i ⴚ 3) ⴚ 8(2i ⴙ 3)

35.

9(2 ⴚ j) ⴙ 3(5 ⴙ 2j) ⴝ 2(7 ⴚ 2j) ⴚ 4( j ⴚ 1)

36.

34.8k ⴙ 0.2(k ⴚ 4) ⴝ 1.2 ⴚ 9(2 ⴚ 3k)

37.

0.1(2m ⴙ 3) ⴚ 4m ⴝ 1.1(2 ⴚ 3m) ⴚ 2.4

38.

0.5(4n ⴚ 4) ⴝ 1 ⴙ 3n

18

Practice Workbook

Algebra 1

1.

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CLASS

DATE

Practice 3.6 Using Formulas and Literal Equations Solve for the indicated variable. 1.

x ⴙ y ⴝ z, for y

2.

P ⴚ Q ⴝ ⴚR, for Q

3.

J ⴙ K ⴝ ⴚL, for J

4.

E ⴚ F ⴝ G, for F

5.

m ⴝ nq, for n

6.

ⴚwr ⴝ a, for w

7.

tu ⴝ v ⴙ w, for u

8.

x ⴝ yz ⴚ w, for z

9.

b ⴝ c ⴙ de, for d

10.

gh ⴚ i ⴝ j, for h

q

11.

p ⴝ r , for r

12.

ab c ⴝ d, for b

13.

2m ⴙ 3 ⴝ n, for m

14.

7 ⴚ 4k ⴝ j, for k

16.

r ⴙ t ⴝ u, for t

18.

4 ⴚ q ⴝ r, for p

6g f ⴝ h, for g 2 17. w ⴚ y ⴝ z, for w 15.

s

p

s

Use the formula V ⴝ d for Exercises 19–21. 19.

Substitute s ⴝ 10, and d ⴝ 5 in the formula, and solve for V.

20.

Substitute s ⴝ 25, and V ⴝ 5 in the formula, and solve for d.

21.

Substitute V ⴝ 8, and d ⴝ 7 in the formula, and solve for s.

Use the formula V ⴝ IR for Exercises 22–24. 22.

Substitute I ⴝ 5, and R ⴝ 10 in the formula, and solve for V.

23.

Substitute I ⴝ 5, and V ⴝ 15 in the formula, and solve for R.

24.

Substitute V ⴝ 240, and R ⴝ 60 in the formula, and solve for I.

Use the formula v ⴝ u ⴙ 10t for Exercises 25–26. 25.

Substitute u ⴝ 16, and t ⴝ 4 in the formula, and solve for v.

26.

Substitute v ⴝ 28, and t ⴝ 5 in the formula, and solve for u.

Algebra 1

Practice Workbook

19

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CLASS

DATE

Practice 4.1 Using Proportional Reasoning Solve each proportion. 1.

12 x 18 ⴝ 36

2.

30 90 27 ⴝ x

3.

n 15 26 ⴝ 78

4.

40.5 5 t ⴝ6

5.

m 12 35 ⴝ 100

6.

1.5 8 6 ⴝr

7.

45.2 f 30 ⴝ 12

8.

15 25 90.5 ⴝ x

9.

n 14 35.2 ⴝ 25.8

10.

50.9 3 16 ⴝ j

11.

r 1.5 85 ⴝ 30

12.

7 n 16.6 ⴝ 14

Tell if each statement is a true proportion. 13.

14 70 3 ⴝ 15

14.

7 3.5 25 ⴝ 50

15.

9 12 32 ⴝ 40

16.

10 25 60 ⴝ 150

17.

13 11 24 ⴝ 35

18.

7 21 18 ⴝ 6

19.

32 20 42 ⴝ 21

20.

19 9.5 30 ⴝ 15

21.

Rearrange the numbers to write three more true proportions. 22.

4 12 5 ⴝ 15

23.

7 14 12 ⴝ 24

24.

6 8 21 ⴝ 28

25.

32 48 18 ⴝ 27

26.

8 40 3 ⴝ 15

27.

42 35 36 ⴝ 30

28.

If Dana spent \$160 on 5 concert tickets, how much would 3 tickets cost?

29.

Myron bought 4 oranges for \$1.40. How much would 9 oranges cost?

30.

A recipe uses 2 cups of flour and makes 24 muffins. How many cups of flour are needed to make 30 muffins?

20

Practice Workbook

Algebra 1

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CLASS

DATE

Practice 4.2 Percent Problems Write each percent as a decimal. 1.

15%

2.

3.2%

3.

0.7%

4.

6%

5.

250%

6.

89%

7.

100%

8.

0.01%

11.

0.002

12.

5

16.

360%

Write each decimal as a percent. 9.

0.62

10.

0.041

Write each percent as a fraction in lowest terms. 13.

59%

14.

25%

15.

56%

18.

What percent of 30 is 3?

Draw a percent bar to model each problem.

17.

Find 45% of 90.

What is 20% of 30?

20.

What is 120% of 70?

21.

3 is what percent of 50?

22.

45 is what percent of 500?

23.

15 is 30% of what number?

24.

12 is 40% of what number?

25.

What is 200% of 40?

26.

What is 28% of 130?

27.

A sweater is marked down from an original price of \$45 to \$33.75. By what percent has the original price of the sweater been marked down?

28.

Mary’s grade on her research paper counts as 20% of her final grade in English. If there are a total of 400 points possible, how many points can she earn for her research paper?

29.

The school newspaper reported that 32% of the student body is in athletics. If the student body consists of 2000 students, how many students are in athletics?

Algebra 1

Practice Workbook

21

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DATE

Practice 4.3 Introduction to Probability Two number cubes were rolled 150 times. Find each experimental probability. 1.

a sum less than 4 appeared 15 times

2.

a sum of 7 appeared 11 times

3.

a sum of 6 or greater appeared 85 times

Two coins were tossed 10 times with the outcomes shown in the table below. Trial

1

2

3

4

5

6

7

8

9

10

Coin 1

H

H

T

T

H

T

H

H

T

T

Coin 2

T

T

T

H

T

H

H

T

H

T

Use the data above to find each experimental probability.

At least one coin shows tails.

5.

Both coins show the same side of the coin.

6.

4.

A survey was conducted to find out how students get to school. The results of the survey are shown in the table below. Method of transportation

School bus

Car

Bicycle

Walk

87

71

25

45

Number of students

Use the the data above to find each experimental probability. 7.

A student rides a bus to school.

8.

A student walks to school.

9.

A student rides to school in a car or in a bus.

10.

A student rides a bicycle or walks to school.

11.

A student does not walk to school.

22

Practice Workbook

Algebra 1

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CLASS

DATE

Practice 4.4 Measures of Central Tendency Find the mean, median, mode(s), and range for each data set. 1.

13, 13, 10, 8, 7, 6, 4, 5 mean

2.

median

range

median

mode(s)

range

median

mode(s)

range

median

mode(s)

range

16, 18, 39, 200, 31, 39 mean

mode(s)

130, 140, 135, 125, 160, 175 mean

5.

median

2, 5, 4, 1, 6, 7, 4, 3, 2, 1 mean

4.

range

20, 30, 35, 24, 36, 47, 48 mean

3.

mode(s)

The Sleep Shop conducted a survey to determine the average number of hours that people sleep at night. The results are shown at right. Use this data for Exercises 6–12. 6.

Make a frequency table for the data.

Number of Hours Spent Sleeping at Night 5 9 8 6 9 10

8 8 10 8 8 7

6 7 7 8 7 8

7 5 7 7 5 8

4 9 8 8 9 6

Find the measures of central tendency for the data. 7. 11.

mean

8.

median

9.

mode

10.

range

Which measure of central tendency do you think gives the best indication of the number of hours the “typical” person spends sleeping each night? Explain.

12.

Suppose that another person was surveyed and said that he spends 3 hours sleeping at night. How would this affect the mean, median, mode, and range?

Algebra 1

Practice Workbook

23

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Practice 4.5 Graphing Data The graphs below show the monthly CD sales for two different music stores. Carl’s Music Place Monthly CD Sales

The Music Store Monthly CD Sales

\$20,000

\$40,000

\$15,000

\$30,000

\$10,000

\$20,000

\$5000

\$10,000

\$0 1.

J

F

M

A

M

\$0

J

F

M

A

M

During which month were the sales at Carl’s Music Place the greatest? What were the sales?

2.

During which month were the sales at Carl’s Music Place the least?

3.

What were the sales? During which month were the sales at The Music Store the greatest? What were the sales? 4.

During which month were the sales at The Music Store the least? What were the sales?

5.

What were the CD sales for Carl’s Music Place for January through May?

6.

What were the CD sales for The Music Store for January through May?

7.

Which store appears to have a longer bar to represent April sales? Which company actually had greater sales in April?

8.

24

Describe how displaying the graphs together can be misleading.

Practice Workbook

Algebra 1

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DATE

Practice 4.6 Other Data Displays In the table at right are the ages of the first 42 presidents of the United States when they were sworn into office.

1.

In the space below, make a stem-and-leaf plot of the data.

57

61

57

57

58

57

61

54

68

51

49

64

50

48

65

52

56

46

54

49

50

47

55

55

54

42

51

56

55

51

54

51

60

62

43

55

56

61

52

69

64

46

2.

What is the range of the data?

3.

What is the median of the data?

4.

What are the lower and upper quartiles for this data?

5.

What is the mean of the data?

6.

What is the mode of the data?

7.

What is the average age of a president of the United States when he is sworn into office? What measure of central tendency do you think best answers this question? Why?

8.

In the space below, construct a box-and-whisker plot for this data.

Algebra 1

Practice Workbook

25

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DATE

Practice 5.1 Linear Functions and Graphs For each relation, identify the domain and range, and state whether it is a function. 1.

(1, 2), (3, 4), (5, 6), (7, 8), (9, 13)

(6, 3), (9, ⴚ4), (8, ⴚ4), (3, 3), (0, 3)

2.

a.

domain:

a.

domain:

b.

range:

b.

range:

c. 3.

c.

(7, 1), (10, 7), (0, 8), (2, 17), (7, 3)

(14, 2), (16, 0), (18, ⴚ2), (20, 0), (22, 2)

4.

a.

domain:

a.

domain:

b.

range:

b.

range:

c. 5.

c.

(1.7, 7), (1.5, 5), (1.3, 3), (1.1, 1), (1.9, 9)

( 12 , 2), ( 13 , 3), ( 14 , 4), ( 15 , 5), (1, 1)

6.

a.

domain:

a.

domain:

b.

range:

b.

range:

c.

(4, 2), (9, 3), (4, ⴚ2), (9, ⴚ3), (5, 25)

(1.2, 17), (1.56, 1987), (0.67, 98), (0.988, 1)

8.

a.

domain:

a.

domain:

b.

range:

b.

range:

c.

c.

Complete each ordered pair so that it is a solution to 6x ⴚ y ⴝ 7. 9.

(4,

)

10.

(⫺4,

12.

(3,

)

13.

(

15.

(2,

)

16.

(12,

18.

(

19.

(

21.

(6,

22.

(

26

, 11) )

Practice Workbook

)

11.

(0,

, ⫺1)

14.

(13,

17.

(

, 5)

20.

(8,

, ⫺19)

23.

(

)

) ) , ⫺10) ) , 17)

Algebra 1

7.

c.

Back Print NAME

CLASS

DATE

Practice 5.2 Defining Slope Examine the graphs below. Which lines have a positive slope? Which have a negative slope? Which have neither? y

1.

y

2.

y

3.

x

x

x

↔ AB ↔ 7. EF ↔ 9. IJ ↔ 11. MN

↔ CD ↔ 8. GH ↔ 10. KL ↔ 12. PQ

A

C D H

B

Find the slope of each line. 13.

rise: ⴚ5; run: ⴚ5

14.

rise: 2; run: 3

15.

rise: ⴚ3; run: 4

16.

rise: ⴚ2; run: ⴚ5

F

E

6.

G K

x

y

Use the graph to find the slope of each line. 5.

y

4.

O

x L

I

M

P N Q

J

Find the slope of the line containing each pair of points. 17.

A(3, 9), B(1, 5)

18.

A(7, 5), B(2, 4)

19.

A(ⴚ3, 10), B(ⴚ5, ⴚ4)

20.

A(5, 2), B(2, ⴚ1)

21.

A(3, ⴚ2), B(ⴚ1, 3)

22.

A(ⴚ1, 3), B(5, 3)

23.

A(1, 8), B(ⴚ1, 7)

24.

A(2, 6), B(3, ⴚ4)

25.

A(0, 4), B(3, ⴚ2)

26.

A(6, ⴚ1), B(5, 6)

27.

A(ⴚ9, 9), B(7, ⴚ2)

28.

A(3, 7), B(ⴚ1, 0)

Algebra 1

Practice Workbook

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DATE

Practice 5.3 Rate of Change and Direct Variation

1.

What was the greatest speed that Michael traveled ?

2.

What does the horizontal segment of the graph represent? How long does Michael stay at this speed?

Speed (mph)

The graph at right shows the speed at which Michael traveled on a highway.

65 60 55 50 45 40 35 30 25 20 15 10 5 0

20

40 60 80 100 120 Time (minutes)

3.

What does the segment with a negative slope tell you about Michael’s speed?

4.

What does the segment with a positive slope tell you about Michael’s speed?

5.

y ⴝ 15 when x ⴝ 5

6.

y ⴝ 2 when x ⴝ 8

7.

y ⴝ 9 when x ⴝ 3

8.

y ⴝ 7 when x ⴝ 1.4

9.

y ⴝ 18 when x ⴝ 11

10.

y ⴝ 21 when x ⴝ 18

11.

y ⴝ 42 when x ⴝ 7

12.

y ⴝ 8 when x ⴝ 56

13.

y ⴝ 12 when x ⴝ 22

14.

y ⴝ 10 when x ⴝ 40

28

Practice Workbook

In Exercises 1–10, y varies directly as x. Find the constant of variation and write an equation for the direct variation.

Algebra 1

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Practice 5.4 The Slope-Intercept Form Give the coordinates of the point where each line crosses the y-axis. 1.

y ⴝ 3x ⴙ 4

3.

y ⴝ 2x

1

2.

y ⴝ 2x ⴚ 3

4.

yⴝ2ⴚx

Write an equation for the graph of each line. y

5.

–6

–4

y

6.

6

6

4

4

2

2

–2 O –2

2

4

6

x

–6

–4

–2 O –2

–4

–4

–6

–6

2

4

6

x

Write an equation for each line. 7.

with a slope of 2 and a y-intercept of 4

8.

with a slope of ⴚ3 and a y-intercept of 1

9.

through (0, ⴚ4) and with a slope of 2 1

10.

through (0, 6) and with a slope of 2

11.

with a slope of ⴚ4 and a y-intercept of ⴚ3

12.

through (0, 1) and with a slope of 1.5

3

Write an equation for the line containing each pair of points. 13.

(3, 8), (2, 6)

14.

(0, ⴚ6), (ⴚ3, 3)

15.

(ⴚ2, ⴚ4), (5, ⴚ1)

16.

(ⴚ1, ⴚ2), (ⴚ3, ⴚ4)

Algebra 1

Practice Workbook

29

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Practice 5.5 The Standard and Point-Slope Forms Write each equation in standard form. 1.

2x ⴝ ⴚ5y ⴙ 11

2.

3y ⴝ ⴚx ⴚ 20

3.

4x ⴚ 7y ⴙ 15 ⴝ 0

4.

9x ⴝ 6y

5.

2x ⴙ 10 ⴝ 3y ⴚ 1

6.

2x ⴝ 2 y ⴙ 3

1

Find the x- and y-intercepts for each equation. 7.

xⴙyⴝ5

9.

4x ⴚ 3y ⴝ 12

10.

x ⴚ 3y ⴝ 6

11.

x ⴚ y ⴝ ⴚ3

12.

4x ⴝ ⴚ5y

13.

2x ⴙ y ⴝ 1

14.

xⴝ3y

15.

x 4 ⴚyⴝ2

16.

x ⴝ ⴚ6y ⴚ 2

18.

x ⴚ 2y ⴝ 2

8.

3x ⴙ 5y ⴝ 15

2

Use intercepts to graph each equation. 17.

2x ⴚ y ⴝ ⴚ4

y

y

–4 –3 –2 –1 O –1 –2 –3 –4

4 3 2 1

4 2

1 2 3 4

x

–4

–2

O

2

4

x

–2 –4

Write an equation in standard form for each line. 19.

through (4, 5) and with a slope of 1

20.

crosses the x-axis at x ⴝ ⴚ3 and the y-axis at y ⴝ 6

21.

through (1, 6) and with a slope of 2

22.

through (3, 7) and (0, ⴚ2)

23.

through (1, 5) and (ⴚ3, 1)

30

Practice Workbook

Algebra 1

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Practice 5.6 Parallel and Perpendicular Lines Write the slope of a line that is parallel to each line. 1.

y ⴝ 2x ⴚ 5

2.

y ⴝ ⴚx ⴙ 2

3.

3x ⴙ y ⴝ 10

4.

5x ⴚ y ⴝ 11

5.

x ⴙ 2y ⴝ 6

6.

2x ⴚ 3y ⴝ 9

7.

4x ⴙ y ⴝ 3

8.

x ⴙ 2y ⴝ 14

Write the slope of a line that is perpendicular to each line. 1

y ⴝ 4x ⴙ 6

10.

y ⴝ ⴚ5 x ⴚ 3

11.

xⴙyⴝ7

12.

6x ⴚ y ⴝ 14

13.

x ⴙ 7y ⴝ ⴚ21

14.

5x ⴚ 4y ⴝ 12

15.

y ⴝ 3x ⴙ 2

16.

2y ⴝ ⴚ2x ⴚ 8

9.

1

Write an equation in slope-intercept form for a line containing the point (6, ⴚ2) and 17.

parallel to the line 2x ⴙ y ⴝ 5.

18.

perpendicular to the line y ⴝ ⴚ3x ⴙ 4.

Write an equation in slope-intercept form for a line containing the point (ⴚ6, 5) and 19.

parallel to the line x ⴙ 2y ⴝ 6.

20.

perpendicular to the line 3x ⴚ 4y ⴝ ⴚ8.

Write an equation for a line containing the point (ⴚ3, 2) and 21.

parallel to the line y ⴝ ⴚ4.

22.

perpendicular to the line y ⴝ ⴚ4.

Write an equation for the line that contains the point (ⴚ1, 2) and is 23.

parallel to the line y ⴝ x ⴚ 6.

24.

perpendicular to the line y ⴝ ⴚx.

Algebra 1

Practice Workbook

31

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Practice 6.1 Solving Inequalities State whether each inequality is true or false. 1.

58ⴚ2

2.

ⴚ1 ⴚ 1  0

3.

ⴚ1  5 ⴚ 6

4.

ⴚ1 ⴙ 2  3

5.

ⴚ4 ⴚ 2  4

6.

86ⴚ4

7.

7ⴚ91

8.

12  9 ⴚ 10

9.

3  ⴚ8 ⴙ 11

Solve each inequality. 10.

x ⴙ 5  ⴚ3

11.

t ⴚ 5  ⴚ2

12.

8 ⴙ y  ⴚ1

13.

cⴙ2 1

14.

qⴚ3 3

15.

x ⴙ 0.8  1

16.

0.75  ⴚ0.5 ⴙ d

17.

x ⴙ 4.9  0.45

18.

3.35  ⴚ4.85 ⴙ n

19.

yⴙ4 8

20.

5 2 6 xⴙ3

21.

2 7 5  t ⴚ 10

1

1

3

1

Write an inequality that describes the points on each number line. –8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

–8

–6

–4

–2

0

2

4

6

8

x

23.

x

24.

x

25.

x

26.

x

27.

x

28.

32

x

22.

Practice Workbook

Algebra 1

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Practice 6.2 Multistep Inequalities Write an inequality that corresponds to each statement. 1.

x is less than y.

2.

W is greater than B.

3.

a is less than or equal to 10.

4.

x is greater than or equal to 100.

5.

r is positive.

6.

q is nonnegative.

7.

M cannot equal 0.

8.

V is between 4.5 and 4.6 inclusive.

Tell whether each statement is true or false.

6.9  6.9

10.

9.66  9.606

11.

10.2  10.02

12.

1 1 2 3

13.

8.91  8.901

14.

0  ⴚ1

15.

1 1 7 5

16.

ⴚ5  ⴚ2

17.

ⴚ6  ⴚ4

9.

Solve each inequality. 18.

xⴙ34

19.

m ⴚ 10  50

20.

Tⴚ58

21.

7 ⴚ N  16

22.

6x  ⴚ12

23.

x ⴙ 12  10

24.

3.5b  ⴚ7

25.

2x  6

26.

n 5  20

27.

r ⴚ2  7

28.

ⴚ5t  45

29.

x 4 ⴙ 7  10

30.

ⴚx 5 ⴙ 4  ⴚ1

31.

6x ⴚ 2  4

32.

xⴙ38ⴚx

33.

x ⴚ 1  ⴚ5

34.

ⴚ5x  2x ⴚ 6

35.

7ⴚx3

36.

16 ⴙ 2  9

37.

14  4 ⴚ 3

Algebra 1

m

j

Practice Workbook

33

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Practice 6.3 Compound Inequalities Solve each compound inequality. 1.

4p  ⴚ2 and 2 ⴙ p  ⴚ5

2.

3m  9 or 2m  8

3.

x 2  4 and 3x  9

4.

a ⴙ 4  1 or a ⴙ 1  0

5.

1 ⴚ1 x x 8  2 and 6  3

6.

x 1 4  16 or 2x ⴚ 2  3

7.

2x ⴚ 1  1 and 6x ⴙ 4  16

8.

x 2 ⴙ 1  7 or x ⴚ 11  7

9.

3w ⴚ 2  3 and 2 ⴙ 1  2

10.

6k ⴚ 1  2 or 2k ⴙ 2  2

3w

1

1

Graph each compound inequality.

x  4 or x  6

12.

x –8

–6

–4

–2

0

2

4

6

8

x  ⴚ5 or x  ⴚ2

–8

–6

–4

–2

0

2

4

6

8

13.

ⴚ5  x  4

–8

–6

–4

–2

0

2

4

6

8

14.

ⴚ6  x  6

–8

–6

–4

–2

0

2

4

6

8

15.

x  ⴚ4 or x  0

–8

–6

–4

–2

0

2

4

6

8

16.

x  ⴚ8 or x  ⴚ7

–8

–6

–4

–2

0

2

4

6

8

17.

x  ⴚ4 or x  2

–8

–6

–4

–2

0

2

4

6

8

18.

7x8

–8

–6

–4

–2

0

2

4

6

8

19.

ⴚ1  x  2

–8

–6

–4

–2

0

2

4

6

8

34

Practice Workbook

x

x

x

x

x

x

x

x

Algebra 1

11.

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Practice 6.4 Absolute-Value Functions Find each of the following. 1.

ⱍ17 ⴚ 3ⱍ

2.

ⱍ3 ⴚ 17ⱍ

3.

ⱍ3 ⴚ (ⴚ17)ⱍ

4.

ⱍⴚ3 ⴚ (ⴚ17)ⱍ

5.

ⴚⱍ17 ⴚ 3ⱍ

6.

ⴚⱍ3 ⴚ 17ⱍ

7.

ⱍ21 ⴚ 5ⱍ

8.

ⱍ5 ⴚ 21ⱍ

9.

ⱍ5 ⴚ (ⴚ21)ⱍ

10.

ⱍⴚ5 ⴚ (ⴚ21)ⱍ

11.

ⴚⱍ21 ⴚ 5ⱍ

12.

ⴚⱍ5 ⴚ 21ⱍ

13.

ⱍ9 ⴚ 13ⱍ

14.

ⱍⴚ19 ⴚ 13ⱍ

15.

ⱍ13 ⴚ 19ⱍ

16.

ⱍ13 ⴚ 13ⱍ

17.

ⱍ5 ⴚ 29ⱍ

18.

ⱍⴚ7 ⴚ (ⴚ11)ⱍ

19.

ⴚⱍ31 ⴚ 23ⱍ

20.

ⴚⱍ11 ⴚ 37ⱍ

21.

ⱍ23 ⴚ 41ⱍ

Find the domain and range of each function. 22.

y ⴝ ⱍxⱍ

23.

y ⴝ ⴚⱍxⱍ

24.

y ⴝ ⱍ6xⱍ

25.

y ⴝ 6ⱍxⱍ

26.

y ⴝ ⴚ6ⱍxⱍ

27.

y ⴝ ⱍx ⴙ 6ⱍ

28.

y ⴝ ⴚⱍx ⴙ 6ⱍ

29.

y ⴝ ⱍxⱍ ⴙ 6

30.

y ⴝ 6 ⴚ ⱍxⱍ

31.

y ⴝ ⱍxⱍ ⴚ 6

32.

y ⴝ ⴚⱍxⱍ ⴚ 6

33.

y ⴝ ⱍ6x ⴙ 6ⱍ

34.

y ⴝ ⴚⱍ1 ⴚ 6xⱍ

35.

y ⴝ ⱍ6x ⴚ 1ⱍ

Algebra 1

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35

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Practice 6.5 Absolute-Value Equations and Inequalities Find the values of x that solve each absolute-value equation. Check your answers.

ⱍx ⴙ 2ⱍ ⴝ 5 3. ⱍx ⴚ 7ⱍ ⴝ 4 5. ⱍ4x ⴚ 2ⱍ ⴝ 6 7. ⱍⴚ4 ⴙ xⱍ ⴝ 7 1.

ⱍx ⴙ 6ⱍ ⴝ 7 4. ⱍx ⴚ 3ⱍ ⴝ 5 6. ⱍ3x ⴙ 5ⱍ ⴝ 11 8. ⱍx ⴚ 2.75ⱍ ⴝ 0.05 2.

Find the values of x that solve each absolute-value inequality. Graph each answer on the number line provided. Check your answers.

ⱍx ⴙ 2ⱍ  7

–16 –12

–8

–4

0

4

8

12

16

10.

ⱍx ⴙ 1ⱍ  8

–8

–6

–4

–2

0

2

4

6

8

11.

ⱍⴚ2 ⴚ xⱍ  4

–8

–6

–4

–2

0

2

4

6

8

12.

ⱍx ⴙ 1ⱍ  4

–8

–6

–4

–2

0

2

4

6

8

13.

ⱍx ⴚ 3ⱍ  2

–8

–6

–4

–2

0

2

4

6

8

14.

ⱍ4 ⴚ xⱍ  5

–4

–2

0

2

4

6

8

10

12

15.

ⱍx ⴙ 2ⱍ  2

–8

–6

–4

–2

0

2

4

6

8

16.

ⱍx ⴚ 5ⱍ  1

–8

–6

–4

–2

0

2

4

6

8

17.

ⱍx ⴙ 2ⱍ  2

–8

–6

–4

–2

0

2

4

6

8

36

Practice Workbook

Algebra 1

9.

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Practice 7.1 Graphing Systems of Equations Solve by graphing. Round solutions to the nearest tenth if necessary. Check algebraically. 1.

xⴙyⴝ4 2x ⴚ y ⴝ 5

2.

xⴙyⴝ0 3x ⴚ 2y ⴝ 10

y

2x ⴙ y ⴝ 7 xⴙyⴝ3

y

y

6

6

4

4

4

2

2

2

2

4

6

x

–6 –4 –2 O –2

2

4

6

x

–6 –4 –2 O –2

–4

–4

–4

–6

–6

–6

xⴙyⴝ1 2x ⴚ 2y ⴝ 6

5.

3x ⴙ 2y ⴝ 9 4x ⴚ y ⴝ 1

6

– 6 –4 –2 O –2

4.

3.

6.

y 6

4

4

4

2

2

2

4

6

x

–6 –4 –2 O –2

6

4

6

x

y

6

2

4

3x ⴚ 4y ⴝ ⴚ4 6x ⴚ 2y ⴝ 1

6

– 6 –4 –2 O –2

2

2

4

6

x

–6 –4 –2 O –2

–4

–4

–4

–6

–6

–6

2

x

Use algebra to determine whether the point (1, 4) is a solution for each pair of equations. 7.

yⴝxⴙ3 y ⴝ 2x ⴚ 2

8.

y ⴝ 3x ⴙ 1 y ⴝ ⴚx ⴙ 5

9.

y ⴝ 5x ⴚ 1 y ⴝ ⴚ2x ⴙ 6

Use algebra to determine whether the point (ⴚ2, 6) is a solution for each pair of equations. 10.

yⴝxⴙ8 y ⴝ 4x ⴚ 2

Algebra 1

11.

xⴙyⴝ4 xⴚyⴝ8

12.

4x ⴙ y ⴝ ⴚ2 y ⴝ ⴚx ⴙ 4

Practice Workbook

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Practice 7.2 The Substitution Method Solve and check each system by using the substitution method. 1.

3.

5.

7.

9.

11.

13.

15.

y ⴝ 2x 2x ⴙ y ⴝ ⴚ12

2.

y ⴝ 2x ⴙ 1 x ⴙ 3y ⴝ 31

4.

2x ⴚ 3y ⴝ ⴚ25 3x ⴙ y ⴝ 1

6.

2x ⴙ 5y ⴝ ⴚ7 3x ⴚ y ⴝ ⴚ2

8.

xⴚyⴝ4 2x ⴚ 3y ⴝ 6

10.

x ⴚ y ⴝ 10 2x ⴙ 3y ⴝ 5

12.

x ⴝ y ⴚ 4.2 2x ⴚ 3y ⴝ ⴚ9

14.

4x ⴚ y ⴝ ⴚ2 ⴚ8x ⴙ y ⴝ 3

16.

yⴝxⴙ3 3x ⴙ y ⴝ 11 xⴙyⴝ3 4x ⴚ 2y ⴝ 18 x ⴚ 2y ⴝ ⴚ3 4x ⴚ 3y ⴝ 8 2x ⴚ y ⴝ ⴚ11 3x ⴚ 6y ⴝ 6 3x ⴙ y ⴝ ⴚ3 x ⴚ 3y ⴝ 11 2x ⴙ y ⴝ 2 4x ⴚ 2y ⴝ ⴚ4 ⴚ2x ⴚ y ⴝ 4 x ⴙ y ⴝ ⴚ3 2x ⴚ 2y ⴝ 2 3x ⴙ y ⴝ ⴚ9 Copyright © by Holt, Rinehart and Winston. All rights reserved.

Graph each system and estimate the solution. Then use the substitution method to get an exact solution. 17.

y ⴝ 2x 2x ⴙ y ⴝ 7

18.

xⴙyⴝ2 x ⴚ 2y ⴝ 0

y 6

6

4

4

2

2

–6 –4 –2 O –2

38

y

2

4

6

x

–6 –4 –2

2

6

x

–2

–4

–4

–6

–6

Practice Workbook

4

Algebra 1

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Practice 7.3 The Elimination Method Solve each system of equations by elimination, and check your solutions. 1.

3.

5.

7.

9.

11.

13.

15.

x ⴙ y ⴝ 10 xⴚyⴝ2

2.

4x ⴙ 2y ⴝ 2 5x ⴙ 2y ⴝ 4

4.

3x ⴙ 2y ⴝ 8 2x ⴚ 6y ⴝ 42

6.

3x ⴙ 4y ⴝ 22 x ⴚ 5y ⴝ ⴚ37

8.

2x ⴚ 5y ⴝ ⴚ19 3x ⴙ 2y ⴝ 0

10.

2x ⴚ 3y ⴝ 6 x ⴙ 3y ⴝ 12

12.

xⴙyⴝ0 2x ⴚ y ⴝ 12

14.

x ⴚ 2y ⴝ 11 2x ⴙ 2y ⴝ ⴚ8

16.

x ⴚ 3y ⴝ ⴚ13 ⴚx ⴙ 4y ⴝ 15 5x ⴚ 2y ⴝ 3 5x ⴙ y ⴝ ⴚ9 x ⴙ 2y ⴝ ⴚ1 4x ⴙ 3y ⴝ ⴚ9 2x ⴙ y ⴝ ⴚ1 7x ⴚ 5y ⴝ 5 4x ⴙ 3y ⴝ 27 3x ⴙ 4y ⴝ 29 x ⴙ 5y ⴝ ⴚ13 2x ⴚ 5y ⴝ ⴚ19 2x ⴙ 2y ⴝ ⴚ8 3x ⴚ 3y ⴝ 18 2x ⴚ y ⴝ ⴚ6 2x ⴙ 3y ⴝ 14

Solve each system of equations by using any method. 17.

19.

21.

23.

2x ⴚ 7y ⴝ 5 5x ⴚ 4y ⴝ ⴚ1

18.

x ⴝ 5y 3x ⴚ 4y ⴝ 11

20.

1 1 xⴙ3yⴝ4 2

ⴚ3y ⴝ x ⴚ 22 7x ⴚ 2y ⴝ 6 9x ⴚ 3y ⴝ 6

Algebra 1

22.

24.

5x ⴚ 7y ⴝ ⴚ16 4x ⴚ 2y ⴝ ⴚ20 0.3x ⴚ 0.5y ⴝ 2 0.3x ⴙ y ⴝ ⴚ4 2 1 3x ⴙ 4 y ⴝ 2

2x ⴙ y ⴝ 4

0.7x ⴚ 1.6y ⴝ 15 0.3x ⴙ 0.4y ⴝ 1

Practice Workbook

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Practice 7.4 Consistent and Inconsistent Systems Solve each system algebraically. 1.

3.

5.

7.

9.

xⴙyⴝ5 ⴚ2x ⴚ 2y ⴝ ⴚ10

2.

2x ⴚ y ⴝ 1 xⴙyⴝ5

4.

2y ⴝ ⴚx ⴚ 4 2x ⴝ ⴚ4y ⴚ 8

6.

3x ⴚ 2y ⴝ 6 ⴚ6x ⴙ 4y ⴝ ⴚ12

8.

4x ⴙ y ⴝ 10 y ⴝ ⴚ4x ⴙ 5

10.

x ⴙ 2y ⴝ 6 x ⴙ 2y ⴝ ⴚ4 3x ⴙ y ⴝ 5 3x ⴙ y ⴝ ⴚ2 4x ⴚ 2y ⴝ ⴚ2 y ⴝ 2x ⴙ 1 xⴚyⴝ2 ⴚx ⴙ y ⴝ ⴚ2 2x ⴙ y ⴝ 3 4x ⴝ 6 ⴚ y

Determine whether each system is dependent, independent, or inconsistent.

13.

15.

17.

19.

21.

23.

40

2x ⴙ y ⴝ 8 y ⴝ ⴚ2x ⴙ 8

12.

y ⴙ 4 ⴝ ⴚ5x y ⴝ 6x ⴚ 7

14.

6x ⴚ 2y ⴝ ⴚ10 y ⴝ 3x ⴙ 2

16.

y ⴙ 4x ⴝ 3 2y ⴝ 8x ⴙ 6

18.

y ⴝ 3x ⴙ 1 3x ⴝ 1 ⴚ y

20.

4ⴝxⴚy 8 ⴙ 2y ⴝ 2x

22.

4x ⴚ 2y ⴝ 1 2x ⴚ 4y ⴝ ⴚ1

24.

Practice Workbook

3x ⴚ y ⴝ 3 y ⴝ 3x ⴚ 9

11.

3x ⴚ 2y ⴝ ⴚ5 4y ⴝ 6x ⴙ 10 y ⴙ 6x ⴝ 18 y ⴝ ⴚ7x ⴙ 2 xⴚyⴝ3 2y ⴝ 2x ⴙ 6 3x ⴝ y ⴙ 2 3y ⴝ x ⴙ 2 x ⴙ 5y ⴝ 10 y ⴝ 5x ⴚ 10 5x ⴚ 2y ⴝ 4 5x ⴚ 4 ⴝ 2y

Algebra 1

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Practice 7.5 Systems of Inequalities Graph the common solution of each system on your own graph paper. Choose a point from the solution and use it to check both inequalities. 1.

3.

5.

7.

9.

11.

yxⴙ4 y2

2.

y3 x  ⴚ2

4.

yxⴚ3 y  ⴚ2x ⴙ 1

6.

4x ⴙ y  2 2x ⴚ y  4

8.

5x ⴚ y  3 4x ⴙ y  0

10.

2x ⴙ 3y  0 3x ⴚ y  ⴚ3

12.

xⴙy0 y  ⴚ1 yxⴚ2 y  ⴚx ⴙ 2 y  3x ⴚ2y  5x x ⴙ 2y  4 3x ⴚ y  2 3x ⴚ 5y  ⴚ10 x ⴙ 4y  4 3x ⴙ 2y  6 x ⴚ y  ⴚ3

Write the system of inequalities that represents the shaded region. Use the points shown to find equations for the boundary lines. y

13.

y

14.

(2, 5) (5, 3)

(–4, 3)

(1, 3)

(4, 4)

(–2, 1) (1, 1) O

x

x

O (3, –3)

Algebra 1

Practice Workbook

41

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Practice 7.6 Classic Puzzles in Two Variables The tens digit of a 2-digit number is twice the units digit. The sum of the digits is 12. Find the original number.

2.

Olga has 5 times as many dimes as nickels. If she has \$3.30, how many of each coin does she have?

3.

Milk that is 4% butterfat is mixed with milk that is 1% butterfat to obtain 18 gallons of milk that is 2% butterfat. How many gallons of each type of milk are needed?

4.

A banker invested a portion of \$10,000 at 5% interest per year and the remainder at 4% interest per year. If the banker received \$470 in interest after 1 year, how much was invested at each rate?

5.

The sum of Nora’s age and her grandmother’s age is 71. Four times Nora’s age is 6 less than her grandmother’s age. Find their ages.

6.

Sailing with the current, a boat takes 3 hours to travel 48 miles. The return trip, against the current, takes 4 hours. Find the average speed of the boat for the entire trip and the speed of the current.

7.

A coin bank contains nickels, dimes, and quarters totaling \$5.45. If there are twice as many quarters as dimes and 11 more nickels than quarters, how many of each coin are in the bank?

8.

Find the two-digit number whose tens digit is 3 less than the units digit. The original number is 6 more than 4 times the sum of the digits.

9.

A daughter is 28 years younger than her father. In 5 years, the father will be 3 times as old as his daughter. How old is each now?

10.

A chemist has a solution that is 20% peroxide and another solution that is 70% peroxide. She wishes to make 100 L of a solution that is 35% peroxide. How much of each solution should she use?

42

Practice Workbook

1.

Algebra 1

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Practice 8.1 Laws of Exponents: Multiplying Monomials Find the value of each expression. 1.

55

2.

29

3.

63

4.

93

5.

1002

6.

65

7.

107

8.

33

9.

48

11.

162

12.

13. 102 ⴢ 105

14.

a7 ⴢ a12

15. c 3 ⴢ c 8

16.

d7 ⴢ d 9

17.

x2 ⴢ x8

18.

w3 ⴢ w5

19.

a2 ⴢ a6

20.

10a ⴢ 10b

10.

124

204

Simplify each product.

Simplify each product. 21.

(2x 2)(4x 3y 2)

22.

(ⴚ3a2b)(6ab4c)

23.

(7q 5)(12q 3r 5)

24.

(11c 8)(ⴚ10c4d)

25.

(9x10z 2)(5x 5y 3)

26.

(ⴚ8f 6g)(ⴚ7f 2g5h)

27.

(1.3a6 b11c 5)(0.5a 2bc 3)

28.

(4.7r 6s 2)(2.1r 11s)

29.

(ⴚ2x 2z)(ⴚ2y 2z)(ⴚ2xyz)

30.

(a x b yc z)(ar b sc t )

1

The area, A, of a triangle is given by A ⴝ 2 bh, where b is the base and h is the height. Find the area of the triangle given the values of b and h. 31.

h ⴝ 5x, b ⴝ 2x

32.

h ⴝ x3, b ⴝ x4

33.

h ⴝ 3x4, b ⴝ 4x7

34.

h ⴝ 12a3, b ⴝ 10a2

Algebra 1

Practice Workbook

43

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Practice 8.2 Laws of Exponents: Powers and Products Simplify each expression. 1.

(4y)2

2.

(52)3

3.

(ⴚy 5)4

4.

(a2)5

5.

(y 2)3

6.

(w 2)2

7.

(w 4)6

8.

(ⴚ8c 5)2

9.

(ⴚ3h 9)3

11.

(ⴚc 5h6)3

12.

10.

(ⴚy 4d 6)8

(ⴚ15h 9k 7)2

13.

(k 9)5(k 3)2

14.

(3y 6)2(x 5y 2z)

15.

(4h3)2(ⴚ2g 3h)3

16.

(14a4b6)2(a6b3)7

Evaluate each monomial for x ⴝ 5, y ⴝ ⴚ1, and z ⴝ ⴚ4.

y4

18.

3x3

19.

2y 2

20.

z2

21.

(yz)2

22.

(yx)2

23.

x 2z 2

24.

yx

25.

ⴚy x

26.

What is the area of a square if each edge of the square has a length of 3a5?

27.

What is the area of a rectangle if one side has a length of 12x 3 and the other side has a length of 6x 2 ?

17.

Find the volume of the cube for each edge length, e. 28.

e ⴝ 5y 4

29.

e ⴝ 3x 7y 5 e

44

Practice Workbook

Algebra 1

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Practice 8.3 Laws of Exponents: Dividing Monomials Use the Quotient-of-Powers Property to simplify each quotient. Then find the value of the result. 1.

106 10 2

417

68

2. 14 4

9210

4. 207 9

5.

3. 3 6

2 yⴙ1 2y

6.

8 yⴙ3 8y

Simplify each expression. Assume that the conditions of the Quotient-of-Powers Property are met.

11.

16.

6r 3 2r

17.

ⴚ40s6 20s 3

18.

21d 18e 5 7d 11e 3

19.

ⴚ16w 7r 2 ⴚ4wr

20.

a 5b 5c 5 ⴚa 2 b 3c 4

21.

4.2x 4y 14 0.6x 9y 9

10.

13.

3 3

( xy ) ( 3wg ) ( 30d 5d )

7.

6

3

6

5

4

8.

14.

( d5c )2

9.

2

ⴚ4s6 3 t 3r 5

( ) ( ⴚ24t 8t )

6 3

3

12.

( 4dc ) 5

ⴚ2d11f 6 2 c 18

( ) ( )

d 11 f 16 2 15. d6f 6

Evaluate each quotient given x ⴝ 2, y ⴝ ⴚ2, and z ⴝ 10. 22.

x3 x

23.

y4 y

24.

x 3y xy3

25.

z4x 2y zxy 2

26.

(yz)2 z

27.

y 3(3zx)2 9x 3

28.

z xⴙ1 zx

30.

( xzy )

Algebra 1

z xⴙx

29. yⴙ3 z

3

Practice Workbook

45

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Practice 8.4 Negative and Zero Exponents Evaluate each expression. 1.

2ⴚ4

2.

(ⴚ2)4

3.

ⴚ24

4.

ⴚ2ⴚ4

5.

(ⴚ2)ⴚ4

6.

3ⴚ2

7.

10ⴚ4

8.

ⴚ72

9.

(ⴚ7)2

10.

(ⴚ10)3

11.

(ⴚ8)ⴚ2

12.

(ⴚ3)ⴚ3

Write each of the following without negative or zero exponents: 14.

y0

15.

aⴚ3

16.

2nⴚ2

17.

(x 2y 3)0

18.

ⴚxⴚ2xⴚ3

19.

aⴚ1bⴚ2c 3

20.

ⴚc 3dⴚ4

21.

m5mⴚ2

22.

k ⴚ4 k 7

24.

ⴚa 3aⴚ6aⴚ5

x ⴚ1

26.

70 (xy)0

yⴚ6 27. 2 y

28.

rt ⴚ4 t3

29.

wⴚ8 wⴚ2

30.

3qⴚ5 qⴚ5

31.

ⴚ2aⴚ4 a 2b

33.

(2a3)(3a5) aⴚ2

23. r ⴚ2sⴚ2t 4

25.

5

5qⴚ4

32. 2 ⴚ2 qs

xⴚ4 x 3

35. ⴚ2 4 x x

46

13. xⴚ1

Practice Workbook

34.

(7dⴚ6)(ⴚ4dⴚ2) 2dⴚ4

36.

ⴚz3zⴚ6 ⴚ3z 2

Algebra 1

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Practice 8.5 Scientific Notation Write each number in scientific notation. 1.

200,000

2.

500,000,000

3.

210,000

4.

40,000

5.

6,500,000,000

6.

840,000,000

7.

466,000,000,000

8.

37,500

9.

0.20

10.

0.0008

11.

0.000076

12.

0.00645

13.

0.00000362

14.

0.000978

Write each number in customary notation. 15.

5 ⴛ 103

16.

6 ⴛ 105

17.

9 ⴛ 104

18.

5.6 ⴛ 107

19.

8.56 ⴛ 1010

20.

3.56 ⴛ 108

21.

6 ⴛ 10ⴚ2

22.

6.7 ⴛ 10ⴚ5

23.

8.76 ⴛ 10ⴚ6

24.

9.22 ⴛ 10ⴚ8

(4 ⴛ 102)(3 ⴛ 102)

26.

(6 ⴛ 104)(2 ⴛ 105)

27.

(2 ⴛ 103) ⴙ (4 ⴛ 103)

28.

(7 ⴛ 107) ⴙ (5 ⴛ 107)

29.

(7 ⴛ 105) ⴚ (2 ⴛ 105)

30.

(9 ⴛ 106) ⴚ (2 ⴛ 106)

31.

12 ⴛ 104 2 ⴛ 10 2

32.

6 ⴛ 106 2 ⴛ 103

33.

(2 ⴛ 103)(4 ⴛ 102) 4 ⴛ 10 4

34.

(8 ⴛ 1010 )(6 ⴛ 102) 2 ⴛ 10 8

Algebra 1

Practice Workbook

47

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DATE

Practice 8.6 Exponential Functions Graph each of the following: 1.

y ⴝ 7x

2.

y ⴝ 0.1x

3.

y ⴝ 1.5x

y

y

y

6

6

6

4

4

4

2

2

2

–4 –2 O –2

2

x

4

–4 –2 O –2

–4 –6

2

4

x

–4 –2 O –2

–4

–4

–6

–6

2

4

2

4

x

Graph each function. In each case, describe the effect of 1 in the transformation of the parent function. 4.

y ⴝ 2x ⴙ 1

5.

y ⴝ 2xⴙ1

6.

y

y ⴝ 1 ⴢ 2x

y

y

6

6

6

4

4

4

2

2

2

2

4

x

–4 –2 O –2

2

4

x

–4 –2 O –2

–4

–4

–4

–6

–6

–6

x

x

(1)

If f (x) ⴝ 2 , find the following values for the function: 7. 11.

ƒ(2) ƒ(ⴚ3)

8. 12.

ƒ(0) ƒ(ⴚ4)

9. 13.

ƒ(ⴚ1)

10.

ƒ(ⴚ2)

ƒ(4)

14.

ƒ(3)

The population of a city is about 200,000 and is growing at a rate of about 0.6% per year. 15.

What multiplier is used to find the new population each year?

16.

Estimate the population 4 years from now.

48

Practice Workbook

Algebra 1

–4 –2 O –2

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CLASS

DATE

Practice 8.7 Applications of Exponential Functions From 1964 to 1992 the percent of female drivers in the United States rose steadily. The percent increase is modeled by y ⫽ 40(1.03)x, where x is the number of years, beginning with x ⴝ 0 in 1964, and y is the percent increase. 1.

Use the model to estimate the percent increase of female drivers in the United States in 1975.

2.

Estimate the percent increase of female drivers in the United States in the year 2000.

The “Mendelssohn” Stradivarius violin was estimated to be worth approximately \$1,700,000 in 1990. The violin is expected to increase in value by approximately 7.5% each year. 3.

Use a calculator to complete the table. Number of years

0

1

2

3

4

5

Value (in millions)

4.

Find an equation to model the growth in value.

5.

Graph the function from Exercise 4 by using a graphics calculator.

6.

Estimate the value of the violin in the year 2010.

The International Telecommunication Union estimated 130,000,000 telephone subscribers in the United States in 1991. The number of telephone subscribers is estimated to increase 8% each year. 7.

Find a function to model this growth in subscribers.

8.

Use the formula to estimate the number of subscribers in the year 2001.

9.

Graph this function by using a graphics calculator.

10.

Estimate the number of subscribers in the year 2011.

Algebra 1

Practice Workbook

49

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Practice 9.1 Adding and Subtracting Polynomials 1.

Write the polynomials and the sum modeled by the tiles.

+

+

+

+

+ + +

+

+

+ +

– – – – – – – – – – – – – –

Rewrite each polynomial in standard form. 2.

2 ⴚ 8c ⴙ c 2

3.

10 ⴙ m3

4.

5n2 ⴙ 2n ⴙ 3n4 ⴚ n

5.

6x ⴚ 2x3 ⴙ 3x2 ⴙ 1

Write the degree of each polynomial.

125 ⴚ d 3

7.

2s

8.

9a3 ⴚ a2 ⴙ 3a6 ⴚ a

9.

4y 2 ⴙ 3y 5 ⴚ 5 ⴙ 8y 3

15.

3n ⴚ 1 from 2n 2 ⴚ 1

17.

7x3 ⴚ 3x ⴙ 2 ⴚ (x2 ⴙ 2)

6.

Use vertical form to add. 10.

3f 2 ⴚ f ⴙ 7f and 2f 2 ⴚ 3f ⴚ 4

11.

6 ⴙ c and 3c 3 ⴙ c 2 ⴚ 12c ⴚ 6

Use horizontal form to add. 12.

4q ⴙ 2q3 ⴚ 1 and 1 ⴚ 2q ⴙ 6q2

13.

3y 3 ⴚ 3y 2 ⴙ 6y and 2y 3 ⴚ 6y ⴚ 3

Use vertical form to subtract. 14.

4m2 from 3m3 ⴚ 6m2 ⴙ m ⴚ 1

Use horizontal form to subtract. 16.

50

10a2 ⴙ 2a ⴚ 8 ⴚ (10a2 ⴙ 8)

Practice Workbook

Algebra 1

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Practice 9.2 Modeling Polynomial Multiplication

+

+

+

1.

+

+

Write the factors and the product for each model.

+

+ + +

+

+

+ + +

+

+

+ + +

2.

Use the Distributive Property to find each product. 3.

6(x ⴙ 2)

4.

7(x ⴚ 2)

5.

9(2x ⴚ 3)

6.

ⴚ2(3x ⴙ 4)

7.

ⴚ4(x ⴚ 5)

8.

10(2x ⴚ 2)

9.

x(x ⴙ 2)

10.

x(8 ⴚ x)

11.

ⴚx(x ⴙ 3)

12.

6x(x ⴚ 3)

13.

ⴚ2x(x ⴙ 2)

14.

ⴚ4x(ⴚ x ⴙ 5)

Model each product with tiles. Check by substituting values for x. 15.

x(x ⴙ 4)

Algebra 1

16.

2x(2x ⴙ 1)

Practice Workbook

51

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DATE

Practice 9.3 Multiplying Binomials Use the Distributive Property to find each product. 1.

(a ⴙ 4)(a ⴙ 5)

2.

(2n ⴚ 3)(n ⴚ 2)

3.

(t ⴙ 6)(2t ⴚ 3)

4.

(4y ⴚ 1)(2y ⴙ 3)

5.

(4c ⴚ 3)(4c ⴚ 1)

6.

(x ⴙ 2)(x ⴚ 8)

7.

(p ⴚ 7)(6p ⴙ 2)

8.

(8f ⴙ 1)(8f ⴙ 1)

9.

(4x ⴙ 3)(4x ⴚ 3)

10.

(5w ⴚ 6)(5w ⴙ 6)

Use the FOIL method to find each product.

(r ⴚ 1)(r ⴚ 2)

12.

(a ⴚ 7)(a ⴚ 3)

13.

(m ⴚ 4)(m ⴚ 4)

14.

(w ⴙ 0.5)(w ⴚ 0.4)

15.

(s ⴙ 3)(2s ⴚ 9)

16.

(y ⴚ 4)(y ⴙ 4)

17.

(3c ⴚ 5d)(5c ⴙ 3d)

18.

(3m ⴙ 2)(3m ⴙ 4)

19.

(3x ⴙ 2y)(3x ⴚ 2y)

20.

(2m ⴙ 5)(2m ⴙ 5)

21.

(2y ⴚ 1)(3y ⴚ 1)

22.

(2x ⴙ 1)(5x ⴙ 2)

23.

(7s ⴙ 1)(7s ⴙ 1)

24.

(7x ⴙ 1)(7x ⴚ 1)

25.

(m ⴙ n)(m ⴙ n)

26.

(4d ⴚ 2c)(2d ⴙ c)

27.

(0.2x ⴙ 2)(0.1x ⴚ 5)

28.

(5p ⴚ 4q)(5p ⴙ 4q)

29.

(s2 ⴙ t)(s2 ⴚ t)

30.

(s2 ⴙ t)(s2 ⴙ t)

31.

Find the area of the rectangle in terms of x.

x–2 x+6

32.

Find the area of the square in terms of x. x–7

52

Practice Workbook

Algebra 1

11.

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DATE

Practice 9.4 Polynomial Functions Show that each equation is true or false by substituting the integers ⴚ1, 0, and 1 for x. 1. x2 ⴚ x ⴚ 12 ⴝ (x ⴚ 4)(x ⴙ 3)

2. x2 ⴙ 7x ⴙ 10 ⴝ (x ⴙ 5)(x ⴚ 2)

3. x2 ⴚ 6x ⴙ 9 ⴝ (x ⴚ 3)2

4. x2 ⴚ 36 ⴝ (x ⴙ 6)(x ⴚ 6)

5. x2 ⴙ 5x ⴙ 25 ⴝ (x ⴙ 5)2

6.

4x2 ⴚ 16t 2 ⴝ (2x ⴚ 4t)(2x ⴙ 4t)

Write a function for the indicated measurement of each geometric solid. 7.

the surface area of a cube with an edge 3x centimeters long

8.

the volume of a cube with an edge x inches long

9.

the surface area of a rectangular solid with a base length of 5 inches and a base width of 3 inches

10.

the volume of a rectangular solid with a base length of 4.5 centimeters and a base width of 3.2 centimeters

11.

the surface area of a cylinder with a height of 7 inches and a radius of x inches

12.

the volume of a cylinder with a height of 1.3 meters and a diameter of x meters

Algebra 1

Practice Workbook

53

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DATE

Practice 9.5 Common Factors Identify each polynomial as prime or not prime. 1.

9x2 ⴙ 24x ⴙ 15

2.

9a2 ⴙ 24a

3.

9m2 ⴙ 16

4. x2 ⴙ 5x ⴚ 6

5.

2x2 ⴙ 2x ⴙ 4

6.

4x2 ⴙ 25y 2

8.

6r 3 ⴙ 3r 2 ⴚ 7r

Factor each polynomial by using the GCF. 7.

3x2 ⴚ 9x

9.

6w4 ⴙ 3w2 ⴚ 9

10.

3q2 ⴙ 6q5 ⴙ 9q

11.

18b3 ⴚ 36b2 ⴚ 9

12.

3v 6 ⴚ 9v 4 ⴙ 147v 2

13.

xy ⴚ 2x2y ⴙ xy 3

14.

10wz2 ⴚ 5wz ⴙ 15w 2z

Write each as the product of two binomials.

y(y ⴙ 1) ⴙ 2(y ⴙ 1)

16.

3(c ⴙ d ) ⴚ a(c ⴙ d)

17.

2(x ⴙ w) ⴚ z(x ⴙ w)

18.

6(x ⴚ 2) ⴙ y(x ⴚ 2)

19.

a(a ⴚ b) ⴚ b(a ⴚ b)

20.

3x(x ⴙ 4) ⴚ 2(x ⴙ 4)

21.

4(x ⴚ 2y) ⴙ x(x ⴚ 2y)

22.

z(4 ⴚ w) ⴙ y(4 ⴚ w)

23.

7x(x ⴚ 1) ⴙ (x ⴚ 1)

24.

mn(r ⴙ 1) ⴚ (r ⴙ 1)

15.

Factor by grouping. 25.

4ax ⴚ bx ⴙ 4ay ⴚ by

26.

2pq2 ⴙ 4pq ⴚ 2q ⴚ 4

27.

3a ⴙ 3 ⴚ a2 ⴚ a

28.

6m3 ⴙ 4m ⴚ 9m2 ⴚ 6

29.

3m ⴚ 12 ⴙ m3 ⴚ 4m2

30.

ab 2 ⴙ 5a ⴚ 6b 2 ⴚ 30

31.

2cd ⴚ c ⴚ 6d ⴙ 3

32.

4 ⴚ 2x ⴙ 6 ⴚ 3x

33.

2xz ⴙ 2yz ⴙ x ⴙ y

34.

mx ⴙ 5m ⴙ nx ⴙ 5n

35.

xy ⴙ 2y ⴙ x ⴙ 2

36.

3x2 ⴙ 3xy ⴚ 2xy ⴚ 2y 2

54

Practice Workbook

Algebra 1

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Practice 9.6 Factoring Special Polynomials Use the generalization of a perfect-square trinomial or the difference of two squares to find each product. 1.

(x ⴚ 1)2

2.

(2x ⴙ 3)2

3.

(a ⴙ 5)2

4.

(3g ⴙ 1)2

5.

(2a ⴚ 5)2

6.

(x ⴚ y)2

7.

(x ⴙ 2y)2

8.

(3m ⴚ n)2

9.

(x ⴚ 3)(x ⴙ 3)

10.

(4y ⴙ 1)(4y ⴚ 1)

(5x ⴙ 2)(5x ⴚ 2)

12.

(6r ⴚ s)(6r ⴙ s)

13. x2 ⴚ 25

14.

y 2 ⴚ 49

15.

2x2 ⴚ 2

16.

4y 2 ⴚ 16

17.

16y 2 ⴚ 25

18.

121 ⴚ x2

19.

9 ⴚ 16y 2

20. x2 ⴚ 6x ⴙ 9

11.

Factor each polynomial completely.

21. x2 ⴙ 10x ⴙ 25

22.

y 2 ⴚ 16y ⴙ 64

23. z2 ⴚ 20z ⴙ 100

24.

64x 2 ⴚ 48xy ⴙ 9y 2

25.

25 ⴚ 10a ⴙ a2

26.

4m2 ⴙ 4m ⴙ 1

27.

81r 2s2 ⴚ 100t 4q 4

28.

16x2 ⴙ 24x ⴙ 9

29.

x 2 ⴙ 2xy ⴙ y 2

30.

4a2 ⴙ 4ab ⴙ b 2

31.

y 2 ⴚ x2

32.

25a2 ⴚ 1

33.

1 ⴚ x2y 4

34.

144c2 ⴚ 120cd ⴙ 25d 2

35.

6a 2 ⴚ 216b 2

36.

49x ⴚ xy 2

37.

12x4 ⴚ 12

38.

b 4 ⴚ 2b 2 ⴙ b 2 ⴚ 2

39.

4c2 ⴚ 24c ⴙ 36

40.

4m4n2 ⴙ 4m3n2 ⴙ m2n2

Algebra 1

Practice Workbook

55

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DATE

Practice 9.7 Factoring Quadratic Trinomials Write each trinomial in factored form. 1. x2 ⴙ x ⴚ 30

2.

m2 ⴙ 9m ⴙ 20

3. c 2 ⴚ c ⴚ 72

4.

d 2 ⴚ 7d ⴙ 12

6.

f 2 ⴚ 2f ⴚ 48

5.

y 2 ⴙ y ⴚ 156

For each polynomial, write all of the factor pairs of the third term, and then circle the pair that would successfully factor the polynomial. 7.

n2 ⴚ 8n ⴙ 15

9. s 2 ⴙ 5s ⴙ 4

8. t 2 ⴚ 121 10.

q 2 ⴚ 2q ⴚ 35

Write each trinomial as a product of its factors. Use factoring patterns, graphing, or algebra tiles to assist you in your work. 11.

g 2 ⴚ 3g ⴚ 40

12.

h 2 ⴙ 6h ⴚ 40

13. j 2 ⴙ 22j ⴙ 40

14. k2 ⴚ 39k ⴚ 40

15. x2 ⴚ x ⴚ 12

16.

a2 ⴚ 9a ⴙ 14

18. x2 ⴚ 5x ⴚ 6

19. x2 ⴚ 8x ⴙ 15

20.

21. x2 ⴚ 9x ⴚ 36

22. x2 ⴚ x ⴚ 42

23. x2 ⴚ 81

24. x2 ⴙ 17x ⴙ 60

25. x2 ⴙ 4x ⴚ 12

26. x2 ⴙ 14x ⴚ 32

27. x2 ⴙ 12x ⴙ 35

28. x2 ⴚ x ⴚ 72

29. x2 ⴙ 17x ⴙ 72

30. x2 ⴚ 17x ⴙ 72

31. x2 ⴙ x ⴚ 72

32. x3 ⴙ 7x2 ⴙ 12x

p2 ⴙ 18p ⴙ 45

33.

2x2 ⴙ 6x ⴙ 3

34.

6x2 ⴙ 8x ⴚ 30

35.

5x2 ⴙ 7xy ⴙ 2y 2

36.

14x2 ⴙ 23xy ⴙ 3y 2

56

Practice Workbook

17.

y 2 ⴚ 7y ⴚ 18

Algebra 1

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Practice 9.8 Solving Equations by Factoring Identify the zeros for each function. 1.

y ⴝ (x ⴙ 4)(x ⴚ 3)

2.

y ⴝ (x ⴙ 4)(x ⴙ 4)

3.

y ⴝ (x ⴙ 6)(x ⴚ 7)

4.

y ⴝ (x ⴚ 5)(x ⴚ 2)

5.

y ⴝ (x ⴙ 21)(x ⴚ 16)

6.

y ⴝ x(x ⴚ 12)

7.

y ⴝ (2x ⴙ 5)(x ⴙ 1)

8.

y ⴝ (3x ⴙ 6)(x ⴚ 4)

9.

y ⴝ x(5x ⴙ 1)

10.

y ⴝ (2x ⴚ 3)(3x ⴚ 2)

Solve by factoring. 11. x2 ⴙ 5x ⴙ 6 ⴝ 0

12. x2 ⴙ x ⴚ 20 ⴝ 0

13. x2 ⴙ 6x ⴚ 7 ⴝ 0

14. x2 ⴚ 4 ⴝ 0

15. x2 ⴙ 6x ⴝ ⴚ9

16. x2 ⴙ x ⴚ 12 ⴝ 0

17. x2 ⴙ 16x ⴙ 64 ⴝ 0

18. x2 ⴙ 8x ⴝ 9

19. x2 ⴙ 2x ⴝ 3

20. x2 ⴚ 5x ⴝ 6

21. x2 ⴙ 18x ⴝ ⴚ81

22. x2 ⴚ 25 ⴝ 0

23.

2x2 ⴙ 11x ⴙ 5 ⴝ 0

25. x2 ⴙ 8x ⴝ 0

24.

3x2 ⴙ 5x ⴙ 2 ⴝ 0

26. x2 ⴚ 8x ⴝ ⴚ16

27.

2x2 ⴙ 9x ⴙ 10 ⴝ 0

29.

The area of the rectangle is 40 square centimeters. Find the value of x.

28.

3x2 ⴙ 8x ⴙ 4 ⴝ 0

x x+6

30.

The area of the square is 16 square centimeters. Find the value of x.

Algebra 1

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x–4

57

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Practice 10.1 Graphing Parabolas Describe how the graph of each function differs from the graph of the parent function, y ⴝ x 2 . 1.

y ⴝ 2(x ⴙ 5)2

2.

y ⴝ (x ⴚ 1)2 ⴙ 5

3.

y ⴝ ⴚ3(x ⴙ 1)2

4.

y ⴝ (x ⴙ 6)2

5.

y ⴝ ⴚ(x ⴙ 3)2 ⴚ 2

6.

y ⴝ 2 (x ⴚ 4)2

1

Determine the vertex and axis of symmetry for each function, and then sketch a graph from the information. 7.

y ⴝ ⴚ(x ⴚ 5)2

y 6

y ⴝ (x ⴚ 1)2 ⴙ 2

y 6

4

4

2

2 4

2

x

6

–4 –2 O –2

–4

–4

–6

–6

y ⴝ 2(x ⴚ 3)2

y

10.

6

4

4

2

2 2

4

x

4

2

4

x

y

y ⴝ 3(x ⴙ 2)2 ⴚ 1

6

– 4 –2 O –2

2

–4 –2 O –2

–4

–4

–6

–6

x

Find the zeros of each polynomial function. Check by graphing. 11.

y ⴝ x 2 ⴚ 2x ⴚ 15

12.

y ⴝ x 2 ⴙ 2x ⴚ 15

13.

y ⴝ x 2 ⴙ 8x ⴙ 15

14.

y ⴝ x 2 ⴙ 5x ⴚ 14

15.

y ⴝ x 2 ⴚ 11x ⴙ 30

16.

y ⴝ x 2 ⴚ 3x ⴚ 4

58

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Algebra 1

–2 O –2

9.

8.

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Practice 10.2 Solving Equations of the Form ax 2 ⴝ k Find each square root. Round answers to the nearest hundredth. 1.

2.

3.

5.

6.

7.

4.

8.

Solve each equation for x. Round answers to the nearest hundredth. 9.

x 2 ⴝ 16

10.

x 2 ⴝ 900

11.

x 2 ⴝ 75

12.

x2 ⴝ 4

13.

x 2 ⴝ 49

14.

x 2 ⴝ 25

15.

(x ⴚ 2)2 ⴝ 16

16.

(x ⴙ 2)2 ⴝ 16

17.

x2 ⴚ 4 ⴝ 0

18.

4 ⴝ (x ⴙ 3)2

19.

ⴚ(x ⴙ 3)2 ⴙ 4 ⴝ 0

20.

(x ⴚ 2)2 ⴚ 36 ⴝ 0

21.

(x ⴚ 3)2 ⴝ 18

22.

x 2 ⴙ 1 ⴝ 17

23.

x2 ⴙ 2 ⴝ 5

24.

(x ⴙ 5)2 ⴝ 7

4

1 9

Find the vertex, axis of symmetry, and zeros of each function. Sketch the graph. 25.

f(x) ⴝ (x ⴚ 1)2 ⴚ 1

Algebra 1

26.

g(x) ⴝ (x ⴙ 2)2 ⴚ 4

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Practice 10.3 Completing the Square Use algebra tiles to complete the square for each binomial. Draw a sketch of your algebra-tile model. Write each perfect-square trinomial in the form x 2 ⴙ bx ⴙ c. 1.

x 2 ⴚ 6x

2.

x 2 ⴙ 2x

3.

x 2 ⴚ 4x

4.

x 2 ⴙ 10x

Complete the square. 5.

x 2 ⴙ 8x

6.

x 2 ⴚ 8x

7.

x 2 ⴙ 11x

8.

x 2 ⴚ 11x

Rewrite each function in the form y ⴝ (x ⴚ h)2 ⴙ k. 10.

y ⴝ x 2 ⴙ 4x ⴙ 4 ⴚ 4

11.

y ⴝ x 2 ⴙ 18x ⴙ 81 ⴚ 81

12.

y ⴝ x 2 ⴚ 18x ⴙ 81 ⴚ 81

13.

y ⴝ x 2 ⴚ 24x ⴙ 144 ⴚ 144

14.

y ⴝ x 2 ⴙ 22x ⴙ 121 ⴚ 121

y ⴝ x 2 ⴚ 4x ⴙ 4 ⴚ 4

9.

Refer to the equation y ⴝ x 2 ⴙ 6x for Exercises 15 and 16. 15.

Complete the square and rewrite in the form y ⴝ (x ⴚ h)2 ⴙ k.

16.

Find the vertex and maximum (or minimum) value.

Rewrite each equation in the form y ⴝ (x ⴚ h)2 ⴙ k. Find the vertex of each quadratic function. 17.

f(x) ⴝ x 2 ⴚ 3

18.

f(x) ⴝ x 2 ⴚ 2

19.

f(x) ⴝ x 2 ⴙ 2x ⴚ 8

20.

f(x) ⴝ x 2 ⴚ 4x ⴙ 3

60

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Algebra 1

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Practice 10.4 Solving Equations of the Form x 2 ⴙ bx ⴙ c ⴝ 0 Find the zeros of each function. Graph to check. 1.

y ⴝ x 2 ⴚ 13x ⴙ 42

2.

y ⴝ x 2 ⴙ 13x ⴙ 42

3.

y ⴝ x 2 ⴚ x ⴚ 42

4.

y ⴝ x 2 ⴙ 7x ⴙ 12

5.

y ⴝ x 2 ⴚ x ⴚ 12

6.

y ⴝ x 2 ⴙ x ⴚ 12

8.

x 2 ⴚ 10x ⴙ 21 ⴝ 0

Solve each equation by factoring. 7.

x 2 ⴚ 4x ⴚ 60 ⴝ 0

9.

x 2 ⴙ 5x ⴙ 4 ⴝ 0

10.

x 2 ⴙ 2x ⴚ 24 ⴝ 0

11.

x2 ⴚ x ⴚ 6 ⴝ 0

12.

x 2 ⴚ 5x ⴙ 4 ⴝ 0

13.

x 2 ⴙ 11x ⴙ 30 ⴝ 0

14.

x 2 ⴙ 2x ⴚ 8 ⴝ 0

15.

x 2 ⴙ 6x ⴙ 9 ⴝ 0

16.

x 2 ⴚ 2x ⴙ 1 ⴝ 0

17.

x 2 ⴙ x ⴚ 30 ⴝ 0

18.

x 2 ⴙ 5x ⴚ 14 ⴝ 0

Solve each equation by completing the square. 19.

x 2 ⴙ 5x ⴙ 6 ⴝ 0

20.

x 2 ⴙ 3x ⴙ 2 ⴝ 0

21.

x 2 ⴙ x ⴚ 12 ⴝ 0

22.

x 2 ⴙ 7x ⴙ 10 ⴝ 0

23.

x 2 ⴚ 2x ⴝ 3

24.

x 2 ⴙ 4x ⴝ 5

25.

x 2 ⴙ 6 ⴝ 7x

26.

x 2 ⴙ 24 ⴝ 11x

Find the point(s) where the graphs intersect. Graph to check. 27.

29.

yⴝ4 y ⴝ x2

28.

y ⴝ 7x ⴚ 35 y ⴝ x 2 ⴚ 3x ⴚ 10

30.

Algebra 1

y ⴝ ⴚx ⴚ 5 y ⴝ x 2 ⴙ 3x ⴚ 10 yⴝxⴚ2 y ⴝ x 2 ⴚ 7x ⴙ 10

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Practice 10.5 The Quadratic Formula Identify a, b, and c for each quadratic equation. 1.

x 2 ⴙ 3x ⴙ 2 ⴝ 0

2.

x 2 ⴚ 2x ⴙ 1 ⴝ 0

3.

x 2 ⴙ 7x ⴚ 3 ⴝ 0

4.

x 2 ⴚ 5x ⴙ 3 ⴝ 0

5.

3x 2 ⴚ 4 ⴝ 0

6.

2x 2 ⴙ 15x ⴝ 0

7.

10x 2 ⴙ 1 ⴙ 6x ⴝ 0

8.

7x ⴙ x 2 ⴚ 2 ⴝ 0

9.

x 2 ⴝ 36

10.

x 2 ⴙ 36 ⴝ 12x

x 2 ⴚ 6x ⴝ 0

12.

3x 2 ⴝ 5x

11.

Find the value of the discriminant and determine the number of solutions for each equation. 13.

4x 2 ⴙ 3x ⴙ 1 ⴝ 0

14.

x 2 ⴙ 5x ⴙ 1 ⴝ 0

15.

x 2 ⴙ 2x ⴚ 6 ⴝ 0

16.

2x 2 ⴙ 2x ⴙ 4 ⴝ 0

17.

x 2 ⴚ 5x ⴙ 1 ⴝ 0

18.

7 ⴚ x 2 ⴙ 6x ⴝ 0

19.

x 2 ⴚ 4x ⴙ 4 ⴝ 0

20.

3 ⴚ 4x ⴙ 2x 2 ⴝ 0

21.

3x 2 ⴚ 4x ⴚ 2 ⴝ 0

22.

2x 2 ⴚ 5x ⴚ 4 ⴝ 0

23.

3x 2 ⴚ 8 ⴝ 0

24.

6x 2 ⴚ 5x ⴙ 1 ⴝ 0

25.

x 2 ⴚ 8x ⴙ 8 ⴝ 0

26.

x2 ⴚ 5 ⴝ 0

Use the quadratic formula to solve each equation. Give answers to the nearest hundredth. Check by substitution.

Choose any method to solve each quadratic equation. Give answers to the nearest hundredth. 27.

x2 ⴚ x ⴚ 2 ⴝ 0

28.

x 2 ⴚ 7x ⴙ 12 ⴝ 0

29.

x 2 ⴙ 3x ⴙ 2 ⴝ 0

30.

x 2 ⴚ 25 ⴝ 0

31.

3x 2 ⴙ 2x ⴚ 5 ⴝ 0

32.

x 2 ⴙ 3x ⴙ 1 ⴝ 0

33.

2x 2 ⴚ 10x ⴙ 8 ⴝ 0

34.

x 2 ⴙ 5x ⴙ 4 ⴝ 0

62

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Algebra 1

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Practice 10.6 Graphing Quadratic Inequalities Solve each quadratic inequality by using the Zero Product Property. Graph the solution on a number line. 1.

x 2 ⴚ 3x ⴚ 40  0

2.

x 2 ⴙ 9x ⴙ 14  0

3.

x 2 ⴙ 2x ⴙ 1  0

4.

x 2 ⴚ x ⴚ 30  0

6.

x 2 ⴙ 3x ⴙ 2  0

5.

x 2 ⴚ x ⴚ 12  0

Graph each quadratic inequality on the grid provided. Shade the solution region. 7.

y  x2 ⴚ 4

8.

y  ⴚx 2 ⴙ 4 y

y

x

x

9.

y  x 2 ⴙ 4x

10. y

y  x 2 ⴙ 4x ⴙ 4 y

x

x

Algebra 1

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63

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Practice 11.1 Inverse Variation Determine whether each of the following is an example of inverse variation: 1.

q

pⴝ3

2.

p ⴝ 3q

3.

3

pⴝq

For Exercises 4 –7, y varies inversely as x. 4.

If y is 6 when x is 10, find x when y is 12.

5.

If x is 25 when y is 5, find y when x is 5.

6.

If x is ⴚ12 when y is ⴚ6, find x when y is 6.

7.

If y is ⴚ0.5 when x is 40, find x when y is 2. The time required to complete an engine overhaul varies inversely as the number of people who work on the job. It takes 4 hours for 6 students to complete an engine overhaul. If they all work at the same rate, how long would it take 2 students to complete the job?

9.

The intensity with which an object is illuminated varies inversely as the square of its distance from the light source. At 1.5 feet from a light bulb, the intensity of the light is 60 units. What is the intensity at 1 foot?

8.

The customary unit of power is horsepower. A horse doing average work can pull 550 pounds a distance of 1 foot in 1 second. The horsepower, H, in feet per second needed to lift 100 pounds 10 feet can be modeled by 103

the rational equation H ⴝ t , where t is time in seconds. 10. Complete the table. Time (seconds)

5

10

15

20

25

30

Horsepower 11.

Find the products of time and horsepower. Describe the products.

12.

What is the relationship between time and horsepower?

64

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Practice 11.2 Rational Expressions and Functions For what values are these rational expressions undefined? 1.

2a ⴙ 5 2a

2.

3d ⴙ 7 2d ⴚ 3

3.

eⴚ9 eⴚ7

4.

5z ⴙ 6 z(6z ⴚ 1)

5.

3w ⴙ 4 (w ⴙ 4)(w ⴚ 1)

6.

7y ⴙ 2 5y 2 ⴙ 10y

9.

ⴚ2f ⴙ 8 6f

12.

fⴚ1 f (f ⴙ 3)

Evaluate each rational expression for f ⴝ 3 and f ⴝ 0. Write undefined if appropriate. 7.

4f ⴚ 1 2f ⴚ 3

8.

10.

3f ⴚ 7 fⴚ3

11.

2f ⴙ 5 fⴙ3 2f 2f (f ⴚ 3)

1

Describe the transformations applied to the graph of f (x) ⴝ x to create the graph of each rational function below. List any values for which the function is undefined. 2

13.

g(x) ⴝ x ⴚ 4

14.

g(x) ⴝ x ⴙ 4 ⴚ 2

1

Graph each rational function. State any restrictions. 15.

2

f(x) ⴝ x ⴚ 3

Algebra 1

16.

1

f(x) ⴝ x ⴙ 4

17.

1

f(x) ⴝ x ⴙ 3 ⴙ 3

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Practice 11.3 Simplifying Rational Expressions For what values of the variable is each rational expression undefined? 1.

nⴚ2 2ⴚn

2.

(w ⴚ 2)(w ⴚ 3) (w ⴙ 5)(w ⴚ 4)

3.

10m m

4.

6 x(x 2 ⴙ 2x ⴙ 1)

Write the common factors. 5.

5ⴢ3 2ⴢ5

6.

a4b ab

7.

(r ⴙ 2)(r ⴙ 3) r(r ⴙ 3)

8.

(x ⴙ 3)2 x2 ⴚ 9

9.

y2 ⴚ y ⴚ 6 y2 ⴚ 9

3ⴚk

10. 2 k ⴚ 2k ⴚ 3

Simplify. 11.

x3 3x

12.

2(x ⴙ y) 8(x ⴙ y)2

13.

aⴙ4 2a ⴙ 8

14.

8w ⴚ 12 4

15.

pⴙ7 p 2 ⴚ 49

16.

64 ⴚ x 2 8ⴚx

17.

h2 ⴙ h ⴚ 12 h 2 ⴙ 5h ⴙ 4

18.

fⴙg 3(f ⴙ g)3

19.

3x 2 ⴚ 12x ⴚ 15 3x 2 ⴚ 18x ⴙ 15

20.

5z3 ⴚ 125z 10z2 ⴚ 250

21.

2x 2 ⴙ 16x ⴙ 32 xⴙ4

66

Practice Workbook

y 2 ⴚ 25

22. 2 y ⴚ 10y ⴙ 25

Algebra 1

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Practice 11.4 Operations With Rational Expressions

Perform the indicated operations. Simplify and state the restrictions on the variables. 1.

3 4 5z ⴙ 5z

2.

6 2 xⴚ3 ⴙxⴚ3

3.

5a 2a aⴙb ⴚaⴙb

4.

x 1 xⴚ1 ⴚxⴚ1

5.

1 2 p ⴚq

6.

c d 3d ⴙ 3c

7.

4 m mn ⴢ 2

8.

y 2 12 6 ⴢ y3

9.

x3 x2 ⴙ 6 12

10.

a2 (a ⴚ 3) 3ⴚa

11.

a3 a (a ⴙ 1)2 ⴙ (a ⴙ 1)2

12.

t 2 ⴙ 2t 3t ⴚ 6 t2 ⴚ 4 ⴢ t

13.

y 2 ⴙ 5y ⴙ 6 y ⴢ y2 yⴙ2

14.

3x 2 3x ⴚ 2 ⴚ 3x ⴚ 2

15.

m2 ⴚ n2 mn m 2n 2 ⴢ 1

16.

1 x x ⴙ 1 ⴙ x2 ⴚ 1

17.

3x 2 2ⴚx 1 ⴚ x2 ⴚ 1 ⴚ x2

18.

8b ⴚ 40 b ⴙ 5 ⴢ b 2 ⴚ 25 8

20.

x ⴚ3xy x ⴙ y ⴚ (x ⴙ y)2

6

19. 2 c ⴚ 3c

2c 2 ⴚ 2c ⴚ 12 6c ⴙ 12

21.

4 ⴙ x2 ⴚ 6

3x

22.

3 z zⴚ1 ⴙ1ⴚz

23.

4 1 xⴚ3 ⴢx

24.

nⴙ4 12 16 ⴢ n2 ⴚ 16

25.

2 3x ⴙ x 2 ⴙ 4x ⴚ 5 xⴙ5

26.

3d d d2 ⴚ 9 ⴙ 3 ⴙ d

Algebra 1

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Practice 11.5 Solving Rational Equations Solve the following rational equations by finding the lowest common denominator: 2 29 y ⴙ3ⴝ y

2.

z z 2 ⴚ7ⴝ3

3.

1 3 5 x ⴙx ⴝ4

4.

2x x 3 ⴚ2 ⴝ5

5.

3 ⴚ 5c 3c ⴚ 6 8 ⴙ 5 ⴝ1

6.

1 xⴚ3 4 ⴚ 8x ⴝ 0

7.

1 2 1 xⴙ6 ⴝxⴙ9 ⴚxⴙ3

8.

yⴚ1 ⴚy ⴚ 2 ⴝ y yⴙ1

9.

4b ⴙ 5 6b ⴙ 1 2b ⴙ 1 ⴝ 3b ⴚ 1

10.

x 5 x2 ⴚ 3 ⴝ x ⴙ 4

11.

6 a ⴚ1ⴝa

12.

y y ⴙ yⴚ5 yⴚ5 ⴝ3

13.

3x ⴚ 1 xⴚ5 4 ⴝ 5 ⴚ2

14.

4w 2w 3w ⴚ 2 ⴙ 3w ⴙ 2 ⴝ 2

15.

2 1 11 x ⴙ 4 ⴝ 12

16.

12 24 x 2 ⴚ 16 ⴚ 3 ⴝ x ⴚ 4

18.

m 2 1 m 2 ⴚ 1 ⴙ m ⴙ 1 ⴝ 2m ⴚ 2

1

17. 2 r ⴚ1

2

ⴝ r2 ⴙ r ⴚ 2

3

1.

yⴙ3

19.

t 1 17 t ⴚ 5 ⴝ t ⴙ 5 ⴚ 25 ⴚ t 2

20.

2 ⴚ y 2 ⴙ 5y ⴙ 6 ⴝ y ⴙ 2

21.

qⴚ3 qⴚ3 ⴝ 4ⴙq 7

22.

g gⴙ7 ⴝ 1 ⴙ gⴚ2 gⴙ2

Solve the following rational equations by graphing: 23.

3x x 5 ⴝ2 ⴚ1

24.

x xⴚ3 4 ⴙ 3 ⴝ6

25.

1 1 2 xⴙ2 ⴙxⴚ3 ⴝx

26.

2x ⴚ 6 xⴚ1 3x ⴙ 1 ⴝ 4x ⴚ 4

68

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Algebra 1

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Practice 11.6 Proof in Algebra Give a reason for each step.

Proof 3x ⴙ 2(x ⴙ 4) ⴝ 13 1.

3x ⴙ 2x ⴙ 8 ⴝ 13

2.

5x ⴙ 8 ⴝ 13

3.

5x ⴙ 8 ⴚ 8 ⴝ 13 ⴚ 8

4.

5x ⴙ 0 ⴝ 5

5.

5x ⴝ 5

6.

5x 5 5 ⴝ5

7.

xⴝ1 ⴚa

a

Give a reason for each step in the proof that b ⴝ ⴚb .

Proof

8. 9. 10.

ⴚa 1 b ⴝ ⴚa b

()

(

1

ⴝⴚ aⴢb

)

a

ⴝ ⴚb

Give a reason for each step in the proof that ⴚa(b ⴙ c) ⴝ ⴚab ⴚ ac.

Proof 11.

ⴚa(b ⴙ c) ⴝ ⴚab ⴙ ⴚac ⴝ ⴚab ⴚ ac

12.

Prove each of the following statements. Give a reason for each step on a separate piece of paper. 13.

If ⴚ6x ⴚ 2 ⴝ ⴚ8x ⴚ 4, then x ⴝ ⴚ1.

14.

If 3(n ⴚ 2) ⴝ 9, then n ⴝ 5.

Algebra 1

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Practice 12.1 Operations With Radicals Simplify each radical expression by factoring. 1.

2.

3.

4.

5.

6.

8.

9.

10.

12.

11.

Simplify each radical expression. Assume that all variables are non-negative and that all denominators are nonzero.

14.

15.

16.

x3 y6

13.

x5 y9

18.

3兹27 ⴚ 5兹3

19.

20.

(5 ⴙ 兹5) ⴙ (2 ⴚ 兹3)

(2兹3)2 23. (兹12 ⴙ 2 )(兹12 ⴚ 2 ) 2 25. (兹3 ⴙ 2 ) 21.

70

Practice Workbook

) 24. 兹3(2 ⴙ 兹12 ) 2 26. ( 兹3 ⴙ 兹12 ) 22.

(

2 兹3 ⴙ 兹12

Algebra 1

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Practice 12.2 Square-Root Functions and Radical Equations Solve each equation algebraically. Be sure to check your solution. 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

12.

11.

Use graphing technology or sketch the graphs on your graph paper to solve each equation, if possible.

13.

4兹x ⴝ ⴚx ⴚ 3

14.

Solve each equation, if possible. If not possible, explain why. 15.

5x 2 ⴝ 125

16.

x 2 ⴚ 1 ⴝ 120

17.

4x 2 ⴝ 120

18.

19.

x 2 ⴙ 169 ⴝ 0

20.

21.

22.

23.

Algebra 1

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Practice 12.3 The Pythagorean Theorem Complete the table. Use a calculator and round each answer to the nearest tenth.

Leg 1.

21

3.

6.5

5.

13

Leg

Hypotenuse 75

63 28

11.

48

2.

7.2

7. 9.

Leg

4.

20

85

6.

33

65

8.

45

0.63

13.

Leg

Hypotenuse

80

82 29

44 48

10.

10

80

12.

1 5

0.87

14.

0.036

60

24

1 3 0.077

15.

16.

17. 48

36

17

x

25

x

Solve for x.

x 8 7

18.

A picket fence has a gate that is 48 inches wide and 62 inches high. Find the length, to the nearest inch, of a diagonal brace for the gate.

19.

The base of a 15-foot ladder is placed 9 feet from a wall. If the ladder leans against the wall, how high will it reach?

20.

Cynthia drove 56 miles due south and 90 miles due west. If she drives in a straight line back to the point where she started, how far will she drive?

72

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Practice 12.4 The Distance Formula For each figure, find the coordinates of Q and the lengths of the three sides of the triangle. Decide whether the triangle is scalene, isosceles, equilateral, or right. 1.

2. y

y Q Q P

R

x P

R x

Find the distance between the two given points. 3.

A(ⴚ2, 8), B(10, ⴚ1)

4.

M(17, 14), N(20, 10)

5.

X(ⴚ7, ⴚ1), Y(ⴚ6, ⴚ1)

6.

D(ⴚ3, 0), E(3, 2)

Find the coordinates of the midpoint of the segment. 7.

AB, with A(ⴚ3, 5) and B(3, 7)

8.

MN, with M(ⴚ4, 3) and N(3, ⴚ5)

9.

XY, with X(ⴚ4, 5) and Y(ⴚ2, 1)

10.

CD, with C(6, ⴚ4) and D(4, 6)

11.

FG, with F(7, ⴚ1) and F(5, ⴚ2)

The midpoint of PQ is M. Find the missing coordinates. 12.

P(52, ⴚ5), Q(16, 19), M(

14.

P(

Algebra 1

), Q(4, 8), M(10, 7)

)

13.

P(6, ⴚ2), Q(

15.

P(ⴚ2, 25), Q(

), M(9, 4) ), M(1, 18)

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Practice 12.5 Geometric Properties Find an equation of a circle with its center at the origin and with the given radius. 1.

2.

Sketch each circle on the grid provided. Then find the equation of the circle. 3.

center at (4, 0) and radius of 3

4.

center at (ⴚ4, 0) and radius of 3

y

y

4 4 2 2 2

O

4

x

6

–6

–2

–4

–2

x

O –2

–4

center at (0, 4) and radius of 3

6.

center at (0, ⴚ4) and radius of 3

y

y

6

–4

–2

–2

O

4

–2

2

–4

O

5.

2

4

x

2

4

x

–6

Identify the center and the radius of each circle. 7.

74

(x ⴚ 1)2 ⴙ y 2 ⴝ 4

Practice Workbook

8.

(x ⴙ 1)2 ⴙ (y ⴚ 2)2 ⴝ 4

Algebra 1

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Practice 12.6 The Tangent Function Use a calculator to find the tangents of the following angles to the nearest tenth: 1.

18°

2.

48°

3.

118°

4.

150°

8.

0.9657

Find the corresponding angles, to the nearest degree, for the following tangent approximations: 5.

0.2867

6.

0.7265

7.

28.64

Use the given information to find the length, to the nearest hundredth, of the indicated side. 9.

B

If angle A is 30° and side b is 6 feet, find a.

c

a 10.

If angle B is 60° and side b is 16 feet, find a.

C

b

A

Use the diagram to find each height to the nearest hundredth. 11.

Find the height of the building. 45 °

12.

Find the height of the tree.

35 ° 60 ft 100 ft

13.

2

If a road has a 2% grade, its slope is 100 . What is the measure, to the nearest tenth, of the angle at which the road inclines?

14.

What is the slope of a line that makes an angle of 45° with the x-axis?

15.

A mast on a sailboat supports a 28-foot tall sail. If the boom holding the bottom of the sail is 18 feet long, what angle does the base of the sail make with its outer edge? Round your answer to the nearest degree.

Algebra 1

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Practice 12.7 The Sine and Cosine Functions Evaluate each expression to the nearest ten-thousandth. 1.

sin 65°

2.

sin 85°

3.

cos 32°

4.

cos 15°

5.

sin 12°

6.

sin 50°

7.

cos 39°

8.

cos 89°

9.

sin 76°

10.

sin 82°

11.

cos 49°

12.

cos 61° B

For Exercises 13–20, use right triangle ABC shown at right. Find the indicated angle measure or length. Round your answer to the nearest tenth.

b ⴝ 6, c ⴝ 8, m∠B ⴝ

14.

a ⴝ 8, c ⴝ 15, m∠B ⴝ

15.

b ⴝ 6, c ⴝ 9, m∠A ⴝ

16.

a ⴝ 8, c ⴝ 14, m∠B ⴝ

17.

b ⴝ 7, c ⴝ 10, m∠B ⴝ

18.

m∠B ⴝ 40°, c ⴝ 30, b ⴝ

19.

m∠B ⴝ 52°, c ⴝ 18, a ⴝ

20.

m∠A ⴝ 46°, c ⴝ 9, b ⴝ

C

c

b

A

13.

a

What angle measure has each approximate sine value? Round each answer to the nearest tenth of a degree. 21.

0.5992

22.

0.8387

23.

0.0872

24.

0.2419

25.

0.1139

26.

0.7408

What angle measure has each approximate cosine value? Round each answer to the nearest tenth of a degree. 27.

0.3746

28.

0.8988

29.

0.0087

30.

0.9885

31.

0.5490

32.

0.0523

76

Practice Workbook

Algebra 1

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Practice 12.8 Introduction to Matrices

Perform the following matrix operations. If a solution is not possible, explain why. 1.

3.

5.

ⴚ4 10 ⴚ5 ⴚ31 ⴚ13 ⴚ8 ⴚ 4 ⴚ17 17 20 16 ⴚ23

2.3 ⴚ5.2 ⴚ4.6 ⴚ1.9 ⴙ ⴚ3 ⴚ 0.2 6 ⴚ1.7 10

1 3 7. 3 ⴚ4

1 4 1 2

2 ⴙ 31 2

2.

4.

6.

1.2 冤 ⴚ0.9

8.

ⴚ1 1 4

4 7 15 8 2 ⴙ 3 13 17 1 5

38 55 ⴚ14 ⴚ7 ⴚ33 ⴚ5 44 2 ⴚ28 ⴙ ⴚ13 40 50 9 ⴚ9 26 16 ⴚ21 ⴚ6

3.4 7 ⴚ2 1.5 ⴙ 6 7 9.2 ⴚ1.3

2 3.1 ⴚ [6 1.8 19] 4.5

Matrices M and N are equal. Find the values of w, x, y, and z. 9.

Mⴝ

10.

Mⴝ

Algebra 1

16 24 3x , Nⴝ 1.8 18 6z

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Practice 13.1 Theoretical Probability An integer from 1 to 40 is drawn at random. Find the probability that it is 1.

odd.

2.

even.

3.

a multiple of 4.

4.

prime.

5.

odd AND a multiple of 5.

6.

odd OR a multiple of 5.

The letters in the word constitution are written on index cards and placed in a brown bag.

7.

A letter is selected at random. Find the probability that it is a vowel.

8.

What is the probability of selecting the letter T?

9.

What is the probability of selecting a consonant?

10.

Find the probability that the name of a state chosen at random begins with the letter B.

North Dakota

Nebraska New Hampshire New York New Jersey North Carolina

Liked drink

Disliked drink

Total

Boys

16

14

30

Girls

19

10

29

Total

35

24

59

A student who was surveyed is chosen at random. What is the theoretical probability that the student 12.

is a girl?

13.

liked the lunch?

14.

is a girl AND liked the lunch?

15.

is a girl OR liked the lunch?

78

Practice Workbook

Algebra 1

11.

Find the probability that the name of a state chosen at random begins with the letter N.

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CLASS

DATE

Practice 13.2 Counting the Elements of Sets List the integers from 1 to 10 inclusive that are 1.

odd.

2.

multiples of 2.

3.

odd AND multiples of 2.

4.

odd OR multiples of 2.

List the integers from 1 to 20 inclusive that are 5.

multiples of 4.

7.

multiples of 4 AND multiples of 3.

8.

multiples of 4 OR multiples of 3.

9.

Draw a Venn diagram that shows the multiples of 3 and the multiples of 5 from 1 to 30 inclusive.

6.

10.

Which numbers are multiples of 3 AND of 5?

11.

How is this shown in the Venn diagram?

multiples of 3.

A marketing representative gave supermarket customers a sample taste of a new soft drink. The results are shown in the table. Liked drink

Disliked drink

Total

Men

16

14

30

Women

19

10

29

Total

35

24

59

12.

How many customers are men?

13.

How many customers disliked the new soft drink?

14.

How many customers are men AND disliked the soft drink?

15.

How many customers are men OR disliked the soft drink?

Algebra 1

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Practice 13.3 The Fundamental Counting Principle Jerry has 4 T-shirts, 2 pairs of jeans, and 3 pairs of shoes that can be worn together in any combination. 1.

How many ways are there for Jerry to choose an outfit?

2.

How many outfits can include a blue T-shirt, assuming that it is one of the 4 T-shirts?

3.

How many outfits can include a pair of black jeans, assuming that it is one of the 2 pairs of jeans?

4.

How many outfits can include a pair of brown shoes, assuming that it is one of the 3 pairs of shoes?

How many ways are there to arrange the letters in each of the following words?

cat

6.

math

7.

sport

8.

problem

9.

The Camachos are decorating their kitchen. There are 7 different wallpaper patterns from which to choose. There are 5 borders that coordinate with each wallpaper pattern. How many combinations are possible?

10.

Members of the pep club are selling carnations. They are selling red, pink, or white carnations in packages of 2, 4, or 6. If all carnations in a package must be the same color, how many choices are offered?

11.

A popular car model comes in 5 different colors, with a standard or automatic transmission, and with or without a sports package. How many different types of cars are available in this model?

12.

How many ways are there to name the

A

B

C

given line? 13.

80

Name all of these ways.

Practice Workbook

Algebra 1

5.

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DATE

Practice 13.4 Independent Events Ten cards numbered from 1 to 10 are placed in a bag. One card is drawn and replaced. Then a second card is drawn. Find the probability that 1.

both are even.

2.

both are odd.

3.

both are prime.

4.

the first one is odd AND the second is even.

5.

the first one is even AND the second is odd.

6.

the first one is prime AND the second is even.

7.

the first one is prime AND the second is odd.

8.

the first one is even AND the second is prime.

9.

the first one is odd AND the second is prime.

10.

neither number is prime.

One number is selected from the list 2, 4, 6, and 8. Another is selected from the list 6, 7, and 8. Find the probability that 11.

both are odd.

12.

they are the same.

13.

their sum is odd.

14.

the number from the second list is greater than the number from the first list.

Use the area model at right to find the probability that 15.

B occurs.

16.

D occurs.

17.

B occurs OR D occurs.

Algebra 1

A

B

C

D

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Practice 13.5 Simulations Suppose that the Denver Nuggets and the New York Knicks are in the basketball championship finals and that each team has an equal chance of winning a given game. The finals end when one team wins 4 out of 7 games. Simulate the finals for at least 10 trials. 1.

Describe the three steps of the simulation.

2.

Complete the chart below to give game-by-game results for each of the 10 trials. Use random numbers generated by a coin toss or by technology. Use W for a Knicks’ win and L for a Knicks’ loss. Trial

1

2

3

4

5

6

7

5 6 7 8 9 10

Use your results from the basketball championship simulation to find the experimental probability of each of the following: 3.

The Nuggets win the finals.

4.

The Knicks win the finals in 4 games.

5.

The finals last 7 games.

6.

A team wins the finals after losing the first 2 games.

82

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Practice 14.1 Graphing Functions and Relations Are the relations in Exercises 1– 4 functions? Why or why not? 1.

{(3, 5), (1, 0), (9, 5), (2, 0)}

2.

{(ⴚ1, ⴚ2), (3, 5), (1, 2), (ⴚ1, 7)} y

3.

y

4.

x

O x

O

Find the domain and range of each function. 5.

{(3, 6), (11, 8), (2, 6), (1, 0)}

6.

{(ⴚ2, 5), (ⴚ5, 5), (3, 5), (0, 5)}

7.

{(ⴚ4, 3), (2, 0), (3, 1), (1, 1)}

Let f (x) ⴝ 6x. Evaluate. 8.

f(2)

9.

f(ⴚ1)

10.

f(0.5)

Evaluate each function given x = 3. 11.

f(x) ⴝ x 2

12.

g(x) ⴝ ⴚ2x

13.

f(x) ⴝ x

14.

h(x) ⴝ ⴚ4ⱍxⱍ

15.

k(x) ⴝ 2x 2 ⴚ 1

16.

g(x) ⴝ x 2 ⴚ 3

1

For each function, identify the independent variable. Then describe the domain and range. 17.

f(x) ⴝ x ⴚ 3

Algebra 1

18.

f(x) ⴝ (x ⴙ 1)2

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Practice 14.2 Translations Identify the parent function. State what type of transformation is applied to the graph of each function. Then draw a carefully labeled graph. (Hint: Remember to plot a few points to help you see what happens to the parent function.) 1.

y ⴝ 0.5x 2

2.

y ⴝ ⴚ3ⱍxⱍ

y

3

yⴝx

y

y

6

6

6

4

4

4

2

2

2

–4 –2 O –2

4.

3.

2

4

x

– 4 –2 O –2

2

4

x

–4 –2 O –2

–4

–4

–4

–6

–6

–6

y ⴝ 2x ⴚ 2

5.

y

y ⴝ ⱍx ⴚ 1ⱍ 6

4

4

2

2 4

x

– 4 –2 O –2

–4

–4

–6

–6

x

y ⴝ INT(x ⴙ 2)

2

4

x

x

Consider the parent function f (x) ⴝ 2x. Note that f (1) ⴝ 2, so the point (1, 2) is on the graph. State how the graph of the parent function is translated to obtain the graph of each function below. 7.

f(x) ⴝ 2 x ⴚ 1

8.

f(x) ⴝ 2 x ⴙ 4

9.

f(x) ⴝ 2 (x ⴚ1)

10.

f(x) ⴝ 2 (x ⴙ 2)

The point (2, 4) is on the graph of f (x). Find the new coordinates of the point after each transformation has been applied to the function. 11.

vertical translation by 2

12.

horizontal translation by 3

13.

horizontal translation by ⴚ4

14.

vertical translation by ⴚ5

84

Practice Workbook

Algebra 1

2

4

y

y

6

–4 –2 O –2

6.

2

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DATE

Practice 14.3 Stretches Given the function y ⴝ 2ⱍx ⱍ, y

1.

identify the parent function.

2.

sketch the graphs of the function and the parent function on the axes at the right.

3.

6 4 2

explain how the graph of the parent function was changed

–4 –2 O –2

by the 2.

2

4

2

4

x

–4 –6

3

Given the function y ⴝ x , 4. 5.

6.

y

identify the parent function.

6

sketch the graphs of the function and the parent function on the axes at the right.

4 2

explain how the graph of the parent function was changed

–4 –2 O –2

by the 3.

x

–4

Tell whether each function is a stretch of the parent function. 7.

x2

yⴝ 4

8.

8

yⴝx

9.

1

y ⴝ ⱍxⱍ ⴚ 2

Write an equation for each graph. 10.

11.

(–2, 6)

(1, 3) (1, 3)

( 6, ) 1 2

(–3, –1)

(–

Algebra 1

1 2

)

, –6

Practice Workbook

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Practice 14.4 Reflections Graph each function. 1.

y ⴝ ⴚ2x 2

2. y

ⱍxⱍ yⴝⴚ 2

3. y

ⴚ3

yⴝ x

y

6

6

6

4

4

4

2

2

2

–4 –2 O –2

2

4

x

– 4 –2 O –2

2

4

x

–4 –2 O –2

–4

–4

–4

–6

–6

–6

2

4

x

State whether the following functions have graphs that are vertical reflections of the parent function: 4.

y ⴝ x2 ⴚ 1

5.

y ⴝ ⴚ2ⱍxⱍ

6.

y ⴝ ⴚINT(x)

1 ⴚx ⴚ 2

8.

y ⴝ ⴚx

9.

yⴝxⴚ1

7.y ⴝ

10.

y ⴝ (ⴚx) ⴚ 1

13.

yⴝ ⴚx ⴚ2

1

11.

y ⴝ 2ⱍⴚx ⴙ 1ⱍ

12.

y ⴝ INT(x ⴚ 1)

14.

y ⴝ (ⴚx ⴚ 1)2

15.

y ⴝ ⱍx ⴚ 1ⱍ

State whether the following functions have graphs that are horizontal reflections of the parent function:

For Exercises 16–17, find f (2) and use this information to tell which kind of reflection (horizontal or vertical) is applied to the function y ⴝ 3x ⴙ 2. 16.

f(x) ⴝ ⴚ(3x ⴙ 2)

17.

f(x) ⴝ 3(ⴚx) ⴙ 2

For Exercises 18–19, find f (3) and use this information to tell which kind of reflection (horizontal or vertical) is applied to the function y ⴝ (x ⴚ 1)2. 18.

86

f(x) ⴝ ⴚ(x ⴚ 1) 2

Practice Workbook

19.

f(x) ⴝ (ⴚx ⴚ 1)2

Algebra 1

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Practice 14.5 Combining Transformations Sketch the graph of each function. 1.

f(x) ⴝ INT(x ⴚ 2)

2.

g(x) ⴝ ⴚx ⴙ 1

y

y

6

6

4

4

4

2

2

2

2

4

x

–4 –2 O –2

2

4

x

–4 –2 O –2

–4

–4

–4

–6

–6

–6

p(x) ⴝ 2 x ⴚ 1

5.

k(x) ⴝ (x ⴚ 2)2

y

6.

y

4

4

4

2

2

2

x

–4 –2 O –2

2

4

x

y

6

4

4

1

6

2

2

h(x) ⴝ x ⴚ 1

6

h(x) ⴝ ⱍx ⴚ 4ⱍ

6

– 4 –2 O –2

4.

3.

y

2

4

O

x

–4 –2

x

–2

–4

–4

–4

–6

–6

–6

Explain what happens to the point (4, 8) on the graph of y ⴝ 2x when the transformations are applied in the order given. (Hint: If you are not sure, draw a sketch.) 7.

a vertical stretch of 2, followed by a vertical translation of 2

8.

a vertical translation of 2, followed by a vertical stretch of 2

9.

a horizontal translation of 5, followed by a vertical stretch of 3

10.

a vertical stretch of 3, followed by a horizontal translation of ⴚ5

Algebra 1

Practice Workbook

87