Document 1804509

Chapter 8,
continued
3x(x 1 2)
3x
3x 2 1 6x
2. }
5 }}
5}
x24
(x 2 4)(x 1 2)
x 2 2 2x 2 8
X
-2
-1
0
1
2
3
4
X=-2
Y1
ERROR
.6
0
-1
-3
-9
ERROR
Y2
1
.6
0
-1
-3
-9
ERROR
4x 2 2 8x x 1 3
x22
4x 2 2 8x
5. } 4 } 5 } + }
x13
5x 1 15 x 2 2
5x 1 15
4x(x 2 2)(x 1 3)
4x
5 }}
5}
5
5(x 1 3)(x 2 2)
X
-3
-2
-1
0
1
2
3
X=-3
Y1
ERROR
-1.6
-.8
0
.8
ERROR
2.4
Y2
-2.4
-1.6
-.8
0
.8
1.6
2.4
(x 1 1)(x 1 4)
x11
x 2 1 5x 1 4
3. }
5 }}
5}
x23
(x 1 4)(x 2 3)
x 2 1 x 2 12
X
-4
-3
-2
-1
0
1
2
X=-4
Y1
ERROR
.33333
.2
0
-.3333
-1
-3
Y2
.42857
.33333
.2
0
-.3333
-1
-3
x 2 2 3x 2 10 x2 1 2x 2 3
6. }
+}
x2 1 3x 1 3
x2 1 x 2 2
(x 2 5)(x 1 2)
(x 1 3)(x 2 1)
(x 1 2)(x 2 1)
5 }}
+ }}
2
x 1 3x 1 3
(x 2 5)(x 1 2)(x 1 3)(x 2 1)
(x 2 5)(x 1 3)
(x 1 3x 1 3)(x 1 2)(x 2 1)
x 1 3x 1 3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
5 }}}
5 }}
2
2
(x 1 3)(x 2 1)
x21
x13 x21
4. }
+}
5 }}
5}
x13
5x 2(x 1 3)
5x 2
5x 2
X
-3
-2
-1
0
1
2
3
X=-3
Y1
ERROR
-2.4
-.4
0
0
.8
3.6
X
-2
-1
0
1
2
3
4
X=-2
Y1
ERROR
-12
-5
ERROR
-1.154
-.5714
-.2258
Y2
-7
-12
-5
-2.286
-1.154
-.5714
-.2258
Y2
-7.2
-2.4
-.4
0
0
.8
3.6
Lesson 8.5
8.5 Guided Practice (pp. 582–585)
5
725
2
1
7
1. } 2 } 5 } 5 } 5 }
12x
12x
12x
6x
12x
3
1
211
1
2
2. }2 1 }2 5 }
5 }2 5 }2
3x
3x 2
3x
x
3x
3x
x
4x 2 x
4x
3. } 2 } 5 } 5 }
x22
x22
x22
x22
2(x 2 1 1)
2x 2 1 2
2
2x 2
4. }
1}
5}
5}
52
2
2
2
x 11
x 11
x2 1 1
x 11
5. 5x 3
10x 2 2 15x 5 5x(2x 2 3)
LCM 5 5x 3(2x 2 3)
Algebra 2
Worked-Out Solution Key
437
Chapter 8,
continued
2
x
12. }
2
}13
x
6. 8x 2 16 5 8(x 2 2) 5 2 (x 2 2)
12x 2 1 12x 2 72 5 12(x 2 1 x 2 6)
2
x
}
2
}13
x
}24
}24
3
5
LCM 5 (23)(3)(x 1 3)(x 2 2) 5 24(x 1 3)(x 2 2)
}
}
(x 2 3)(x 1 5)
x15
x15
13. }}
5 }}
+ }}
1
2
1
2
} 1 } (x 2 3)(x 1 5)
}1}
x15
x15
x23
x23
3 7
4x
21 2 4x
1
1 4x
21
3
7. } 2 } 5 } + } 2 } + } 5 } 2 } 5 }
7
7 4x
4x 7
28x
28x
28x
4x
3(x 2 3)
5 }}
2(x 1 5) 1 x 2 3
x
x
1
1
8. }2 1 }
5 }2 1 }
3x(3x 2 4)
9x 2 2 12x
3x
3x
3(x 2 3)
5 }}
2x 1 10 1 x 2 3
x
3x 2 4
x
3(x 2 3)
5 }2 + }
1}
+}
3x(3x 2 4) x
3x 2 4
3x 2 4
3x (3x 2 4)
x2
3x (3x 2 4)
5}
1}
2
2
2
denominator is called a complex fraction.
2. To add rational expressions with unlike denominators,
5
first find a common denominator. Then rewrite each
rational expression using the common denominator.
Finally, add the numerators.
x13
5 }}
+}1}
+}
(x 2 4)(x 1 3) 12
12(x 2 4) x 1 3
5
15 1 5
20
5
15
3. } 1 } 5 } 5 } 5 }
4x
4x
4x
x
4x
5x 1 15
12(x 2 4)(x 1 3)
12x
12(x 2 4)(x 1 3)
5 }} 1 }}
x24
4
x
4. }2 2 }2 5 }
16x
16x 2
16x
17x 1 15
5 }}
12(x 2 4)(x 1 3)
9 2 2x
2x
9
5. } 2 } 5 }
x11
x11
x11
6
x11
10. }
2}
x2 2 4
x 2 1 4x 1 4
3x(x 1 2)
6x
3x 2 1 6x
3x2
6. } 1 } 5 } 5 }
x28
x28
x28
x28
x22
6
x12
5 }}
+ } 2 }}
+}
(x 1 2)(x 1 2) x 2 2
(x 1 2)(x 2 2) x 1 2
x2 2 x 2 2
(x 1 2) (x 2 2)
6x 1 12
(x 1 2) (x 2 2)
5 }}
2 }}
2
2
2
x 2 x 2 2 2 (6x 1 12)
5 }}
2
(x 1 2) (x 2 2)
x 2 2 x 2 2 2 6x 2 12
(x 1 2) (x 2 2)
5 }}
2
2
x 2 7x 2 14
(x 1 2) (x 2 2)
5
x
x
}2}
6
3
}
7
x
}2}
10
5
9. 3x, 3(x 2 2)
LCM 5 3x(x 2 2)
10. 2x 2
4x 1 12 5 4(x 1 3) 5 22(x 1 3)
LCM 5 4x 2(x 1 3)
LCM 5 2x(x 2 5)
60
+}
60
10x 2 20x
5}
12x 2 42
210x
5}
12x 2 42
2(25x)
5}
2(6x 2 21)
25x
5}
6x 2 21
25x
5}
3(2x 2 7)
438
(2x 1 1)(2x 1 1)
4x 2 2 1
1
4x 2
8. } 2 } 5 } 5 }} 5 2x 1 1
2x 2 1
2x 2 1
2x 2 1
2x 2 1
11. 2x, 2x(x 2 5)
5 }}
2
x
x
}2}
3
6
11. }
7
x
}2}
10
5
5(x 1 3)
15
5x 1 15
5x
7. } 1 } 5 } 5 } 5 5
x15
x13
x13
x13
Algebra 2
Worked-Out Solution Key
12. 24x 2 5 23(3)(x 2)
8x 2 2 16x 5 8x(x 2 2) 5 23(x)(x 2 2)
LCM 5 23(3)(x2)(x 2 2) 5 24x 2(x 2 2)
13. x
x25
x 2 2 25 5 (x 1 5)(x 2 5)
LCM 5 x(x 1 5)(x 2 5)
14. 9x 2 2 16 5 (3x 1 4)(3x 2 4)
3x 2 2 2x 2 8 5 (3x 1 4)(x 2 2)
LCM 5 (3x 1 4)(3x 2 4)(x 2 2)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
6
x11
5 }}
2 }}
(x 1 2)(x 1 2)
(x 1 2)(x 2 2)
x11
8.5 Exercises (pp. 586–588)
1. A fraction that contains a fraction in its numerator or
5
x
12x 2 48
x 2 x 2 12
5
x
5 }}
1}
(x 2 4)(x 1 3)
12(x 2 4)
9. }
1}
2
12
5}
3x 1 7
Skill Practice
x 1 3x 2 4
3x (3x 2 4)
5}
2
x
2(1 2 2x)
3
3
5 (22)(3)(x 1 3)(x 2 2)
1
3x
2 2 4x
x
+ }x 5 }
5}
2 1 3x
2 1 3x
Chapter 8,
continued
215x
12
12
215x
23. }
1}
5 }}
1}
x24
x24
(x 2 4)(x 2 4)
x2 2 8x 1 16
15. D; 3x 2 2 9x 5 3x(x 2 3)
6x 2 5 2(3)(x 2)
7
7 5
72
35
107
12 6
12
16. } 1 } 5 } + } 1 } + } 5 } 1 } 5 }
5x 6
6x
6x 5
30x
30x
30x
5x
x24
12x 2 48
215x
5 }}
1 }}
(x 2 4)(x 2 4)
(x 2 4)(x 2 4)
5
8
5 3x
8
4
17. }2 2 } 5 }2 + } 2 } + }
4x
4x 3x
4
3x
3x
32
15x
32 2 15x
5 }2 2 }2 5 }
12x
12x
12x2
23x 2 48
(x 2 4)
5}
2
23(x 1 16)
5}
2
(x 2 4)
x24 x24
12
12
x24
x
18. } 2 } 5 } + } 2 } + }
5x
5x
5(x 2 4)
5(x 2 4) x
x24
2
x 2 8x 1 16
x13
x2 2 5
x13
x 25
24. }
2}
5 }}
2}
2
x
1
7
x17
(x
1
7)(x 2 2)
x 1 5x 2 14
2
12x
5}
2}
5x(x 2 4)
5x(x 2 4)
x2 2 5
x13
x 2 20x 1 16
5 }}
5x(x 2 4)
x2 2 5
3
x2 2 5 2 (x2 1 x 2 6)
5 }}
(x 1 7)(x 2 2)
x18
5 }}
1}
+}
x23 x18
(x 1 8)(x 2 3)
x2 2 5 2 x 2 2 x 1 6
5 }}
(x 1 7)(x 2 2)
3x 1 24
12
5 }}
1 }}
(x 1 8)(x 2 3)
(x 1 8)(x 2 3)
2x 1 1
5 }}
(x 1 7)(x 2 2)
3(x 1 12)
3x 1 36
5 }}
5 }}
(x 1 8)(x 2 3)
(x 1 8)(x 2 3)
3
1
1
3
x16
x14
20. } 2 } 5 } + } 2 } + }
x16
x14 x16
x16 x14
x14
3x 1 18
x14
5 }}
2 }}
(x 1 4)(x 1 6)
(x 1 4)(x 1 6)
x2 1 x 2 6
5 }}
2 }}
(x 1 7)(x 2 2)
(x 1 7)(x 2 2)
3
3
12
12
19. }
1}
5 }}
1}
x23
x23
(x 1 8)(x 2 3)
x 2 1 5x 2 24
12
x22
5 }}
2}
+}
x17 x22
(x 1 7)(x 2 2)
2
25. You must have a common denominator before you can
add values in the numerator.
x
x12
4
x25
x
x12
4
x25
x25
x25
x12
x12
}1}5}+}1}+}
x 2 2 5x
4x 1 8
5 }}
1 }}
(x 1 2)(x 2 5)
(x 1 2)(x 2 5)
3x 1 18 2 (x 1 4)
5 }}
(x 1 4)(x 1 6)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
12
215x
5 }}
1}
+}
x24 x24
(x 2 4)(x 2 4)
LCM 5 6x2(x 2 3)
x2 2 x 1 8
5 }}
(x 1 2)(x 2 5)
3x 1 18 2 x 2 4
5 }}
(x 1 4)(x 1 6)
x2 1 4
2x
x2 1 4
2x
26. C; } 2 }
5}
2 }}
x14
(x 1 4)(x 2 4)
x14
x 2 2 16
2x 1 14
5 }}
(x 1 4)(x 1 6)
2x
x24
x2 1 4
5}
+ } 2 }}
x14 x24
(x 1 4)(x 2 4)
2(x 1 7)
5 }}
(x 1 4)(x 1 6)
2x 2 2 8x
9
2x
2x
9
x23
x11
21. } 1 } 5 } + } 1 } + }
x11
x23 x11
x11 x23
x23
x2 1 4
5 }}
2 }}
(x 1 4)(x 2 4)
(x 1 4)(x 2 4)
2x 2 2 8x 2 (x 2 1 4)
9x 1 9
2x 2 2 6x
5 }}
1 }}
(x 2 3)(x 1 1)
(x 2 3)(x 1 1)
5 }}
(x 1 4)(x 2 4)
2x 2 1 3x 1 9
5 }}
(x 2 3)(x 1 1)
5 }}
(x 1 4)(x 2 4)
2x2 2 8x 2 x 2 2 4
x 2 2 8x 2 4
5 }}
(x 1 4)(x 2 4)
15
15
x14
x14
22. }
2}
5 }}
2}
x22
x22
(x 1 2)(x 2 2)
x2 2 4
15
x14
x12
5 }}
2}
+}
x22 x12
(x 1 2)(x 2 2)
15x 1 30
x14
5 }}
2 }}
(x 1 2)(x 2 2)
(x 1 2)(x 2 2)
x 1 4 2 (15x 1 30)
5 }}
(x 1 2)(x 2 2)
x 1 4 2 15x 2 30
5 }}
(x 1 2)(x 2 2)
214x 2 26
22(7x 1 13)
5 }}
5 }}
(x 1 2)(x 2 2)
(x 1 2)(x 2 2)
Algebra 2
Worked-Out Solution Key
439
Chapter 8,
continued
3
x21
x13
30. }
2}
1}
x25
x13
x2 2 25
x13
3
x21
5 }}
2}
1}
x25
x13
(x 1 5)(x 2 5)
x11
x
27. }
1}
x2 1 6x 1 9
x2 2 9
x11
x
5 }}
1 }}
(x 1 3)(x 2 3)
(x 1 3)(x 1 3)
x13
x11
x23
x 2 1 3x
x 2 2 2x 2 3
5 }}
1 }}
(x 1 3)(x 1 3)(x 2 3)
(x 1 3)(x 1 3)(x 2 3)
2x 2 1 x 2 3
5 }}
(x 1 3)(x 1 3)(x 2 3)
x13
(2x 1 3)(x 2 1)
5 }}
2
(x 1 3) (x 2 3)
3
x25
(x 2 4)(x 2 8)
5 }}
2 }}
(x 2 4)(x 1 2)
x13
x25
x28
x12
5 }}
+ } 2 }}
+}
(x 2 4)(x 1 2) x 2 8
(x 2 4)(x 2 8) x 1 2
x 2 2 3x 2 10
x2 2 5x 2 24
2 }}
5 }}
(x 2 4)(x 1 2)(x 2 8)
(x 2 4)(x 1 2)(x 2 8)
x2 2 5x 2 24 2 (x 2 2 3x 2 10)
5 }}}
(x 2 4)(x 1 2)(x 2 8)
2
2
x 2 5x 2 24 2 x 1 3x 1 10
5 }}}
(x 2 4)(x 1 2)(x 2 8)
22x 2 14
5 }}
(x 2 4)(x 1 2)(x 2 8)
22(x 1 7)
5 }}
(x 2 4)(x 1 2)(x 2 8)
5x
2
x12
29. } 1 } 1 }
x
3x 2 1
x24
x 1 2 x(3x 2 1)
2 (x 2 4)(3x 2 1)
5}
+ } 1 }x + }}
x 2 4 x(3x 2 1)
(x 2 4)(3x 2 1)
5x
(x 1 5)(x 2 5)
(x 1 5)(x 2 5)
(x 2 1)(x 2 1 8x 1 15)
x 2 1 6x 1 9
5 }}
2 }}
(x 1 5)(x 2 5)(x 1 3)
(x 1 5)(x 2 5)(x 1 3)
3(x 2 2 25)
1 }}
(x 1 5)(x 2 5)(x 1 3)
x 2 1 6x 1 9 2 (x 3 1 7x 2 1 7x 2 15) 1 3x 2 2 75
(x 1 5)(x 2 5)(x 1 3)
5 }}}}
x25
x13
28. }
2 }}
x 2 2 12x 1 32
x2 2 2x 2 8
x13
(x 1 5)(x 1 3)
(x 1 5)(x 1 3)
1}
+ }}
x13
(2x 1 3)(x 2 1)
5 }}
(x 1 3)(x 1 3)(x 2 3)
x21
x13
5 }}
+}2}
+ }}
x25
(x 1 5)(x 2 5) x 1 3
x(x 2 4)
x(x 2 4)
1}
+}
3x 2 1
x(3x2 1 5x 2 2)
2(3x 2 2 13x 1 4)
5x 2(x 2 4)
5 }}
1 }}
1 }}
x(x 2 4)(3x 2 1)
x(x 2 4)(3x 2 1)
x(x 2 4)(3x 2 1)
3x 3 1 5x 2 2 2x
6x 2 2 26x 1 8
5x 3 2 20x 2
5 }}
1 }}
1 }}
x(x 2 4)(3x 2 1)
x(x 2 4)(3x 2 1)
x(x 2 4)(3x 2 1)
8x3 2 9x 2 2 28x 1 8
5 }}
x(x 2 4)(3x 2 1)
x 2 1 6x 1 9 2 x 3 2 7x 2 2 7x 1 15 1 3x 2 2 75
(x 1 5)(x 2 5)(x 1 3)
5 }}}}
2x 3 2 3x 2 2 x 2 51
(x 1 5)(x 2 5)(x 1 3)
5 }}
x
3
31. }
4
10 1 }x
2
15 2 }x
x
3
}
4
10 1 }x
}26
}26
5
3x
x2 2 18x
x(x 2 18)
+}
5}
5}
30x 1 12
6(5x 1 2)
3x
2
15 2 }x
5(15x 2 2)
75x 2 10
5x
32. }
5}
+}
5}
5}
x
x
5x
x(x 1 20)
x 2 1 20x
}14
}14
5
5
16
16
}
}
x(x 2 2)(x 1 1)
x22
x22
}
}
33.
5 4
+ }}
6 x(x 2 2)(x 1 1)
6
4
}
}1
}1}
x
x11
x
x11
16x(x 1 1)
5 }}}
4x(x 2 2) 1 6(x 2 2)(x 1 1)
16x(x 1 1)
5 }}
2
2
4x 2 8x 1 6(x 2 x 2 2)
16x(x 1 1)
5 }}
2
2
4x 2 8x 1 6x 2 6x 2 12
16x(x 1 1)
5 }}
2
10x 2 14x 2 12
16x(x 1 1)
5 }}
2
2(5x 2 7x 2 6)
8x(x 1 1)
5 }}
(5x 1 3)(x 2 2)
7
1
8x 2 20
2x 2 5
34. }}
x
}
2x 2 5
7
1
2x 2 5
4(2x 2 5)
}}
x
}
2x 2 5
}2}
}2}
5
7
1
}2}
2x 2 5
4(2x 2 5) 4(2x 2 5)
}}
5
+}
x
4(2x 2 5)
}
2x 2 5
427
5}
4x
23
5}
4x
440
Algebra 2
Worked-Out Solution Key
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
x
5 }}
+ } 1 }}
+}
(x 1 3)(x 2 3) x 1 3
(x 1 3)(x 1 3) x 2 3
Chapter 8,
6
3
x22
x 24
}}
35.
1
3
}1}
x22
x12
}2}
2
continued
5
3
6
x22
(x 1 2)(x 2 2)
}}
1
3
}1}
x22
x12
5
3
6
x22
(x 1 2)(x 2 2)
}}
1
3
}1}
x22
x12
x2 1 3x 2 18
4
}
x2 1 10x 1 24
}}
4
} 2 }}
} 2 }}
x 2 1 3x 2 18
4
}
x 2 1 10x 1 24
}}
4
}
}
5
x 2 1 3x 2 18
x 1 10x 1 24
5 }}
2
(x 1 2)(x 2 2)
(x 1 2)(x 2 2)
+ }}
(x 1 6)(x 2 3)
5 }}
(x 1 6)(x 1 4)
3(x 1 2) 2 6
x23
5 }}
3(x 2 2) 1 (x 1 2)
5}
x14
3x 1 6 2 6
5 }}
3x 2 6 1 x 1 2
3x
5}
4x 2 4
x
1
x
x 11
38. }
5
}
x
}2}
21
5}
5
}
x
1
3x 2 3
36. }}
x14
5
}2}
x11
x 2 2 3x 2 4
5}
5
}
x
x
1
x
}2}+}
11x
x
} x
1
3(x 2 2 1)
}}
x14
5
} 2 }}
(x 2 4)(x 1 1)
x11
x
}
5}
5
}
x
5
x2
1
x
11x
}
5
}
x
5
x2
1
x
11x
}
5
}
x
}2}
1
3(x 1 1)(x 2 1)
}}
x14
5
} 2 }}
(x 2 4)(x 1 1)
x11
}}
1
3(x 1 1)(x 2 1)
}}
x14
5
} 2 }}
(x 2 4)(x 1 1)
x11
}}
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
5
}2}
3(x 1 1)(x 2 1)(x 2 4)
3(x 1 1)(x 2 1)(x 2 4)
+ }}
x24
15(x 2 1)(x 2 4) 2 3(x 1 4)(x 2 1)
x24
15(x 2 2 5x 1 4) 2 3(x 2 1 3x 2 4)
5 }}}
x24
15x 2 75x 1 60 2 3x 2 9x 1 12
5 }}}
2
2
1 1 x 2 x3
2x 3 1 x 1 1
5}
5(x 1 1)
3 2 2x
x
39. }
1
2
}2 2 }
x 3 1 x2
x
}
3
5
3 2 2x
x
}
1
2
}2 2 }
x3 1 x2
x
}
3
x3(x 3 1 x 2)
+}
3 3
2
x (x 1 x
)
(3 2 2x)(x 3 1 x 2)
5 }}
3
2
3
2x(x 1 x ) 2 x
x24
5 }}
12x 2 2 84x 1 72
3x 3 1 3x 2 2 2x 4 2 2x 3
5 }}
2x 4 1 2x 3 2 x 3
x24
12(x 2 7x 1 6)
5 }}
2
22x 4 1 x 3 1 3x 2
2x 1 x
5 }}
4
3
x24
12(x 2 6)(x 2 1)
5 }}
x 2(22x 2 1 x 1 3)
37. Sample answer:
x2 2 x 2 6
x 1 4x
}
x12
}
x
x(1 1 x)
x(1 1 x)
+}
5}
5(1 1 x)
5 }}}
}
2
x
1
}2}
11x
x
}
x
}
2
5
x
1
}2}
1
x
}
x11
3x
5}
4(x 2 1)
5
4
+ }4
5 }}
3
x (2x 1 1)
}
5
x2 2 x 2 6
x(x 1 4)
}
x12
}
x
22x 2 1 x 1 3
5 }}
x(2x 1 1)
5 }}
x(2x 1 1)
5
x2 2 x 2 6
}
x(x 1 4)
}
x12
}
x
2(2x 2 2 x 2 3)
x(x 1 4)
x(x 1 4)
+}
2(2x 2 3)(x 1 1)
5 }}
x(2x 1 1)
x2 2 x 2 6
5 }}
(x 1 2)(x 1 4)
(x 2 3)(x 1 2)
5 }}
(x 1 2)(x 1 4)
x23
5}
x14
Algebra 2
Worked-Out Solution Key
441
Chapter 8,
continued
40. }}
5
6
}
1 3x 2 1
21
3
1
2x 2 1
x
}
3
6
}1}
1
x
}12
x
When R1 5 2000 and R2 5 5600,
5
3
1
2x 2 1
x
}
3
6
}1}
x
1 1 2x
3
1
2x 2 1
x
}}
3
6
x
}+}1}
1 1 2x
x
x }
The total resistance when R1 5 2000 ohms and
R2 5 5600 ohms is about 1473.7 ohms.
3x22 1 (2x 2 1)21
x
12
}2 1 }
R1R2
R1R2
1
1
42. Rt 5 }
5}
+}
5}
1
1
1
1
R
1 R1
R
R
2
1 2
}1}
}1}
R
R
R
R1
}2 1 }
R1R2
2
}2 1 }
5
3
1
2x 2 1
x
}
3
6x
}1}
x
1 1 2x
3
1
2x 2 1
x
}
3
6x
}1}
x
1 1 2x
11,200,000
11i
}2 1 }
}2 1 }
(2000)(5600)
1
Pi
Pi
43. a. M 5 }}
5}
1
1 12t
}
1 2 (1 1 i)12t
1 2 1}2
x
5
2
1
5}
5}
ø 1473.7
Rt 5 }
R 1R
5600 1 2000
7600
}
x
5
2
(1 1 i)12t
Pi
Pi(1 1 i)12t
5}
+}
5}
12t
12t
1
12}
12t
(1 1 i)
2
x (2x 2 1)(1 1 2x)
+ }}
2
x (2x 2 1)(1 1 2x)
3(2x 2 1)(1 1 2x) 1 x2(1 1 2x)
5 }}}
3
6x (2x 2 1) 1 3x(2x 2 1)(1 1 2x)
3(4x 2 1) 1 x 1 2x
2
2
3
5 }}
4
3
2
12x 2 6x 1 3x(4x 2 1)
12x2 2 3 1 x 2 1 2x 3
12x 2 6x 1 12x 2 3x
5 }}
4
3
3
2x 3 1 13x 2 2 3
5 }}
12x4 1 6x3 2 3x
(1 1 i)
(1 1 i)
21
b. When P 5 15,500, i 5 0.005, and t 5 4,
Pi(1 1 i)12t
15,500(0.005)(1 1 0.005)12(4)
M 5 }}
5 }}}
12t
12(4)
(1 1 i)
21
(1 1 0.005)
21
48
77.5(1.005)
ø 364.02
5}
48
(1.005) 2 1
Your monthly payment will be $364.02 if you borrow
$15,500 at an annual interest rate of 0.5% and repay
the loan over 4 years.
391t 2 1 0.112
44. a. A 5 }}
0.218t 4 1 0.991t 2 1 1
2x 3 1 13x 2 2 3
3x(4x 1 2x 2 1)
(2x 1 1)(x2 1 6x 2 3)
5 }}
2
3x(2x 2 1)(2x 1 2x 1 1)
Problem Solving
391(t 2 1)2 1 0.112
b. A 5 }}}
0.218(t 2 1)4 1 0.991(t 2 1)2 1 1
c.
d
d
41. T 5 } 1 }
a2j
a1j
d
a1j
d
a2j
5}
+}1}
+}
a2j a1j
a1j a2j
ad 1 dj
ad 2 dj
2ad
5 }}
1 }}
5 }}
(a 2 j)(a 1 j)
(a 1 j)(a 2 j)
(a 2 j)(a 1 j)
When d 5 2468, a 5 510, and j 5 115,
2ad
2(510)(2468)
T 5 }}
5 }}
(a 2 j)(a 1 j)
(510 2 115)(510 1 115)
Amount
Amount
Total
amount of 5 after one 1 after two
dose
doses
aspirin
391t 2 1 0.112
5 }}
0.218t 4 1 0.991t 2 1 1
391(t 2 1)2 1 0.112
1 }}}
4
2
0.218(t 2 1) 1 0.991(t 2 1) 1 1
2,517,360
5}
ø 10.2.
(395)(625)
The total time needed to fly from New York to
Los Angeles and back if d 5 2468 miles, a 5 510 miles
per hour, and j 5 115 miles per hour is about 10.2 hours.
d. Using the graph from part (c) and the maximum
feature, you get a maximum value of about 369, which
occurs when t ø 2.209. The time after the second dose
has been taken is t 2 1 ø 2.209 2 1 ø 1.209. Since
0.209 3 60 ø 13, the greatest amount of aspirin is
in the bloodstream about 1 hour 13 minutes after the
second dose has been taken.
442
Algebra 2
Worked-Out Solution Key
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
5 }}
3
2
Chapter 8,
continued
1
45. 4th expression: 1 1 }}
1
2 1 }}
1
Mixed Review for TAKS
46. B;
21}
1
2 1 }1
a 2 1 b2 5 c 2
2 1 }2
x 2 1 (x 1 4)2 5 202
1
5th expression: 1 1 }}
1
2
x 1 x 2 18x 1 16 5 400
2 1 }}
1
2x 2 1 8x 2 384 5 0
2 1 }}
1
21}
1
}
2b 6 Ïb 2 2 4ac
2 1 }1
x 5 }}
2a
2 1 }2
1
1
2 1 }2
2 1 }2
}}
28 6 Ï82 2 4(2)(2384)
2(2)
2
1 1 }1 5 1 1 }1 + }2
5 }}
}
28 6 Ï 3136
5}
4
2
2
2
511}
5 1 1 }5 5 1}5 5 1.4
411
1
1
28 6 56
5}
4
11}
5 1 1 }2
1
2 1 }1
2 1 }5
2 1 }2
x 5 12
1
5 1 1 }2 + }5 5 1 1 }
10 1 2
2 1 }5
5
12
5
12
47. G;
}
5 1 1 } 5 1} 5 1.416
1
1
21}
1
21}
12
x 5 216
Because x must be positive, x 5 12. So, the length of the
shorter leg is 12 centimeters.
5
5
or
3x 2 4y 5 218
5x 1 2y 5 24
35
3 23
y53
2 1 }2
1
3x 2 4y 5 218
12
12
}
}
511}
5 + 12 5 1 1 24 1 5
3x 2 4(3) 5 218
21}
12
12
3x 2 12 5 218
3x 5 26
12
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
511}
5 1}
ø 1.4137931
29
29
1
1
29
1
x 5 22
The solution is (22, 3).
1
29
511}
511}
+}
1 1 }}
1
12
12
2 1 }}
21}
2 1 } 29
21}
1
29
2 1 }1
2 1 }2
Lesson 8.6
8.6 Guided Practice (pp. 590–592)
29
511}
58 1 12
29
2
x27
3
5x
1.
}5}
511}
70
3(x 2 7) 5 2(5x)
29
5 1}
ø 1.4142857
70
3x 2 21 5 10x
1
1
2 1 }}
1
21}
70
27x 2 21 5 0
511}
1 1 }}
1
29
2 1 }}
1
12
226y 5 278
1 1 }}
511}
5
1
2 1 }1
15x 2 20y 5 290
215x 2 6y 5
27x 5 21
x 5 23
21}
1
Check:
2 1 }1
2 1 }2
1
3
5(23)
21}
70
70
3
215
2
210
}0}
70
511}
511}
140 1 29
169
70
2
23 2 7
}0}
70
511}
+}
29 70
1
1
2}5 5 2}5 5 1}
ø 1.4142012
169
}
The expressions approach Ï 2 ø 1.4142135 . . ..
Algebra 2
Worked-Out Solution Key
443