460 ( )

Chapter 8,
continued
2. H;
Distance against current
Distance with current
}} 1 }} 5 time
Speed with current
Speed against current
2
2
x13
x23
2(x 2 3)
2(x 1 3)
}} 1 }} 5 1.25
(x 1 3)(x 2 3)
(x 1 3)(x 2 3)
2(x 2 3) 1 2(x 1 3)
}} 5 1.25
(x 1 3)(x 2 3)
} 1 } 5 1.25
2x 2 6 1 2x 1 6
x 29
4x
}
5 1.25
x2 2 9
}}
5 1.25
2
1.25(x 2 2 9) 5 4x
1.25x 2 2 11.25 5 4x
1.25x 2 2 4x 2 11.25 5 0
4(1.25x 2 2 4x 2 11.25) 5 0
5. B;
Volume of rectangular prism:
V 5 *wh
5 (6x)(6x)(8x 2 3)
5 36x 2(8x 2 3)
Volume of cylinder:
V 5 :r 2h
5 :(3x)2(8x 2 3)
5 :(9x 2)(8x 2 3)
5x 2 16x 2 45 5 0
The ratio of the volume of the rectangular prism to the
4
volume of the inscribed cylinder is }
F
.
:
Volume of cube 5 s 3 5 (2r)3 5 8r 3
(5x 1 9)(x 2 5) 5 0
5x 1 9 5 0
9
x 5 2}5
or
x2550
or
x55
4
}:r 3
Volume of sphere
3
}} 5 }
3
Volume of cube
8r
4
3
}
}:
5 8
Because x must be positive, x 5 5. Your speed in still
water is 5 miles per hour.
4
1
5 }3 : + }8
3. D;
:
50
5}
6
t5}
1}
s15
s
50s
s(s 1 5)
50s 1 250
s 1 5s
100s 1 250
5}
s 2 1 5s
50s
s 1 5s
5}
1}
2
2
The expression that represents the total time of the
100s 1 250
.
cyclist’s round trip is }
s 2 1 5s
4. F;
Amount of zinc
% zinc
Amount of copper 5 }} 2 Amount of zinc
x
25 5 }
2x
0.45
x
0.45(25) 5 0.451 }
2 x2
0.45
11.25 5 x 2 0.45x
11.25 5 0.55x
20.45 ø x
You need about 20.45 ounces of zinc to make brass.
ø 0.52
The ratio of the volume of the sphere to the volume of
the cube is about 0.52.
Chapter 8 Review (pp. 603–606)
1. If two variables x and y are related by an equation of
a
the form y 5 }x where a Þ 0, then x and y show inverse
variation.
z
2. The expression } represents the constant of variation.
xy
p (x)
3. A function of the form f (x) 5 } where p(x) and
q(x)
q(x) are polynomials and q(x) Þ 0 is called a rational
function.
complex fractions.
2
x11
}
x24
2
3
5. When you rewrite the equation } 5 } as
x21
x
3(x 2 1) 5 2x, you are cross-multiplying.
a
6. y 5 }
x
a
5
y 5 }x
5
5 5 }1
5}
23
55a
5 2}3
5
y 5 }x
Algebra 2
Worked-Out Solution Key
1
x
}
4. Sample answer: The fractions }
and }}
are
2
1
3
}14
}1}
x
x11
5
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
50(s 1 5)
s(s 15)
5}1}
460
4
:
: (9x 2)(8x 2 3)
4
6. Volume of sphere 5 } :r 3
3
2
50
36x 2(8x 2 3)
Volume of prism
Volume of cylinder
}} 5 }} 5 }F
Chapter 8,
7.
continued
a
24
y 5 }x
y5}
x
a
24
26 5 }
24
5}
23
24 5 a
5 28
3x 2 2
12. f (x) 5 }
x24
x 2 4 5 0 l x 5 4, so x 5 4 is a vertical asymptote.
3
a
y 5 }c 5 }1 5 3 is a horizontal asymptote.
24
y
y5}
x
45
a
8.
y 5 }x
y5}
x
45
a
18 5 }
5
2
5
181 }2 2 5 a
5 215
45 5 a
45
y5}
x
a
28
y 5 }x
y5}
x
a
212
28
}5}
5}
23
The numerator has no real zeros, so there is no
x-intercept. The denominator has no real zeros, so there
is no vertical asymptote.
m 5 0 and n 5 2, so m < n and y 5 0 is a horizontal
asymptote.
x
y
23
}
22
1
8
2121 }3 2 5 a
2
5 }3
24(2) 5 a
28 5 a
28
y5}
x
4
10. y 5 }
x23
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
The domain is all real numbers except 4, and the range is
all real numbers except 3.
5
13. y 5 }
x2 1 1
9(5) 5 a
2
3
x
22
5}
23
}
9.
2
y
1
2
0
5
2
1
3
}
1
x
21
1
2
y
4x 2
14. y 5 }
x21
1
x
21
4x 2 5 0 l x 5 0, so 0 is an x-intercept.
x 2 1 5 0 l x 5 1, so x 5 1 is a vertical asymptote.
m 5 2 and n 5 1, so m > n and the graph has no
horizontal asymptote.
The domain is all real numbers except 3, and the range is
all real numbers except 0.
1
11. y 5 } 1 2
x15
y
x
y
21
22
0
0
1
2
3
}
2
}
1
21
x
The domain is all real numbers except 25, and the range
is all real numbers except 2.
y
5
22
x
22
18
2
16
3
18
Algebra 2
Worked-Out Solution Key
461
Chapter 8,
continued
6x 2
15. h(x) 5 }
x22
6x2 5 0 l x 5 0, so 0 is an x-intercept.
x 2 2 5 0 l x 5 2, so x 5 2 is a vertical asymptote.
m 5 2 and n 5 1, so m > n and the graph has no
horizontal asymptote.
y
21
22
0
0
1
26
3
54
4
48
5
50
10
4
x
23
2}3
21
22
0
2}3
1
22
3
2
2}3
}
26
3
22
2}3
0
2}
20
1
2}6
10
}
15
y
35
24
2
6
1
3
1
53
15
33
}
20
x 2 2 1 5 0 l x 2 5 1 l x 5 61, so 1 and 21
are x-intercepts.
x 1 4 5 0 l x 5 24, so x 5 24 is a vertical
asymptote.
1
2
m 5 2 and n 5 1, so m > n and there is no horizontal
asymptote.
x
x
22
8
0
3
2
1
2}4
}
80x 5y
5 + 16 + x 2 + x 3 + y
16x 3
80x4 xy
}}
19. }
+ }2 5 }
5}
2 3 5
2
2
3
5x y
5+x +y+y
y2
y
5x
2
6(x 2 16)
x23
x 2 3 6x 2 2 96
20. } + }
5}
+ }}
2(x 2 4) (x 1 3)(x 2 3)
2x 2 8
x2 2 9
x23
(2)(3)(x 2 3)(x 1 4)(x 2 4)
5 }}}
(2)(x 2 4)(x 1 3)(x 2 3)
3(x 1 4)
(x 2 8)(x 1 5) 5 0
or
x 5 25
The vertical asymptotes are x 5 8 and x 5 25.
1
m 5 2 and n 5 2, so m 5 n and y 5 }1 5 1 is a
horizontal asymptote.
5}
x13
20x 2 2 5x
16x 2 2 8x 1 1
21. }}
4}
3
2
15x 3
x 2 7x 1 12x
16x2 2 8x 1 1
15x 3
x 2 7x 1 12x 20x 2 5x
(4x 2 1)(4x 2 1)
15x 3
5 }}
+}
x(x 2 2 7x 1 12) 5x(4x 2 1)
5 }}
+}
3
2
2
(4x 2 1)(4x 2 1)(5x)(3x)(x)
5 }}}
x(x 2 4)(x 2 3)(5x)(4x 2 1)
3x(4x 2 1)
5 }}
(x 2 4)(x 2 3)
Algebra 2
Worked-Out Solution Key
6(x 1 4)(x 2 4)
(x 1 3)(x 2 3)
5}
+ }}
2(x 2 4)
x2 2 3x 2 40 5 0
x1550
x
8
The numerator has no real zeros, so there is no
x-intercept.
x58
2
25 224
23
or
5
27 216
21
x2850
g(x)
y
y
x2 1 6
17. y 5 }
2
x 2 3x 2 40
462
x
x2 2 1
18. g(x) 5 }
x14
The numerator has no real zeros, so there is no
x-intercept. The denominator has no real zeros,
so there is no vertical asymptote.
m 5 0 and n 5 2, so m < n and y 5 0 is a horizontal
asymptote.
y
28
h(x)
28
16. y 5 }
x2 1 3
x
y
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
x
x
Chapter 8,
continued
x 2 2 13x 1 40
22. }}
4 (x 2 2 5x 2 24)
x 2 2 2x 2 15
x 2 2 13x 1 40
1
x 2 2x 2 15 x 2 5x 2 24
(x 2 8)(x 2 5)
1
5 }}
+ }}
(x 2 5)(x 1 3) (x 2 8)(x 1 3)
5 }}
+}
2
2
(x 2 8)(x 2 5)
5 }}}
(x 2 5)(x 1 3)(x 2 8)(x 1 3)
1
(x 1 3)
5 }2
3(x 1 4)(x 1 3)
5x
3(x 2 1 7x 1 12)
5x
29.
5}
1 }}
6x(x 1 3)
6x(x 1 3)
5(x 1 2) 5 7x
9(x 2 1) 5 4(3x)
5x 1 10 5 7x
9x 2 9 5 12x
23 5 x
Check:
5
7
}0}
5
512
}0}
23 2 1
4
24
4
}0}
151
21 5 21 6
2
}5}
2x 1 5
x12
x 5 21
x23
Check:
5x 2 2 15x
6
2(21) 1 5
2
21 1 2
4x 2 9
}0}
6
3
2
1
4x 2 9
}0}
5 }}
1 }}
(x 1 8)(x 2 3)
(x 1 8)(x 2 3)
252
5x 2 2 11x 2 9
5 }}
(x 1 8)(x 2 3)
x 1 12
3
30.
5x
x12
25. }
2}
x2 2 9
x 2 1 4x 1 3
x 2 1 14x 1 24 5 6x 1 9
x23
5x
x 2 1 8x 1 15 5 0
x11
5 }}
+ } 2 }}
+}
(x 1 3)(x 1 1) x 2 3
(x 1 3)(x 2 3) x 1 1
2
x 2x26
(x 1 5)(x 1 3) 5 0
x1550
2
5x 1 5x
5 }}
2 }}
(x 1 3)(x 2 3)(x 1 1)
(x 1 3)(x 2 3)(x 1 1)
or
x 5 25
x 2 2 x 2 6 2 (5x 2 1 5x)
5 }}
(x 1 3)(x 2 3)(x 1 1)
x 2 2 x 2 6 2 5x 2 2 5x
5 }}
(x 1 3)(x 2 3)(x 1 1)
x 5 23
Check x 5 23:
2(25) 1 3
25 1 12
}0}
3
25 1 2
2(23) 1 3
23 1 12
}0}
3
23 1 2
7
3
27
23
}0}
7
3
7
3
353
24x 2 2 6x 2 6
}0}
22(2x 2 1 3x 1 3)
}5}
5 }}
(x 1 3)(x 2 3)(x 1 1)
2x
x14
31.
2
2x
26. } 5 }
x
9
x1350
or
Check x 5 25:
5 }}
(x 1 3)(x 2 3)(x 1 1)
9
3
23
21
23x
4x 2 3
}5}
2x(4x 2 3) 5 (23x)(x 1 4)
2x 2 5 18
8x 2 2 6x 5 23x 2 2 12x
x2 5 9
11x 2 1 6x 5 0
x 5 63
Check x 5 3:
Check x 5 23:
2(3)
9
2
3
}0}
6
9
2
3
} 0 2}
2
3
2
3
2}3 5 2}3 } 5 } 2x 1 3
x12
}5}
(x 1 12)(x 1 2) 5 3(2x 1 3)
5x
5 }}
2 }}
(x 1 3)(x 1 1)
(x 1 3)(x 2 3)
}0}
29
9
1 0 }7
22x 5 2
5}
+ } 1 }}
x18 x23
(x 1 8)(x 2 3)
}0}
3(23)
9
22x 1 10 5 12
4x 2 9
5x
4x 2 9
5x
24. } 1 }
5}
1 }}
x18
(x 1 8)(x 2 3)
x18
x 2 1 5x 2 24
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
29 5 3x
55x
4x 1 10 5 6x 1 12
3x 2 1 26x 1 36
x12
10 5 2x
Check:
5 }}
6x(x 1 3)
x12
3x
9
}5}
2(2x 1 5) 5 6(x 1 2)
5x
3x 2 1 21x 1 36
5}
1 }}
6x(x 1 3)
6x(x 1 3)
5x
x21
4
28.
}5}
7
5
x14
5
x
x 1 4 3(x 1 3)
23. } 1 } 5 } + } 1 } + }
2x
6(x 1 3) x
2x
6(x 1 3)
3(x 1 3)
5}
1 }}
6x(x 1 3)
6x(x 1 3)
7
x12
5
x
27.
2(23)
9
2
23
26
9
2
3
2
2
x(11x 1 6) 5 0
x50
or
11x 1 6 5 0
6
x 5 2}
11
Algebra 2
Worked-Out Solution Key
463
Chapter 8,
continued
34.
Check x 5 0:
23(0)
4(0) 2 3
}0}
0
4
0
23
21 2}
11 2
3x 2 2 3x 5 12 1 2x 2 2 2
6
2
x 2 3x 2 10 5 0
}0}
6
6
2}
14
23
4 2}
11
11
1
2
(x 2 5)(x 1 2) 5 0
18
}
11
}
57
2}
11
18
12
2}
0 2}
57
38
6
6
2}
5 2}
19
19
x2550
or
x55
or
Check x 5 22:
3(5)
511
}0}
12
2
12
24
}0}12
5
2
6 5 6 5
2
35.
2(x 1 7)
x14
2x 1 20
2x 1 8
2(x 1 7)
x14
2x 1 20
2(x 1 4)
12
3
}225}
65x
F
Check:
G
2(x 1 7)
F
2x 1 20
2(x 1 4)
2(x 1 4) }
2 2 5 2(x 1 4) }
x14
3
5
}1}03
6
2
G
4(x 1 7) 2 4(x 1 4) 5 2x 1 20
1
2
}1}03
4x 1 28 2 4x 2 16 5 2x 1 20
12 5 2x 1 20
6
2
}03
28 5 2x
353
24 5 x
8(x 2 1)
4
}
5}
x12
x2 2 4
33.
8(x 2 1)
4
}} 5 }
x12
(x 1 2)(x 2 2)
F
8(x 2 1)
(x 1 2)(x 2 2)
G
4
(x 1 2)(x 2 2) }} 5 (x 1 2)(x 2 2)1 }
x 1 22
8(x 2 1) 5 4(x 2 2)
8x 2 8 5 4x 2 8
Check:
2(24 1 7)
24 1 4
4x 5 0
x50
2(24) 1 20
2(24) 1 8
}220}
6
0
12
0
}220}
Division by 0 is undefined, so x 5 24 is an extraneous
solution, and the equation has no solution.
36. a.
4x 2 8 5 28
b.
Total free
Total free
60 1 x
4
5}
75 1 x
throws attempted
throws made
60 1 x
75 1 x
} 5 0.82
60 1 x 5 0.82(75 1 x)
Check:
4
012
}
0}
2
4
2
}0}
252
464
26
21
}225}
5x 1 6 5 6x
28
24
12
(22) 2 1
}0}12
}5}
2
0 24
3(22)
22 1 1
12
5 21
15
6
3
x
8(0 2 1)
x 5 22
}0}
12
2
3
5
2x }2 1 }x 5 2x(3)
5
2
x1250
Check x 5 5:
}1}53
1
G
3x 2 2 3x 5 12 1 2(x 2 2 1)
231 2}
11 2
6
(x 1 1)(x 2 1)
3x(x 2 1) 5 12 1 2(x 1 1)(x 2 1)
6
5
2
F
3x
:
Check x 5 2}
11
32.
12
(x 1 1)(x 2 1)
12
(x 1 1)(x 2 1)1 x}
5 (x 1 1)(x 2 1) }} 1 2
1 12
050
0
3x
x11
} 5 }} 1 2
}0}
12
2}
11
}
38
}
11
12
x 21
Algebra 2
Worked-Out Solution Key
60 1 x 5 61.5 1 0.82x
60 1 0.18x 5 61.5
0.18x 5 1.5
}
x 5 8.3
The player must make 9 consecutive free throws to
raise her free-throw percentage to at least 82%.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2(0)
014
3x
x11
}5}
12
2
Chapter 8,
continued
2
7. y 5 } 2 3
x15
Chapter 8 Test (p. 607)
1.
10
a
y 5 }x
y5}
x
2 5 }5
5}
4
10 5 a
5 }2
y
x
22
10
a
5
10
The domain is all real numbers except 25, and the range
is all real numbers except 23.
y5}
x
2.
2
a
216
y 5 }x
y5}
x
a
21
8. y 5 } 2 1
x24
216
85}
22
y
5}
4
216 5 a
1
5 24
5
216
x
y5}
x
15
a
3.
y 5 }x
y5}
x
15
a
10 5 }3
}
5}
4
3
10 }2 5 a
15
5}
4
2
1 2
15 5 a
1
1
2x 1 1 5 0 l x 5 2}2 , so x 5 2}2 is a
a
18
a
y 5 }x
1
21
5 2}2 is a horizontal asymptote.
y 5 }c 5 }
2
y5}
x
f(x)
18
a
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
62x
9. f (x) 5 }
2x 1 1
vertical asymptote.
15
y5}
x
4.
The domain is all real numbers except 4, and the range is
all real numbers except 21.
6 5 }3
5}
4
18 5 a
5}
2
9
2
2
x
18
y5}
x
a
5.
214
y 5 }x
y5}
x
a
24
7
2
214
}5}
5}
4
7
7
2
}(24) 5 a
5 2}2
214
y5}
x
6.
15
32x
a
x
5
y5}
a
15
32(4)
}5}
3
8
}
4
5}
1 2
5 3
8 4
15
} } 5a
5}
128
15
32
}5a
15
}
15
32
}
y5 5}
x
32x
1
is all real numbers except 2}2.
4
10. y 5 }
x2 1 2
The numerator has no real zeros, so there is no
x-intercept. The denominator has no real zeros,
so there is no vertical asymptote.
214 5 a
y5}
1
The domain is all real numbers except 2}2 , and the range
m 5 0 and n 5 2, so m < n and y 5 0 is a horizontal
asymptote.
x
y
22
}
21
2
3
4
}
3
0
2
1
}
2
y
1
21
x
4
3
2
}
3
Algebra 2
Worked-Out Solution Key
465
Chapter 8,
continued
x2 2 4
11. y 5 }
x 2 1 8x 1 15
15. x 2 2 4x 5 x(x 2 4)
x 2 2 2x 2 8 5 (x 2 4)(x 1 2)
x 2 4 5 0 l x 5 4 l x 5 62, so 2 and 22
are x-intercepts.
2
2
LCM 5 x(x 2 4)(x 1 2)
16. 2x 1 6 5 2(x 1 3)
x 2 1 8x 1 15 5 0
x 3 1 10x 2 1 21x 5 x(x2 1 10x 1 21) 5 x(x 1 3)(x 1 7)
(x 1 5)(x 1 3) 5 0
x1550
or
x 5 25
LCM 5 2x(x 1 3)(x 1 7)
x1350
or
6y 2
3x 2y 2xy 3
3x2y
17. }
4 }3 5 }
+}
2xy
4x 3y 5 6y 2
4x 3y 5
x 5 23
The vertical asymptotes are x 5 25 and x 5 23.
6x 3y 4
1
m 5 2 and n 5 2, so m 5 n and y 5 }1 5 1 is a horizontal
asymptote.
x
5}
3 7
24x y
6x 3y 4
5 }}
3
4
3
6+4+x +y +y
y
y
1
4y
5 }3
4
26
32
}
3
24
212
7
2}2
5
21
x
x24
211
5
5}
x13
9
5
2}2
}
22
0
1
2}8
2
0
(x 2 5)(x 2 3)
x 2 2 8x 1 15
x14
x14
19. }}
+ } 5 }}
+ }}
(x 1 4)(x 1 8) (x 1 5)(x 2 5)
x 2 1 12x 1 32 x 2 2 25
(x 2 5)(x 2 3)(x 1 4)
5 }}}
(x 1 4)(x 1 8)(x 1 5)(x 2 5)
1
x23
5 }}
(x 1 8)(x 1 5)
x 2 2 11x 1 28
20. }}
4 (x 2 2 16)
x 2 1 5x 1 4
x2 1 3
12. g(x) 5 }
2x 2 1
The numerator has no real zeros, so there is no x-intercept.
1
1
x 2 2 11x 1 28
x 1 5x 1 4
1
x 2 16
(x 2 7)(x 2 4)
1
(x 1 4)(x 2 4)
5 }}
+}
2
2
2x 2 1 5 0 l x 5 }2, so x 5 }2 is a vertical asymptote.
+ }}
5 }}
(x 1 4)(x 1 1)
m 5 2 and n 5 1, so m > n and there is no horizontal
asymptote.
5 }}}
(x 1 4)(x 1 1)(x 1 4)(x 2 4)
x
f (x)
26
23
21
2}3
0
23
1
4
2
}
7
4
4
x27
(x 1 4) (x 1 1)
5 }}
2
3x 2 (4x 1 1)
4x 1 1
3x
21. } 2 } 5 }}
x15
x15
x15
1
22
7
3
x(x 1 5)
LCM 5 x(x 2 3)(x 1 5)
14. 4x 2(x 2 2) 5 (22)(x 2)(x 2 2)
8x(x 1 2) 5 23(x)(x 1 2)
LCM 5 23(x2)(x 2 2)(x 1 2) 5 8x 2(x 2 2)(x 1 2)
Algebra 2
Worked-Out Solution Key
(x 2 7)(x 2 4)
g(x)
13. (x 2 3)(x 1 5)
466
(x 2 4)(x 1 1) x 2 6
x 2 2 3x 2 4 x 2 6
18. }
+ } 5 }}
+}
(x 2 6)(x 1 3) x 1 1
x 2 2 3x 2 18 x 1 1
(x 2 4)(x 1 1)(x 2 6)
5 }}
(x 2 6)(x 1 3)(x 1 1)
x
3x 2 4x 2 1
5}
x15
2x 2 1
5}
x15
2
4
2
x16
x23
4
22. } 1 } 5 } + } 1 } + }
x16
x23 x16
x16 x23
x23
4x 1 24
2x 2 6
1 }}
5 }}
(x 2 3)(x 1 6)
(x 2 3)(x 1 6)
6x 1 18
5 }}
(x 2 3)(x 1 6)
6(x 1 3)
5 }}
(x 2 3)(x 1 6)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
28
Chapter 8,
continued
6
3x
6
3x
23. }
2}
5 }}
2}
x14
x14
(x 1 4)(x 2 3)
x2 1 x 2 12
3x
6
x23
2}
+}
5 }}
x14 x23
(x 1 4)(x 2 3)
3x
Check x 5 3:
Check x 5 2:
311
13
1
}1}0}
3
316
316
}1}0}
1
9
6x 2 18
3x 2 (6x 2 18)
23(x 2 6)
2x
x25
4x 2 20
2x
6x 2 20
2(3x 2 10)
5 }}
5 }}
(x 1 5)(x 2 5)
(x 1 5)(x 2 5)
x23
2x 1 4
}5}
622
4
5
4
5
}5}
a
28. I 5 }2
r
50m 1 30
0 5 (x 2 9)(x 1 2)
5}
m
x1250
C
x 5 22
Check x 5 9:
Check x 5 22:
3
912
}0}
923
2(9) 1 4
3
22 1 2
}0}
6
22
3
0
}0}
22 2 3
2(22) 1 4
25
0
}0}
3
3
}5}
11
11
Average cost (dollars)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
8
10
c 5 }}}}
Number of months
0 5 x 2 2 7x 2 18
80
Division by 0 is undefined, so 22 is an extraneous
solution. The only solution is x 5 9.
40
20
13
x16
13
x 1 x 2 1 7x 1 6 5 13x
x 2 1 8x 1 6 5 13x
x 2 2 5x 1 6 5 0
(x 2 3)(x 2 2) 5 0
x2350
or
x2250
x53
or
x52
2
4
6
8
Number of months
m
After 5 months, the average cost will be $56.
Monthly fee + Number of months 1 Setup fee
1}
5 x(x 1 6)1 }
x(x 1 6)1 }
x 2
x16
x 1 62
x 1 (x 1 6)(x 1 1) 5 13x
0
30. Let c be the average cost and m be the number of months.
}1}5}
x11
(5, 56)
60
0
1
4
5
}0}
Monthly fee + Number of months 1 Installation fee
6x 1 12 5 x 2 2 x 2 6
x11
x
612
0}
Check: }
621
614
29. Let c be the average cost and m be the number of months.
3(2x 1 4) 5 (x 1 2)(x 2 3)
1
x16
x12
x14
x56
5 }}
1 }}
(x 1 5)(x 2 5)
(x 1 5)(x 2 5)
26.
13
8
x 2 8 5 22
5}
+ } 1 }}
x15 x25
(x 1 5)(x 2 5)
3
11
13
8
}5}
2x 2 8 5 x 2 2
2x
2x
4
4
24. } 1 }
5}
1 }}
x15
x15
(x 1 5)(x 2 5)
x 2 2 25
or
13
8
x 2 1 2x 2 8 5 x 2 1 x 2 2
5 }}
(x 1 4)(x 2 3)
or
3
2
1
8
(x 2 2)(x 1 4) 5 (x 2 1)(x 1 2)
23x 1 18
x59
13
216
}5}
5 }}
(x 1 4)(x 2 3)
x2950
13
9
x22
x21
27.
3x 2 6x 1 18
5 }}
(x 1 4)(x 2 3)
3
x12
13
9
211
2
}1}0}
}5}
5 }}
(x 1 4)(x 2 3)
25.
13
9
}1}0}
2 }}
5 }}
(x 1 4)(x 2 3)
(x 1 4)(x 2 3)
4
4
3
1
216
c 5 }}}}
Number of months
99m 1 50
5}
m
99m 1 50
100 5 }
m
100m 5 99m 1 50
m 5 50
You would need to use this service for 50 months in order
for your average monthly cost to fall to $100.
Algebra 2
Worked-Out Solution Key
467
Chapter 8,
continued
TAKS Practice (pp. 610–611)
5. A;
2
(21, 3); parallel to y 5 2}5 x 2 1
1. B;
* 5 20 2 2 5 18 in.
2
m1 5 2}5
w 5 12 2 2 5 10 in.
2
h 5 8 2 2 5 6 in.
m2 5 m1 5 2}5
Surface area 5 2B 1 Ph
Let (x1, y1) 5 (21, 3).
5 2(18)(10) 1 [2(18) 1 2(10)](6)
y 2 y1 5 m2(x 2 x1)
5 360 1 56(6)
2
y 2 3 5 2}5 (x 2 (21))
5 360 1 336
5 696
2
y 2 3 5 2}5 (x 1 1)
The surface area of the new packaging is
696 square inches.
2. G;
2
2
13
y 5 2}5 x 1 }
5
Volume 5 :r 2h
1960 5 :(12)2h
5y 5 22x 1 13
1960 5 144:h
2x 1 5y 5 13
1960
144:
6. F;
}F
5h
a2 1 b2 5 c2
4.3 ø h
x 2 1 402 5 (50 2 x)2
The swimming pool is about 4.3 feet tall.
2
x 1 1600 5 2500 2 100x 1 x 2
3. B;
The scale factor of n AED to n ABC is 8 : 24, or 1 : 3.
Let x be the perimeter of n ABC.
40
x
}5}
100x 1 1600 5 2500
100x 5 900
x59
The part of the flagpole that remains standing is
9 feet tall.
x 5 120
7. A; The line passes through (0, 5) and (24, 0).
The perimeter of n ABC is 120 units.
025
4. F;
Find the surface area to paint on each part of the silo.
5
y 2 5 5 }4 (x 2 0)
5 :r*
5 :(15)(17)
5
y 2 5 5 }4 x
ø 801.11
5
Cylinder surface area 5 (2:r 2 1 2:rh) 2 2:r 2
2}4 x 1 y 2 5 5 0
5 2:rh
5
241 2}4x 1 y 2 5 2 5 0
5 2:(15)(40)
5x 2 4y 1 20 5 0
ø 3769.91
5x 2 4y 5 220
2
Total surface area ø 801.11 1 3769.91 ø 4571 ft .
1 gallon
400 ft
So, the painter needs 12 gallons of paint.
5
y 2 y1 5 m(x 2 x1)
Cone surface area 5 (:r 2 1 :r*) 2 :r 2
4571 ft2 + }
ø 11.4
2
25
m5}
5}
5 }4
24 2 0
24
8. H;
h
tan 608 5 }
40
40 + tan 608 5 h
69 ø h
The tree is about 69 feet tall.
468
Algebra 2
Worked-Out Solution Key
h
608
40
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
1
3
2
y 2 3 5 2}5 x 2 }5
Chapter 8,
continued
9. C;
50
3
x
4.5
}5}
3x 5 50 + 4.5
50 + 4.5
x5}
3
x 5 75
It takes 75 pounds of force to stretch the spring
4.5 inches.
10. J;
y 5 2x 2 produces the narrowest parabola when graphed
2
because {2{ > {21.5{ > {2}3 { > {0.5{.
11. C;
The domain of the relation shown is all values of x that
are greater than or equal to 1, or x q 1.
12. J;
94 1 85 1 89 1 90 1 s
5
}} q 90
358 1 s
5
} q 90
358 1 s q 450
s q 92
To achieve a final grade of A, Lisa’s score on the fifth
exam must be greater than or equal to 92, so s q 92.
13. C;
3y 5 15(x 2 5)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
y 5 5(x 2 5)
y 5 5x 2 25
The slope of the line is 5.
14. Price 1 Sales tax 5 Total cost
212.50 1 212.50x 5 227.91
212.50x 5 15.41
x ø 0.073
The sales tax to the nearest percent is 7%.
Algebra 2
Worked-Out Solution Key
469