Algebra Homework

PLEASE SHOW ALL WORK ON HOW YOU GOT TO ANSWER

I WILL EMAIL YOU THE PAGES FOR THE ASSIGNMENTS

Assignment 7

Page 46 – 47; 20 -100 Multiples of 10

Page 355 – 356; 5 – 10, 19 – 24, and 43 – 46

Assignment 8

Instructions to students: Complete this assignment as specified below and submit by 11:59 PM on 1/5/2019.

Page 313 – 314; 9 – 45 Multiples of 3

Page 325; 15 – 45 Multiples of 3

Assignment 9

Instructions to students: Complete this assignment as specified below and submit by 11:59 PM on 1/5/2019.

Page 332; 12 – 36 Multiples of 3, and 51, 60

Page 337; 3 – 30 Multiples of 3

Assignment 4

Page 169; 11, 15, 19, 23, 27, 31, 35, 39, 43, and 47

Assignment 3

Page 133; 59 – 68

Page 126; 71 – 79, 81 – 83

Section 3.3 Linear Functions: Graphs and Alice
59
S
תח
0
200
10.000
1200
b) Since m is a function of s. s will be on the horizontal axis and will be on the
vertical axis. We will graph this function by plotting points. We select values for s
and find the corresponding values for m. The table in the margin shows three or
dered pairs which we will plot and then draw the graph shown in Figure 3.42.
c) By reading our graph carefully, we can estimate that when the store’s sales are
$15,000, Rob’s monthly salary is about $1700.
Now Try Exercise 53
20.000
2200
m(s) = 200 + 0.108
$2500 –
52000
Monthly salary
51500
$1000+
$500+
10
15
S
5
20
Sales ($1000s)
FIGURE 3.42
EXERCISE SET 3.3
Math XL
MyMathlab
MathXL
MyMathLab
re
ed
51
Warm-Up Exercises
Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
linear
domain
range
x-intercept
y-intercept
horizontal
vertical
constant
standard form
fail
pass
real numbers
1. The domain, or set of x-coordinates, of every linear function 6. The graph of an equation of the form x = a, where a is a real
is all
symbolized R.
number, is a
line.
2. The
or set of y-coordinates, of every lin- 7. An equation of the form r = a
will always
ear function f(x) = ax + b,a # 0, is all real numbers, sym-
the vertical line test and therefore will
bolized R.
never define a function.
3. The
is the point where the graph crosses 8. A function of the form f(x) = b, where b is a real number, is
the x-axis.
known as a
function.
4. The
is the point where the graph crosses 9. A function of the form f(x) = ax + b, where a and b are
the y-axis.
real numbers, is known as a
function.
5. The graph of an equation of the form y = b, where b is a real 10. The
of a linear equation is ax + by = c.
number, is a
line.
ber
ion
ob-
His
12. 7x = 3y – 6
1
14. 2(x – 3+
Practice the Skills
Write each equation in standard form.
11. y = – 4x + 3
13.3(x – 2) = 4(y – 5)
Graph each equation using the x- and y-intercepts.
15. f(x) = 2x + 3
16. y = x – 5
20. 2x – 3y = 12
24. 6x + 12 y = 24
5. S.
18. f(x) = -6x + 5
1
22. x + y = 2
he
19. 2y = 4x + 6
23. 15x + 30y = 60
27. 120x – 360y = 720
Graph each equation.
1
17. y = -2x + 1
4
21.
3
x = y – 3
25. 0.25x + 0.50y = 1.00
1 1
29. -xt
3 4
26.-1.6y = 0.4x + 9.6
3
30. xt
2
28. 250 = 50x – 50 y
y = 12
im
31. f(x) =
32. y
1
х
2
36.-10x + 5y = 0
33. y = -2x
37. 6x – 9y = 0
34. g(r) = 4x
38. 18.r + 6y = 0
35. 2x + 4y = 0
Graph each equation
39. y = 4
41. X -4
45. x = 0
42. x = 4
46. 8(x) = 0
43. y = -1.5
on 1
40. y = -4
44. f(x) = -3
48. x = -3.25
47. x
2
1005 Hong it in the subMISSION,
Chapter 1 Basic Concepts
87
46
16.
86
1
37
15. 35
1
Practice the Skills
Avaluate each expression
20.
Simplify e-
77. (32)
3-2
14. 32.39
24. (32)
34
19.
81. (b
E
E
SE
53
23. (2′)
28.
3)
85. (
17. 9
21. 15°
18. 72
22. 24°
26. (6-5)
(9)
27.
89. 3
d) -(-3)-2
93.
25. (2.4)
c) -3-2
d)-(-4)
97.
Evaluate each expression.
29. a) 32
b) (-3)-2
c)-4-3
d)
101
b) (-4)
-()
-(
c)
30. a) 4
–
3-2
-1
d)
b)
5
3
105
31. a)
(6)
()
(
b)
Simplify each expression and write the answer without negative exponents. Assume that all bases represented by variables are nonzero
32. a)
10
d) -(-5.x)”
d) (-7y)”
d) 3(xyz)”
d) x + y
33. a) 5.rº
34. a) 7yº
35. a) 3.xyz
36. a) rº + yo
c) (-5.x)”
c) -7yº
c) 3x(yz)º
c) x + y^
b) -5.rº
b) (7y)
b) (3xyz)
b) (x + y)”
Simplify each expression and write the answer without negative exponents.
8
9
40.
1
39.
5×2
13×3
37. 7y
38.
y?
17mn
44.
43.
41.
2
3a
b-3
42.
10r4
-1
y у
15ab5
3c-3
9-10-1
8-12
5x2y3
47.
48.
xly
45.
46.
у
Simplify each expression and write the answer without negative exponents.
49. 25.2-7
50. a.a
51. xo.x+
52. x.x
7-5
->
53.
8
85
54.
4
4-1
56.
55. 1
mo
5w 2
57.
58.
ms
59.
60.
-3
P
W?
61. 3a 2.4a
62. (-804)(-3v-5)
63. (-3p ?)(-p)
65. (5rºs-2)(-2rºs2)
66. (-6p+q°)(2p)
*67. (2x*y)(4x’y 5)
64. (2x-*y*)(6x *y)
27xy?
68.
9xy
(x-2)(4x)
72.
69.
33x®y 4
11x?y2
70.
16x-2y3z-2
– 2x y
Oxy 423
71.
-3x y z
.
Evaluate each expression.
73. a) 4(a + b)
74. a) -3° + (-3)
b) 4aº + 46°
b) -3° – (-3)
75. a) 4-1 – 3-1
c) (4a + 4b)
e) -3° + 3º
c) 2.4″‘ + 3.5
c) 3.52 + 2-4
d) -4° + 45°
d) -3° -3°
b) 4-! + 3-1
76. a) 52 + 4-1
b) 5-2-4-1
d) (2-4) + (3.5)
d) (3:5)? – (2-4)
Section 1.5 Exponents
47
77. (39)
Simplify each expression and write the answer without negative exponents.
78. (52)
79. (3%)-2
81. (b)-2
82. (-c)”
85. (-5x )
86. – 11(x )
87. 4-2 + 8-1
89. 3.4-2 + 9.8-1
90. 5.2-3 + 7.4-2
45
91.
80. (22)
84. (-x)”
88. 5-1 + 2-1
93. (4x?y ?)
2c3
92.
(5)
94. (4x²y?)?
95. (5p 9 )
96. (854-42
98. 8(x’y 1)
3x2y4\3
E
102.
5min
10m’n?
9x 2
yos
104.
()
ху
106.
-3
or
xy-2)2
zero.
112.
3
97. (-3g *k”) –
99.
5j
3x
4k
100.
101.
4xy
103.
Sx
105.
4x²y) –
14x²y
107.
3xy
7xz
108.
109.
xy-320-1
110.
4x-ly-273-2
x-1y2z4
111.
9x4y6z4-2
-abc-
3-3
2xy?z-3)
3xy ?
113.
4abc+
(2x-‘y-2)-3
114.
(3x +y?)
115.
(2xy-z-3)?
(5x-y3)2
116.
(2x*y)
(9x-yz)-1
Problem Solving
too
117. r2. rSa+3
Simplify each expression. Assume that all variables represent nonzero integers.
118. y2m+3. y5m-7
119. w2a-5. w3a-2
120. d-4x+7. d5x-6
121.
122.
ym-
123. (x3p+5)(x20–3 124. (521-3)(s*+5)
125, x(x+2)
30ma+bnb-a
126. y3b+2. y26+4
127.
128.
бma-bna+b
8x°-4 yd +6
129. a) For what values of x is xt > x3?
2 -2
133. a) Is
equal to
?
b) For what values of x is x4 < x3? 3 3 c) For what values of x is x4 = x?? b) Will (x) ? equal (-x)? for all real numbers x except 0? d) Why can you not say that x4 > x??
Explain your answer.
2
130. Is 3- greater than or less than 2-8? Explain.
134. a) Is
equal to
?
3
3
131. a) Explain why (-1)” = 1 for any even number n.
b) Will (x)} equal (-x) 3 for any nonzero real number x?
b) Explain why (-1)” = -1 for any odd number n.
Explain.
132. a) Explain why (-12) is positive.
c) What is the relationship between (-x) and (x)-for
any nonzero real number x?
b) Explain why (-12) is negative.
x 2203
Jsm-1
ymm-1
0-4
24x¢+3yd+4
-2
–
3)
-3
2-3
yoz-2)-1
Determine what exponents must be placed in the shaded area to make each expression true. Each shaded area may represent a different ex
ponent. Explain how you determined your answer.
x
z12
x
137.
135.
136.
x 10y2
xky z
ху
rºy 2 )2
x-2y3z
.18
x18yo
= X
7
x-*y
Challenge Problems
We will learn in Section 7.2 that the rules of exponents given in this section also apply when the exponents are rational numbers. Usin
information and the rules of exponents, evaluate each expression.
4
15/83
140.
112
x1/2 3/2
139.
1/4
.
138.
-1
X
2
x 1/2 y
+2y-32
142.
(* ** 5/2
141.
ry,5/3
und in the sub SSION
(Chapter 5 Review Exercises
Chapter 5 Review Exercises
355
15.1]
1. 3.r? + 9
3. 8x – x + 6
one, b) write the polynomial in descending order of the variable x, and c) give the degree of the polynomial.
Determine whether each expression is a polynomial. If the expression is a polynomial, a) give the special name of the polynomial if it has
5b)
2. 5x + 4x – 7
4. -3 – 10x2y + 6xy + 2x*
Perform each indicated operation.
20m + 16)
7. (2a – 3b – 2) – (-a + 5b – 9)
–
11. Add x2 – 3x + 12 and 4×2 + 10x – 9.
13. Find P(2) if P(x) = 2×2 – 3x + 19
5. (x2 – 5x + 8) + (2x + 6)
6. (7x² + 2x – 5) – (2x? – 9x – 1)
8. (4×3 – 4×2 – 2x) + (2x + 4×2 – 7x + 13)
9. (3x+y + 6xy – 5y?) – (4y2 + 3xy)
10. (-8ab + 2b2 – 3a) + (-12 + 5ab + a)
12. Subtract 3a²b – 2ab from -7a²b – ab.
14. Find P(-3) if P(x) = x – 3×2 + 4x – 10
Perimeter In Exercises 15 and 16, find a polynomial expression for the perimeter of each figure.
x² – x + 7
x² +7
15.
16.
x² + 1
13x + 8
9x + 5
x2 + x + 19
x² + 2x + 3
Use the following graph to work Exercises 17 and 18. The graph shows Social Security receipts and outlays from 1997 through 2025.
Social Security Receipts and Outlays
$2000
$1600
Receipts
Outlays
$1200
Dollars (billions)
$800
$400
0
97 98 99 00 01 02 03 04 05 06 10 15 20 25
Year
Source: Social Security Administration
17. Social Security Receipts The function R(t) = 0.78t? +
20.28t + 385.0, where t is years since 1997 and 0 st s 28,
gives an approximation of Social Security receipts, R(t), in
billions of dollars.
a) Using the function provided, estimate the receipts in
2010.
b) Compare your answer in part a) with the graph. Does the
18. Social Security Outlays The function (t)
7.32+ + 383.91, where t is years since 1997 and
gives an approximation of Social Security out!
billions of dollars.
a) Using the function provided, estimate th
2010.
b) Compare your answer in part a) with the g
graph support your answer?
graph support your answer?
20. – 3xy?(x + xy – 4y)
150 + 1)(10a – 3)
(5.2)
Det og goes wrong
356
Chapter 5 Polynomials and Polynomial Functions
Volume
71.
23. (x + 8y)
–
25. (2x – 1)(5x + 4y)
27. (2a +90)
29. (7x + 5y)(7* – $y)
31. (4x + 6)(4xy – 6)
33. f(x + 3x) + 27
35. (3 + 4x – 6)(2x – 3)
24. (a – 116)
26. (2py – 7)(3pq + 7r)
28. (4x – 3y)
30. (2a – 56°) (2a + 5b”)
32. (9a – 25+)(90+ 20)
34. ((2p – 9) – 51
36. (4x + 6x – 2)(+ 3)
Area In Exercises 37 and 38, find an expression for the total area of each figure
38.
37.
(5.5)
73.
75.
77.
79.
81.
4
2
83
85
87
40. f(x) = 2x – 4,8(x) = ? – 3
42. f(x) = – 2, 8(x) = x + 2
Ar
8
44.
388
1253
For each pair of functions, find a) (g)(x) and b) (f.g)(3).
39. f(x) = x + 1,8(x) = 1 – 3
41. f(x) = r + x – 3.8(x) = x – 2
(5.3) Divide
4.x’ys
43.
20xy
45pq – 25q2 – 159
45.
5q
2rºy2 + 8r+ y2 + 12xy
47.
8xy
49. (2x – 3x + 4x + 17x + 7) = (2x + 1)
51. (r + r – 22) = (x – 3)
46.
7a- – 16a + 32
4
48. (8.r? + 14.x – 15) = (2x + 5)
50. (4a – Ta? – 5a + 4) = (2a – 1)
52. (4.rº + 12x + x – 9) = (2x + 3)
Use synthetic division to obtain each quotient.
53. (3.rº – 2x + 10) = (x – 3)
54. (2y – 10y + y – 2) = (y + 1)
55. (r – 18) + (x – 2)
56. (2x + x2 + 5x – 3) + (–)
59. (32 – 6) +(3-5)
Determine the remainder of each division problem using the Remainder Theorem. If the divisor is a factor of the dividend, so
57. (r? – 4x + 13) – (x – 3)
58. (2x – 6x² + 3x) = (x + 4)
3x –
60. (2x* – 6.rº – 8) = (x + 2)
(5.4) Factor out the greatest common factor in each expression.
61. 4x² + 8x + 32
62. 15.rº + 6.r* – 12.rºy
63. 10ab3 – 14a²b6
64. 24xy*23 + 12.xyz? – 30x®y?z?
Factor by grouping.
65. 5r² – xy + 30xy – 6y2
66. 12a + Sab + 15ab + 1062
67. (2x – 5)(2x + 1) – (2x – 5)(x – 8)
68. 7x(3x – 7) + 3(3x – 7)
Area In Exercises 69 and 70, A represents the area of the figure. Find an expression, in factored form, for the difference of the areas of
the geometric figures
.
69.
70.
A = 13x(5x + 2)
A = 7(5x + 2)
A = 14 + 18
A = 7x + 9