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F G GF
Chapter 5,
7. p(1)
4
p(2)
2
p(3)
6
p(4)
22
continued
8. (3x4y22)23 5 (3)23(x4)23( y22)23
p(5)
56
Power of a product property
4
16
34
1st order differences
Power of a power property
y6
6
12
18
6
6
2nd order differences
5}
3 12
Negative exponent property
3rd order differences
5}
12
Simplify and evaluate power.
Cubic function: p(t) 5 at 3 1 bt 2 1 ct 1 d
Use (1, 4): a(1) 1 b(1) 1 c(1) 1 d 5 4
3
2
3x
y6
27x
322
3 22
9. }
5}
4
422
1 2
42
3
a1b1c1d54
5 }2
Use (2, 2): a(2)3 1 b(2)2 1 c(2) 1 d 5 2
Use (3, 6): a(3) 1 b(3) 1 c(3) 1 d 5 6
2
27a 1 9b 1 3c 1 d 5 6
16
F
64a 1 16b 1 4c 1 d 5 22
GF G F G
X
1
1
1
1
8
4
2
1
27
9
3
1
64 16
4
1
B
4
a
b
5
6
d
22
X 5 A21B
Using a graphing calculator, the solution is a 5 1,
b 5 23, c 5 0, and d 5 6. So, the profit can be modeled
by p(t) 5 t 3 2 3t 2 1 6.
2. A solution of a polynomial equation is repeated if a
factor is raised to a power greater then 1 or the factor
is repeated.
Simplify and evaluate power.
1
xy
Negative exponent property
26 5
2x y
1
12. }
5 }8 x26 2 3y5 2 (22)
16x3y22
Quotient of powers property
1
5 }8x29y7
Simplify exponents.
y7
5 }9
Negative exponent property
8x
13. f(x) 5 2x4
x
22
21
0
1
2
f (x)
216
21
0
21
216
y
2
22
4. The function f has 4 2 1 5 3 turning points.
52
Power of a power property
5}
8 8
c 3 10n where 1a c <10 and n is an integer.
7
x
y
5}
8
3. A number is in scientific notation if it is in the form
5. 22 + 25 5 22 1 5
Power of quotient property
28
Chapter 5 Review (pp. 402–406)
function has a local maximum or a local minimum.
Quotient of powers property
5 4 3 104
1 2
When t 5 7, p(t) 5 (7)3 2 3(7)2 1 6 5 $202.
1. At each of its turning points, the graph of a polynomial
5 4 3 107 2 3
(x2)24
x2 24
11. }
5}
22
y
( y22)24
2
c
Simplify and evaluate powers.
8
8 3 107
107
10. }3 5 } 3 }3
2
2 3 10
10
Use (4, 22): a(4)3 1 b(4)2 1 c(4) 1 d 5 22
A
Negative exponent property
5}
9
8a 1 4b 1 2c 1 d 5 2
3
Power of a quotient property
x
Product of powers property
Simplify and evaluate power.
5 128
6. (32)23(33) 5 32633
5 3 2613
23
53
1
3
5 }3
1
5}
27
7. (x22y5)2 5 (x22)2( y 5)2
24 10
5x y
y10
5}
4
x
314
Algebra 2
Worked-Out Solution Key
Power of a power property
Product of powers property
Simplify exponent.
Negative exponent property
Simplify and evaluate power.
Power of a product property
Power of a power property
Negative exponent property
14. f(x) 5 x3 2 4
x
22
21
0
1
2
f (x)
212
25
24
23
4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
22
5 323x212y6
Chapter 5,
continued
21. 64x 3 2 8 5 (4x 2 2)(16x 2 1 8x 1 4)
y
5 8(2x 2 1)(4x2 1 2x 1 1)
2
22. 2x 2 12x 3 1 10x 5 2x(x4 2 6x 2 1 5)
5
x
1
5 2x(x2 2 1)(x2 2 5)
5 2x(x 2 1)(x 1 1)(x2 2 5)
23. 2x 3 2 7x 2 2 8x 1 28 5 x 2(2x 2 7) 2 4(2x 2 7)
5 (2x 2 7)(x2 2 4)
5 (2x 2 7)(x 2 2)(x 1 2)
15. f(x) 5 x3 1 2x 1 3
24. V 5 *wh
x
22
21
0
1
2
f (x)
29
0
3
6
15
When * 5 x, w 5 x 2 4, and h 5 3x 1 2:
V 5 x(x 2 4)(3x 1 2) 5 3x3 2 20x2 2 8x
Graph y 5 3x2 2 10x2 2 8x and y 5 240.
y
6
x
1
Intersection
X=6
Y=240
16. F 5 20.907t 4 1 28.0t 3 2 258t 2 1 902t 1 12,700
t
0
2
4
6
8
From the graph, the volume of the sculpture is 240 cubic
inches when x 5 6. So, the dimensions of the sculpture
should be 6 inches long by 6 2 4 5 2 inches wide, and
3(6) 1 2 5 20 inches high.
x26
f (t) 12,700 13,681 13,740 13697 14,025
t
10
ww
25. x2 1 3x 2 1q x3 2 3x2 2 x 2 10
12
x3 1 3x2 2
Fish caught
(millions of pounds)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
In 1999, the fish caught
for human consumption
was greater than
14.5 billion pounds.
F
16,000
15,000
14,000
13,000
12,000
0
26x2 2 18x 1 6
18x 2 16
Years since 1990
2
5x261}
.
So, }}
2
2
26. 2x2 2 2q 4x4 2 0x3 2 17x2 1 9x 2 18
2 4x2
4x4
5 5x 2 x 1 3 1 x 2 9x 1 4x
2
213x2 1 9x 2 18
5 6x 3 2 9x 2 1 3x 1 3
18.
13
2}
2
2x2
www
17. (5x 2 x 1 3) 1 (x 3 2 9x 2 1 4x)
3
18x 2 16
x 1 3x 2 1
x 2 3x 2 x 2 10
x 1 3x 2 1
3
0 2 4 6 8 10 12 t
3
3
x
26x2 1 0x 2 10
f (t) 14,850 15,948
213x2 1 0x 1 13
(x 3 1 4x 2 2 5x) 2 (4x 3 1 x 2 2 7)
9x 2 31
5 x 3 1 4x 2 2 5x 2 4x 3 2 x 2 1 7
5 23x 3 1 3x 2 2 5x 1 7
19. (x 2 6)(5x 2 1 x 2 8)
5 (x 2 6)5x 2 1 (x 2 6)x 2 (x 2 6)8
4x 2 17x 1 9x 2 18
2x 2 2
4
2
27. 5
2
211
13
244
10
25
40
21
8
24
5 5x 3 2 30x2 1 x 2 2 6x 2 8x 1 48
5 5x 3 2 29x 2 2 14x 1 48
20. (x 2 4)(x 1 7)(5x 2 1)
5 (x2 1 3x 2 28)(5x 2 1)
5 (5x 2 1)x2 1 (5x 2 1)3x 2 (5x 2 1)28
13
9x 2 31
2x 2 2
5 2x2 2 }
1}
.
So, }}
2
2
2
2
4
2x3 2 11x2 1 13x 2 44
5 2x 2 2 x 1 8 2 }
.
So, }}
x25
x25
5 5x3 2 x2 1 15x2 2 3x 2 140x 1 28
5 5x3 1 14x2 2 143x 1 28
Algebra 2
Worked-Out Solution Key
315
Chapter 5,
0
2
215
10
210
20
244
118
210
22
259
128
5
5
34. f(x) 5 2x4 2 x3 2 42x 1 16x 1 160
Possible rational zeros: 61, 62, 64, 65, 68, 610,
616, 620, 632, 640, 680,
5x4 1 2x2 2 15x 1 10
So, }}
5
x12
128
5x3 2 10x2 1 22x 2 59 1 }
.
(x 1 2)
29. 22
1
1
25
22
24
22
14
224
27
12
0
Test x 5 4:
4 2 21
242
16
160
8
28
256
2160
7
214
240
0
2
f (x) 5 (x 2 4)(2x 1 7x 2 14x 2 40)
3
5
2
}
2
f(x) 5 x3 2 5x2 2 2x 1 24 5 (x 1 2)(x2 2 7x 1 12)
5 (x 1 2)(x 2 3)(x 2 4)
30. 8
1
2
211
14
80
8
224
280
210
0
23
1
24
4
9
0
24
24
0
9
0
12
16
0
5 (x2 1 3x 2 4)(x 2 5)
5 x3 2 2x2 2 19x 1 20
36. f(x) 5 (x 1 1)(x 1 1)(x 2 6)(x 2 3i)(x 1 3i)
5 (x2 1 2x 1 1)(x 2 6)[x2 2 (3i)2]
5 (x3 2 4x2 2 11x 2 6)(x2 1 9)
2
5 x5 2 4x4 2 2x 3 2 42x2 2 99x 2 54
}
}
37. f(x) 5 (x 2 2)(x 2 7)[x 2 (3 2 Ï 5 )][x 2 (3 1 Ï 5 )]
7
233
218
212
30
18
25
23
0
2
40
35. f(x) 5 (x 1 4)(x 2 1)(x 2 5)
2
2
30
5
5 (x 2 1)(3x 2 2)(3x 1 2)
32. 26
5
The zeros are 24, 22, }2 , and 4.
f (x) 5 9x 2 9x 2 4x 1 4 5 (x 2 1)(9x 2 4)
3
240
5 2(x 2 4)(2x 2 5)(x 1 4)(x 1 2)
2
29
214
5 2(x 2 4)(2x 2 5)(x2 1 6x 1 8)
5 (x 2 8)(x 2 5)(x 1 2)
9
7
5
5 (x 2 8)(x2 2 3x 2 10)
31. 1
2
f(x) 5 (x 2 4)1 x 2 }2 2(2x2 1 12x 1 16)
f (x) 5 x 2 11x 1 14x 1 80
3
5
1
6160, 6}2 , 6}2
f (x) 5 2x3 1 7x2 2 33x 2 18
5 (x 1 6)(2x2 2 5x 2 3)
5 (x 1 6)(2x 1 1)(x 2 3)
}
}
5 (x2 2 9x 1 14)[(x 2 3) 1 Ï 5 ][(x 2 3) 2 Ï5 ]
}
5 (x2 2 9x 1 14)[(x 2 3)2 2 (Ï5 )2]
5 (x2 2 9x 1 14)(x2 2 6x 1 4)
5 x4 2 15x3 1 72x2 2 120x 1 56
38. R 5 20.0040t 4 1 0.088t 3 2 0.36t 2 2 0.55t 1 5.8
When R 5 7:
0 5 20.0040t 4 1 0.088t 3 2 0.3t 2 2 0.55t 2 1.2
33. f (x) 5 x3 2 4x2 2 11x 1 30
Possible rational zeros: 61, 62, 63, 65, 66, 610, 615,
630
Test x 5 2:
2 1 24
211
30
2
24
230
22
215
0
1
f (x) 5 (x 2 2)(x2 2 2x 2 15) 5 (x 2 2)(x 1 3)(x 2 5)
The zeros are 23, 2, and 5.
316
Algebra 2
Worked-Out Solution Key
Zero
X=7.9866171 Y=0
From the graph, there is only one real zero: t ø 7.99.
So, the revenue became greater than 7 million near the
end of the seventh year.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
28. 22
continued
Chapter 5,
continued
f(x) 5 22x 3 2 3x 2 2 1
39.
2. (2x22y3)25
x-intercept: x ø 21.68
5 225(x22)25( y3)25
Power of a product property
Local maximum: (0, 21)
5 225x10y215
Power of a power property
Local minimum: (21, 22)
10
x
2y
5}
5 15
Negative exponent property
x10
32y
5}
15
40.
Simplify and evaluate power.
24 22
(x )
x24 22
3. }
5}
y2
(y 2)22
x8
5}
y24
1 2
Power of a quotient property
Power of a power property
5 x 8y 4
f(x) 5 x 1 3x 2 x 2 8x 1 2
4
3
3(xy)
2
4. }3 5 }3
27x 2 5y
27x 2 5y
x-intercepts: x ø 0.25, x ø 1.34
Local minimums: (22, 6), (0.88, 23.17)
f (2)
221
26
215
f (3)
240
219
24
f(4)
257
217
f(5)
266
29
8
2
Power of a product property
5. f (x) 5 2x3
Local maximum: (21.13, 7.06)
41. f (1)
Negative exponent property
3x 3y 3
3
f(6)
261
5
x
f (x)
22
21
0
8
1
0
2
21 28
y
1st order differences
14
1
2nd order differences
2
6
6
3rd order differences
6
21
x
Cubic function: f (x) 5 ax 1 bx 1 cx 1 d
3
2
a(1)3 1 b(1)2 1 c(1) 1 d 5 26
a 1 b 1 c 1 d 5 26
a(2) 1 b(2)2 1 c(2) 1 d 5 221
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
3
8a 1 4b 1 2c 1 d 5 221
a(3) 1 b(3) 1 c(3) 1 d 5 240
3
2
6. f (x) 5 x4 2 2x2 2 5x 1 1
x
22
21
0
f (x)
19
5
1
27a 1 9b 1 3c 1 d 5 240
2
25 21
y
a(4)3 1 b(4)2 1 c(4) 1 d 5 257
F GF G F G
1
1
64a 1 16b 1 4c 1 d 5 257
a
1 1 1
26
8
4
2
1
b
27
9
3
1
c
64 16
4
1
d
A
5
221
6
240
257
X
5
B
X
5
A21B
Using a graphing calculator, the solution is a 5 1,
b 5 28, c 5 2, and d 5 21. A polynomial function is
f (x) 5 x3 2 8x2 1 2x 2 1.
1
7. f (x) 5 x5 2 x4 2 9
x
22
f (x)
257 211 29 29
Chapter 5 Test (p. 407)
1. x3 + x2 + x24 5 x3 1 2 2 4
5x
x
21
0
1
2
7
y
Product of powers property
Simplify exponents
8
21
x
Algebra 2
Worked-Out Solution Key
317
Chapter 5,
continued
18. f (x) 5 4x4 2 8x3 2 19x2 1 23x 2 6
8. (2x3 1 5x2 2 7x 1 4) 1 (x3 2 3x2 2 4x)
Possible rational zeros: 61, 62, 63, 66,
5 2x3 1 5x2 2 7x 1 4 1 x3 2 3x2 2 4x
3
1
5 3x 1 2x 2 11x 1 4
3
1
6}2, 6}2, 6}4, 6}4
2
9. (3x3 2 4x2 1 3x 2 5) 2 (x2 1 4x 2 8)
Test x 5 22: 22
5 3x3 2 4x2 1 3x 2 5 2 x2 2 4x 1 8
28
219
23
26
28
32
226
6
216
13
23
0
4
5 3x3 2 5x2 2 x 1 3
10. (3x 2 2)(x 1 4x 2 7)
2
4
5 (3x 2 2)x2 1 (3x 2 2)4x 2 (3x 2 2)7
5 3x3 2 2x2 1 12x2 2 8x 2 21x 1 14
f (x) 5 (x 1 2)(4x3 2 16x2 1 13x 2 3)
5 3x3 1 10x2 2 29x 1 14
Test x 5 3: 3
4
216
13
23
12
212
3
24
1
0
11. (3x 2 5)3 5 (3x)3 2 3(3x)2(5) 1 3(3x)(52) 2 53
5 27x3 2 15(9x2) 1 9x(25) 2 125
5 27x3 2 135x2 1 225x 2 125
12. 4
3
3
214
16
222
12
28
32
22
8
10
4
f (x) 5 (x 1 2)(x 2 3)(4x2 2 4x 1 1)
5 4(x 1 2)(x 2 3)1 x 2 }2 2
1 2
1
The real zeros are 22, }2 , and 3.
3x3 2 14x2 1 16x 2 22
10
5 3x2 2 2x 1 8 1 }
.
So, }}
x24
x24
2x 1 2x 1 3
www
4
3
q
13. 3x 2 3x 1 2 6x 1 0x 1 7x2 1 4x 2 17
2
5 x3 2 6x2 1 5x 1 12
6x 2 6x 1 4x
3
2
20. f(x) 5 (x 2 6)(x 2 2i)(x 1 2i)
6x3 1 3x2 1 4x
5 (x 2 6)[x2 2 (2i)2]
6x 2 6x 1 4x
5 (x 2 6)(x2 1 4)
3
2
9x 1 0x 2 17
2
5 x3 2 6x2 1 4x 2 24
9x 2 9x 1 6
2
}
5 2x2 1 2x 1 3 1 }
.
So, }}
2
2
14. 8x3 1 27 5 (2x)3 1 33 5 (2x 1 3)(4x2 2 6x 1 9)
2
2
2
16. x3 2 3x2 2 4x 1 12 5 x2(x 2 3) 2 4(x 2 3)
5 (x 2 3)(x2 2 4)
5 (x 2 3)(x 2 2)(x 1 2)
17. f (x) 5 x 1 x 2 22x 2 40
2
Possible rational zeros: 61, 62, 64, 65, 68, 610, 620,
640
Test x 5 22: 22
1
1
5 (x2 1 4x 1 3)(x2 2 2x 2 4)
5 x4 1 2x3 2 9x2 2 22x 2 12
}
5 (x 2 1)(x 1 1)(x2 1 6)
3
}
5 (x2 1 4x 1 3)[(x 2 1)2 2 (Ï 5 )2]
1
222
240
22
2
40
21
220
0
[x 2 (4 2 Ï10 )]
}
5 [(x 2 1) 2 3i][(x 2 1) 1 3i][(x 2 4) 2 Ï10 ]
}
[(x 2 4) 1 Ï10 ]
}
5 [(x 2 1)2 2 (3i)2][(x 2 4)2 2 (Ï10 )2]
5 (x2 2 2x 1 10)(x2 2 8x 1 6)
5 x4 2 10x3 1 32x2 2 92x 1 60
23. f(x) 5 x3 2 5x2 1 3x 1 4
f (x) 5 (x 1 2)(x2 2 x 2 20) 5 (x 1 2)(x 2 5)(x 1 4)
The real zeros are 22, 5, and 24.
x-intercepts: x ø 20.6, x ø 1.6, x 5 4
Local maximum: (0.3, 4.5)
Local minimum: (3, 25)
318
Algebra 2
Worked-Out Solution Key
}
22. f(x) 5 [x 2 (1 1 3i)][x 2 (1 2 3i)][x 2 (4 1 Ï 10 )]
15. x 1 5x 2 6 5 (x 2 1)(x 1 6)
4
}
}
5 (x2 1 4x 1 3)[(x 2 1) 1 Ï5 ][(x 2 1) 2 Ï 5 ]
9x 2 23
3x 2 3x 1 2
6x 1 7x 1 4x 2 17
3x 2 3x 1 2
2
}
21. f(x) 5 (x 1 3)(x 1 1)[x 2 (1 2 Ï 5 )][x 2 (1 1 Ï 5 )]
9x 2 23
4
5 (x2 2 2x 2 3)(x 2 4)
5 x3 2 2x2 2 3x 2 4x2 1 8x 1 12
2
4
19. f(x) 5 (x 1 1)(x 2 3)(x 2 4)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
3
Chapter 5,
continued
F GF G F G
24. f(x) 5 x4 1 3x3 2 x2 2 6x 1 2
1
1
1
1
a
0
8
4
2
1
b
27
27
9
3 1
c
d
5 24
21
X
5
64 16
4
1
A
5 A B
X
x-intercepts: x ø 0.34, x ø 1.14
Using a graphing calculator, the solution is a 5 2,
b 5 27, c 5 0, d 5 5. A cubic function is
f(x) 5 2x3 2 7x2 1 5.
Local maximum: (20.88, 5.06)
Local minimums: (22.16, 1.83), (0.79, 21.50)
25. f (1)
f (2)
1
3
22
f (3)
1
f(4)
3
0
2
f (5)
7
f(6)
13
6
4
GDP
27. Per Capita GDP 5 }
Population
1.099 3 1013
2.91 3 10
1st order differences
5}
8
2nd order differences
5}
3}
8
2.91
1013
10
1.099
2
2
2
2
Quadratic function: f(x) 5 ax 2 1 bx 1 c
5 0.378 3 105
a(1) 1 b(1) 1 c 5 3 la 1 b 1 c 5 3
5 3.78 3 104
2
a(2) 1 b(2) 1 c 5 1 l4a 1 2b 1 c 5 1
2
28. Let V represent the total number of U.S. households with
a(3)2 1 b(3) 1 c 5 1 l9a 1 3b 1 c 5 1
both television and VCRs.
V5T+P
a 1 b 1 c 5 3 lc 5 3 2 a 2 b
20.205x2 1 8.36x 1
4a 1 2b 1 c 5 1
3
9a 1 3b 1 c 5 1
20.250x3 1 10.20x2 1 2.42x
3a 1 b 5 22
20.250x3 2 5.56x2 1 645.3x 1 152.26
9a 1 3b 1 (3 2 a 2 b) 5 1
8a 1 2b 5 22
The number of households with televisions and VCRs
can be modeled by V(x) 5 20.250x3 2 5.56x2 1
645.3x 1 152.26.
3a 1 b 5 22 lb 5 23a 2 2
8a 1 2b 5 22
29.
8a 1 2(23a 2 2) 5 22 la 5 1
b 5 23(1) 2 2 5 25
c 5 3 2 1 2 (25) 5 7
Volume
(Cubic
inch)
1040
0
27
f(3)
24
3
f(4)
21
25
10
12
f(6)
185
105
59
34
22
12
f(5)
80
46
12
1st order differences
Cubic function: f(x) 5 ax 3 1 bx 2 1 cx 1 d
a(1)3 1 b(1)2 1 c(1) 1 d 5 0 l
a1b1c1d50
a(2) 1 b(2) 1 c(2) 1 d 5 27 l
3
2
8a 1 4b 1 2c 1 d 5 27
a(3) 1 b(3) 1 c(3) 1 d 5 24 l
3
2
27a 1 9b 1 3c 1 d 5 24
a(4) 1 b(4) 1 c(4) 1 d 5 21 l
3
2
64a 1 16b 1 4c 1 d 5 21
5
+ (x 1 2) + (2x 2 3)
x
2
0 5 2x3 1 x2 2 6x 2 1040
Test possible rational solutions:
8
2
2nd order differences
3rd order differences
Width
Height
+ (inch) +
(inch)
1040 5 2x 1 x 2 6x
The quadratic function is f (x) 5 x 2 5x 1 7.
f (2)
27
Length
5 (inch)
3
2
26. f (1)
1.98
1.22x 1 76.9
215.76x2 1 642.9x 1 152.26
4a 1 2b 1 (3 2 a 2 b) 5 1
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
B
21
2
1
26
21040
16
136
1040
130
0
17
0 5 (x 2 8)(2x 1 17x 1 130)
2
x 2 8 5 0 or 2x2 1 17x 1 130 5 0
}}
217 6 Ï172 2 4(2)(130)
x 5 8 or x 5 }}
2(2)
}
217 6 iÏ751
5 }}
4
The only reasonable solution is x 5 8. So, the volume
of the prism can be modeled by V(x) 5 2x3 1 x2 2 6x.
When V 5 1040, the prism has a length of 8 in., width of
8 1 2 5 10 in., and a height of 2(8) 2 3 5 13 in.
Algebra 2
Worked-Out Solution Key
319
Chapter 5,
continued
TAKS Practice (pp. 410–411)
1. A;
(3x 1 9)8 1 1128 1 (6x 2 15)8 1 748 5 3608
3x 1 9 1 112 1 6x 2 15 1 74 5 360
2. F;
Area 5 Area of circle 2 Area of square
}
12. F;
2x 1 3y 5 29
3y 5 22x 2 9
y 5 2}3x 2 3
5:22
2
The slope is 2}3, so 2x 1 3y 5 29 is parallel to
ø 1.14
The shaded region has an area of about 1.14 square units.
3. B;
All interior angles 5 (n 2 2) + 1808
5 (12 2 2) + 1808
5 10 + 1808
5 18008
18008
5 1508.
Each interior angle 5 }
12
The measure of each interior angle is 1508.
2
y 5 2}3x 1 2.
Supporters
Supporters
13. C; }} 5 }}
Number surveyed
Number surveyed
75
125
x
800
}5}
125x 5 60,000
x 5 480
About 480 people would support spending money to
improve a community park.
14. c 5 classroom instruction, d 5 driving, x 5 observation
4. J;
mŽx 5 1808 2 848 2 428 5 548
c 1 d 1 x 5 46
c 5 3d
3
}r 5 54
5
d5x14lx5d24
r 5 90
5. A; The pattern is created by translations.
6. H;
c 1 d 1 x 5 46
3d 1 d 1 (d 2 4) 5 46
5d 5 50
Door
Number
1 admission +
sold
ticket price
s 5 25x 1 35(530 2 x)
7. D; y 5 2x 2 2 13x 1 20
0 5 (2x 2 5)(x 2 4)
5
x 5 }2
x54
or
5
The x-intercepts are x 5 }2 and x 5 4.
8. G;
The number of students at Lakeview High School
is 2x 2 20.
9. B; 25y 5 4(x 1 1)
25y 5 4x 1 4
4
4
y 5 2}5 x 2 }5
4
The slope of the line is 2}5 .
10. F;
The variable n represents the least of the three even
numbers.
Algebra 2
Worked-Out Solution Key
d 5 10
The student spends 10 hours driving.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Advance
Amount
Number
from ticket 5 admission +
sold
ticket price
sales
320
The commission Val is paid is dependent on his total
sales.
2
2
5 :(1) 2 (Ï 2 )
2
11. B;
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