Algebra Question

Midterm Exam.

Find attached a pdf document with the 19 questions of the exam. I need it ready before 10/22/2023

MAT-103 Midterm Exam – SUMMER 2023
Multiple Choice
1) Write the set in set-builder notation.
–8
–6
A [–4, 2)
–4
–2
0
2
B
4
8 x
6
D [–4, 2]
C
7
2) Find the additive and multiplicative inverse of 11 .
A
B
C
4
additive inverse: 11 ;
multiplicative inverse: 0
additive inverse:  11 ;
7
11
multiplicative inverse: 7
D
additive inverse:  7 ;
11
11
additive inverse: 7 ;
multiplicative inverse:  11
11
7
multiplicative inverse: 7
3) Identify the property demonstrated by the equation 6 + 12 = 18.
A Commutative Property B Closure Property C Distributive Property
by rationalizing the denominator.
4) Simplify
A
B
C
D
5) Simplify the expression
.
B
A
C
6) Simplify the expression
A 0 B –1 C 1 D 3
B
8) Simplify the expression
A 3.25
D
.
7) Simplify the expression
A
. Assume all variables are nonzero.
C
D
. Write the answer in scientific notation.
10–11 B 3.25 10–9 C 3.25 10–10 D 3.25 1011
1
D Associative Property
MAT-103 Midterm Exam – SUMMER 2023
9) The commercial jet that travels from Miami to New York averages about 300 mi/h. The air distance from
Miami to New York is 1092 miles. Write a function to represent the distance d remaining on the trip t
hours after takeoff.
B
A
C
D
10) Determine whether the data set could represent a linear function.
x
0
1
2
3
f(x)
–1
2
5
8
A The data set is constant.
function.
B Cannot be determined
C No, the data set does not represent a linear
D Yes, the data set could represent a linear function.
11) Graph the line with slope 1 that passes through (3, 3).
A
B
y
–15 –12 –9
–6
15
15
12
12
9
9
6
6
3
3
–3
–3
3
6
9
12
15
x
–3
–3
–6
–9
–12
–12
–15
–15
D
15
12
12
9
9
6
6
3
3
–3
–3
3
6
9
12
15
x
3
6
9
12
15
x
3
6
9
12
15
x
y
15
–6
2
–6
–9
y
–6
–15 –12 –9
–6
C
–15 –12 –9
y
–15 –12 –9
–6
–3
–3
–6
–9
–9
–12
–12
–15
–15
MAT-103 Midterm Exam – SUMMER 2023
12) Find the intercepts of
A
, and graph the line.
x-intercept:  , y-intercept:
11
4
C
19
4
x-intercept:  4 , y-intercept: 4
11
y
–10 –8
B
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
D
19
x-intercept: –4, y-intercept: 4
2
4
6
8
10
x
8
10
x
x-intercept: –4, y-intercept: 4
y
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–10 –8
–6
–4
–2
–2
–4
–6
–8
2
4
6
8
10
x
–6
–4
–2
–2
2
4
6
–4
–6
–8
–10
–10
3
1
MAT-103 Midterm Exam – SUMMER 2023
13)Write the function
in slope-intercept form. Then graph the function.
A
C
y
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–6
–4
–2
–2
2
4
6
–10 –8
x
8
–6
–4
–2
–2
2
4
6
8
x
2
4
6
8
x
–4
–4
–6
–6
–8
–8
–10
–10
B
D
y
–10 –8
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
14) Determine if
is vertical or horizontal. Then graph.
A
C
The line is horizontal.
The line is horizontal.
y
–5
4
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
MAT-103 Midterm Exam – SUMMER 2023
B
D
The line is vertical.
The line is vertical.
y
–5
–4
–3
–2
15) Solve
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
x
5
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
x
1
2
3
4
5
1
2
3
4
5
x
1
2
3
4
5
x
for y. Graph the solution.
A
C
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
B
D
y
–5
5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
MAT-103 Midterm Exam – SUMMER 2023
16) Let
be the transformation, vertical translation 5 units down, of
B
A
C
17) Solve the inequality
. Write the rule for
.
D
and graph the solution set.
A
C
–10 –8
–6
–4
–2
0
2
4
6
8
10
B
–10 –8
–6
–4
–2
0
2
4
6
8
10
–10 –8
–6
–4
–2
0
2
4
6
8
10
D
–10 –8
–6
–4
–2
0
2
4
6
8
10
18) Anchorage, Alaska and Augusta, Georgia have very different average temperatures. This is a table of the
average monthly temperature in each city. Make a scatter plot for the temperature data, identify the
correlation, and then sketch a line of best fit and find its equation.
Anchorage
Augusta
Jan
15
44
Feb
19
47
Average Temperatures (ºF)
Mar Apr May Jun Jul Aug
26
26
47
54
58
56
56
63
71
78
81
80
Sep
48
75
Oct
35
64
Dec
16
47
C Negative correlation
A Positive correlation
Augusta
Augusta
72
72
60
60
48
48
36
36
24
6
Nov
21
55
36
48
Anchor.
24
36
48
Anchor.
MAT-103 Midterm Exam – SUMMER 2023
B Positive correlation
Augusta
Augusta
72
72
60
60
48
48
36
36
24
19) Translate1111111
D Negative correlation
36
48
Anchor.
24
so that the vertex is at (–3, 2). Then graph.
A
C
y
–10 –8
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
B
2
4
6
8
x
2
4
6
8
x
D
y
–10 –8
7
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
36
48
Anchor.
MAT-103 Midterm Exam – SUMMER 2023
Multiple Choice
1) Write the set in set-builder notation.
–8
–6
A [–4, 2)
–4
–2
0
2
B
4
8 x
6
D [–4, 2]
C
7
2) Find the additive and multiplicative inverse of 11 .
A
B
C
4
additive inverse: 11 ;
multiplicative inverse: 0
additive inverse:  11 ;
7
11
multiplicative inverse: 7
D
additive inverse:  7 ;
11
11
additive inverse: 7 ;
multiplicative inverse:  11
11
7
multiplicative inverse: 7
3) Identify the property demonstrated by the equation 6 + 12 = 18.
A Commutative Property B Closure Property C Distributive Property
by rationalizing the denominator.
4) Simplify
A
B
C
D
5) Simplify the expression
.
B
A
C
6) Simplify the expression
A 0 B –1 C 1 D 3
B
8) Simplify the expression
A 3.25
D
.
7) Simplify the expression
A
. Assume all variables are nonzero.
C
D
. Write the answer in scientific notation.
10–11 B 3.25 10–9 C 3.25 10–10 D 3.25 1011
1
D Associative Property
MAT-103 Midterm Exam – SUMMER 2023
9) The commercial jet that travels from Miami to New York averages about 300 mi/h. The air distance from
Miami to New York is 1092 miles. Write a function to represent the distance d remaining on the trip t
hours after takeoff.
B
A
C
D
10) Determine whether the data set could represent a linear function.
x
0
1
2
3
f(x)
–1
2
5
8
A The data set is constant.
function.
B Cannot be determined
C No, the data set does not represent a linear
D Yes, the data set could represent a linear function.
11) Graph the line with slope 1 that passes through (3, 3).
A
B
y
–15 –12 –9
–6
15
15
12
12
9
9
6
6
3
3
–3
–3
3
6
9
12
15
x
–3
–3
–6
–9
–12
–12
–15
–15
D
15
12
12
9
9
6
6
3
3
–3
–3
3
6
9
12
15
x
3
6
9
12
15
x
3
6
9
12
15
x
y
15
–6
2
–6
–9
y
–6
–15 –12 –9
–6
C
–15 –12 –9
y
–15 –12 –9
–6
–3
–3
–6
–9
–9
–12
–12
–15
–15
MAT-103 Midterm Exam – SUMMER 2023
12) Find the intercepts of
A
, and graph the line.
x-intercept:  , y-intercept:
11
4
C
19
4
x-intercept:  4 , y-intercept: 4
11
y
–10 –8
B
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
D
19
x-intercept: –4, y-intercept: 4
2
4
6
8
10
x
8
10
x
x-intercept: –4, y-intercept: 4
y
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–10 –8
–6
–4
–2
–2
–4
–6
–8
2
4
6
8
10
x
–6
–4
–2
–2
2
4
6
–4
–6
–8
–10
–10
3
1
MAT-103 Midterm Exam – SUMMER 2023
13)Write the function
in slope-intercept form. Then graph the function.
A
C
y
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–6
–4
–2
–2
2
4
6
–10 –8
x
8
–6
–4
–2
–2
2
4
6
8
x
2
4
6
8
x
–4
–4
–6
–6
–8
–8
–10
–10
B
D
y
–10 –8
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
14) Determine if
is vertical or horizontal. Then graph.
A
C
The line is horizontal.
The line is horizontal.
y
–5
4
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
MAT-103 Midterm Exam – SUMMER 2023
B
D
The line is vertical.
The line is vertical.
y
–5
–4
–3
–2
15) Solve
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
x
5
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
x
1
2
3
4
5
1
2
3
4
5
x
1
2
3
4
5
x
for y. Graph the solution.
A
C
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
B
D
y
–5
5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
MAT-103 Midterm Exam – SUMMER 2023
16) Let
be the transformation, vertical translation 5 units down, of
B
A
C
17) Solve the inequality
. Write the rule for
.
D
and graph the solution set.
A
C
–10 –8
–6
–4
–2
0
2
4
6
8
10
B
–10 –8
–6
–4
–2
0
2
4
6
8
10
–10 –8
–6
–4
–2
0
2
4
6
8
10
D
–10 –8
–6
–4
–2
0
2
4
6
8
10
18) Anchorage, Alaska and Augusta, Georgia have very different average temperatures. This is a table of the
average monthly temperature in each city. Make a scatter plot for the temperature data, identify the
correlation, and then sketch a line of best fit and find its equation.
Anchorage
Augusta
Jan
15
44
Feb
19
47
Average Temperatures (ºF)
Mar Apr May Jun Jul Aug
26
26
47
54
58
56
56
63
71
78
81
80
Sep
48
75
Oct
35
64
Dec
16
47
C Negative correlation
A Positive correlation
Augusta
Augusta
72
72
60
60
48
48
36
36
24
6
Nov
21
55
36
48
Anchor.
24
36
48
Anchor.
MAT-103 Midterm Exam – SUMMER 2023
B Positive correlation
Augusta
Augusta
72
72
60
60
48
48
36
36
24
19) Translate1111111
D Negative correlation
36
48
Anchor.
24
so that the vertex is at (–3, 2). Then graph.
A
C
y
–10 –8
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
B
2
4
6
8
x
2
4
6
8
x
D
y
–10 –8
7
–6
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
36
48
Anchor.