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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Commutative Property of Addition
)
Property of Addition
ⴝ 68 ⴙ ⴝ 2.
35(3 ⴙ 5) ⴝ 35 ⴢ ⴝ
ⴙ
ⴢ5
Property
ⴙ
ⴝ
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1.
w
p
u
f
2
1
h
1
1
Algebra 1
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Practice 3.4 Solving Multistep Equations
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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.
9 21 12 ⴝ 28 Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
17.
Find 45% of 90.
Find each answer. 19.
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.
Neither coin shows heads.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7.
c.
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
27
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CLASS
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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CLASS
DATE
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
–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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CLASS
DATE
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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DATE
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
58ⴚ2
2.
ⴚ1 ⴚ 1 0
3.
ⴚ1 5 ⴚ 6
4.
ⴚ1 ⴙ 2 3
5.
ⴚ4 ⴚ 2 4
6.
86ⴚ4
7.
7ⴚ91
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
x
22.
Practice Workbook
Algebra 1
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CLASS
DATE
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Solve each inequality. 18.
xⴙ34
19.
m ⴚ 10 50
20.
Tⴚ58
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.
xⴙ38ⴚx
33.
x ⴚ 1 ⴚ5
34.
ⴚ5x 2x ⴚ 6
35.
7ⴚx3
36.
16 ⴙ 2 9
37.
14 4 ⴚ 3
Algebra 1
m
j
Practice Workbook
33
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DATE
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.
7x8
–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
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11.
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CLASS
DATE
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Practice Workbook
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
9.
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CLASS
DATE
Practice 7.1 Graphing Systems of Equations Solve by graphing. Round solutions to the nearest tenth if necessary. Check algebraically. 1.
再
xⴙyⴝ4 2x ⴚ y ⴝ 5
2.
再
xⴙyⴝ0 3x ⴚ 2y ⴝ 10
y
再
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.
再
3x ⴙ 2y ⴝ 9 4x ⴚ y ⴝ 1
y Copyright © by Holt, Rinehart and Winston. All rights reserved.
再
6
– 6 –4 –2 O –2
4.
3.
6.
再
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.
再
yⴝxⴙ3 y ⴝ 2x ⴚ 2
8.
再
y ⴝ 3x ⴙ 1 y ⴝ ⴚx ⴙ 5
9.
再
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.
再
yⴝxⴙ8 y ⴝ 4x ⴚ 2
Algebra 1
11.
再
xⴙyⴝ4 xⴚyⴝ8
12.
再
4x ⴙ y ⴝ ⴚ2 y ⴝ ⴚx ⴙ 4
Practice Workbook
37
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CLASS
DATE
Practice 7.2 The Substitution Method Solve and check each system by using the substitution method. 1.
3.
5.
7.
9.
11.
13.
15.
再 再 再 再 再 再 再 再
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.
再 再 再 再 再 再 再 再
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.
再
y ⴝ 2x 2x ⴙ y ⴝ 7
18.
再
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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CLASS
DATE
Practice 7.3 The Elimination Method Solve each system of equations by elimination, and check your solutions. 1.
3.
5.
7.
9.
11.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
13.
15.
再 再 再 再 再 再 再 再
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.
再 再 再 再 再 再 再 再
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.
再 再
再 再
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.
再 再
再 再
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
39
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CLASS
DATE
Practice 7.4 Consistent and Inconsistent Systems Solve each system algebraically. 1.
3.
5.
7.
9.
再 再 再 再 再
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.
再 再 再 再 再
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
再 再 再 再 再 再 再
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
再 再 再 再 再 再 再
3x ⴚ y ⴝ 3 y ⴝ 3x ⴚ 9
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11.
再 再 再 再 再 再
yxⴙ4 y2
2.
y3 x ⴚ2
4.
yxⴚ3 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.
再 再 再 再 再 再
xⴙy0 y ⴚ1 yxⴚ2 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
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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
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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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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 ?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Perform each computation. Write your answers in scientific notation. 25.
(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
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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.
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Algebra 1
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–4 –2 O –2
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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
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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
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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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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Practice 9.2 Modeling Polynomial Multiplication
+
–
–
–
+
+
–
–
–
1.
+
+
Write the factors and the product for each model.
+
+ + +
+
+
+ + +
+
+
+ + +
2.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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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
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Practice Workbook
Algebra 1
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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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
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Practice Workbook
Algebra 1
Copyright © by Holt, Rinehart and Winston. All rights reserved.
–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.
兹1
2.
兹81
3.
5.
兹30
6.
兹18
7.
兹16 兹110
4.
兹225
8.
兹55
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
再 再
yⴝ4 y ⴝ x2
28.
y ⴝ 7x ⴚ 35 y ⴝ x 2 ⴚ 3x ⴚ 10
30.
Algebra 1
再 再
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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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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?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Practice Workbook
Algebra 1
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
ⴢ
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Practice Workbook
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
兹144
2.
兹72
3.
兹288
4.
兹4000
5.
兹3264
6.
兹8775
Express each radical expression in simplest radical form. 7.
兹8 兹14
8.
9.
兹12 兹6
10.
兹72 兹6
兹162 兹3
12.
兹500 兹50
11.
兹3 兹27
Simplify each radical expression. Assume that all variables are non-negative and that all denominators are nonzero.
兹m 6n
14.
兹a 8 b 6
15.
兹
16.
兹
x3 y6
Copyright © by Holt, Rinehart and Winston. All rights reserved.
13.
x5 y9
If possible, perform each indicated operation and simplify your answer. 17.
兹12 ⴙ 3兹3
18.
3兹27 ⴚ 5兹3
19.
兹1 ⴙ 兹25 兹2
20.
(5 ⴙ 兹5) ⴙ (2 ⴚ 兹3)
Simplify each radical expression.
(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.
兹x ⴚ 7 ⴝ 3
2.
兹7 ⴚ x ⴝ 3
3.
兹ⴚx ⴚ 7 ⴝ 3
4.
兹x ⴚ 3 ⴝ x
5.
兹2x ⴙ 3 ⴝ 兹x ⴙ 7
6.
兹2x ⴙ 3 ⴝ 5
7.
兹5 ⴙ x ⴝ 3
8.
兹11 ⴚ 10x ⴝ 9
9.
兹3x ⴚ 2 ⴝ ⴚ1
10.
兹x ⴚ 2 ⴝ 3
兹2x ⴙ 1 ⴝ x ⴚ 1
12.
兹2x ⴙ 15 ⴝ x
11.
Use graphing technology or sketch the graphs on your graph paper to solve each equation, if possible.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
13.
4兹x ⴝ ⴚx ⴚ 3
14.
兹x ⴙ 0.1 ⴝ 1.0
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.
兹x ⴝ ⴚ49
19.
x 2 ⴙ 169 ⴝ 0
20.
兹x ⴙ 20 ⴝ 5
21.
兹2x ⴝ 50
22.
兹x ⴚ 1 ⴙ 6 ⴝ 2
23.
兹x ⴙ 4 ⴝ 1
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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?
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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)
Practice Workbook
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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.
radius of 9
2.
radius of 4
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Perform the following matrix operations. If a solution is not possible, explain why. 1.
冤 12 69 冥 ⴙ 冤 34 110 冥
3.
冤
5.
冤 冥 冤 冥 冤 冥
冥 冤
ⴚ4 10 ⴚ5 ⴚ31 ⴚ13 ⴚ8 ⴚ 4 ⴚ17 17 20 16 ⴚ23
冥
2.3 ⴚ5.2 ⴚ4.6 ⴚ1.9 ⴙ ⴚ3 ⴚ 0.2 6 ⴚ1.7 10
冤 冥 冤 冥
1 3 7. 3 ⴚ4
1 4 1 2
2 ⴙ 31 2
2.
冤 90
4.
冤
6.
1.2 冤 ⴚ0.9
8.
冤 冥
ⴚ1 1 4
冥 冤
4 7 15 8 2 ⴙ 3 13 17 1 5
冥
冥 冤
38 55 ⴚ14 ⴚ7 ⴚ33 ⴚ5 44 2 ⴚ28 ⴙ ⴚ13 40 50 9 ⴚ9 26 16 ⴚ21 ⴚ6
冥 冤
3.4 7 ⴚ2 1.5 ⴙ 6 7 9.2 ⴚ1.3
冥
冥
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
冤 wy ⴚⴙ 17 2x5z 冥, N ⴝ 冤 1218 2635 冥
10.
Mⴝ
冤 8w 2y
Algebra 1
冥
冤
16 24 3x , Nⴝ 1.8 18 6z
冥
Practice Workbook
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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
Nevada New Mexico
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11.
Find the probability that the name of a state chosen at random begins with the letter N.
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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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5.
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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.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Practice Workbook
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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
1 2 3 4 Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Practice Workbook
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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
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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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
Back Print NAME
CLASS
DATE
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
– 4 –2 O –2 Copyright © by Holt, Rinehart and Winston. All rights reserved.
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
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