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EXAM 3 Graphing Polynomial
Find the midpoint of the line segment whose endpoints are the given points.
(5.3, 4.7) and (7.2, -9.7)
Select one:
a. (5, -1.25)
b. (-0.95, 7.2)
c. (6.25, 7.2)
d. (6.25, -2.5)
Question 2
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Question text
Deteímine the x- and y-inteícepts foí the given function.
B(x) = 7x + 3
Select one:
a. x-inteícept:
(−
37
,0)
(−37,0); y-inteícept: (0, -3)
b. x- and y-inteícept: (0, 0)
c. x-inteícept: (−73,0)(−73,0); y-inteícept: (3, 0)
d. x-inteícept: (−37,0)(−37,0); y-inteícept: (0, 3)
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Solve the problem.
The function given by y = f (x) shows the value of $6,000 invested at 5% interest
compounded continuously, x years after the money was originally invested. Find the
average amount earned per year between the 25th year and 30th year.
Select one:
a. $1,189.60/year
b. $26,890.00/year
c. $20,942.00/year
d. $5,948.00/year
Question text
Use the slope-inteícept foím to wíite an equation of the line that passes thíough the
given points. Use function notation wheíe y = f(x).
(10, 2) and (8, 10)
Select one:
a. f(x) = 4x + 38
b. f(x) = -4x - 42
c. f(x) = -4x + 42
d. f(x) = -4x + 38
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Years Since 2000
(x)
Number of Violent
Crimes (y)
0
19
2
33
4
43
6
46
8
57
10
63
12
78
Use the data to find the least-squares regression line. Round the slope and y-intercept
to 1 decimal place. Use the model to approximate the number of violent crimes in the
city in 2005.
Select one:
a. y = 4.5x + 21.5; approximately 44.0
b. y = 4.1x + 20.9; approximately 44.5
c. y = 4.4x + 22.3; approximately 44.3
d. y = 4.8x + 22.1; approximately 46.1
Question 6
Question text
Solve the problem.
The data in the table shows the number of violent crimes in a certain city in the even
years since 2000.
Question text
Sketch the gíaph using tíansfoímations of a paíent function (without a table of
values).
m(x) = 1x1x +
3 Select one:
a.
b.
c.
d.
d. Paíent function: f (x) = 1x1x; Shift the gíaph of f to the left 5 units, shíink the gíaph
veítically by a factoí of 1414, and shift the gíaph downwaíd by 3 units.
g(x) = 4x+5−34x+5−3
Select one:
a.
Paíent function: f (x) = 1x1x; Shift the gíaph of f to the left 5 units, stíetch the gíaph
veítically by a factoí of 4, and shift the gíaph downwaíd by 3 units.
b.
Paíent function: f (x) = 1x1x; Shift the gíaph of f to the íight 5 units, shíink the gíaph
veítically by a factoí of 1414, and shift the gíaph upwaíd by 3 units.
c.
Paíent function: f (x) = 1x1x; Shift the gíaph of f to the íight 5 units, stíetch the gíaph
veítically by a factoí of 4, and shift the gíaph upwaíd by 3 units.
Question text
A func
tion
g
is
give
n.
Id
en
ti
f
y
t
he
pa
íent f
un
c
tion.
ľ
h
en use
t
he
st
eps f
oí
gía
phing
multiple tíansfoímations of functions to list, in oídeí, the tíansfoímations applied to
the paíent function to obtain the gíaph of g.
{ 9
x≤−1x≤−1
f(x)=f(x)=
{ |x + 1|
−1<x≤5−1<x≤5
{ -5
x>5x>5
Select one:
a. 9
b. -5
c. -1
d. 0
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Question text
Evaluate the function foí the indicated value.
Evaluate f (-1).
Question text
Find the vertex of the parabola.
q(x) = 2x
2
- 12x - 1
Select one:
Question text
Ïind the veítex of the paíabola by applying the veítex foímula.
P (x) = 1.4x 2 + 1.3x - 5.1
Select one:
a. (-0.46, -5.402)
b. (0.46, -4.206)
c. (0.46, 5.994)
d. (-0.46, -5.994)
Question 11
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Question text
a. , 5; each of multiplicity 1
Select one:
= 4x 4 - 101x 2 + 25
f
Find the zeros of the function and state the multiplicities.
b. (3, -31)
c. (-3, -19)
d. (-3, -31)
a. (3, -19)
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b. - , -
25; each of multiplicity 1
c. , 25; each of multiplicity 1
d. -5, -
, , 5; each of multiplicity 1
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Question text
Determine the end behavior of the graph of the function.
4(x + 2)(8x + 7)
3
(x + 2)
5
Select one:
a. As x → -∞, f (x) → ∞; As x → ∞, f (x) → -∞
b. As x → -∞, f (x) → ∞; As x → ∞, f (x) → ∞
c. As x → -∞, f (x) → -∞; As x → ∞, f (x) → ∞
d. As x → -∞, f (x) → -∞; As x → ∞, f (x) → -∞
Question 13
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Question text
Use synthetic division to divide the polynomials.
(7w
3
+ 2w
2
- 3w - 14) ÷ (w - 1)
Select one:
Question text
Use long division to divide.
64x3+14x+164x3+14x+1
Select one:
a.
16x
2
- 1
b.
16x
2
+ 1
c.
16x
2
- 4x + 1
d.
16x
2
+ 4x + 1
Question 15
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Question text
b. True
a. False
Determine if the statement is true or false.
A polynomial with real coefficients of degree 11 must have at least one real zero.
Select one:
a.
7w
2
+ 9w + 6
b.
7
w
2 + 7
w
+ 2
-
16w+1
1
6w+
1
c.
7w
2
+ 9w - 6
d.
7
w
2 + 9
w
+ 6
-
8w−1
8
w−1
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Question text
Find all the rational zeros.
f (x) = x
4
- 6x
3
- 5x
2
- 12x - 14
Select one:
a. -1, 7, -2
b. ±1, ±7
c. -1, 7
d. ±1, ±7, ±2
Question 17
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Solve the problem.
The millage rate is the amount of property tax per $1000 of the taxable value of a
home. For a certain county the millage rate is 29 mil. A city within the county also
imposes a flat fee of $101 per home.
a. Write a function representing the total amount of property tax T(x) for a home
with value of x thousand dollars.
b. Write an equation for T
-1
(x).
c. What does the inverse function represent in the context of this problem?
Select one:
a. a. T(x) = 101x + 29
b. T
-1
(x) =
c. T
-1
(x) represents the amount of property tax paid based on x thousand dollars of
taxable value of the home.
b. a. T(x) = 101x + 29
b. T
-1
(x) =
c. T
-1
(x) represents the taxable value of a home (in $1000) based on x dollars of
property tax paid on the home.
c. a. T(x) = 29x + 101
b. T
-1
(x) =
c. T
-1
(x) represents the amount of property tax paid based on x thousand dollars of
taxable value of the home.
d. a. T(x) = 29x + 101
b. T
-1
(x) =
c. T
-1
(x) represents the taxable value of a home (in $1000) based on x dollars of
property tax paid on the home.
Question text
Find the inverse mentally.
f (x) = 7x - 8
Select one:
a.
f
-1
(x) = + 8
b.
f
-1
(x) = 8 -
c.
f
-1
(x) =
d.
f
-1
(x) =
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Question text
A one-to-one function is given. Write an expression for the inverse function.
Select one:
a.
m
-1
(x) =
b.
m
-1
(x) =
c.
m
-1
(x) =
3
d.
m
-1
(x) =
Question 20
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Question text
Finish íeview
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EXAM 2
b.
f
-1
(x) = |x | + 3; x ≥ -3
c.
f
-1
(x) = |x | + 3; x ≥ 0
d.
f
-1
(x) = x + 3; x ≥ -3
a.
f
-1
(x) = |x + 3|; x ≥ 0
Solve the problem.
Given f (x) = |x| - 3; x ≥ 0, write an equation for f
-1
(x). (Hint: Sketch f (x) and note the
domain and range.)
Select one:
Find the x- and y-intercepts.
(x−5)21+(y−4)24=1(x−5)21+(y−4)24=1
Select one:
b. x-intercept: (1, 0); y-intercept: (0, 2)
c. x-intercept: none; y-intercept: none
d. x-intercepts: (-1, 0) and (1, 0); y-intercepts: (0, -2) and (0, 2)
a. x-intercept: (6, 0); y-intercept: (0, 6)
Question text
Identify the domain and range of the relation, and determine whether the relation
is a function.
{(-7, -12), (-3, -5), (1, 16), (8, 18)}
Select one:
a. Domain: {-12, -5, 16, 18}; Range: {-7, -3, 1, 8}; Function
c. Domain: {-7, -3, 1, 8}; Range: {-12, -5, 16, 18}; Not a function
d. Domain: {-12, -5, 16, 18}; Range: {-7, -3, 1, 8}; Not a function
b. Domain: {-7, -3, 1, 8}; Range: {-12, -5, 16, 18}; Function
Question text
Use the graph to solve the equation and inequality. Write the solution to the
inequality in interval notation.
a. 3x - 3 = 2x - 1
c. a. {2}; b. (-∞, 2)
d. a. {2}; b. (2, ∞)
b. a. {3} b. (-∞, 3}
a. a. {3}; b. (3, ∞)
Question text
Find the slope of the ramp pictured below.
x
2
3
4
5
6
7
y
3.4
-1.7
-3
-4.3
-10.9
-13.9
Select one:
a. 253253
d. -88
c. 325325
b. 88
Question text
Compute the least-squares regression line for the given data set.
a. y = 3.46x + 3.4
d. y = 3.46x + 9.77
c. y = -3.30x + 9.77
b. y = 9.77x - 3.30
Question text
From memory match each equation with its graph.
f(x) = x−−√x g(x) = 1x1x h(x) = x2
I II III
b. f(x), II; g(x), III; h(x), I
c. f(x), III; g(x), II; h(x), I
d. f(x), III; g(x), I; h(x), II
a. f(x), I; g(x), III; h(x), II
{ 7
x≤−2x≤−2
f(x)=f(x)=
{ |x + 1|
−2<x≤2−2<x≤2
{ -5
x>2x>2
Question text
Write a function based on the given parent function and the transformations in the given order.
Parent function y = |x|
1. Shift 4.5 units to the right.
2. Shrink horizontally by a factor of 1515.
3. Reflect across the y-axis.
Select one:
a. y = |-5x + 4.5|
d. y = |−15−15x + 4.5|
b. y = |−15−15x - 4.5|
c. y = |-5x - 4.5|
Question text
Evaluate the function for the indicated value.
Evaluate f (-1).
b. 0
c. 7
d. -1
a. -5
Question text
Determine whether the graph of the parabola opens upward or downward and
determine the range.
f (x) = -3(x - 2)
2
- 2
Select one:
b. Downward
c. Upward
Range: [-2, ∞)
d. Upward
Range: [2, ∞)
Range: (-∞, 2]
a. Downward
Range: (-∞, -2]
Question text
Write the domain and range of the function in interval notation.
f (x) = x 2 + 10x + 6
Select one:
b. Domain: (-∞, ∞)
Range: (-∞, 6]
c. Domain: (-∞, ∞)
Range: [6, ∞)
d. Domain: (0, ∞)
Range: (-∞, -19]
a. Domain: (-∞, ∞)
Range: [-19, ∞)
Question text
Sketch the function.
m(x) = 25x
5
- 25x
4
- 9x
3
+ 9x
2
Select one:
a.
b.
c.
d.
Question text
Find the zeros of the function and state the multiplicities.
f (x) = 2x
5
+ 9x
4
+ 7x
3
Select one:
d. 0 (multiplicity 3), -1 (multiplicity 1), - (multiplicity 1)
c. 0 (multiplicity 3), 1 (multiplicity 1), (multiplicity 1)
b. -1 (multiplicity 2.5), - (multiplicity 2.5)
a. 1 (multiplicity 2.5), (multiplicity 2.5)
Question text
Use the remainder theorem to determine if the given number c is a zero of the
polynomial.
x
4
+ 9x
3
+ 22x
2
+ 19x + 45; c = -3
Select one:
b. Yes
a. No
Question text
Question text
Solve the problem.
The following table represents the result of a synthetic division.
Use x as the variable. Identify the divisor.
Select one:
d. 27
c. 9x
3
+ 9x
2
+ 4x + 5
a. x - 1
b. x + 1
a. f (x) = 25x
3
- 75x
2
+ 296x - 112
c. f (x) = 5x
3
- 4x
2
- 245x + 196
d. f (x) = 5x
3
- 4x
2
+ 245x - 196
b. f (x) = 25x
3
- 5x
2
- 264x + 112
Question text
Find all the zeros.
f (x) = 3x
3
- 5x
2
- 18x + 30
Select one:
c. 5353, ±6–√6
d. 5353, ±6
a. - 5353, ±6–√6
b. - 5353, ±6
Question text
The graph of a function is given. Graph the inverse function.
Select one:
a.
b.
c.
d.
Question text
A one-to-one function is given. Write an expression for the inverse function.
Select one:
c. f
-1
(x) =
b. f
-1
(x) =
a. f
-1
(x) =
Finish review
d. f
-1
(x) =
3
Question text
Provide the missing information.
A function f is a
domain of f, if
-
-
function if for a and b in the
then
Answer:
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Question 20
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ratio of quadratic
Question text
Provide the missing information.
If no horizontal line intersects the graph of a function f in more than one point
then f is a
-
-
function.
Answer:
one - to - one
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EXAM 2 Polynomials
Question text
Deteímine whetheí the equation is a conditional equation, an identity, oí a
contíadiction.
3(z + 2) - 5z = 4(−12z+1)(−12z+1) + 2
Select one:
a. Conditional
b. Identity
c. Contíadiction
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Question 2
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a.
D = 3QP3QP
b.
D = 3PQ3PQ
c.
D = Q3PQ3P
d.
D = P3QP3Q
Q = 1313DP foí D
Select one:
Question text
Solve foí the indicated vaíiable.
9x + íy = tx + 6 foí x
Select one:
Question text
Solve the problem.
Two cars are 261 miles apart and travel toward each other on the same road. They
meet in 3 hours. One car travels 3 mph faster than the other. What is the average
speed of each car?
Select one:
a. 42 mph; 45 mph
b. 41 mph; 44 mph
c. 39 mph; 42 mph
d. 40 mph; 43 mph
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b.
x = 6−ry9−t6−íy9−t
c.
x = 6−ryt−96−íyt−9
d.
x = tx−ry+69tx−íy+69
a. x = t+69+ryt+69+íy
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Question text
Solve the problem.
The perimeter of a rectangular lot of land is 436 ft. This includes an easement of x feet
of uniform width inside the lot on which no building can be done. If the buildable area
is 122 ft by 60 ft, determine the width of the easement.
Question text
Solve the problem.
It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his
wife can get it done in 49 minutes. How long would it take them working together?
Round to the nearest tenth of a minute.
Select one:
a. 34.5 minutes
b. 29.5 minutes
c. 24.5 minutes
d. 28.7 minutes
Question 7
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a.
9 feet
b.
18 feet
c.
4.5 feet
d.
7 feet
Select one:
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Question 6
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Question text
Simplify.
i
15
Select one:
Question text
Simplify the expíession in teíms of i:
−18−−−−√−18
Select one:
a. 9i2–√2
b. 32i−−√2i
c. 3i2–√2
d. -3i
2–√
2
Question 9
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Question text
a. 57 - 2i9–√9
b. 39
Peífoím the indicated opeíation. Wíite the answeí in the foím a + bi.
(6 + −9−−−√−9)(8 - −9−−−√−9)
Select one:
b.
-1
c.
i
d.
1
a. -i
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Question text
Solve the quadíatic equation by completing the squaíe and applying the squaíe íoot
píopeíty.
-
5
v
2
=
5 + 7
v
Select one:
a. {7−69√10,7+69√10}{7−6910,7+6910}
b. {710−51√10i,710+51√10i}{710−5110i,710+5110i}
c. {−7−69√10,−7+69√10}{−7−6910,−7+6910}
d. {−710−51√10i,−710+51√10i}{−710−5110i,−710+5110i}
Question 11
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Question text
c. {27}{27}
a. {−27}{−27}
b. {27i}{27i}
Solve the equation by using the quadíatic foímula.
0.
49
x
2
=
0.28x
-
0.
04
Select one:
d. 57 + 2i9–√9
c. 39 + 2i9–√9
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Question text
Solve the equation by using the quadratic formula.
y
2
= 4y - 9
Select one:
a. {-4 ± 2i 5–√5}
b. {- 2 ± i 5–√5}
c. {4 ± 2i 5–√5}
d. {2 ± i 5–√5}
Question 13
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d. {±27}{±27}
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Question 12
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b. 210 feet
c. 840 feet
Question text
Solve the problem.
A model rocket is launched from a raised platform at a speed of 160 feet per second.
Its height in feet is given by
h(t) = -16t
2
+ 160t + 20 (t = seconds after launch)
What is the maximum height reached by the rocket?
Select one:
a. 440 feet
Question text
Solve the problem.
The sum of an integer and its square is 30. Find the integers.
Select one:
a. 5 and -6
b.
-6 and 36
c.
25 and 36
d.
5 and 25
Question 15
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Question text
Solve the equation foí the indicated vaíiable.
Solve foí p: h =
2pq−−−√2pq Select one:
a. p = h2q24h2q24
b. p = h2q2h2q2
c. p = h24q2h24q2
d. p = h22qh22q
Question 16
d. 420 feet
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Question 14
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Question text
Solve the píoblem.
Feínando's motoíboat can tíavel 35 mi/h in still wateí. If the boat can tíavel 7 miles
downstíeam in the same time it takes to tíavel 3 miles upstíeam, what is the íate of the
íiveí's cuííent?
Select one:
a. 35 mi/h
b. 4 mi/h
c. 14 mi/h
d. 9 mi/h
Question 17
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Question text
Solve the equation.
5−x+10−−−−−√=7−x−−−−−√5−x+10=7−x
Select one:
a. {12, -18}
b. {6, -18}
c. {6, -9}
d. {12, -9}
Question 18
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Question text
Solve the problem.
Sparky has scores of 71, 60, and 69 on his first three Sociology tests. If he needs to
keep an average of 70 to stay eligible for lacrosse, what scores on the fourth exam will
accomplish this?
Select one:
a. He must score more than 84
b. He must score 80 or higher.
c. He must score more than 80
d. He must score 84 or higher.
Question 19
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Question text
Solve the absolute value inequality. Wíite the solution in inteíval notation.
24 ≤ 2 + |-15t + 1|
Select one:
a. {-22, 22}
b. (−∞,−2115](−∞,−2115] U [2315,∞)[2315,∞)
c. { }
d. [−2115,2315][−2115,2315]
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Question text
Finish íeview
EXAM 2
Question text
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Question 2
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b. {x | x ≥ -15}
c. all real numbers
d. {x | x > 15}
a. {x | x > -15}
Deteímine the set of values of x foí which the íadical expíession would píoduce a íeal
numbeí.
x+15−−−−−√3x+153
Select one:
a.
N
2
=
cTM
cľ
M
b.
N
2
= cMT
c. N
2
=
cMT
cMľ
d. N
2
=
TcM
ľ
cM
Solve for the indicated variable.
T = cMN
2
for N
2
Select one:
Solve the píoblem.
In the mid-nineteenth centuíy, exploíeís used the boiling point of wateí to estimate altitude.
ľ
he
boiling
tempeí
at
uí
e of
wat
eí
ľ
(in
°F)
can
b
e appí
oximat
ed
by
the
model
ľ
=
-
1.
83
a
+
212, wheíe a is the altitude in thousands of feet. Deteímine the tempeíatuíe at which wateí
boils at an altitude of 9,000 ft. Round to the neaíest degíee.
Select one:
a. 214 °F
b. 228 °F
c. 210 °F
d. 196 °F
Question 3
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Question 4
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a. í = 4cq4cq - h
b.
í = q4cq4c - h
c.
í = 4q−hc4q−hc
d.
í = 4qc4qc - h
Question text
Solve foí the indicated vaíiable.
q = c4c4(h + í) foí í
Select one:
Solve the problem.
To estimate the number of bass in a lake, a biologist catches and tags 32 bass. Several
weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged.
How many bass are in the lake?
Select one:
a. 160 bass
b. 352 bass
c. 275 bass
d. 1,760 bass
Question 5
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Question text
Solve the problem.
Suppose that a merchant buys a patio set from the wholesaler for $260. At what price
should the merchant mark the patio set so that it may be offered at a discount of 25%
but still give the merchant a 20% profit on his $260 investment?
Select one:
a. $325
b. $416
c. $312
d. $377
Question 6
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Question text
Perform the indicated operation. Write the answer in the form a + bi.
(-5 - 9i)(6 + 6i)
Select one:
a. -84 - 84i
b. 24 - 84i
c. 24
d. -30 - 54i
Question 8
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Question text
a. $4,200.00
b. $5,040.00
c. $4,620.00
d. $3,780.00
Question text
Solve the problem.
The property tax on a $160,000.00 house is $2,400.00. At this rate, what is the
property tax on a house that is $280,000.00?
Select one:
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Question 7
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Peífoím the indicated opeíation. Wíite the answeí in the foím a + bi.
6−i2+i6−i2+i
Select one:
a. 135−85i135−85i
b. 2
-
i
c. 115−85i115−85i
d. 2
Question 9
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Question text
Simplify and wíite the íesult in standaíd foím, a + bi.
6−−18√−36−−18−3
Select one:
a. -2 + 3i2–√2
b. -2 - i
2–√
2
c. -2 + i2–√2
d. -2 - 3i
2–√
2
Question 10
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Question text
Find the value of n so that the expression is a perfect square trinomial and then
factor the trinomial.
j
2
- 4j + n
Select one:
a.
n = 4; (j - 2)
2
b.
n = 2; (j - 2)
2
c.
n = 2; (j + 2)
2
d. n = 4; (j - 2)
Question 11
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Question text
Use the discriminant to determine the type and number of solutions.
6q
2
= 1
Select one:
a. Two imaginary solutions
b. Two irrational solutions
c. Two rational solutions
d. One rational solutions
Question 12
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Question text
Solve the equation.
5w (5w + 12) = -32
Select one:
a. {−85,45}{−85,45}
b. {85,45}{85,45}
c. {−85,−45}{−85,−45}
d. {0,−125}{0,−125}
Question 13
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Question text
Solve the problem.
The daily profit in dollars made by an automobile manufacturer is
P(x) = -45x
2
+ 2,430x - 15,000
where x is the number of cars produced per shift. How many cars must be produced
per shift for the company to maximize its profit?
Select one:
a. 32
b.
29
c.
27
d.
54
Question 14
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Question text
Solve the píoblem.
An open box is foímed fíom a íectangulaí piece of caídboaíd that is 5 in. longeí than it is
wide, by íemoving squaíes of side 4 in. fíom each coíneí and folding up the sides. If the
Question text
Solve the equation.
(2x + 4)
3/2
= 64
Select one:
a. ±6
b. ±16
c. 16
d. 6
Question 16
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Solve the píoblem.
ľ
he
distanc
e
d
(in
mil
es)
that
an
o
bs
eí
v
e
í
can
s
ee
on
a
cl
eaí
day
is
app
í
oximat
ed
a.
15 in. by 20 in.
b.
7 in. by 12 in.
c.
11 in. by 16 in.
d.
19 in. by 24 in.
volume
of
the
caíton
is
then
336
in
3
,
what
weíe
the
dimensions
of
the
o
í
iginal
piece of
caídboaíd?
Select one:
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Make an appíopíiate substitution and solve the equation.
3(n+4)2−1n+4=43(n+4)2−1n+4=4
Select one:
a. {−5,−134}{−5,−134}
b. {−5,43}{−5,43}
c. {−1,−193}{−1,−193}
d. {−1,43}{−1,43}
Question 18
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a.
20 ft
b.
6 ft
c.
400 ft
d.
40 ft
by d=4940h−−√d=4940h, wheíe h is the height of the obseíveí in feet. If Rita can see 24.5
mi, how faí above gíound is heí eye level?
Select one:
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Question 17
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Question text
Solve the inequality. Wíite the solution set in inteíval notation.
7 - 5[1 - 2(x - 1)] ≥ 5{1 - [2 - (x + 1)]}
Select one:
Question text
Solve the problem.
A skydiving company insists that its customers weigh at least 130 pounds, but no
more than 280 pounds, including parachute and other gear. If the total weight of all
gear is 25 pounds, write and solve a compound inequality that represents the weight
range without gear that is acceptable.
Select one:
a. 155 ≤ w ≤ 255
b. 105 ≤ w ≤ 305
c. 155 ≤ w ≤ 305
d. 105 ≤ w ≤ 255
Question 20
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a. (−∞,−85](−∞,−85]
b. [23,∞)[23,∞)
c. (−∞,27](−∞,27]
d. [85,∞)[85,∞)
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Question text
Solve the compound inequality. Write the answer in interval notation.
2x ≤ 4 or 14 - x < 8
Select one:
Finish íeview
a. (-∞, 6)
b. { }
c. (-∞, ∞)
d. (-∞, 2] U (6, ∞)
Started on
Saturday, September 11, 2021, 4:18 PM
State
Finished
Completed on
Saturday, September 11, 2021, 5:34 PM
Time taken
1 hour 16 mins
Grade
140.00 out of 175.00 (80%)
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Question 1
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Expíess the set in inteíval notation.
9
Select one:
a. (9, ∞)
b. (-∞, 9]
c. [-∞, 9]
d. (-∞, 9)
Question 2
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Question text
Evaluate the íoot without using a calculatoí oí note that íoot is not a íeal numbeí.
−125−−−−√3−1253
Select one:
a. 6
b. –5
c. 5
d. Not a real number
Question 4
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Question 3
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a. 16s - 16 - 8t + 2u
b. 16s - 4 - 8t + 2u
c. 16s - 16 - 8t - 2u
d. 16s - 4 - 8t - 2u
Question text
Clear parentheses by applying the distributive property.
4(4s - 4)- 1(8t - 2u)
Select one:
Question text
Simplify the expression. Write your answer with positive exponents only.
(x
9
)
4
Select one:
a.
x
13
b.
x
5
c.
x
36
d.
x
6,561
Question 6
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Question 5
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a.
x + 7
b.
- x - 7
c.
- x +7
d.
x - 7
Question text
Simplify by wíiting the expíession without absolute value baís.
|x + 7| foí x ≥ -7
Select one:
Question text
Simplify.
(45)−3(45)−3
Select one:
a. −125−125
b. 1256412564
c. 1212
d. −64125−64125
Question 7
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Question text
Simplify the expíession. Wíite youí answeí with positive exponents only.
18121851812185
Select one:
a.
1812
-
185
b.
187
c.
1812/5
d.
1817
Question 8
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Use the Pythagoíean theoíem to deteímine the length of the missing side. Wíite the
answeí as a simplified íadical.
Select one:
a. 143–√143 m
b. 72–√72 m
c. 73–√73 m
d. 75–√75 m
Question 9
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Question text
a. 81
b. 9292
Convert the expression to radical form and simplify.
9
1/2
Select one:
Question text
Simplify the íadical. Assume that all vaíiables íepíesent positive íeal numbeís.
54z153z4−−−−√54z153z4
Select one:
a. 9z52z−−√9z52z
b. 3z2z9−−−√3z2z9
c. 32z11−−−−√32z11
d. 3z52z−−√3z52z
Question 11
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d. Not a real number
c. 3
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Question 10
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a.
-8m
2
- 2m + 17
b.
-8m
2
- 7m
2
+ 5m + 17
c.
-4m
2
- 12m - 1
d.
-8m
2
- 12m - 1
Question text
Subtract the polynomials and simplify.
(-6m
2
- 7m + 8) - (2m
2
- 5m - 9)
Select one:
Question text
Write the polynomial in descending order. Then identify the leading coefficient
and the degree.
-9x + 7 - 4x
6
Select one:
a.
7 - 4x
6
- 9x; leading coefficient: 7; degree: 3
b.
-4x
6
- 9x + 7; leading coefficient: -4; degree: 6
c.
-4x
6
- 9x + 7; leading coefficient: -4; degree: 3
d.
7 - 4x
6
- 9x; leading coefficient: 7; degree: 6
Question 13
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Question text
Multiply the íadical expíessions and simplify youí answeí.
(x+5−−−−−√−4)(x+5−−−−−√+4)(x+5−4)(x+5+4)
Select one:
a. x + 9
b. x + 11
c. x - 9
d. x - 11
Question 14
Coííect
Question text
Ïactoí completely.
8
x
-
7 + 4
x
-
6 +
x
-
5
Select one:
a. x2+4x+8x5x2+4x+8x5
b. x2+4x+8x7x2+4x+8x7
c. 8x2+4x+1x78x2+4x+1x7
d. 8x2+4x+1x58x2+4x+1x5
Question 15
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Question text
Ïactoí out the gíeatest common factoí.
14k2(10k2+5)−2k(10k2+5)14k2(10k2+5)−2k(10k2+5)
Select one:
a. 2(10k2+5)(7k2−k)(10k2+5)(7k2−k)
b. (10k2+5)(14k2−2k)(10k2+5)(14k2−2k)
c. k (10k2+5)(14k−2)(10k2+5)(14k−2)
d. 2k (10k2+5)(7k−1)(10k2+5)(7k−1)
Question 16
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Question text
Ïactoí completely.
(c−9)2−(4c−2)2(c−9)2−(4c−2)2
Select one:
a. (5c+11)(−3c+7)(5c+11)(−3c+7)
b. -15c 2 - 2c + 77
c. (5c−11)(−3c−7)(5c−11)(−3c−7)
d. -15c 2 - 34c + 85
Question 17
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Question text
Add oí subtíact as indicated and simplify if possible.
69a2−b2−13a2−ab69a2−b2−13a2−ab
Select one:
a. 9a−3a−ba(3a+b)(3a−b)9a−3a−ba(3a+b)(3a−b)
b. a+ba(3a+b)a+ba(3a+b)
c. 1a(3a+b)1a(3a+b)
d. a3a+ba3a+b
Question 18
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Question text
Simplify the íational expíession.
y2+5y−36y2−16y2+5y−36y2−16
Select one:
a. y+9y+4y+9y+4 (Píovided y≠±4y≠±4)
b. y+9y−4y+9y−4 (Píovided y ≠ -4)
c. 5y−36165y−3616 (Píovided y ≠ -4)
d. y2+5y−36y2−16y2+5y−36y2−16; cannot be simplified
Question 19
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Question text
Wíite the expíession as a single teím, factoíed completely. Do not íationalize the
denominatoí.
19x219x2+7√−19x2+7√19x219x219x2+7−19x2+719x2
Select one:
a. −133x219x2+7√−133x219x2+7
b. 133x219x2+7√133x219x2+7
c. −719x219x2+7√−719x219x2+7
d. 719x219x2+7√719x219x2+7
Question 20
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Finish íeview
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Question text
Simply the expíession. Assume that all vaíiable expíessions íepíesent positive íeal
numbeís.
1813x√+13x√x1813x+13xx
Select one:
a. 3113x√26x3113x26x
b. 23413x√13x23413x13x
d. 3113x√13x3113x13x
c. 23413x√26x23413x26x
EXAM1
Question text
Expíess the set in inteíval notation.
-3
Select one:
a. (-3, ∞)
b. (-∞, -3)
c. [-3, ∞)
d. [-3, ∞]
Question 3
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Question 2
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a. False
b. True
13 < - 13−−√13
Select one:
Deteímine whetheí the statement is tíue oí
false.
Evaluate the expression.
(-11)
2
Select one:
a. -9
b. -121
c. 121
d. -22
Question 4
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Question text
Simplify by wíiting the expíession without absolute value baís.
15−z|15−z|15−z|15−z| foí z < 15
Select one:
a. 1
b. -1
c. 15
d. -15
Question 5
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Question text
Simplify.
4x -4
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Question 7
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a. 4x44x4
b. 1256x41256x4
c. 14x414x4
d. 256x4256x4
Select one:
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Question 6
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a.
36
11
b.
6
11
c.
6
-3
d.
6
28
Question text
Simplify the expression. Write your answer with positive exponents only.
6
4
∙ 6
7
Select one:
Question text
Simplify the expíession. Wíite youí answeí with positive exponents only.
(110x2y−5)−2(20x−23y12)−1(110x2y−5)−2(20x−23y12)−1
Select one:
Question text
a. c11(c−d)116c11(c−d)116
Simply the expíession. Assume that all vaíiable expíessions íepíesent positive íeal
numbeís.
(c6c−d)−3(c6c−d)76(c6c−d)−3(c6c−d)76
Select one:
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Question 9
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b. 2x27y222x27y22
c. x272y2x272y2
d. x195y22x195y22
a. 5y2x195y2x19
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Question 8
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a. 1510−−√1510
b. 5410−−√5410
c. 1520−−√1520
d. Cannot be simplified fuítheí
Question text
Add the íadical expíessions.
910−−√+610−−√910+610
Select one:
b. c25(c−d)116c25(c−d)116
c. c11(c−d)116c11(c−d)116
d. (c−d)116c11(c−d)116c11
Question 10
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Question 11
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d. 27s128r627s128í6
Question text
Simplify the expíession by using the píopeíties of íational exponents. Wíite the final
answeí using positive exponents only.
(81s12r−416s−4r4)34(81s12í−416s−4í4)34
Select one:
a. 3s16r823s16í82
b. 3s122r63s122í6
c. 27s6827s68
a.
-
514
514
p
2
-
1514
1514
pq
+
47
47
q
2 + 3
Select one:
Question text
Subtíact the polynomials and simplify.
(27p2−12pq+314q2+14)−(914p2+47pq−514q2+11)(27p2−12pq+314q2+14)−(914p2+47pq
−514q2+11)
Question text
Choose the polynomial that is described.
A monomial in one variable of degree 4
Select one:
a. 4n
b.
-9t
3
- 3n
c.
-9t
3
- 4t
2
- 3n - 8
d.
-9t
4
Question 13
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Question text
c.
24t
11
u
8
a.
24t
28
u
15
b.
11t
11
u
8
Multiply the polynomials by using the distributive property.
(8t
7
u
3
)(3t
4
u
5
)
Select one:
b.
-
514
514
p
2
-
1514
1514
pq
+
47
47
q
2 + 25
c.
1314
1314
p
2 +
114
114
pq
-
17
17
q
2 + 25
d.
-
514
514
p
2 +
114
114
pq
-
17
17
q
2 + 25
Flag question
Question 12
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Question text
Ïactoí completely.
5x
7/2
-
52
52x
-7/2
Select one:
a. 5x7/2(2x−1)25x7/2(2x−1)2
b. 5252
c. 5(2x7−1)2x7/25(2x7−1)2x7/2
d. 5x7/22(2x−1)5x7/22(2x−1)
Question 15
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Question text
Factor the polynomial by grouping (if possible).
5n
2
p - 10np - 5n
2
+ 10n
Select one:
a.
(5n
2
- 10n)(p - 1)
b. 5n(n - 2)(p - 1)
c. 5np(n - 2) - 5n(n - 2)
d. Cannot be factored
Question 16
Coííect
d.
24t
3
u
-2
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Question 14
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Question text
Ïactoí completely.
x
(2
x
+ 1)
-
2/3 + (2
x
+ 1)1/3
Select one:
a. 1
b. 3x(2x+1)2/33x(2x+1)2/3
c. (3x+1)1/3(2x+1)2/3(3x+1)1/3(2x+1)2/3
d. 3x+1(2x+1)2/33x+1(2x+1)2/3
Question text
Add oí subtíact as indicated and simplify if possible.
−2y2y2+5y+y−32y2+y−10−2y2y2+5y+y−32y2+y−10
Select one:
a. 1−y(2y+5)(y−2)1−y(2y+5)(y−2)
b. −2y2+y−32y3+5y2−10−2y2+y−32y3+5y2−10
c. −3y2+y+1y(2y+5)(y−2)−3y2+y+1y(2y+5)(y−2)
d. −y−34y2+6y−10−y−34y2+6y−10
Question 18
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Question text
Divide the íational expíessions.
4y−1y2−4÷1−4yy+24y−1y2−4÷1−4yy+2
Select one:
a. 16y2−1y−216y2−1y−2
b. (4y−1)(1−4y)(y−2)(y+2)2(4y−1)(1−4y)(y−2)(y+2)2
c. 1y−21y−2
d. 12−y12−y
Question 19
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Question text
Add oí subtíact as indicated and simplify if possible.
16y2+−78y16y2+−78y
Select one:
a. −648y3−648y3
b. −21y+424y2−21y+424y2
c. −1724y2−1724y2
d. −614y3−614y3
Question 20
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Finish íeview
EXAM 2
Solve the píoblem.
if n > 0, then 9n - | 9n |
= Select one:
a. 9n
b. n
c.
1
d.
0
Question 2
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Question text
Add oí subtíact as indicated and simplify if possible.
t2−8t−3−−4t+13t−3t2−8t−3−−4t+13t−3
Select one:
a. t+72t+72
b. t2+4t+5t−3t2+4t+5t−3
d. t + 7
c. t2−4t+5t−3t2−4t+5t−3
Question text
Solve the problem.
A new diet program guarantees you will lose 1.6 lb per week. A male with a starting
weight of 220 lb is modeled by
W = 220 - 1.6t
where t is the number of weeks after starting the diet.
Use the model to determine the male's weight after 19 weeks.
Select one:
a. 218.4 lb
b. 189.6 lb
c. 208.6 lb
d. 170.6 lb
Question 3
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List the elements of A ∩ B.
A = {-29, 14, 13, -20, 11, -2} and B = {-27, -10, 13, 11}
Select one:
a. {13}
b. {13, 11}
c. {-29, 14, 13, -20, 11, -2, -27, -10}
d. { }
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Solve the problem.
A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each
day, including the first. Write an equation that expresses the cost y of renting this saw
if it is rented for x days.
Select one:
a. y = 3.75x + 6.50
b. y = 6.50x + 3.75
c. y = 3.75(x + 6.50)
d. y = 3.75x - 6.50
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Answer the question.
How many miles (to the nearest hundredth of a mile) is a trip that is 1.5 × 10
6
inches?
Select one:
a. 11.835 miles
b. 47.34 miles
c. 2,367.42 miles
d. 23.67 miles
Question 6
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Simplify the expíession. Wíite youí answeí with positive exponents only.
(4vw
−3
x
2
)
2
(2v
3
w
2
x
−2
)
4
⋅
(4vw−3x
2)2(2
v3w2x
−2)4⋅ (
-
v
3
w
2
x
-
4)
-
3 Select
one:
a. x16v19w8x16v19w8
b. −x24v19w20−x24v19w20
c. x24v23w8x24v23w8
d. −4x16v23w20−4x16v23w20
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a.
6q9p3r66q9p3í6
b.
6q9r6p36q9í6p3
Simplify.
6p−3r6q−96p−3í6q−9
Select one:
Question text
Evaluate the íoot without using a calculatoí oí note that íoot is not a íeal numbeí.
8–√383
Select one:
a. 3
b. 2
c. -2
d. Not a íeal numbeí
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b. 5
c. -5
d. Not a real number
a. 6
Evaluate the íoot without using a calculatoí oí note that íoot is not a íeal numbeí.
625−−−√46254
Select one:
d.
6
p
3
í
6
q
9
c. 6p3r6q96p3í6q9
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Simplify the expíession by using the píopeíties of íational exponents. Wíite the final
answeí using positive exponents only.
(t2t−6)12(t2t−6)12
Select one:
a. t
-
2
b. t
7
c.
t
-
5
d.
t
4
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Question text
Subtract the polynomials and simplify.
Subtract (-7m
3
- 6m - 6) from (-5m
3
- 4m - 8).
Select one:
a.
-2m
3
- 2m + 2
b.
2m
3
+ 2m - 2
c.
2m
3
- 10m - 14
d.
-5m
3
+ 7m
2
+ 2m - 2
Question 12
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Choose the polynomial that is described.
A trinomial in one variable of degree 3
Select one:
a.
4r
2
- 9t + 7
b.
3r
2
+ 4t - 9
c.
4r
3
d.
4r
3
- 9t + 7
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Add the polynomials and simplify.
(4m
4
- 8m
3
- 7m) + (4m
4
- 7m
2
- 5m)
Select one:
a.
4m
4
- 4m
3
- 7m
2
- 12m
b.
8m
4
- 8m
3
- 7m
2
- 2m
c.
8m
4
- 8m
3
- 7m
2
- 12m
d.
8m
4
- 8m
3
- 14m
2
- 5m
Question 14
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Question text
Factor the sum or difference of cubes.
125r
3
+ 8
Select one:
a.
(5r + 2)
2
(5r - 2)
b.
(5r - 2)(25r
2
+ 10r + 4)
c.
(5r + 2)(25r
2
- 20r + 4)
d.
(5r + 2)(25r
2
- 10r + 4)
Question 15
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Factor completely.
9x
4
+ 21x
3
- 9x
2
- 21x
Select one:
a. -3x(3x + 7)(x + 1)(x - 1)
b. 3x(3x - 7)(x + 1)(x - 1)
c. 3x(3x + 7)(x +1)(x - 1)
d.
3x(3x + 7)(x + 1)
2
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Factor the polynomial by grouping (if possible).
3rs - 5cr - 15cs + 25c
2
Select one:
a. c(3s - 5c)(r - 5)
b.
r(3s - 5c) - 5(3cs - 5c
2
)
c. (3s - 5c)(r - 5c)
d. Cannot be factored
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Simplify the complex fíaction.
m2+6m+52m12+52mm2+6m+52m12+52m
Select one:
a. 1212
b. m+52mm+52m
c. m + 1
d. m + 5
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Simplify the complex fíaction.
150x+11015+125x150x+11015+125x
Select one:
a. 125x125x
b. 2
c. 1212
d. 12x12x
Question 19
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Simply the expíession. Assume that all vaíiable expíessions íepíesent positive íeal
numbeís.
y−33y√+33√y−33y+33
Select one:
a. y√−33−−√y−33
b. y−33−−√y−33
c. y√+33−−√y+33
d. y+33−−√y+33
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Simplify the íational expíession.
x3−5x2+2x−103x2−75x3−5x2+2x−103x2−75
Select one:
a. x2+23(x+5)x2+23(x+5) (Píovided x ≠ -5)
b. x3+2x−7−12x3+2x−7−12 (Píovided x ≠ -5)
c. x2+23x−15x2+23x−15 (Píovided x ≠ -5)
d. x3−5x2+2x−103x2−75x3−5x2+2x−103x2−75; cannot be simplified
Finish íeview
EXAM 3
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a. (-∞, -9)
b. (-9, ∞)
c. [-9, -7]
d. (-9,-7]
-9 -7
Select one:
Expíess the set in inteíval
notation.
Question text
Expíess the set in inteíval notation.
3 9
Select one:
a. [3, 9)
b. (3, 9]
c. (-∞, 3)
d. [3,9]
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a. (-∞, 6)
b. [6, 7)
c. [6, 7]
d. (6, 7]
6 7
Select one:
Question text
Expíess the set in inteíval
notation.
Question text
Simplify.
4
-2
Select one:
a. 2
b. -16
c. 116116
d. -8
Question 6
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Question text
Perform the indicated operation and write the answer in scientific notation.
(1.2 ×10
6
)(3.8 ×10
7
)
a.
u ≥ 10
b.
u > 10
c.
u < 10
d.
u ≤ 10
Write the statement as an inequality.
u is at least 10.
Select one:
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Select one:
a.
4.56 × 100
13
b.
4.56 × 10
13
c.
4.56 ×10
42
d.
5 × 10
13
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Peífoím the indicated opeíation and wíite the answeí in scientific notation.
31.5×10164.5×10631.5×10164.5×106
Select one:
a. 27 × 10 10
b. 27 × 10 22
c. 7 × 10 10
d. 7 × 10 22
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a. −12x3y415xy−−−−√−12x3y415xy
Multiply the íadical expíessions and simplify youí answeí.
−36x6y3−−−−−√⋅210xy6−−−−−√−36x6y3⋅210xy6
Select one:
Question text
b. (18y−1)2y−−√(18y−1)2y
a. 172y3−2y−−−−−−−√172y3−2y
Subtíact the íadical expíessions. Assume that all vaíiables íepíesent positive íeal
numbeís.
372y3−−−−√−2y−−√372y3−2y
Select one:
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c. −24x3y415xy−−−−√−24x3y415xy
d. −24xyx5y7−−−−√−24xyx5y7
b. −1215x7y9−−−−−−√−1215x7y9
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Question 9
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a. 62–√62
b. 17−−√17
c. 362–√362
d. 26–√26
Question text
Multiply the íadical expíessions and simplify youí answeí.
9–√⋅8–√9⋅8
Select one:
Question text
Multiply the polynomials by using the distributive property.
(n - 6p)(n
2
- 5np + 3p
2
)
Select one:
a.
n
3
+ 22n
2
p
2
- 18p
3
b.
n
3
- 6np + 33np
2
- 18p
3
c.
n
3
- 11n
2
p + 33np
2
- 18p
3
d.
n
3
- 6p - 5np - 18p
3
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c. 372y3−2y−−−−−−−−√372y3−2y
d. Cannot be simplified fuítheí
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Question 11
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a.
64y
2
+ 144y + 81 - z
2
b.
64y
2
+ 144y - 16yz + 81- 19z
2
c.
64y
2
+ 81 - z
2
d.
64y
2
+ 288y + 81 - z
2
Question text
Multiply.
[(-8y - 9) + z][(-8y - 9)- z]
Select one:
Question text
Write an expression for the area and simplify your answer.
[The figure is not necessarily drawn to scale.]
Select one:
a.
12x
2
+ 51x - 54
b.
12x
2
- 3x - 54
c.
12x
2
+ 3x - 54
d.
12x
2
- 54
Question 14
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Question text
Factor completely.
x
2
+ 3xy - 4y
2
- 5y + 5x
Select one:
a. (x - y)(x + y + 5)
b. (x - y)(x + 4y - 5)
c. (x - y)(x - 4y + 5)
d. (x - y)(x + 4y + 5)
Question 15
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Question text
Factor the trinomial completely by using any method. Remember to look for a
common factor first.
2w
3
- 16w
2
x + 32wx
2
Select one:
a. 2w(w - 4x)(w + 4x)
b.
2w(w - 4x)
2
c.
2w
2
(1 - 4x)
2
d. Prime
Question 16
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Question text
Factor out the greatest common factor.
12r
2
s - 24rs
2
+ 18rs
Select one:
Question text
Wíite the expíession as a single teím, factoíed completely. Do not íationalize the
denominatoí.
1 - 10x
-3
+ 23x
-12
Select one:
a. x3−10x3+23x3x3−10x3+23x3
b. 1−10x9+23x121−10x9+23x12
c. x12−10x9+23x12x12−10x9+23x12
d. x12−10x3+23x12x12−10x3+23x12
Question 18
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a. 3rs(4r - 8s + 6)
b.
6r(2rs - 4s
2
+ 3s)
c. 2rs(6r - 12s - 12)
d. 6rs(2r - 4s + 3)
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Question 17
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a. −13x√x−13xx
Question text
Rationalize the denominatoí.
−13x√−13x
Select one:
Question text
Simplify the expíession, if possible.
(32t+1−t2t2+5t+2)(t+2)(32t+1−t2t2+5t+2)(t+2)
Select one:
a. 2t+6(2t+1)(t+2)2t+6(2t+1)(t+2)
Question text
Wíite the domain of the íational expíession in set-buildeí notation.
1x−141x−14
Select one:
a. {x | x ≠ 14, x ≠ -1}
b. {x | x = 14}
c. {x | x ≠ -14}
d. {x | x ≠ 14}
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b. 3t+6t+23t+6t+2
c. 3t+62t+13t+62t+1
b. xx√−13xx−13
c. 169x169x
d. Alíeady íationalized.
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Finish íeview
.
d. 2t+62t+12t+62t+1
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