Document 1804710

Chapter 3,
continued
Lesson 3.5
3. B;
s 5 320t 2 2300, s 5 440t 2 3500
3.5 Guided Practice (pp. 188–190)
320t 2 2300 5 440t 2 3500
10 5 t
The average annual salaries were equal in 1990 1 10, or
the year 2000.
5
4. G;
Let x 5 number of 4-seat tables.
5
Let y 5 number of 6-seat tables.
x 1 y 5 20
3 24
24x 2 4y 5 280
4x 1 6y 5 90
4x 1 6y 5 90
5 11
8
26
1 25
23
1
4
22 28
G
G
511
11 1 (25)
4 1 (22)
26 1 (28)
814
25
6
6
2
214
12
G
F GF G
F
G
F G
F G
F
G
F G
0
2
7 22
y55
GF
22 1 (23)
23
2
0
2 23
5 214
1
24 2 2
There are five 6-seat tables.
022
22 2 0
5 7 2 (23)
23 2 5 1 2 (214)
5. D;
Let x 5 number of small chairs.
26 22
Let y 5 number of large chairs.
5
51x 1 70y a 2000
10 22
28 15
80x 1 110y q 2750
2000
Choice D: 51(24) 1 70(8)a
1784 a 2000 2750
80(24) 1 110(8)q
2 21
3. 24 27
22
2800 q 2750 4.
3
6s 1 8(5 2 s) 5 34
s53
The student spends three hours skating.
7. Let s 5 the price of a soda.
Let p 5 the price of a pretzel.
Let h 5 the price of a hot dog.
Equation 1: s 1 p 1 2h 5 7
Equation 2: 2s 1 p 1 2h 5 8
Equation 3: s 1 4h 5 10
7
24(6)
4
12
24
5
F
F
8
0
4 21
23 25
24(1)
24(0) 24(25)
28 224
28
5
Equation 1: 6s 1 8b 5 34
22s 5 26
0 25
24(22)
Let b 5 the number of hours bicycling.
b552s
1
5 24(27)
6. Let s 5 the number of hours skating.
Equation 2: b 1 s 5 5
23
6
24(2) 24(21) 24(23)
The store can buy and sell 24 small chairs and
8 large chairs.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
4
24
2.
2y 5 10
s 1 p 1 2h 5
F
F
F
22
1.
1200 5 120t
20
GF
1
22 22
0
6
G
3(4) 1 (22)
3(21) 1 (22)
3(23) 1 0
3(25) 1 6
GF
5
10 25
29 29
G
F GF G
F
GF G
95 114
5. B 2 A 5
316
125 100
215
2 278 251
205 300
225 270
95 2 125
114 2 100
5 316 2 278
215 2 251
205 2 225 300 2 270
5
230
14
38
236
220
30
This matrix represents the change in the number of DVD
racks sold from last month to this month.
22s 2 p 2 2h 5 28 Multiply Equation 2 by 21.
2s
5 21
s5 1
1 1 4h 5 10
h 5 2.25
The price of one hotdog is $2.25.
Algebra 2
Worked-Out Solution Key
133
Chapter 3,
(F
GF
F
23x 21
4
1
y
22
F
9
24
3
25
G)
G
G
G
23x 1 9
25
21
y13
22(23x 1 9)
22(25)
22(21) 22(y 1 3)
F
6x 2 18
10
2
22y 2 6
6x 2 18 5 12
5
5
5
5
F
F
F
F
12
10
2 218
12
10
2 218
12
10
2 218
12
10
2 218
G
G
G
G
F GF G
F
GF G
7 23
9.
12
y5
526
24 2 6
11 2 5
4
2(21)
10. 2
F
6
11. 23
26
5.
10
28
5 23
5
2
12
5 1 (28)
2 1 10
21 1 (26)
813
G
5 2 3 23 2 (24)
5
2
1
7.
F GF G
F
GF
0.1
4.4
6.2
0.7
5
1
14. }
2
2.4 20.6
1
6.1
3.1
8.1 21.9
1.2 1 2.4
5.3 1 (20.6)
0.1 1 6.1
4.4 1 3.1
6.2 1 8.1
0.7 1 (21.9)
5
3.6
6.2
4.7
7.5
14.3 21.2
0 15
26
212
221
9
G
F
F
F
5
24(22)
11
24 1 }
2
24 1 }7 2
5.4
1.6
0 23
G
8.1
1.5(1.6)
1.5(0) 1.5(23)
23 5.1
2.4
0 24.5
G
8 12
22
20 21 0
G
F G
F G
10
28
2
1
2
1
2
1
2
} (8)
} (12)
} (20)
1
2
} (21)
1
2
} (0)
1
2
}(10)
1
2
}(2)
21
4
1
6
10 2}2
0
5
1
24
4
G
8
3.4
22
}(28)
5
24(23)
222 27
} (22)
matrix to a 3 3 2 matrix.
Algebra 2
Worked-Out Solution Key
23(23)
2
1.5(5.4)
F
8. This operation is not possible. You cannot add a 3 3 3
134
23(4) 23(7)
1.5(22) 1.5(3.4)
5
2 3 1 matrix from a 2 3 2 matrix.
5.3
5
2
5
6. This operation is not possible. You cannot subtract a
1.2
23(25)
}
12
}
13. 1.5
3 24
25
23(2) 23(0)
7
4
11
2
}
28
5
27 11
22
5
2}8
5
23
10 2 12 28 2 (23)
6 212
4 7 23
24 2}8 2
23 12
5
8
5
24(2)
13.1 .
5
2(4)
2(3) 2(26)
F G
F1
F G
5
21.2
3
6
210
22
2 0 25
12. 24
3. The final matrix has the wrong dimensions.
28 10
25
14 21
2 23 22
the dimensions and then compare the corresponding
elements. If they are the same, then the matrices
are equal.
1
5
3 26
5
2. To determine if two matrices are equal, first compare
22
5
GF
G
F G
F GF
G
F
G
21
are 3 3 4.
21 8
6
5
6
23 2 2
1. The dimensions of a matrix with 3 rows and 4 columns
5 2
22
729
Skill Practice
4.
2
5
3.5 Exercises (pp. 190–193)
F G
F GF GF
F G
F GF G
F
GF G
9
5 12 2 (22)
The solution is x 5 5 and y 5 6.
It should be
5
11
24
22y 2 6 5 218
x5 5
2
1
2
1
2
G
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
6. 22
continued
Chapter 3,
F
15. 22.2
F
F
continued
6
3.1 4.5
21
0 2.5
5.5 21.8 6.4
22.2(6)
G
22. D 2 2C 5
22.2(3.1)
22.2(4.5)
22.2(0) 22.2(2.5)
5 22.2(21)
22.2(5.5) 22.2(21.8) 22.2(6.4)
5
213.2 26.82
2.2
0
17. B 2 A 5
5
5 24
3 21
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
5
0
24 1 (212)
3 1 (26)
21 1 0
18 212
5
0 2 (21)
4(5) 2 18
29
2
3
0
26
}(18)
5
5
F
F
F
5
2
3
2
3
}(26)
25.
2
}3(0)
7.2
1
5
3.4
28.8
1.8 1 7.2
21.5 1 0 10.6 1 (25.4)
28.8 1 2.1 3.4 1 (21.9)
9
5
21.5 5.2
1.5 3.3
26.7
21. C 1 3D 5
13
0 1 3.3
3.6
3
226.6
19.7 28.7
3.3
F
F
3.4
7.2
0
0 25.4
2.1 21.9
1.8 1 3(7.2)
3.3
21.5 1 3(0) 10.6 1 3(25.4)
28.8 1 3(2.1) 3.4 1 3(21.9)
3.3 2 2(0)
G
1.8 21.5 10.6
3.4
28.8
7.2
0
25.4
2.1 21.9
3.3
0.5(1.8) 2 7.2
0
G
21 3x
5
24
10.7
GF
G
21 218
5
5
2y
G
0.5(0) 2 3.3
2y 5 24
x 5 26
y 5 22
6
22x
F
1 28
G F
12
22x 1 2(5)
5 21
6
27
6 1 2(21)
1 1 2(27) 28 1 2(6)
F
G
G
3x 5 218
F
G
0.5(21.5) 2 0 0.5(10.6) 2 (25.4)
3.6 23.3
26.5
4
GF
GF
GF
5
5
5
213 4
y54
29
4
213
y
29
4
213
y
29
4
213
y
G
G
G
19
x5}
2
19
The solution is x 5 }
and y 5 4.
2
26.
2
F
F GF
8 2x
5
2
6
2(8) 2 3
2(5) 2 10
3
29
10 24y
2(2x) 2 (29)
F
22x 1 9 5 4
5
x 5 }2
GF G
GF G
GF G
5
5
2(6) 2 (24y)
13 22x 1 9
1.8 21.5 10.6
28.8
G
0 2 2(21.5) 25.4 2 2(10.6)
22x 1 10 5 29
0 25.4
3.3
0
G
2.1 2 2(28.8) 21.9 2 2(3.4)
0
2.1 21.9
3.4
22x 1 10
1.8 21.5 10.6
20. C 1 D 5
1.8 21.5 10.6
28.8
0
24
3.3
The solution is x 5 26 and y 5 22.
12 28
5
2.1 21.9
26.3 20.75
24.
18 24
}(212)
25.4
0.5(28.8) 2 2.1 0.5(3.4) 2 (21.9)
2 24
4(21) 2 0
18 212
5
0
26
4(24) 2 (212)
4(3) 2 (26)
1
18 212
2
3 21
21
13 28
0
7.2 2 2(1.8)
2
3 21
18 2 5 212 2 (24)
5 24
23
F
7.2
23. 0.5C 2 D 5 0.5
23 216
5
5 24
2
0
26
18 212
26
26 2 3
2
2
19. } B 5 }
3
3
5
1
5 1 18
18. 4A 2 B 5 4
5
GF
G
F
F
5
G
GF G
GF G
GF G
F GF G
F
GF G
F GF
G
F G
F
G
F
G
F
G
F
G
F
G
F
G
F
G
F
G
5
F
F
F
F
25.5
3.96 214.08
212.1
16. A 1 B 5
5
29.9
G
22
F
0
12 1 4y
13
0 16
13
4
0 16
13
5
4
4
0 16
12 1 4y 5 16
y51
5
The solution is x 5 }2 and y 5 1.
0 1 3(3.3)
23.4 21.5 25.6
22.5 22.3
9.9
Algebra 2
Worked-Out Solution Key
135
Chapter 3,
F GF
F
GF
F GF
21 2
4x
5
3 6
4x(21)
4x(2)
8 216
12x
5
24x
3y
224
8x
24x
3y
224
5
4x(3) 4x(6)
8 216
8 216
3y
224
G
G
G
d.
3X 2
F
3y 5
24x
x 5 22
3y 5
24(22)
3b 2 (26)
3c 2 2
3d 2 1
y 5 20.25
X5
Problem Solving
30. a.
5
F G F G
F GF G
F
GF G
23 2
4 23
a 1 (25)
d 1 (23)
5
7 28
5
5
23
b10
c14
2
5 2
0
25
X1
7 28
5
5
5
23
a 5 12, b 5 28, c 5 27, and d 5 8.
G
F GF G
F
GF G
X5
b.
F
X2
3
5
0
a22
b23
c25
d20
5
5
8
30
19
16
20
14
29
39
36
31
32
42
29 20
12
17
25
16
28 40
32
21
30 2 29 19 2 20
5 2 12 16 2 17
20 2 25 14 2 16
29 2 28 39 2 40
36 2 32 31 2 21
0
5
1
21
27 21 25
22
1 21
F
4
Mid-size
6
Mini-van
Suv
6
21 3
c.
4
3
23 1
2X 1
4 7
5
2a 1 (23) 2b 1 1
2c 1 4
2d 1 7
8 29
32
40
24
34
18
25
0
22
8 29
5
0
10
X5
F
10
4 23
G
34.56
18
25
19
22
5
Downtown
Mall
b. M 1 J 5
5
5
F
F
F
F
B
31
42 18
22
25 11
31
42 18
25 11
19.44
C
GF
GF
1
A
B
25
36 12
38
32 15
32 15
18 1 12
22 1 38
25 1 32
11 1 15
78 30
57 26
G
G
G
36 12
38
42 1 36
56
C
25
31 1 25
60
27
June (J )
A
22
43.2
25.92 36.72
20.52 23.76
May(M)
a 5 211, b 5 10, c 5 4, and d 5 23.
211
40
24 34
After an 8% increase: 1.08
10
G
F GF G
19
33. a.
G
Highway mpg
32
F G
F GF G
F
GF G
X5
9
G
10
a 5 10, b 5 9, c 5 4, and d 5 3.
10
G
G
32 2 32 47 2 42
Economy
21 3
8
47
5
City mpg
8
2
32
32.
12 28
27
F
F
F
F
31. Change in sales 5 Sales for 2004 2 Sales for 2003
5 10.1
,B5
F G
2}3 3
17
29. Sample answer:
25 4
2
219
2}
1
3
5 9.6 1 0.50
A5
213 15
5
G
G
17
2
3x 2 2y 5 3(3.2) 2 2(20.25)
10 3
2
219
a 5 2}3, b 5 3, c 5 2}
, and d 5 1.
3
The solution is x 5 22 and y 5 216.
x 5 3.2
1
2
213 15
5
3a 2 11
y 5 216
3y 5 20.75
GF
GF
11 26
2
24x 5 8
28. C; 2x 5 6.4
F
G
This matrix represents the total sales for May and June.
136
Algebra 2
Worked-Out Solution Key
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
27.
continued
Chapter 3,
continued
F
1 56
1
c. }(M 1 J) 5 }
2 60
2
78 30
57 26
GF
5
28
39 15
30
28.5 13
G
7. 2x 2 y 2 3z 5
2x 2 3y 5 10 l x 5 210 2 3y
34. No, the matrix A 1 B does not give meaningful
2(210 2 3y) 2 y 2 3z 5 5
information. The team size in each matrix is an average,
but the sum of the two averages is not an average.
35. A 5
3A 5
F
F
1
1
5
5
1
4
1
4
3
3 15
3 12
G
15
3 12
5
x 1 2y 2 5z 5 211
27y 2 3z 5 25
(210 2 3y) 1 2y 2 5z 5 211
y
2y 2 5z 5 21
27y 2 3z 5 25
G
2y 2 5z 5 21
27y 2 3z 5 25
7y 1 35z 5 7
3 (27)
2
32z 5 32
2
x
The height of the large rectangle is three times the
height of the small rectangle, and the width of the large
rectangle is three times the width of the small rectangle.
Therefore, the large rectangle is nine times the size of the
small rectangle.
z5 1
27y 2 3(1) 5 25 l y 5 24
x 1 2(24) 2 5(1) 5 211 l x 5 2
The solution is (2, 24, 1).
8.
Mixed Review for TAKS
x 1 y 1 z 5 23
22x 2 2y 2 2z 5 6
3 (22)
4x 2 5y 1 2z 5 16
4x 2 5y 1 2z 5 16
2x 2 7y
36. C;
42 students chose only running as their favorite activity.
2x 2 3y 1 z 5 9
37. F;
4x 2 5y 1 2z 5 16
y
5 22
4x 2 5y 1 2z 5 16
When the y-intercept is decreased, the line shifts to the
left, so the x-intercept also decreases.
2x 2 7(22)
Quiz 3.3–3.5 (p. 193)
1.
5 22
24x 1 6y 2 2z 5 218
3 (22)
5 22 l x 5 4
4 1 (22) 1 z 5 23 l z 5 25
2.
y
The solution is (4, 22, 25).
y
9.
2x 2 4y 1 3z 5 1
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
22x 1 5y 2 2z 5 2
y1 z53
1
4.
y
2
1
x
y
22x 1 5y 2 2z 5 2
y1 z5 3
x
21
6x 1 2y 1 10z 5 19
6x 1 2y 1 10z 5 19
1
x
22
3.
1
x
26x 1 15y 2 6z 5 6
33
17y 1 4z 5 25
24y 2 4z 5 212
3 (24)
17y 1 4z 5
17y 1 4z 5 25
13y
1
25
5 13
y5
1
11z53lz52
1
5.
2x 2 4(1) 1 3(2) 5 1 l x 5 2}2
6.
y
y
The solution is 1 2}2, 1, 2 2.
1
8
10. A 1 B 5
1
21
22
x
x
5
F GF G
F
GF G
F G F G
F
GF G
11. B 2 2A 5
5
2 25
1
3 21
3
24
8 10
2 1 (24)
25 1 3
318
21 1 10
24
3
8 10
24 2 2(2)
22
5
22 22
11
9
2 25
3 21
3 2 2(25)
8 2 2(3) 10 2 2(21)
5
28 13
2 12
Algebra 2
Worked-Out Solution Key
137
Chapter 3,
continued
matrix to a 2 3 3 matrix.
2
13. } C 5
3
5
F
F
2
} (26)
3
2
} (22)
3
2
2
3
}3(1)
2
3
}(24)
4
24
2}3
2
3
2}3
}(21)
6
8
}
2
} (9)
3
2
2}3
G
G
3. AB 5
5
5
F
F
F
1 22
1(5) 1 (22)(22)
g 5 21
7
2
23
0
4
1
21
2
5 23
0
1.4e 1 1.1r 1 1.3g 5 25
25
2e 1 2r 1 2g 5 42
22e 1 r 2 2g 5 0
20.3(14) 2 0.1g 5 24.4 l g 5 2
25 213
5. AB 2 AC 5
2
e 1 14 1 2 5 21 l e 5 5
You should buy 5 pounds of Empire, 14 pounds of Red
Delicious, and 2 pounds of Golden Delicious apples.
2.
3.
F
F
F
8
8
G
32.24 17.68 23.12
22.08 14.56 28.32
G
26 11 25
21 11
7
18 20 28
5.
Hardcover
Paperback
F
7
23
4.
F G
G
R
M
S
C
44
36
38
21
76
44
22
50
12
3.6 Guided Practice (pp. 195–198)
1. AB is defined and has dimensions 5 3 2.
2. AB is not defined because the number of columns in A
does not equal the number of rows in B.
5
1
0
G
21
2
23
0
4
1
21
2
23
0
4
1
4(23) 1 1(21)
G F G)
G F G)
3
22 21
24
5
1
0
23(2) 1 0(21)
14(2) 1 1(21)
21(24) 1 2(1)
21(5) 1 2(0)
2 23(24) 1 0(1)
23(5) 1 0(0)
5
27
24
29
26
10
7
GF G
G
G
213
1
5 221
9
1
1
6. 2}(AB) 5 2}
2
2
5
F
4(5) 1 1(0)
6
G
G
25
12 215
2
20
215
25 213
27 24
29
26
10
7
1
2}2 (27)
1
2}2 (29)
1
2}2 (10)
G
2
4(3) 1 1(22)
38 239
211
24
23(23) 1 0(21)
4(24) 1 1(1)
G
2
21(2) 1 2(21)
22 225
Algebra 2
Worked-Out Solution Key
22 21
G F G)
G
21(3) 1 2(22)
Lesson 3.6
138
2
5 23(3) 1 0(22)
Graphing Calculator Activity 3.5 (p. 194)
1.
9
5 221
22e 1 r 2 2g 5 0
3r
5 42
r 5 14
19 25
3
4(7) 1 1(23)
213
1
20.3r 2 0.1g 5 24.4
32
G (F
GF
5 23(7) 1 0(23)
21.4e 2 1.4r 2 1.4g 5 229.4
e 1 r 1 g 5 21
F
F
F
F
(F
(F
F
F
F
F
F
9
21
3 (21.4)
1.4e 1 1.1r 1 1.3g 5
G
212 221
G
23 21
4 1
21(7) 1 2(23) 21(23) 1 2(21)
Equation 3: r 5 2(g 1 e), or 22e 1 r 2 2g 5 0
r1
23 22
1(1) 1 (22)(23)
Equation 2: 1.4e 1 1.1r 1 1.3g 5 25
e1
G
5
23(5) 1 3(22)
r 5 pounds of Red Delicious apples
g 5 pounds of Golden Delicious apples
Equation 1: e 1 r 1 g 5 21
1
23(1) 1 3(23)
4. A(B 2 C) 5
14. e 5 pounds of Empire apples
GF
3
23
1
2}2 (24)
1
2}2 (26)
1
2}2 (7)
GF G
5
}
7
2
2
9
2
3
}
7
25 2}2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
12. The sum 3A 1 C is not possible. You cannot add a 2 3 2