Add as indicated.
61)
–8.5 + (–2.1)
61)
A)
6.4
B)
–10.6
C)
–6.4
D)
10.6
Multiply as indicated.
62)
2(–1)(9)(–9)
62)
A)
162
B)
2
C)
83
D)
–162
A
Solve the equation to determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
63)
–3(x – 2) + 26 =2x –5(x – 8)
63)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
C
Solve the equation.
64)
–7=8(x + 9) – (7x – 2)
64)
A)
{81}
B)
{– 81}
C)
{18}
D)
{67}
B
Solve the equation. If the solution set is or (–, ), classify the equation as an inconsistent equation or an identity.
65)
5x + 5
15 =x – 3
3–x – 4
15
65)
A)
{–16}
B)
( , ); identity
C)
{–6}
D)
; inconsistent equation
A
B
Determine whether the inequality is true or false.
66)
22 >1
66)
A)
True
B)
False
Simplify the expression using the products to powers rule.
67)
(–4a)3
67)
A)
–12a3
B)
–64a
C)
–64a3
D)
–12a
Evaluate.
68)
Evaluate x2– (xy – y) for x satisfying 2(x + 3)
3=4x + 12 and y satisfying –3y + 42 =5y + 10.
68)
A)
16
B)
25
C)
21
D)
17
Solve the problem.
69)
During a road trip, Tony drove one–third the distance that Lana drove. Mark drives 12 more miles
than Lana drove. The total distance they drove on the trip was 320 miles. How many miles did each
person drive?
69)
A)
Tony drove 396 miles, Lana drove 132 miles, and Mark drove 120 miles.
B)
Tony drove 40 miles, Lana drove 120 miles, and Mark drove 132 miles.
C)
Tony drove 44 miles, Lana drove 132 miles, and Mark drove 144 miles.
D)
Tony drove 132 miles, Lana drove 396 miles, and Mark drove 408 miles.
70)
The median age at which men in a certain county were first married can be modeled by the formula
A =0.0037x2–0.42x +36.58 where x is the number of years after 2000. What would be the
predicted median age at first marriage for men in the year 2057? Round to the nearest tenth of a
year.
70)
A)
24.7 yr
B)
27.2 yr
C)
23.7 yr
D)
26.7 yr
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
71)
Six times the difference of a number and eleven is represented by 6(x –11) and
6
13
{x x is a rational number}
71)
A)
True
B)
False
Simplify the expression using the products to powers rule.
72)
(4a)3
72)
A)
64a3
B)
64a
C)
12a3
D)
12a
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
73)
At what time was the temperature the highest?
73)
A)
5 p.m.
B)
1 p.m.
C)
11 a.m.
D)
2 p.m.
Express the interval in set builder notation and graph the interval on a number line.
74)
(–4, 1)
74)
A)
{x –4 x 1 }
B)
{x –4< x 1 }
C)
{x –4 x <1 }
D)
{x –4< x <1 }
Solve the formula for the specified variable.
75)
I =nE
nr + R for n
75)
A)
n =IR
Ir + E
B)
n =
–R
Ir – E
C)
n = IR(Ir – E)
D)
n =
–IR
Ir – E
Add as indicated.
76)
2
9+ – 1
3
76)
A)
–1
9
B)
–5
9
C)
5
9
D)
1
9
Determine whether the statement is true or false.
77)
Every irrational number is a rational number.
77)
A)
True
B)
False
78)
Every irrational number is a whole number.
78)
A)
True
B)
False
Solve the formula for the specified variable.
79)
P = s1+ s2+ s3 for s3
79)
A)
s3= s1+ P – s2
B)
s3= P – s1– s2
C)
s3= s1+ s2– P
D)
s3= P + s1+ s2
Solve the equation. Express the solution in scientific notation.
80)
x
4×107= – 1.5 ×105
80)
A)
{6 ×1012}
B)
{–6×1035}
C)
{6 ×1013}
D)
{–6×1012}
Divide the expression using the quotient rule.
81)
x7y10
x3y5
81)
A)
x3y4
B)
x4y5
C)
xy5
D)
x3y5
Find the absolute value.
82)
|–10|
82)
A)
–10
B)
10
C)
–10
D)
10
Solve the equation. Express the solution in scientific notation.
83)
(4.2 ×10–10)x =8.5 ×10–4
83)
A)
{1.27 × 107}
B)
{2.02 × 10–14 }
C)
{2.02 × 10–6}
D)
{2.02 × 106}
Simplify the expression using the products to powers rule.
84)
(x9y)2
84)
A)
x11y
B)
x18y
C)
x11y3
D)
x18y2
Subtract as indicated.
85)
9– 15
85)
A)
6
B)
–24
C)
–6
D)
24
Divide as indicated or state that the division is undefined.
86)
14 ÷ – 7
2
86)
A)
49
B)
–49
C)
4
D)
–4
Express the interval in set builder notation and graph the interval on a number line.
87)
(–, 7.5)
87)
A)
{x x 7.5}
B)
{x x >7.5}
C)
{x x 7.5}
D)
{x x <7.5}
Solve the problem.
88)
Paul has $15,000 to invest. He puts x dollars in a safe government–insured certificate of deposit
paying 5% per year. He invests the remainder of the money in noninsured corporate bonds paying
12% per year. His total interest earned at the end of the year is given by the algebraic expression
0.05x +0.12(15,000 – x). Simplify this expression.
88)
A)
1800 +0.07x
B)
1800 –0.95x
C)
1800 –0.07x
D)
1800 +0.17x
Find –x for the given value of x.
89)
x = – 2.7
89)
A)
1
–2.7
B)
0
C)
–2.7
D)
2.7
Perform the indicated computation. Write the answer in scientific notation.
90)
9.18 ×10–9
2×107
90)
A)
4.59 ×10–2
B)
9.18 ×10–16
C)
9.18 ×10–2
D)
4.59 ×10–16
Express the interval in set builder notation and graph the interval on a number line.
91)
(–6, )
91)
A)
{x x –6 }
B)
{x x –6 }
C)
{x x > – 6 }
D)
{x x > – 6 }
Write the number in scientific notation.
92)
0.000303
92)
A)
3.03 ×10–4
B)
3.03 ×10–3
C)
3.03 ×104
D)
3.03 ×10–5
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
93)
When 40% of a number is added to the number, the result is 154. What is the number?
93)
A)
110
B)
44
C)
140
D)
29
Solve the equation. Express the solution in scientific notation.
94)
(4.7 ×109)x =9.4 ×107
94)
A)
{2.0 ×1016}
B)
{2.0 ×10–2}
C)
{4 ×10–2}
D)
{4 ×1016}
Use the order of operations to simplify the expression.
95)
(–4) · (2– 5) + (–4) ·7
(–4) · (7– 4)
95)
A)
2
B)
0
C)
49
24
D)
4
3
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
96)
–0.7–0.7 and 6·7>6+7
96)
A)
True
B)
False
Solve the equation.
97)
0.50x – 0.30(20 + x) =0.50(20)
97)
A)
{70}
B)
{80}
C)
{90}
D)
{40}
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
98)
{x x is an integer between –6 and –1} = {–6, –5, –4, –3, –2, –1} and –2.5–
2
98)
A)
True
B)
False
Solve.
99)
The formula N =2x2+5x +1 represents the number of households in a certain city, N, in
thousands, that have a computer, x years after 2005. According to the formula, in what year were
there 53,000 households with computers in this city?
99)
A)
2008
B)
2009
C)
2007
D)
2010
Graph the equation.
29
100)
y =1
2x – 4
100)
A)
B)
C)
D)
Simplify the expression using the power rule.
101)
(x3)–4
101)
A)
–4x12
B)
–x12
C)
1
x12
D)
–4x3
Plot the point in the rectangular coordinate system.
102)
(3,6)
102)
A)
B)
C)
D)
Determine whether the inequality is true or false.
103)
–16 25
103)
A)
True
B)
False
Divide as indicated or state that the division is undefined.
104)
145
–5
104)
A)
–39
B)
–1
29
C)
–29
D)
29
Determine whether the statement is true or false.
105)
Every real number is either rational or irrational.
105)
A)
True
B)
False
Determine whether the inequality is true or false.
106)
24 13
106)
A)
True
B)
False
Provide an appropriate response.
107)
Divide and write the answer in scientific notation: 3 ×10–9
12 ×10–5
107)
A)
2.5 ×10–5
B)
0.25 ×10–4
C)
2.5 ×10–4
D)
2.5 ×105
Use the zero exponent rule to simplify the expression.
108)
–110
108)
A)
11
B)
–1
C)
1
D)
0
109)
–9y0
109)
A)
0
B)
–9
C)
–8
D)
1
Solve the equation.
110)
6(x + 4) + 39 =9x –3(x + 3 ÷ 1.1)
110)
A)
( , )
B)
C)
{30}
D)
{48}
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
111)
Three times the sum of a number and eight is represented by 3(x +8) and
0
{x x is a natural number}
111)
A)
True
B)
False
Find –x for the given value of x.
112)
x = – 6
7
112)
A)
–7
6
B)
–6
7
C)
7
6
D)
6
7
Graph the equation.
33
113)
y = – 1
4x2
113)
A)
B)
C)
D)
Write the number in decimal notation without the use of exponents.
114)
7.567 ×10–6
114)
A)
0.00007567
B)
–7,567,000
C)
0.000007567
D)
0.0000007567
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
115)
At what time was the temperature 73°?
115)
A)
5 p.m.
B)
10 a.m. and 11 a.m.
C)
4 p.m. and 5 p.m.
D)
10 a.m.
Simplify the algebraic expression.
116)
–4x + 2y + 6x + 7y
116)
A)
9x + 2y
B)
2x + 9y
C)
–4x + 6x + 2y + 7y
D)
11xy
35
Solve the equation.
117)
2{12 – [3x – (4x –6)]} = 24 –7(x –6)
117)
A)
{6}
B)
–10
3
C)
10
3
D)
{–6}
Perform the indicated computation. Write the answer in scientific notation.
118)
13.68 ×10–4
3.8 ×10–9
118)
A)
3.6 ×10–13
B)
7.2 ×10–13
C)
3.6 ×105
D)
7.2 ×105
Solve the problem.
119)
Your company uses the quadratic model y = – 11x2+ 350x to represent how many units (y) of a
new product will be sold (x) weeks after its release. How many units can you expect to sell in week
28?
119)
A)
10,108 units
B)
18,424 units
C)
9492 units
D)
1176 units
Use the meaning of the symbols
and
to determine whether the statement is true or false.
120)
–1{ x | x is a rational number}
120)
A)
True
B)
False
Find the absolute value.
121)
0
121)
A)
10
B)
1
C)
0
D)
–1
Solve the equation. Express the solution in scientific notation.
122)
(–3.1 ×10–3)x = (2.5 ×10–9)(6.2 ×104)
122)
A)
{–5×1012}
B)
{–0.5 ×10–1}
C)
{–5×10–8}
D)
{–5×10–2}
Use the indicated property to write an algebraic expression equivalent to the given expression.
123)
2x +19; commutative of addition
123)
A)
19x +2
B)
–2x +19
C)
2x –19
D)
19 +2x
Determine whether the inequality is true or false.
124)
18 5
124)
A)
True
B)
False
Simplify the exponential expression.
125)
–5ym3n
–7ym6n
125)
A)
5
7m3
B)
–2
m3
C)
–2y2n2
m3
D)
1
2m3
Solve the problem.
126)
According to Bode’s law, the distance d of the nth planet from the sun is d =3(2n–2) + 4
10 , in
astronomical units. Find the distance of Mars (n = 4) from the sun.
126)
A)
1.0 units
B)
1.6 units
C)
0.7 units
D)
2.8 units
37
Find the absolute value.
127)
|–3|
127)
A)
3
B)
0
C)
–3
D)
6
Multiply as indicated.
128)
(–8)(–7)(–7)
128)
A)
112
B)
392
C)
–392
D)
–382
C
129)
–3· 0
129)
A)
0
B)
3
C)
–3
D)
–3
A
Simplify the expression using the power rule.
130)
(x7)7
130)
A)
7x49
B)
x49
C)
x14
D)
7x7
B
Use the order of operations to simplify the expression.
131)
72 – 4 ·17 + 96 ÷ (–6)
131)
A)
–12
B)
–1281
C)
–30
D)
1140
A
38
A
Write the English phrase as an algebraic expression. Let x represent the number.
132)
A number divided by 34
132)
A)
34
x
B)
34x
C)
x
34
D)
x –34
Express the interval in set builder notation and graph the interval on a number line.
133)
(–, 3]
133)
A)
{x x 3 }
B)
{x x 3 }
C)
{x x <3 }
D)
{x x <3 }
Provide an appropriate response.
134)
The bar graph shows the percentage of Americans in various age groups who had contact with a
police officer, for anything from an arrest to asking directions, in a recent year.
The mathematical model P = – 0.6x2+ 0.8x + 26.6 describes the percentage of Americans, P, in age
group x who had contact with a police officer. Does the model underestimate or overestimate the
percentage of Americans between the ages of 16 and 19, inclusive, who had contact with a police
officer? By how much?
134)
A)
overestimates by 1.8
B)
underestimates by 0.8
C)
underestimates by 1.8
D)
overestimates by 0.8