Lesson Warm Up 34 1. slope 2. 5 3. 2 Lesson Practice
Lesson Warm Up 34
f.
34
y
1. slope
x
O -8
-4
2. 5
4
8
4
8
4
8
2
4
-4 -8
3. 2 g.
8
y
Lesson Practice 34 x
O -8
a. yes
-4 -4 -8
b. no c.
4
h.
y
8 4
2 -2
2
x
O
x
O -4
y
-8
4
-4 -4 -8
-4
d.
4
i.
y
4
y
2 -2
e.
-4
4
-2
-2
-2
-4
-4
j.
y
4
2 2
y
2
x O
x
O
x
O
x
O
6
-2
-2
2 -2 -4
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–1
Saxon Algebra 2
Lesson k.
8
34
y
4 x
O -8
-4
4
8
-4 -8
l.
;
12 8
P
4 0
Q 4
8
12
3 29 _ y=_ x + 5 5
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–2
Saxon Algebra 2
Lesson Practice 34
14. a.
1. Chuck = 92 quarts, Nikita = 81 quarts 2. ab(x + 2)(x - 1) 25 3. _ 108
15. The vertex of the graph of y = (x + 2)2 is 2 units further to the left.
19 _ ,8 (_ 7 7)
6. 3 + 8x
-2 -6 -4
y
16. about 6.17 km/h
z
1 17. _ 8
7. 1.5 × 10-13 8. 6mx 9.
2x + 5y = -10 x - y = 16 all the coefficients are now whole numbers.
b. (10, -6)
1 4. - _ 2
5.
34
-1
18. 1; 2
2 4 _ x - y = -_ 5
3
10. [29
11
9]
11. B 12. Possible answer: They are identical except that f(x) · g(x) is undefined at the values x = 0, 2 . x = -2, and x = _ 3 13. a. (0, 6.1), (1, 6.13), and (2, 6.16) b. y = 0.03x + 6.1 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–3
Saxon Algebra 2
Lesson
19.
A
AA
-1
-1
34
⎤ ⎡ -1 2 =⎢ ; 3 1 _ _ ⎣ 2 - 4⎦ ⎤ ⎡ ⎡3 8⎤ -1 2 =⎢ 3 1 ⎣2 4⎦ ⎢ _ _ ⎣ 2 - 4⎦
⎡-3 + 4 6 - 6⎤ ⎡1 0⎤ =⎢ =⎢ = I, ⎣-2 + 2 4 - 3⎦ ⎣0 1⎦ ⎡ ⎤ -1 2 ⎡ 3 8⎤ -1 A A=⎢ ⎢ 3 ⎣ 2 4⎦ 1 _ _ ⎣ 2 - 4⎦ ⎤ ⎡ -3 + 4 -8 + 8 ⎡1 0⎤ =⎢ = =I 3 3 ⎣ ⎦ _ _ 0 1 4 - 3⎦ ⎣ 2 - 2
⎢
20. C
24. 15,600
21. Yes; 6(4) - 4 = 24 - 4 = 20
25. All related matrices have determinant 0, so the solutions are 0/0, indicating infinitely many possibilities. The two equations are equivalent, so there are infinitely many solutions.
22. Measurement 3; 8.875 inches 16 1 _ x + 23. y = _ 3 3 12 8
y A
D
4 O B
4
8
C x 12
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–4
Saxon Algebra 2
Lesson
34
26. The student used the Addition Counting Principle instead of the Fundamental Counting Principle. The correct answer is 26 · 25 · 24 · 23 = 358,800. 27. It is a basic quadratic polynomial. 7 is the sum of 3 and 4, and 12 is the product of 3 and 4. So, the factors are in the form (x + u)(x + v) where u + v = 7 and uv = 12. 28. Possible answer: Compress (shrink) the graph of y = x vertically 3 and by a factor of _ 4 then shift (translate) the resulting graph 3 units down. 29. A solution to a linear system of two equations is an ordered pair, not a single number. The pair (2, 1) is the solution to this system. 30. (x)2 + 2(x)(8) + (8)2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–5
Saxon Algebra 2
f.
34
y
1. slope
x
O -8
-4
2. 5
4
8
4
8
4
8
2
4
-4 -8
3. 2 g.
8
y
Lesson Practice 34 x
O -8
a. yes
-4 -4 -8
b. no c.
4
h.
y
8 4
2 -2
2
x
O
x
O -4
y
-8
4
-4 -4 -8
-4
d.
4
i.
y
4
y
2 -2
e.
-4
4
-2
-2
-2
-4
-4
j.
y
4
2 2
y
2
x O
x
O
x
O
x
O
6
-2
-2
2 -2 -4
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–1
Saxon Algebra 2
Lesson k.
8
34
y
4 x
O -8
-4
4
8
-4 -8
l.
;
12 8
P
4 0
Q 4
8
12
3 29 _ y=_ x + 5 5
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–2
Saxon Algebra 2
Lesson Practice 34
14. a.
1. Chuck = 92 quarts, Nikita = 81 quarts 2. ab(x + 2)(x - 1) 25 3. _ 108
15. The vertex of the graph of y = (x + 2)2 is 2 units further to the left.
19 _ ,8 (_ 7 7)
6. 3 + 8x
-2 -6 -4
y
16. about 6.17 km/h
z
1 17. _ 8
7. 1.5 × 10-13 8. 6mx 9.
2x + 5y = -10 x - y = 16 all the coefficients are now whole numbers.
b. (10, -6)
1 4. - _ 2
5.
34
-1
18. 1; 2
2 4 _ x - y = -_ 5
3
10. [29
11
9]
11. B 12. Possible answer: They are identical except that f(x) · g(x) is undefined at the values x = 0, 2 . x = -2, and x = _ 3 13. a. (0, 6.1), (1, 6.13), and (2, 6.16) b. y = 0.03x + 6.1 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–3
Saxon Algebra 2
Lesson
19.
A
AA
-1
-1
34
⎤ ⎡ -1 2 =⎢ ; 3 1 _ _ ⎣ 2 - 4⎦ ⎤ ⎡ ⎡3 8⎤ -1 2 =⎢ 3 1 ⎣2 4⎦ ⎢ _ _ ⎣ 2 - 4⎦
⎡-3 + 4 6 - 6⎤ ⎡1 0⎤ =⎢ =⎢ = I, ⎣-2 + 2 4 - 3⎦ ⎣0 1⎦ ⎡ ⎤ -1 2 ⎡ 3 8⎤ -1 A A=⎢ ⎢ 3 ⎣ 2 4⎦ 1 _ _ ⎣ 2 - 4⎦ ⎤ ⎡ -3 + 4 -8 + 8 ⎡1 0⎤ =⎢ = =I 3 3 ⎣ ⎦ _ _ 0 1 4 - 3⎦ ⎣ 2 - 2
⎢
20. C
24. 15,600
21. Yes; 6(4) - 4 = 24 - 4 = 20
25. All related matrices have determinant 0, so the solutions are 0/0, indicating infinitely many possibilities. The two equations are equivalent, so there are infinitely many solutions.
22. Measurement 3; 8.875 inches 16 1 _ x + 23. y = _ 3 3 12 8
y A
D
4 O B
4
8
C x 12
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–4
Saxon Algebra 2
Lesson
34
26. The student used the Addition Counting Principle instead of the Fundamental Counting Principle. The correct answer is 26 · 25 · 24 · 23 = 358,800. 27. It is a basic quadratic polynomial. 7 is the sum of 3 and 4, and 12 is the product of 3 and 4. So, the factors are in the form (x + u)(x + v) where u + v = 7 and uv = 12. 28. Possible answer: Compress (shrink) the graph of y = x vertically 3 and by a factor of _ 4 then shift (translate) the resulting graph 3 units down. 29. A solution to a linear system of two equations is an ordered pair, not a single number. The pair (2, 1) is the solution to this system. 30. (x)2 + 2(x)(8) + (8)2 © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 34–5
Saxon Algebra 2
