Math 1314 Test 2 Summer 2020 Practice With Solutions
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School
University of Texas *
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Course
1314
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by GeneralPorcupine3551
Math 1314
Practice Test 2 Solutions
NAME____________________
Question
Points Possible
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
Total
100
Make sure to include all work you want graded on your submission
Must Show Work to get full credit.
1.
Solve the following linear equation:
6
x
+
7
=
4
x
+
55
Answer:
6
x
+
7
−
4
x
−
7
=
4
x
+
55
−
4
x
−
7
2
x
=
4 8
x
=
24
2.
The following rational equation has denominators that contain variables. For the equation
1
x
+
3
+
2
=
9
x
+
3
a.
Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable.
Answer:
x
+
3
=
0
x
=−
3
b.
Keeping the restrictions in mind, solve the equation. Answer:
(
1
x
+
3
+
2
)
(
x
+
3
)=
(
9
x
+
3
)
(
x
+
3
)
1
+
2
(
x
+
3
)
=
9
1
+
2
x
+
6
=
9
2
x
=
2
x
=
1
3.
The average cost of tuition and fees at public four-year colleges in the United States can be modelled by the following formula, where T
represents the average cost of tuition and fees for the school year ending x
years after 1996. When will the tuition and fees at public US college’s average $5411?
T
=
165
x
+
2771
Answer:
5411
=
165
x
+
2771
2640
=
165
x
x
=
16
16
+
1996
=
2012
They will average $5411 in 2012
4.
Multiply and write the expression in standard form a
+
bi
.
(
8
+
7
i
)
(
8
−
7
i
)
Answer:
64
−
56
i
+
56
i
−
49
i
2
=
64
+
49
=
113
5.
To solve x
2
−
2
3
x
=
4
9
by completing the square what must be added to both sides of the equation?
Answer:
(
−
2
3
2
)
2
=
(
−
1
3
)
2
=
1
9
6.
Find the x-intercepts of the graph of y
=
x
2
−
2
x
−
35
.
Answer:
x
2
−
2
x
−
35
=
0
(
x
−
7
) (
x
+
5
)
=
0
x
=
7
,
−
5
7.
Solve the quadratic equation x
2
−
2
x
=
4
. Make sure you solutions are simplified.
Answer:
(
−
2
2
)
2
=
(
−
1
)
2
=
1
x
2
−
2
x
+
1
=
4
+
1
(
x
−
1
)
2
=
5
√
(
x
−
1
)
2
=
±
√
5
x
−
1
=
±
√
5
x
=
1
±
√
5
8.
Solve the quadratic equation x
2
+
8
x
+
11
=
0
. Make sure you solutions are simplified.
Answer:
x
2
+
8
x
+
11
=
0
a
=
1
,b
=
8
,c
=
11
x
=
−
8
±
√
8
2
−
4
(
1
)(
11
)
2
(
1
)
=
−
8
±
√
20
2
=
−
8
±
2
√
5
2
=−
4
±
√
5
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9.
The selling price of a refrigerator, $456.50. If the markup is 10% of the dealer’s cost, what is the dealer’s cost of the refrigerator? Answer:
456.50
=
x
+
0.1
x
456.50
=
1.1
x
x
=
415
$415
10. Solve the formula for h
. j
=
h
−
h
−
f
s
m
Answer:
j
(
s
)=
(
h
−
h
−
f
s
m
)
(
s
)
j s
=
hs
−(
h
−
f
)
m
js
−
fm
=
hs
−
hm
+
fm
−
fm
js
−
fm
=
h
(
s
−
m
)
(
js
−
fm
)
s
−
m
=
h
(
s
−
m
)
s
−
m
h
=
js
−
fm
s
−
m