Chapter 1, {

Chapter 1,
continued
4. G; 34 1 3x 5 112
Check:
5
1 5{ 0 291 2}
{21 2}
11 2
11 2
5
{
45
{
0}
11 45
11
45
} 5 }
{
45
0 2}
45
7
2}
7
10
35
}1}
7
7
{
4he solution is2}
Reject }
because it is an
11
7
11
5
}Þ
5
extraneous solution.
or
p < 29
or
p17>2
p > 25
{2q 2 3{a3
15.95
5. C; } ø 5.4
2.95
If you rent at least six videos, you will save money.
6. H; d 5 depth (ft)
0 5 12 2 1.5t
1.5t 5 12
t58
The pool will be empty in 8 hours.
0a2qa6
7. C; Choice A: sides 2, 4, 9 l 2 1 4 > 9 0aqa3
Choice B: sides 3, 6, 9 l 3 1 6 > 9 12. {5 2 r{q4
Choice C: sides 5, 10, 9 l 5 1 10 > 9 5 2 ra24 or
5 2 rq4
2ra29 or
rq9
5 1 9 > 10 2rq21
or
ra1
Final
Final a0.8 + Current 1 0.2 + exam
grade
grade
score
85 a0.8 + 83
1 0.2 +
x
85a66.4 1 0.2x
18.6a0.2x
10 1 9 > 5 8. Let x 5 hours doing office work.
Let y 5 hours doing outside work.
Equation 1: 8x 1 9y 5 399
Equation 2: x 1 y 5 45 l x 5 45 2 y
Substitute for x in Equation 1:
8(45 2 y) 1 9y 5 399
y 5 39
93ax
You need to get a final exam score of 93 or better.
14. Acceptable weights for the container:
{w 2 1.5{a0.025
20.025 a w 2 1.5 a 0.025
1.475 a w a 1.525
Mixed Review for TEKS (p. 59)
1. B; Let c 5 gallons in city.
Let h 5 gallons on highway.
Equation 1: 60c 1 51h 5 675
Equation 2: c 1 h 5 12 l c 5 12 2 h
Substitute for c in Equation 1:
60(12 2 h) 1 51h 5 675
29h 5 245
h55
Five gallons of gas were used on the highway.
You worked 39 hours outside that week.
1
9. a 1 b 1 } (a 1 b) 5 72
2
3
2
3
2
} a 1 } b 5 72
3
2
} (a 1 b) 5 72
a 1 b 5 48
1
1
medium 5 }2 (a 1 b) 5 }2 (48) 5 24
The second longest piece is 24 inches long.
Chapter 1 Review (pp. 61– 64)
1. In a power, the exponent represents the number of times
the base is used as a factor.
2. If substituting a number for a variable in an equation
results in a true statement, then the number is a solution
of the equation.
3. An extraneous solution is an apparent solution that
2. J;
{w 2 3.5{ a 0.25
3.5 2 0.25awa3.5 1 0.25
3.25awa3.75
3. A; 2369aTa2297
38
45
The kicker made 26 field goals.
d 5 12 2 1.5t
p 1 7 < 22
23a2q 2 3a3
13.
7
x 5 26
t 5 time (h)
10. {p 1 7{ > 2
11.
3x 5 78
5
Algebra 2
Worked-Out Solution Key
must be rejected because it does not satisfy the
original equation.
4. Like terms: 3x 2 and 2x 2; 40 and 27
1
5. Sample answer: 5x 1 10 and 101 }
2x 1 1
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
10
55
2}
1}
11
11
5
{21 }7 2 1 5{ 0 291 }7 2
Chapter 1,
continued
6. The procedures are similar when adding and subtracting,
Check:
and when multiplying and dividing with positives. The
procedures are different when multiplying and dividing
with negatives; the inequality symbol reverses, but this
process has no effect on an equation.
7m 1 38 5 25m 2 16
71 2}2 21 38 0 251 2}2 22 16
9
9
45
63
7. Inverse property of multiplication
1 38 0 }
2}
2 2 16
2
8. Identity property of addition
}5}
10. 25x 1 14 2 17 2 6x 5 25x 2 6x 1 14 2 17
21. 48j 1 25 5 12j 2 11
5 19x 2 3
36j 5 236
5 26y 1 3x
j 5 21
12. 6(n 2 2) 2 8n 1 40 5 6n 2 12 2 8n 1 40
22. 8(2n 2 5) 5 3(6n 2 2)
5 22n 1 28
16n 2 40 5 18n 2 6
13. 5(2b 1 3) 1 8(b 2 6) 5 10b 1 15 1 8b 2 48
240 5 2n 2 6
5 10b 1 8b 1 15 2 48
234 5 2n
5 18b 2 33
217 5 n
14. 3g 1 9g 2 2 12g 2 1 g 5 9g 2 2 12g 2 1 3g 1 g
Check:
5 23g 2 1 4g
8(2n 2 5) 5 3(6n 2 2)
15. 7t 4 1 7t 2 2 2t 2 2 9t 4 5 7t 4 2 9t 4 1 7t 2 2 2t 2
8(2(217) 2 5) 0 3(6(217) 2 2)
8(234 2 5) 0 3(2102 2 2)
5 22t 4 1 5t 2
1
+
5+
+
0.40
Number of
1 Base charge
miles
x
1
2.50
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
An expression for the cost of the ride is 2x 1 2.5.
17. 24x 1 16 5 12
Check:
1
241 2}6 21 16 0 12
1
x 5 2}6
24 1 16 0 12
12 5 12 Check:
26y 5 224
26y 1 15 5 29
26(4) 1 15 0 29
224 1 15 0 29
y54
29 5 29 19. 4(q 2 5) 5 16
Check:
4q 2 20 5 16
4(q 2 5) 5 16
4(9 2 5) 0 16
4q 5 36
4(4) 0 16
q59
20.
16 5 16 7m 1 38 5 25m 2 16
12m 1 38 5 216
12m 5 254
9
m 5 2}2
8(239) 0 3(2104)
2312 5 2312 Percent
Total
Price of
Price of
+
1
5
sales tax
cost
jacket
jacket
0.06
+
x
1
x
5 79.49
23.
24x 1 16 5 12
24x 5 24
18. 26y 1 15 5 29
48j 1 25 5 12j 2 11
48(21) 1 225 0 12(21) 2 11
248 1 25 0 212 2 11
223 5 223 5 6n 2 8n 2 12 1 40
5 + Cost per }5 mile
Check:
36j 1 25 5 211
11. 6y 1 12x 2 12y 2 9x 5 6y 2 12y 1 12x 2 9x
16.
13
2
13
2
9. Distributive property
1.06x 5 79.49
x 5 74.99
The cost before taxes is $74.99.
24.
Cost
per
pound
1
Cost
Pounds
+ of green 1 per
pound
peppers
+
x
1
4
Pounds
Total
+ of orange 5 cost
peppers
+
(3 2 x)
5 4.50
x 14(3 2 x) 5 4.50
x 1 12 2 4x 5 4.50
23x 5 27.50
x 5 2.5
You bought 2.5 pounds of green peppers and
3 2 2.5 5 0.5 pound of orange peppers.
25. 10x 1 y 5 7
y 5 7 2 10x
When x 5 3: y 5 7 2 10(3)
y 5 7 2 30
y 5 223
Algebra 2
Worked-Out Solution Key
39
Chapter 1,
continued
26. 8y 2 3x 5 18
s 2 2:r 2 5 2:rh
8y 5 18 1 3x
3
s 2 2:r 2
2:r
}5h
9
3
9
3
When r 5 5 cm and s 5 400 cm 2:
When x 5 2: y 5 }4 1 }8(2)
400 2 2:(5) 2
y 5 }4 1 }4
h 5 }}
2:(5)
y53
h5}
10 :
400 2 50 :
27. xy 2 6y 5 215
40
y(x 2 6) 5 215
h5}
25
:
15
h ø 7.73
y 5 2}
x26
The height h is about 7.73 centimeters.
15
When x 5 5: y 5 2}
526
32.
y 5 15
4x 5 6y 1 9
1
58}3 5 r
4x 2 9 5 6y
2
3
d 5 rt
175 5 r(3)
1
The average speed of the train is 58}3 miles per hour.
3
2
}x 2 } 5 y
3
2
When x 5 9: y 5 }3 (9) 2 }2
3
y 5 6 2 }2
9
y 5 }2
33.
Base
fee
1
180
1
Mileage
Miles
+
rate
over 150
0.25
Total
cost
5
+ (x 2 150) 5 293
180 1 0.25x 2 37.5 5 293
0.25x 1 142.5 5 293
29. 5x 2 2y 5 10
0.25x 5 150.5
5x 5 10 1 2y
x 5 602
5x 2 10 5 2y
Your family drove 602 miles while on vacation.
5
2
34. 2x 2 3 < 21
}x 2 5 5 y
5
When x 5 26: y 5 }2 (26) 2 5
y 5 215 2 5
y 5 220
30. x 2 3xy 5 1
2x < 2
x<1
4
24
22
0
2
0
2
4
6
28
26
24
22
4
35. 7 2 3xq211
23xq218
xa6
x 5 1 1 3xy
x 2 1 5 3xy
8
36. 15x 1 8 > 9x 2 22
x21
}5y
3x
6x 1 8 > 222
25 2 1
When x 5 25: y 5 }
3(25)
26
y5}
215
2
5
y5}
6x > 230
x > 25
0
37. 13x 1 24a16 2 3x
16x 1 24a16
16xa28
1
xa2}2
40
Algebra 2
Worked-Out Solution Key
22
21
0
1
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
9
y 5 }4 1 }8x
28.
s 5 2:rh 1 2:r 2
31.
Chapter 1,
38.
continued
25 < 10 2 x < 5
Check:
25 2 10 < 10 2 x 2 10 < 5 2 10
{81 2}5 21 1{0 31 2}5 2
1
215 < 2x < 25
8
15 > x > 5
5 < x < 15
5
0
8
12
0 2}
1}
11
11 {
11
{2}
{2}35 {0 2}35
0 2}
11
11 {
{}
} Þ 2}
} Þ 2}
1
40. 2x 1 3x > 10
0
22
2x 1 10 > 3x
5x > 10
2
4
3x 1 10 > 2x
10 > x
x>2
x < 10
xa4
3
11
or
x 2 5q1
or
xq6
2
4
6
8
45. {5 2 2y{ > 7
or 3p 1 2 5 27
or
5 2 2y < 27
3p 5 29
or
or
5 2 2y > 7
22y < 212
or
22y > 2
y>6
or
p 5 23
Check:
0
24
5
{31 }3 2 1 2{ 0 7
{3(23) 1 2{ 0 7
{5 1 2{ 0 7
{7{ 0 7
{29 1 2{ 0 7
{27{ 0 7
757
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
3
11
1
x 2 5a21
0
757
9q 2 5 5 2q
or
7q 2 5 5 0
or
11q 2 5 5 0
7q 5 5
or
11q 5 5
5
9q 2 5 5 22q
{
6z 1 5q225
6za20
and
6zq230
10
za}
3
10
25 a z a }
3
and
zq25
33
22
2
{
35
10
0}
2}
11 { 11
11
{}
55
10
10
10
0}
11 { 11
{2}
10
10
10
7
10
11
}5}
10
11
}5}
43. {8r 1 1{ 5 3r
or
5r 1 1 5 0
or
5r 5 21
1
r 5 2}5
or
or
2
4
25.5 a C a 26.5
So, the acceptable circumference of a volleyball should
be between 25.5 inches and 26.5 inches.
Chapter 1 Test (p. 65)
} 1
7
1. 22, 2}, 6.5, Ï 30 , }
4
3
7
1
3
24
23 22 21
8r 1 1 5 3r
0
{C 2 26{a0.5
{}7 2}7 { 0 }7
{}7 { 0 }7
and
47. C 5 Circumference
5
5
91 }
2 5 0 21 }
11 2
11 2
45
1
2
6z 1 5a25
24
Check:
{
8
1
q5}
11
5
5
91 }7 22 5 0 21 }7 2
4
25
5
or
q 5 }7
y < 21
46. {6z 1 5{a25
42. {9q 2 5{ 5 2q
10
7
3
x > 210
41. {3p 1 2{ 5 7
45
3
44. {x 2 5{q1
x 1 10 > 0
2 < x < 10
{
3
no solution.
24
5
p 5 }3
11
Both 2}5 and 2}
are extraneous solutions. There is
11
29a3xa9
3p 5 5
3
5
3
5
2axa
3p 1 2 5 7
8
1
3
16
39. 28a3x 1 1a10
5
1
{2}5 1 }5 {0 2}5
15
4
1 1 0 31 2}
11 2
11 2
{81 2}
{
1
8r 1 1 5 23r
11r 1 1 5 0
11r 5 21
1
r 5 2}
11
0
30 .5
6
1
2
3
4
5
6
7
}
3
9
2. }, 0.8, 25.5, 2Ï 10 , 2}
4
2
25.5
2 10
3
24
26 25 24 23 22 21
9
2
0.8
0
1
2
3
4
5
Algebra 2
Worked-Out Solution Key
41
3.
continued
5 1 (x 2 5) 5 x
5 1 (x 1 (25)) 5 x
Definition of subtraction
5 1 ((25) 1 x) 5 x
Commutative property
of addition
(5 1 (25)) 1 x 5 x
01x5x
x5x
4.
Given
14. 6k 1 7 5 4 1 12k
1
2
10 5 10 }5k
15. 2t 2 2 5 9(t 2 8)
Identity property of addition
2t 2 2 5 9t 2 72
22 5 10t 2 72
70 5 10t
75t
16. 12x 2 28y 5 40
228y 5 40 2 12x
(3d 1 7) 2 d 1 5 5 2d 1 12 Given
10
11.
12.
13.
42
When x 5 5 and y 5 23:
Algebra 2
Worked-Out Solution Key
10
3
10
18
1}
y 5 2}
7
7
8
y 5 }7
17. x 1 4y 5 12
4y 5 12 2 x
1
y 5 3 2 }4x
1
When x 5 2: y 5 3 2 }4 (2)
1
y 5 3 2 }2
7. 5n 1 10 2 8n 1 6 5 (5n 2 8n) 1 (10 1 6)
10.
3
1 }7(6)
When x 5 6: y 5 2}
7
2d 1 12 5 2d 1 12 Combine like terms.
5 23n 1 16
10m 2 4(3m 1 7) 1 6m 5 10m 2 12m 2 28 1 6m
5 (10m 2 12m 1 6m) 2 28
5 4m 2 28
2
2
11 1 q 2 3q 1 18q 2 2
5 (23q 2 1 18q 2) 1 q 1 (11 2 2)
5 15q 2 1 q 1 9
9t 2 1 14 2 17t 1 6t 2 8t 2
5 (9t 2 2 8t 2) 1 (217t 1 6t) 1 14
5 t 2 2 11t 1 14
5(x 2 3y) 1 2(4y 2 x) 5 5x 2 15y 1 8y 2 2x
5 (5x 2 2x) 1 (215y 1 8y)
5 3x 2 7y
5(2u 1 3w) 2 2(5u 2 7w)
5 10u 1 15w 2 10u 1 14w
5 (10u 2 10u) 1 (15w 1 14w)
5 0 1 29w
5 29w
5n 1 11 5 29
Check: 5(24) 1 11 0 29
5n 5 220
220 1 11 0 29
n 5 24
29 5 29 Check:
2(7) 2 2 0 9(7 2 8)
29 0 9(21)
29 5 29 1 }7x
y 52}
7
(3d 1 (2d)) 1 (7 1 5) 5 2d 1 12 Associative property
of addition
4x 2 6y 5 4(5) 2 6(23)
5 20 1 18
5 38
6. When x 5 2 and y 5 4:
3x2 2 9y 5 3(2)2 2 9(4)
5 3(4) 2 36
5 12 2 36
5 224
1
3170416
3 5 6k
3d 1 ((2d) 1 7) 1 5 5 2d 1 12 Commutative
property of addition
9.
1
Inverse property of addition
3d 1 (7 1 (2d)) 1 5 5 2d 1 12 Associative property
of addition
8.
61 }2 2 1 7 0 4 1 121 }2 2
7 5 4 1 6k
Associative property
of addition
(3d 1 7) 1 (2d) 1 5 5 2d 1 12 Definition of
subtraction
5.
Check:
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Chapter 1,
5
y 5 }2
18. 15y 1 2xy 5 230
y (15 1 2x) 5 230
30
y 5 2}
15 1 2x
30
When x 5 5: y 5 2}
15 1 2(5)
30
y 5 2}
25
6
y 5 2}5
19. 25x 2 6 < 19
25x < 25
x > 25
20.
x 1 22q23x 2 10
28
26
24
0
22
4x 1 22q210
4xq232
xq28
28
26
24
22
0
Chapter 1,
21.
continued
26. {3y 1 4{ > 2
5 < 2x 1 3a11
5 2 3 < 2x 1 3 2 3a11 2 3
3y 1 4 < 22
2 < 2xa8
1 < xa4
0
22
2
4
or
3y < 26
or
y < 22
or
6
22. {3d 2 4{ 5 14
or
3d 2 45 14
3d 5 210
or
3d 5 18
or
d56
10
d 5 2}
3
24
27.
10
3 2}
24
3
{ 0 14
{3(6) 2 4{ 0 14
{210 2 4{ 0 14
{214{ 0 14
{18 2 4{ 0 14
{14{ 0 14
14 5 14 or
3f 1 3 5 24
0
21
2
{}3 z 2 5{ < 2
25 < }3 z 2 5 < 5
2
0 < }3 z < 10
14 5 14 0 < z < 15
28.
35f14
or
22
2
f 1 3 5 2(2f 1 4) or f 1 3 5 2f 1 4
f 1 3 5 22f 2 4
23
25 1 5 < }3 z 2 5 1 5 < 5 1 5
23. {f 1 3{ 5 2f 1 4
21 5 f
3f 5 27
0
26
6
12
18
Number of
Cost of
Monthly
+
1
months
router
fee
18
+
n
1
75
The amount of money you spend in n months is given by
18n 1 75.
When n 5 12:
7
f 5 2}3
18n 1 75 5 18(12) 1 75
Check:
5 216 1 75
7
2}3 1 3
{
{
0 2 2}7 1 4
3
1
2
14
2
{2{ 0 22 1 4
2
3
2
3
5 291
{21 1 3{ 0 2(21) 1 4
{}3{ 0 2}3 1 4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2
y > 2}3
23
Check:
2
3y > 22
2
3d 2 4 5 214
{1
3y 1 4 > 2
252
} Þ 2}
7
The solution is 21. Reject 2}3 because it is an extraneous
solution.
You spend $291 in 12 months.
29.
Cost
Hours
Labor
of 5
of
1
+
cost per
parts
labor
hour
Total
cost
45h 1 240 5 420
45h 5 180
h54
24. {10 2 7g{ 5 2g
10 2 7g 5 22g
The repair took 4 hours.
10 2 7g 5 2g
10 5 5g
10 5 9g
25g
}5g
30. Your
rate
10
9
{10 2 7(2){ 0 2(2)
{10 2 71 }9 2 {0 21 }9 2
{10 2 14{ 0 4
{10 2 }9 {0 }9
{24{ 0 4
{}9 {0 }9
10
70
20
20
20
20
20
}5}
9
9
454
25. {x 2 5{a30
1 window
20 min
1 window
15 min
} + t min 1 } +
Check:
10
+ Time 1 Sister’s + Time 5 Windows
washed
rate
1
15
t min 5 12 windows
1
20
} t 1 } t 5 12
t1}
t 5 60(12)
60 1 }
20 2
15
1
1
4t 1 3t 5 720
7t 5 720
720
6
5 102 }7
t5 }
7
It will take about 103 minutes.
230ax25a30
230 1 5ax 2 5 1 5a30 1 5
225axa35
35
225
240
220
0
20
40
Algebra 2
Worked-Out Solution Key
43
Chapter 1,
continued
1
31. V 5 } :r 2h; r 5 2, V 5 45
3
3V 5 :r 2h
11. D;
3
4
} (4x 2 12) 1 2(3x 2 7) 5 3x 2 9 1 6x 2 14
3V
:r
5 9x 2 23
}2 5 h
When r 5 2 in. and V 5 45 in.3:
3V
:F
r
3(45)
13. C; Point Q will be (22, 22) after the rotation, so Q will
be in Quadrant III.
h 5 }2
14. ERA 5 9 + earned runs 4 innings pitched
h5}
2
:(2
12. F; b 5 375 2 4d
9 + earned runs
)
2.25 5 }}
212
135
h5}
F
ø 10.7
4:
477 5 9 + earned runs
The height h of the cone is about 10.7 inches.
} 5 earned runs
TAKS Practice (pp. 68–69)
1. D; h 5 1.5 1 3.5t
477
9
53 5 earned runs
The pitcher gave up 53 runs.
h 5 1.5 1 3.5(12) 5 43.5
In 12 years, the tree will be 43.5 feet tall.
2. H; fee 5 3.9 1 (18 2 10)(0.15)
fee 5 3.9 1 8(0.15)
3. D; total cost 5 number of books 3 price of 1 book
1 2
1
} inch
3
6
4. G; (9 picas) } 5 } inches
2
1 pica
1 25
1
6
}
} inch
(8 picas)
1 pica
4
3
} inches
Area 5 1 }2 21 }3 2 5 2 in.2
The area of the square is 2 square inches.
5. A; V(container) 5 :r 2h 5 : (82)(25) ø 5026.55 cm3
4
4
V(scoop) 5 }3:r3 5 }3:(2.5)3 ø 65.45 cm3
5026.55 cm3
65.45 cm
Scoops in container 5 }
3 ø 76.8
There are about 77 scoops of ice cream in the container.
6. J; The polyhedron has 7 faces, 15 edges, and 10 vertices.
7. B; m 5 6a 1 3c
2280 5 6a 1 3(260)
1500 5 6a
250 5 a
250 adult tickets were sold.
8. F; 30q6 1 2r
9. A; Area of square 5 * + w 5 4 3 4 5 16 ft2
Area of circle 5 :r2 5 :(22) ø 12.57 ft2
Area left over ø 16 2 12.57 ø 3.43 ft2
About 3 square feet of wood is left over.
10. J; p2 5 942 1 502
}
p 5 Ï942 1 502
44
Algebra 2
Worked-Out Solution Key
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
3 4