{

{
1
0
5
1
42
1 58.5
0 130.5
continued
{
1
0
5
48. H;
1
1
0
The pentagonal prism has 15 edges.
Cl 5 }}}
6
Lesson 3.8
3.8 Guided Practice (pp. 210–213)
(130.5 1 292.5 1 0) 2 (210 1 0 1 0)
5 }}}
5 35.5
6
The atomic weights of flourine, sodium, and chlorine are
19, 23, and 35.5, respectively.
F
4
1
1. }
24 2 2 22
70 128 1 70 128
1
0 70
45. a. Area 5 6}
0 70 1
2
124
36
124 36 1
{
1
{
21
6
G F
4
21
22 22
6
1
5}
5
F
8 25
1
2. }
28 2 (220)
5 4786
{
{
F
22
1
3. }
624
1
5 3201
2
The area of the bottom triangular region is 3201 mi .
c. Total area 5 4786 1 3201 5 7987
The total of the Dinosaur Diamond is 7987 mi2.
d. You could connect Vernal, UT, to Moab, UT, to
create a left and right triangular region.
{
1
{
1
x 120
1 100 50 5 5000
1
0
0
6}2F (50x 1 0 1 0) 2 (0 1 0 1 12,000) G 5 5000
1
6}2 (50x 2 12,000) 5 5000
Two possibilities:
1
1. }2 (50x 2 12,000) 5 5000
4
6 21
1
24
4. 2}
0 24
1
2}4
G F
x 5 40
The farmer could put the final post at (40, 120) or
(440, 120).
Mixed Review for TAKS
47. C;
Total pay 5 Salary 1 Bonus + Number of new customers
150
Algebra 2
Worked-Out Solution Key
8 25
4 21
F G
}
2
3
2}
12
1
3
2}
12
5
1
4
1 22
5 }2
1
21
2
1
2
2}2
G
1
5
3
1
24
2}4
}
0
}
24
1
1
6
0
6
1
0
0
1
}
1 23
}
}
24
0
1
6
1
5. A 5
F
2 22
2
0
1
24
}
8
9
1
6
24
6
0
}
9
F
2}4 1 }4
014
011
21 22
4
G F
21
1
22 1 1
X5
0 22 ; A
12 24 26
2}4
X5
X5
1
2. 2}2 (50x 2 12,000) 5 5000
225x 5 21000
12 a c, or c q 12
G
F G
F GF G
F GF G F GF G
F G F
G
23
5
x 5 440
60 a 5c
3
1
4 21
25x 5 11,000
450 a 390 1 5c
}
11
}
1
46.
1
5}
12
5
70
0
36
5 6}2 [(0 1 8680 1 2412) 2 (0 1 0 1 4690)]
x 120
1
6}2 100 50
0
0
2}
22
2}
11
The area of the top triangular region is 4786 mi2.
0 70 1
0
67
0 1 67
124 36 1 124
1
2
11
}
F G F G
5 6}2 [(4900 1 15872 1 0) 2 (8680 1 2520 1 0)]
1
b. Area 5 6}
2
G
1
G
21 21.5 0.5
5 21.5 21.5 0.5
21
22 0.5
G
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Chapter 3,
Chapter 3,
continued
F GF
G
F
G
F G
F
GF G
F
G
F G
F G
F
G
F GF
G
F
Check:
AA21 5
5
2
22
0
21 21.5
0.5
2
0
22
21.5 21.5
0.5
12
24
26
21
0.5
22 1 3 1 0
23 1 3 1 0
22 1 0 1 2
23 1 0 1 4
11021
212 1 6 1 6 218 1 6 1 12
62223
1
0
0
5 0
1
0
0
0
1
12110
0.01307
0.2026 20.0327
0.1503 20.1699
0.1242
2
22
0
0.06535 1 0 2 0.0654
0.5
2
0
22
0.7515 1 0 1 0.2484
21
22
0.5
12
24
26
01323
22 2 4 1 6
21022
01423
1
0
0
5 0
1
0
0
0
1
23
4
5
1
5
0
5
2
2
21
A
ø
0.01307
0.1242
Check:
23
4
5
1
5
0
5
2
2
AA21 ø
20.0654 20.0131
0.01307
0.1634
0.2026 20.0327
0.1503 20.1699
0.1242
23 3 1024
22 3 1024
24
0.99988
25 3 1025
2 3 1024
1 3 1024
0.9999
21.1 3 10
1
0
0
ø 0
1
0
0
0
1
2
1 22
5
3
4
3
5I
0
12 27
; A21 5 220 12
25
8
1.5 21
0.5
3
Check:
21
AA
2
1
22
12
5 5
3
0
4
3
8
24 2 20 2 3
5
27
3
220
12
25
1.5
21
0.5
214 1 12 1 2
62521
60 2 60 1 0
235 1 36 1 0
15 2 15 1 0
48 2 60 1 12
228 1 36 2 8
12 2 15 1 4
1
0
0
5 0
1
0
20.0654 1 0.06535 1 0
0
0
1
20.327 1 0.02614 1 0.3006
G
1.0001
0.1962 1 0.05228 1 0.7515
5
5I
12
27
3
2
1
22
0.0393 1 0.8104 2 0.8495
A21A 5 220
12
25
5
3
0
20.0131 1 1.0130 1 0
1.5
21
0.5
4
3
8
20.0655 1 0.4052 2 0.3398
20.4902 2 0.1308 1 0.621
0.1634 2 0.1635 1 0
0.817 2 0.0654 1 0.2482
5
7. A 5
0.1634
0.2026 20.0327
0.1503 20.1699
F
F G
G
0.99998
2 3 1024
0
25 3 1025
0.9999
21 3 1024
22.6 3 1024
21 3 1024
0.9998
1
0
0
ø 0
1
0
0
0
1
5I
G
2
F
G
F G
F G F G
F GF G
F
G
F G
F GF G
F
G
F G
5
5I
20.0654 20.0131
2
0.6012 2 0.8495 1 0.2484
20.327 1 0 1 0.3268
0.5
31022
5
0.05228 1 1.013 2 0.0654
21.5
5 23 2 3 1 6
0
20.2616 2 0.0655 1 0.3268
21.5
01323
5
5
20.4509 2 0.1699 1 0.621
21
21022
4
1
0.1962 2 0.0131 1 0.817
5I
22 2 3 1 6
GF G
23
5 20.03921 1 0.2026 2 0.1635
A21A 5 21.5
6. A 5
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
22
F
F
0.1634
20.0654 20.0131
A21A 5
24 2 35 1 12
12 2 21 1 9
5 240 1 60 2 20
220 1 36 2 15
32512
1.5 2 3 1 1.5
224 1 0 1 24
40 1 0 2 40
23 1 0 1 4
1
0
0
5 0
1
0
0
0
1
5I
Algebra 2
Worked-Out Solution Key
151
Chapter 3,
F GF G F G
F GF
4
1
3
x
5
10
5
y
21
5 21
1
A21 5 }
17
4
23
X 5 A21B 5
1
5
17
2}
17
}
5
3
4
17
2}
17
}
1
3. }
425
G
5
17
2}
17
10
3
2}
17
4
}
17
21
3
5
22
The solution of the system is (3, 22).
9.
x
6 23
y
26
5
2
y
2
1
4
3
21
X5A B5
F
7
6
1
7. }}
228 2 (224) 24 24
3
2
2
1
1 }2
}
25
8
3
2
}
5
0
m
17
2
2
1
p
5 35
4
3
2
d
69
F G
A movie pass costs $8, a package of popcorn costs $1, and
a DVD costs $17.
7
6
1
5 2}4 24 24
F G
x
y
4
Matrix of constants: 22
2. First, you find the determinant of A. Then, switch the
elements on the downward diagonal and negate the
elements on the upward diagonal. Finally, you
multiply } and the new matrix.
Algebra 2
Worked-Out Solution Key
G
3
2}4
2}2
1
1
F G
5
11
1
1
2}
2}
36
72
F
260
G
F
1
30 260
5 2}
360
6
F G
F GF G
F G
224
224
1
1
1
1
15
2}
60
5
1
21 2 }6
10. }
10
4
2}3 2 1 2}
32
4
4
3
}
G
}6
2}
12
5
}
5
21 2 }6
1
5 }2
5
FG
FG
}
2}
2}
12
24
30
1
9. }}
2720 2 (2360) 6
3.8 Exercises (pp. 214–217)
152
6
2
17
1
det A
7
3
2
3
20 22
1
5 2}
144 12
6
5
1
1. Matrix of variables:
3
F G
20 22
1
8. }
120 2 264 12
8
Skill Practice
F G
7
21
F GF G F G
FG
1
5
2}2
G F
5
1
1 }2
5
6
25
3
9
1
5 2}3 22 27
27
8
2
A B5
9
5
}
The solution of the system is (21, 2).
21
6
3 22
1 21
2 22
1
5 }2
25
5
2
11.
22
4 23
5
21 23
GF G F G
F GF G
F GF G F G
x
1
2
1
5. }
12 2 10 25
21 21
4 23
5 1 3 22
3 22
2
3 21
A21 5 }2
4 23
24 25
5
1
5
1
24
1
5
218
Because {A{ 5 0, }is undefined and A does not
{A{
have an inverse. The system has infinitely many solutions.
F
1
4
5 21 1
1
1 23
A21 5 }0
26
10.
5
3
1
6. }}
221 2 (218) 22
F GF G F G
F G
2 21
4
1
4. }
28 2 (29)
F GF G F G
1
}
F G F GF G
F G F GF G
F G F GF G
F G F G
4
3
4
}
1
5
2
}
2 }2 2 }
12
2
3
1
11. The new matrix should have been multiplied by },
det A
not by det A.
F G F G
F GF
2
4
1
5
21
12. C;
21
1
210 2 (29) 23
}
3
10
2
5
F G
5
6
}
5 24
1
5 }6 21
5
1
1
2 }6
23
3 210
G
2
2 }3
1
3
}
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
8.
continued
Chapter 3,
continued
F GF G
F GF G F
F G F
F
F GF G
F GF G F
F G F
F
F GF G
F GF G F
F G F
F
F GF G
5 21
1
13. }
1 24
1
5 21
5
5 21
1 1
1
4 5
24
1
24
X5
1 0
3
1
14. }
2 22
3
}
2
28
5
6
6
8
3
2
3
1
0
21
0
1
11
21
X5
X5
21
0
}
}
6
4
1
4
1
0
0
1
1
16. 2}
12 21
X5
23
F GF
1
1
2
2}6
}
1
}
12
1
}
4
2}6
1
}
12
G
F G
23 6
1 2
1
0
0
1
}18
X5
9
2
23 2 6
25
2
}
24 29
21
0
}
}
3
2
1
4
23 1 0
9
2
}11
23
11
2
}
1
1
0 2}2
5
X5
0 22
F G F
F
1
0
0
1
X5
GF G
G
G
F GF
F GF G
F G
1 3 22
18. }
3 9 25
5
3
4
110
3
1
19. A21 5
1
2}4
F
F
F
Check:
2
29
3
1
0
0
1
0.9
0.6
20.2
0.2
1
0
5
12
19
}
6
29
12
}
8
2
1
6
}11
1
1
2}
1 }2
12
G
F GF G
F
G
F G
G
GF
G
1 2}3
4
5
0
5
2}3
3
1
6
3
422
2
5 2 }3
2
}
13
3
24
7
}
40
3
210
024
0 2 10
20.3
20.2
0.3
0.9
0.6
0.1
20.2
0.2
0.2
0.6 1 0 2 0.6
0.4 1 0 1 0.6
20.9 1 0.9 1 0
20.6 1 0.6 1 0
0.3 1 0.1 2 0.4
20.6 1 0 1 0.6
0.9 1 0.1 1 0
F G
1
0
0
5 0
1
0
5
12
0
0
1
}
G
G
20.3 1 0.9 1 0.4 20.2 1 0.6 2 0.4
5
}
7
6
022
0.1
3
5 21
0 1 10
0.2
1
4
1
1
}
}
12 4
5
2}6 1 4
10
19
G
0.3
3
F GF G
F
G
F G
18
5
22
1
2
024
12 2 5 15 2 }3
1
}
8
023
X5
0
2}6
4
23 24 22
X5
1
}
6
2
AA21 5 22
1
2
0
5
20.3 20.2
5
3 21
3 1 15 21 1 20
X5
5
2}2 1 }4
0
1
2}2
3 2}3
25
5
2}3
}
2
2
1 2}3
5
2
1
1 2}3
3 21
}12
X5
5
}
}
1
X5
3
610
1
4
X5
4
3
6
}
GF G
G
G
24
24 1 0
0
1
5
0
1
2}2
G
5
2
1
X5
0 22
21
}
X5
2 26
3
}
2
21
3
2
0
}
9
3
5
21
3
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
0
15 2 6
5
2
1
29 26
X5
4
1
15. 2}
4 26
6
24
21
24
3
21
28 2 1 212 1 6
X5
3
}
2
2
1
10 1 1
X5
0 1
GF G
G
G
5 21
24
F G
F GF G F GF
F
1 22 25
17. 2}
2
0
1
G
5I
Algebra 2
Worked-Out Solution Key
153
Chapter 3,
A A5
5
F
F
20.3
GF
0.3
20.2
1
1
22
0.9
0.6
0.1
22
0
3
20.2
0.2
0.2
3
1
0
20.3 1 0.4 1 0.9
G
21
A A5
20.3 1 0 1 0.3
0.9 2 1.2 1 0.3
0.9 1 0 1 0.1
20.2 2 0.4 1 0.6
20.2 1 0 1 0.2
G
5
5 0
1
0
0
0
1
}
}
20.8 3
}
1.1 6
21. 3
20. A21 5
Check:
1
21
AA
0
}
}
0. 3
}
20. 6
2
5 2
1
3
1
4
4
0
5 2
1
1
5
F
4
2
3
4
8
5
10
F G
154
2}3
5
2}6
1
}
3
1
}
6
7
}
6
2
2}3
1
}
6
14
2}3 2 }
1}
3
3
1
0
0
5 0
1
0
0
0
1
Algebra 2
Worked-Out Solution Key
5I
2
1
6
}
4
8
1
5
2
1
7
6
4
3
1
6
G
0
1
0
0
0
1
Check:
AA
G
1
1
2}3 1 0 1 }3
}1}22
8
3
1
3
2}3 1 }6 1 }2
4
3
4
3
8
3
2}3 1 }3 1 }3
2
1
1
1
2
2
2
2
1
3
1
4
4
1
0
2
2
1
3
1
4
4
4
4
1
2
2
2
4
5
2
7
3
2
3
2}3 1 1 1 }3
0 2 }3 1 }3
}221}
5I
20.5
0
0.5
0.125
0.4375
0.21875
0.0625
20.03125
5 22
G
8
2}3 1 4 2 }3
21.0625
1 21
21
4
4
}102}
3
3
}1}2}
0
0
0 1 }3 1 }3
F G
F
F GF
F
1
1
0 1 }3 2 }3
2}6 1 }3 1 }6
5 0
21. A21 5
1
4
3
7
}
}
0.1 6
}
0.1 6
20. 3
}
2}3 2 }6 1 }2
4
}
}
0. 3
}
20. 6
1. 3
2}3
4
7
2}3 1 0 1 }3
1
6
}2}1}
F G
4
1
5
}
}
0.1 6
}
0.1 6
}
}
20.8 3
}
1.1 6
}
2}3
20. 3
21. 3
1
3
2}3 1 }3 2 }3
5I
1. 3
2}3
7
6
}
F G
F
G
F GF
F G
0
4
3
}
0.4 1 0.6 1 0
1
}
5 2}6
GF G
F G
}
}
0.1 6
}
0.1 6
20. 3
F G
F
4
21.8 1 1.8 1 0
0
}
}
0. 3
}
20. 6
1. 3
2}3
0.6 2 0.6 1 0
1
F
}
}
20.8 3
}
21.1 6
21. 3
G
G
2
20.5
0
0.5
3 10
21.0625
0.125
0.4375
3 21
2
0.21875 0.0625 20.03125
20.5 1 1.0625 1 0.4375
0 2 0.125 1 0.125
1 2 3.1875 1 2.1875
0 1 0.375 1 0.625
21.5 1 1.0625 1 0.4375
0 2 0.125 1 0.125
5
0.5 2 0.4375 2 0.0625
21 1 1.3125 2 0.3125
1.5 2 0.4375 2 0.0625
F G
1
0
0
5 0
1
0
0
0
1
5I
G
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
21
continued
Chapter 3,
F
F
GF
0
20.5
A21A 5 21.0625
5
continued
0.5
0.125
0.4375
1 21
22
0.21875 0.0625 20.03125
G
2
3 10
3 21
A21A ø
2
20.5 1 0 1 1.5
F
F
F
0.03425
21.0625 2 0.25 1 1.3125
0.5 1 0 2 0.5
0.08219
0.08219
0.01370
0.34247
20.10960
5
21
0
8
1
12
25
0
5
20.21875 1 0.1875 1 0.03125
G
20.16438 1 0 1 0.1644
1.31506 1 0 2 1.3152
21 1 0 1 1
22. A
0.41095 1 0.65752 2 0.0685
23.28765 1 2.73976 1 0.548
20.03425 1 0.03425 1 0
F G
F
F G
F
F
1
0
0
5 0
1
0
0
0
1
ø
0.17125 1 0.274 2 0.4452
0.4375 1 0.625 2 0.0625
5I
0.03425
21
0.03425
0.08219
0.08219
20.08219 1 0.08219 1 0
21
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
AA
0.65753 1 0.34247 1 0
G
0.08904
0.01370
20.65753 0.34247 20.10960
Check:
G
F
G
F G
F
G
F GF
G
F
G
F G
0
0.99997
0
24
24
1
1
0
0
1
0
0
1
22
5
21
0
8
1
0
12
25
0
0.03425
0.03425
0.08904
0.08219
0.08219
0.01370
20.65753
0.34247
20.10960
G
Check:
20.0685 1 0.41095 1 0.65753
21
AA
0 1 0.65752 2 0.65753
5
5 3 1025
25
1.1 3 10
21.4 3 10
23. A21 5
5I
0.15
0.3
0.05
20.06875
0.1125
0.01875
20.025
20.05
20.175
5
3 28
0
2
1
20.06875 0.1125 0.01875
0 26
20.025 20.05 20.175
4
21
0.411 2 0.41095 1 0
G
0.99998
2 3 10
5
ø 0
ø
G
20.0685 1 0 1 1.06848
1.0625 1 0.375 2 0.4375
22.125 1 1.25 1 0.875
0.08904
20.65753
22
0.21875 2 0.125 2 0.09375
0.03425
0.15
0.3
0.05
0.45 1 0.55 1 0
0.9 2 0.9 1 0
0 1 0.65752 1 0.34247
5 0.3 2 0.275 2 0.025
0.6 1 0.45 2 0.05
0.411 2 0.41095 1 0
20.15 1 0 1 0.15
20.3 1 0 1 0.3
20.0685 1 0.41095 2 0.34247
20.17808 1 0.0685 1 0.10960
0 1 0.1096 2 0.10960
1.06848 2 0.0685 1 0
F
F G
22.0 3 1025
0.99998
25
0.99999
5 3 1025
5 3 1025
5 21.0 3 10
1
0
0
ø 0
1
0
0
0
1
G
0.15 2 0.15 1 0
0.1 1 0.075 2 0.175
G
20.05 1 0 1 1.05
1
0
0
0
5 0
1
0
0.99998
0
0
1
2.0 3 1025
5I
5I
Algebra 2
Worked-Out Solution Key
155
Chapter 3,
0.15
0.3
GF
0.05
3 28
A21A 5 20.06875 0.1125 0.01875
2
20.025 20.05 20.175
21
G
4
1
A21A ø
0 26
0.45 1 0.6 2 0.05
0 1 0.3 2 0.3
0.55 1 0.45 1 0
0 1 0.1125 2 0.1125
F G
F
F GF
F
1
0
0
5 0
1
0
0
0
1
0.2766
ø
G
21.2 1 1.2 1 0
0.2 2 0.2 1 0
24. A
5
20.075 2 0.1 1 0.175
20.2979
0.1489
0.2128
G
1
5
0.2766 20.2340 20.1915
AA21 5 22
2
1
0.3191
F
F G
3 21
6
20.0851
0.1915 20.2979
0.2128
25.
5 20.5532 1 0.6382 2 0.0851
F
20.936 1 0.1915 1 0.7445
A
0.468 1 0.383 1 0.1489
20.766 2 0.2979 1 1.064
0.383 2 0.5958 1 0.2128
20.5745 1 0.2979 1 1.2768
F
F G
1
0
G
1 3 1024
0.9999
0
1.0002
1
0
0
0
1
5I
21 3 1024
1
0
0
ø 0
1
0
G
0
0
1
1.0002
5
y
225
1
1 22
5 2}
15
7
5
4
1
}
2
15
2}
15
7
4
2}
2}
15
15
1
2
15
}
2}
15
10
4
225
7
5
3
2
The solution is (3, 2).
26.
F GF G F G
F GF G
F GF G F G
4
7
x
2
3
y
21
A
G
10
x
5
216
24
3
3 27
1
5 2}2
22
4
5
3
7
2
2}2
}
1
22
The solution (10, 28).
Algebra 2
Worked-Out Solution Key
24 3 10
GF G F G
F GF G
F GF G F G
X 5 A21B 5
156
G
5I
2}
2}
15
15
21 3 1024
0
2 3 1024
X5A B5
1 3 1024
0
1
24
21
5 21 3 1024
1
0
5 23 3 1024
4 21
21
G
1 3 1024
27 22
0.8298 2 0.3191 2 0.5106
20.702 2 0.1915 1 0.8934
1
6
0.3191 1 0.383 1 0.2979
0.9999
1.1064 1 0.3191 2 0.4255
2
3 21
1.2764 2 0.383 2 0.8937
20.0851 1 0.2978 2 0.2128
4
0.1489
22
20.3404 2 0.2978 1 0.6384
20.4255 1 0.1489 1 1.2768
G
5
1.1064 1 0.468 2 0.5745
1.383 2 0.234 2 1.149
20.1915
1
0.2128
1.5955 1 0.1915 2 1.7874
0.1915
20.0851
0.1915 20.2979
0.1489
4
0.2766 2 0.468 1 0.1915
0 2 0.05 1 1.05
20.2340
ø 0
0.3191
5I
0.3191
GF
0.2766 20.2340 20.1915
20.0851
5 20.20625 1 0.225 2 0.01875
21
F
F
0
7
2
2}2
}
1
22
216
24
5
10
28
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
F
F
continued
Chapter 3,
27.
continued
F GF G F G
F GF G
F GF G F G
3 22
x
y
6 25
1 25
2
26
3
A21 5 2}3
5
14
5
2
5
3
2}3
}
X 5 A21B 5
2
2
5
3
2}3
2
21
5
14
5
}
5
32.
1 21
x
y
9 210
4
45
210 1
A21 5 21
29 1
4
45
9 21
33.
F
GF G F G
F GF G
F GF G F G
22 29
4
x
y
16
5
7
3
5
21
A
1
A21 5 }4
16
9
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
9
}
4
4
X 5 A21B 5
1
21 2}2
22
8
1
21 2}2
The solution is (10, 22).
30.
F
x
y
5
21
21
A
GF G F G
F GF G
F GF G F G
2 27
1
5 }3
7
1
2
5
3
1
}
3
7
3
2
}
3
}
5
5
}
3
1
}
3
X 5 A21B 5
7
}
3
2
}
3
26
3
5
23
0
31.
F
GF G F G
F GF G
F GF G F G
1
21
3
1
A21 5 }
19
21
x
y
5
3 21
1
X5A B5
22
225
6
3
19
1
}
19
3
19
1
}
19
1
19
6
}
19
} 2}
5
1
19
6
}
19
} 2}
22
225
5
5
26
10
20
16
5
5
7
5
4
3
2}4
2}4
}
5
4
}
G
F GF G F G
7
5
4
3
2}4
2}4
20
16
5
}
4
5
23
5
F GF G F G
F GF G
F GF G F G
3 25
x
y
21 2
5
2 5
A21 5 1
226
10
2 5
5
1 3
1 3
2 5
X 5 A21B 5
226
10
1 3
5
22
4
The solution is (22, 4).
}
The solution is (23, 0).
6
34. C;
26
5
3
5
G
The solution is (23, 5).
10
22
5
22
38
1
}
4
}
}
5
24 22
2}8
5 27
1
5 }4
23
5
X 5 A21B 5
9
4
4
1
4
}
F GF G F G
x
y
22
8
5
2}8
1
5
8
1
2}4
F GF G F G
F GF
The solution is (25, 29).
29.
5
1
5
8
1
2}4
}
The solution is (26, 10).
25
29
5
22
38
5
5 21
1
5 }8
22
2
X5A B5
9 21
10 21
X 5 A21B 5
x
y
}
10 21
5
5
21
21
5
1
A
21
24
F GF G F G
F GF G
F GF G F G
2
2
21
The solution is (21, 24).
28.
F GF G F G
F GF
35.
F
GF G F G
F G
F GF G F G
1 21 23
5
x
2
2
1
y
23 21
0
z
5 217
8
1
21
A
3
5
5 23 29 216
1
4
7
1
3
5
2
X 5 A B 5 23 29 216
1
4
7
217
21
8
29
5
19
210
The solution is (29, 19, 210).
1
28
The solution is (1, 28).
Algebra 2
Worked-Out Solution Key
157
F
GF G F G
F
G
F
GF G F G
1 28
23
36.
x
18
5 211
217
1 22
1
y
2 22
5
z
A
40.
2.2 23
18
0.2 21
X 5 A21B 5 20.6
0.4 20.8
1
211
A21 5
217
4
21
F
4
5
1
2
3
5 24
22
21
A
F
0.25
z
23
0.1429
ø 1.2143 22.0714 20.0714
21
2
0
FG
G
3
F
F
6
21
0 21
4
F
5
GF G F G
y
5 227
23
z
0.1905
0.0476
0.0476
FG
2
8 27
14
y
225
3
6 25
10
z
216
210
4
ø
4
21 25
4
A21 5
1
F
1
}
}
21.58 3
21.41 6
X 5 A21B 5
y
5 248
2
20.58 3
0.916
}
}
21.41 6
F
FG
G
20.25
20.58 3
0.91 6
}
}
21.41 6
10
0
The solution is (22, 10, 0).
158
Algebra 2
Worked-Out Solution Key
}
1.08 3
G
0.25
22
5
4 22 217
20
8
27
8
25
Problem Solving
F
20.25
}
}
21.58 3
18
60s 1 240t 5 21,000
0.25
21.41 6
27 229
5 22 216
s 1 t 5 200
14
0.75
52
5
t 5 hours in a twin-engine plane
GF G F G
0.75
x
43. s 5 hours in a single-engine plane
x
z
1 27
0
The solution is (23, 8, 1, 25).
The solution is (24, 1, 3).
F
w
1
3
39.
GF G F G
F G
FG
6
X 5 A21B 5
1
2 21
5
23
24
3
4 10
2
2 21
0.9048 20.0952
A21 ø 21.3810
1.1429 20.7143
0.2857
X 5 A21B 5
25
F G
4
The solution is (21, 22, 3).
38.
3
5
14
0
A
220
3
25
5 24
21
x
11
}
}
0.58 3
0. 3
2
22
4 21 21
}
}
2.08 3
0. 3
0.25
42.
21
X5A B5
}
}
0.58 3
0. 3
20.75 20.25
0
41. Sample answer:
4
5
0.5714 20.8571
21
}
}
2.08 3
0. 3
The solution is (3, 3, 25).
GF G F G
y
14
20.75 20.25
5
x
25
5
z
0
X 5 A21B 5
The solution is (22, 4, 21).
2
y
0.25
22
5
GF G F G
F
G
F
GF G F G
0.25
0.2 21
5 20.6
0.4 20.8
1
21.6
37.
F
11
x
6
1
2
1 21
1
21
4 21
2.2 23
21.6
21
continued
}
}
1.08 3
1
s
60
240
t
21
A
GF G
14
248
2
GF G F G
F GF
1
5
240 21
1
5}
180 260
1
21
X5A B5
200
21,000
4
3
}
5
1
2}
180
1
1
180
2}3
F GF
1
}
}
4
3
2}
180
200
1
2}3
1
}
180
21,000
G
GF G
5
150
50
The pilot spent 150 hours flying a single-engine plane
and 50 hours flying a twin-engine plane.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Chapter 3,
Chapter 3,
continued
44. x 5 three-point field goals
b. 3c 1 5m 5 28
7c 1 10m 5 60
3 5
c
y 5 two-point field goals
F GF G F G
F GF
z 5 free throws
7 10
x 1 y 1 z 5 976
3x 1 2y 1 z 5 1680
F GF G F G
1
1
x
976
3
2
1
y
5 1680
0
1 21
z
135
F G
F GF G F G
2}3
A21 5
1 2}3
1
}
1
1
}
2
3
X 5 A21B 5
2}3
X 5 A21B 5
1
976
99
1 2}3
}
1680
5 506
1
1 2}3
1
2}3
135
371
2
3
Dirk made 99 three-point field goals, 506 two-point field
goals, and 371 free throws.
45. a. m 5 number of batches of muffins
r 5 number of batches of rolls
m 1 2r 5 8 (cups of buttermilk)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
b.
1 3
r
3
1
c. A21 5 }
1 21
21
X5A B5
5
22
1
8
11
5
3 22
21
3 22
8
1
11
21
1
5
2
3
The class should make two batches of muffins and
three batches of rolls.
F
78
104
1
2c 1 3m 5 18
0
F GF G F G
F GF G
F GF G F G
3
c
3
5
m
A21 5 1
5
5 23
23
X 5 A21B 5
0.6
25.5 23.8
A
2
5
5 23
23
5 23
18
2
28
23
2
5
6
2
Each cheese costs $6.00 and each meat costs $2.00.
G
GF G F G
28
60
5
4
3.2
F
500
b
t
5
w
0.9348
5
100
0.0223
0.0549
5 20.0039 20.9079
0.0093
0.1086 20.0378
FG
G
2.3
X 5 A21B ø 0.8
1.2
About 2.3 ounces of Bran Crunchies, 0.8 ounces of
Toasted Oats, and 1.2 ounces of Whole Wheat Flakes
should be combined.
5
18
28
3
GF G F G
20.0056
21
3c 1 5m 5 28
2
198
Area per +
sheet
m 5 cost of meat
2}5
t 5 ounces of Toasted Oats
w 5 ounces of Whole Wheat Flakes
78b 1 104t 1 198w 5 500
b 1 0.6w 5 5
22b 1 25.5t 1 23.8w 5 100
48. a. Equation 1:
46 a. c 5 cost of cheese
3
2}5
7
5
}
47. b 5 ounces of Bran Crunchies
22
F GF G F G
F GF G
F GF G F G
m
1
7
}
5
1
cheeses and meats in the various platters may not be
the same, or there may be other factors that affect
cost, such as the cost of the platters on which the food
is served.
m 1 3r 5 11 (number of eggs)
1 2
22
22
Each cheese costs $4.00 and each meat costs $3.20.
1
2
3
}
F
5
c. Sample answer: The costs may differ because the
1 2}3 2}3
21
3
27
1
2
3
21
60
10 25
1
A21 5 2}5
y 2 z 5 135
1
m
28
5
(
Sheets
Sheets of
1 Sheets
1
of red
yellow
of blue
)
Total
area
Area of
Area of
Equation 2: Area 5
1
yellow
blue
of red
Equation 3:
Cost
+
Sheets
Sheets of
1 Cost +
of red
yellow
Sheets
Total
1 Cost +
5
of blue
cost
Algebra 2
Worked-Out Solution Key
159
continued
Mixed Review for TAKS
Equation 1: 0.75r 1 0.75y 1 0.75b 5 9
Equation 2: r 2 y 2 b 5 0
Equation 3: 6.5r 1 4.5y1 8.5b 5 80
b.
F
0.75 0.75
1
21
6.5
4.5
51. B;
GF G F G
FG
0.75
r
21
y
8.5
b
5
Let p 5 pounds of peanuts.
9
Let x 5 total weight.
0
Equation 1: p 1 12 5 x
80
x 2 p 5 12
6
c. X 5 A21B 5
Equation 2: 2.5p 1 4.75(12) 5 4x
2.5
4x 2 2.5p 5 57
3.5
You should buy 6 sheets of red, 2.5 sheets of yellow,
and 3.5 sheets of blue tiles.
49. a. AT 5
5
5
F GF G
F
G
F
G
F GF
G
F
G
F
G
0
1
1
3
5
21
0
1
4
2
011
014
012
21 1 0 23 1 0 25 1 0
1
4
2
21 23 25
AAT 5 A(AT ) 5
0
1
21
0
1
021
5
4
2
21 23 25
023
025
21 1 0 24 1 0 22 1 0
y
(3, 4)
(1, 1)
(21, 21) (1, 21)
AAT
AT
4
2
AAAAT, or A (AAT). This means the triangle will be
rotated 908 clockwise four times from T, or rotated
908 clockwise twice from AAT, so it will be back to its
original position.
BA 5
F
d
ad 2 cb
,B5
2c
d
}
ad 2 cb
}
ad 2 bc
}
ad 2 cb
cd 2 dc
}
ad 2 cb
2ab 1 ba
}
ad 2 cb
2cb 1 da
}
ad 2 cb
ad 2 bc
}
ad 2 bc
2ca 1 ac
}
ad 2 bc
db 2 bd
}
ad 2 bc
2bc 1 ad
}
ad 2 bc
2b
ad 2 cb
a
}
ad 2 cb
}
GF
GF
5
5
G
third number 5 4n 1 2
The sum is 141, so n 1 (3n 2 5) 1 (4n 1 2) 5 141.
53. A;
5x 1 y 5 217
35x 1 7y 5 2119
37
2x 2 7y 5
2x 2 7y 5 8
37x
1 0
0 1
1 0
0 1
G
G
Algebra 2
Worked-Out Solution Key
5I
5I
8
5 2111
x 5 23
5(23) 1 y 5 217 l y 5 22
The solution is (23, 22).
F GF G
F
G
(F GF
(F GF
F
F
F
1 24
2 23
5
0
2
410
1
26 2 8
20 1 0 230 1 4
1
5
1
Because AB 5 BA 5 I, B is the inverse of A.
160
second number 5 3n 2 5
2. AB 1 AC 5
b. To get back to the original triangle, you must find
F
F
first number 5 n
5
(4, 23)
(2, 25)
AB 5
Solve for p.
52. H;
x
(23, 24)
c
p56
The grocer will need 6 pounds of peanuts.
1. 2AB 5 2
1
F G
1.5p 5 9
Quiz 3.6–3.8 (p. 217)
(5, 2)
A
50. A 5
4x 2 2.5p 5 57
21 24 22
Matrix A rotates the triangle 908 clockwise about
the origin.
a b
Multiply Equation 1 by 24.
21 23 25
5
(25, 22)
24x 1 4p 5 248
5
5
5
F GF G
F G
G)
G)
G
G
GF G
1 24
2 23
5
0
2
1 24
5
2
210
2 28
10
4
2 23
0
1
4 214
20 226
1
26 21
2
4
23 2 4
10 1 0 215 1 2
26 2 8 21 2 16
230 1 4
25 1 8
2 2 14 27 2 17
10 2 26 213 1 3
5
212 224
216 210
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Chapter 3,
Chapter 3
F
F
F
(F
F
F
3. A(B 1 C) 5
2 23
5
0
2
5
5
4. (B 2 A)C 5
5
2
4
5
24 2 8
24 2 20
220 1 4
220 1 10
2 23
1
5
212 224
5
1 24
2
1
1
2
G)
10.
1
23
2
216 210
26 21
2
2
4
G
G
{
2
30 2 2
7.
4
5
524
24
3
28
1
G
11.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
3
x
2
7
y
12.
1
22
X 5 A21B 5
9.
22
1
26
5
4
22
2 23
y
A21 5 21
5
23
4
22
3
X 5 A21B 5
2 22
y
5
3 24
2 23
3 24
5
2 23
3
5
3
213
17
3
}
5
24
2
G
24
5
28
5
3
1
1
2
1
}
2
1
1
2
1
}
2
2}4
}
1
1 22
5 2}4
22
7
4
x
5
3
y
3
2}4
2}4
24
3
2}4
28
0
5
4
6
5
225
3
24
25
7
13.
5
3
24
25
7
3
24
6
25
7
225
F GF G F G
F GF
4
1
x
26
1
y
A
1 1
5}
10 6
3
5
21
21
F GF G F G
F GF G
F GF G F G
21
F GF G F G
F GF G
F GF G F G
x
22
22
5
118
2205
The solution is (118, 2205).
1
22
The solution is (4, 22).
3 24
x
X 5 A21B 5
7 23
7 23
22
3 21
A21 5 1
26
5
2
2
The solution is (0, 4).
22
7 23
1
A21 5 }1
5
5
}
F GF G F G
F GF G
F GF G F G
5
23
5
2}3 2}3
2}3 2}3
X 5 A21B 5
{
1
22
5 }
F GF G F G
F GF G
F GF G F G
A
5 (12 1 18 2 45) 2 (260 1 54 1 3) 5 212
8.
1 25
3 26
24
17
21
5
2 21
9 23
6
1 22
3
{
y
213
5
The solution is 1 }
,2 .
3 2
5 (21 1 0 1 18) 2 (24 1 12 1 0) 5 9
2 21
23
6
22
3
25
X5A B5
0
1
3
{
x
21
26 21
26 1 2 21 1 4
1
23
2
6
A
4
0 22
1
4
3 21
GF G F G
F GF G
F GF G F
2
23
21
{22 23 { 5 5(23) 2 (22)(4) 5 27
5
F
24 24
2
0
26 21
1
1
25 21
5
6.
G(F G F
GF G
GF
G F G)F
GF G
GF
1 24
1 24
5
5.
continued
21
X5A B5
5
21
4
22
18
5
1
}
1
10
2}
10
3
5
}
2
5
}
G
F GF G F G
1
}
1
10
2}
10
22
3
}
5
2
}
5
18
5
22
6
The solution is (22, 6).
1
The solution is (3, 1).
Algebra 2
Worked-Out Solution Key
161
Chapter 3,
1
12
2
2
26
1 0
1 12
1 12
3. s 5 pounds of sunflower seed
2
2
26
{
t 5 pounds of thistle seed
s 1 t 5 20
5 6}2 [(0 1 24 1 312) 2 (24 1 0 1 24)] 5 144
F
F
F
The area of the sail is 144 square feet.
Problem Solving Workshop 3.8 (p. 219)
1. 2m 1 p 5 17.75
2m 1 2p 1 d 5 34.50
4m 1 3p 1 2d 5 67.25
(22)R1 1 R3
(21)R1 1 R2
(21)R2 1 R3
F
F
F
F
2
0 A
1
17.75
2
2
1 A 34.50
4
2
3
1
2 A
0 A
2
2
1 A 34.50
0
2
1
1
2 A
0 A
31.75
17.75
0
1
1 A
16.75
0
2
1
1
2 A
0 A
31.75
17.75
0
1
1 A
16.75
0
0
1 A
15
67.25
17.75
G
G
G
G
From the third row, d 5 15. From the second row,
p 1 d 5 16.75, so p 1 15 5 16.75, or p 5 1.75. From
the first row, 2m 1 p 5 17.75, so 2m 1 1.75 5 17.75,
or m 5 8.
A movie pass costs $8, a package of popcorn costs $1.75,
and a DVD costs $15.
m 5 amount in money market funds
s 1 b 1 m 5 18000
100R2
R1 1 (21)R3
(210)R1 1 R2
2R2 1 3R3
(21)R2
1 2}14 2R3
F
F
F
F
F
1
1
0.1 0.07
1 21
1 1 1
5
1 A 18000
0.05 A
1440
21 A
A 18,000
A 144,000
G
0
10
7
0
1
2 2 A 18,000
1
1 A
18,000
0 23 25 A 236,000
0
1
2
1
2 A
1 A
18,000
18,000
0 23 25 A 236,000
G
0
1
0 24 A 218,000
1
1 A 18,000
0
3
5 A 36,000
0
0
1 A
4500
G
G
G
From row 3, m 5 4500. From row 2, 3b 1 5m 5 36,000,
so 3b 1 5(4500) 5 36,000, or b 5 4500. From row 1,
s 1 b 1 m 5 18,000, so s 1 4500 1 4500 5 18,000, or
s 5 9000. You should invest $9000 in stocks, $4500 in
bonds, and $4500 in money market funds.
162
Algebra 2
Worked-Out Solution Key
R2
}
0.45
20
1 A
1
20
0
0.45 A 4.05
1
1 A 20
0
1 A
9
G
G
G
From row 2, t 5 9. From row 1, s 1 t 5 20. So,
s 1 9 5 20, or s 5 11.
The mixture contains 11 pounds of sunflower seed and 9
pounds of thistle seed.
4. x 2 2y 1 4z 5 210
5x 1 y 2 z 5 24
3x 2 6y 1 12z 5 230
(23)R1 1 R3
F
F
4 A 210
1 22
1 21 A
5
3 26
1 22
24
G
G
12 A 230
4 A
210
5
1 21 A
24
0
0
0 A
0
Because row 3 produces the equation 0 5 0, the system
has infinitely many solutions.
Mixed Review for TEKS (p. 220)
1. B;
B5
0.1s 1 0.07b 1 0.05m 5 1440
s2b2m50
(20.34)R1 1 R2
A5
2. s 5 amount in stocks; b 5 amount in bonds
1 A
1
0.34 0.79 A 10.85
0.34s 1 0.79t 5 10.85
F
F
4.5
6
2.5
5.5
8
2.5
4 6.5 3.25
5 8.5 3.25
B2A5
5
2. H;
21
A
5
G
G
F
21
F
F
4 2 4.5
6.52 6
3.25 2 2.5
5 2 5.5
8.5 2 8
3.25 2 2.5
G
20.5
0.5
0.75
20.5
0.5
0.75
}
}
20. 1
}
20. 2
X5A B5
F
G
} 0.}3
}
}
2. 2 20. 4
} 0.}1
4. 4
}
} 0.}3
1. 3 26. 6
}
}
}
2. 2 20. 4
20. 1
} 4.}4 0.}1
20. 2
1. 3 26. 6
FG
25
5
20
40
The person has 40 quarters.
G
GF G
85
13.25
0
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
{
0
1
14. Area 5 6} 12
2
continued