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Math Problems
Algebra 1
Write and solve direct variation equations
The sum of
n
\mathrm{n}
n
and
n
−
1
\mathrm{n}-1
n
−
1
terms of an AP is
441
441
441
and
356
356
356
, respectively. If the first term of the AP is
13
13
13
and the common difference is equal to the number of terms, find the common difference of the AP.
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How many liters of pure water should be added to
150
150
150
liters of a
35
%
35\%
35%
salt water saline solution to make it a
25
%
25\%
25%
salt water saline solution?
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Sanjay has the following data:
\newline
7
,
20
,
5
,
c
7, 20, 5, c
7
,
20
,
5
,
c
\newline
If the mode is
5
5
5
, which number could
c
c
c
be?
\newline
Choices:
\newline
(A)
5
5
5
\newline
(B)
20
20
20
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If
y
y
y
varies directly with
x
x
x
and
y
=
12
y = 12
y
=
12
when
x
=
6
x = 6
x
=
6
, find
y
y
y
when
x
=
4
x = 4
x
=
4
.
\newline
Write and solve a direct variation equation to find the answer.
\newline
y
=
y =
y
=
____
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The price value,
V
V
V
, of a car that is
t
t
t
years old is given by
V
=
f
(
t
)
=
17000
−
3100
t
V=f(t)=17000-3100t
V
=
f
(
t
)
=
17000
−
3100
t
. Find the domain and range of
f
(
t
)
f(t)
f
(
t
)
.
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If a trader purchased a few items and sold all except
10
10
10
items at a profit of
10
%
10\%
10%
on each item and recovered his total cost of purchasing all the items, how many items did the trader purchase?
\newline
A)
90
90
90
\newline
B)
100
100
100
\newline
C)
110
110
110
\newline
D)
120
120
120
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If a trader purchased a few items and sold all except
10
10
10
items at a profit of
10
%
10\%
10%
on each item and recovered his total cost of purchasing all the items, how many items did the trader purchase?
\newline
A)
90
90
90
\newline
B)
100
100
100
\newline
C)
110
110
110
\newline
D)
120
120
120
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If
y
y
y
varies directly with
x
x
x
and
y
=
39
y = 39
y
=
39
when
x
=
3
x = 3
x
=
3
, find
y
y
y
when
x
=
1
x = 1
x
=
1
. Write and solve a direct variation equation to find the answer.
\newline
y = ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
21
y = 21
y
=
21
when
x
=
−
3
x = -3
x
=
−
3
, find
y
y
y
when
x
=
−
2
x = -2
x
=
−
2
. Write and solve a direct variation equation to find the answer.
\newline
y = ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
63
y = 63
y
=
63
when
x
=
7
x = 7
x
=
7
, find
y
y
y
when
x
=
4
x = 4
x
=
4
. Write and solve a direct variation equation to find the answer. Simplify any fractions.
\newline
y = ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
−
100
y = -100
y
=
−
100
when
x
=
−
25
x = -25
x
=
−
25
, find
y
y
y
when
x
=
22
x = 22
x
=
22
. Write and solve a direct variation equation to find the answer.
\newline
y = ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
84
y = 84
y
=
84
when
x
=
12
x = 12
x
=
12
, find
y
y
y
when
x
=
6
x = 6
x
=
6
. Write and solve a direct variation equation to find the answer.
\newline
y = ____
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Identify the rejection region(s). Select the correct choice below.
\newline
A. The rejection regions are
z
<
−
2.33
z<-2.33
z
<
−
2.33
and
z
>
2.33
z>2.33
z
>
2.33
.
\newline
B. The rejection region is
z
>
2.33
z>2.33
z
>
2.33
.
\newline
C. The rejection region is
z
<
2.33
z<2.33
z
<
2.33
.
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If
y
y
y
varies directly with
x
x
x
and
y
=
20
y = 20
y
=
20
when
x
=
5
x = 5
x
=
5
, find
y
y
y
when
x
=
3
x = 3
x
=
3
. Write and solve a direct variation equation to find the answer.
\newline
y
y
y
= ____
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A direct variation includes the points
(
2
,
10
)
(2,10)
(
2
,
10
)
and
(
1
,
n
)
(1,n)
(
1
,
n
)
. Find
n
n
n
. Write and solve a direct variation equation to find the answer.
\newline
n
n
n
= ____
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A direct variation includes the points
(
2
,
18
)
(2,18)
(
2
,
18
)
and
(
1
,
n
)
(1,n)
(
1
,
n
)
. Find
n
n
n
. Write and solve a direct variation equation to find the answer.
\newline
n
n
n
= ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
4
y = 4
y
=
4
when
x
=
2
x = 2
x
=
2
, find
y
y
y
when
x
=
1
x = 1
x
=
1
. Write and solve a direct variation equation to find the answer.
\newline
y
y
y
= ____
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If
y
y
y
varies directly with
x
x
x
and
y
=
16
y = 16
y
=
16
when
x
=
2
x = 2
x
=
2
, find
y
y
y
when
x
=
1
x = 1
x
=
1
. Write and solve a direct variation equation to find the answer.
\newline
y
y
y
= ____
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A direct variation includes the points
(
2
,
12
)
(2,12)
(
2
,
12
)
and
(
1
,
n
)
(1,n)
(
1
,
n
)
. Find
n
n
n
. Write and solve a direct variation equation to find the answer.
\newline
n
=
_
_
_
n = \_\_\_
n
=
___
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If
y
y
y
varies directly with
x
x
x
and
y
=
12
y = 12
y
=
12
when
x
=
4
x = 4
x
=
4
, find
y
y
y
when
x
=
3
x = 3
x
=
3
. Write and solve a direct variation equation to find the answer.
\newline
y
y
y
= ____
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
F
b
−
n
b
=
D
F b-n b=D
F
b
−
nb
=
D
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
f
f
f
. Be sure to take into account whether a letter is capitalized or not.
\newline
n
f
−
q
f
=
8
n f-q f=8
n
f
−
q
f
=
8
\newline
Answer:
f
=
f=
f
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
8
A
−
5
m
=
N
8 A-5 m=N
8
A
−
5
m
=
N
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
g
=
2
m
A
+
n
A
g=2 m A+n A
g
=
2
m
A
+
n
A
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
B
B
B
. Be sure to take into account whether a letter is capitalized or not.
\newline
H
B
−
2
M
3
B
=
g
H B-2 M^{3} B=g
H
B
−
2
M
3
B
=
g
\newline
Answer:
B
=
B=
B
=
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Solve the following equation for
g
g
g
. Be sure to take into account whether a letter is capitalized or not.
\newline
q
=
g
H
3
+
m
q=g H^{3}+m
q
=
g
H
3
+
m
\newline
Answer:
g
=
g=
g
=
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
b
G
+
Q
3
=
r
b G+Q^{3}=r
b
G
+
Q
3
=
r
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
F
F
F
. Be sure to take into account whether a letter is capitalized or not.
\newline
2
n
F
−
R
F
=
M
2 n F-R F=M
2
n
F
−
RF
=
M
\newline
Answer:
F
=
F=
F
=
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
q
=
h
2
(
b
−
n
)
q=h^{2}(b-n)
q
=
h
2
(
b
−
n
)
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
b
D
=
g
b D=g
b
D
=
g
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
d
d
d
. Be sure to take into account whether a letter is capitalized or not.
\newline
j
=
−
h
+
d
j=-h+d
j
=
−
h
+
d
\newline
Answer:
d
=
d=
d
=
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Solve the following equation for
f
f
f
. Be sure to take into account whether a letter is capitalized or not.
\newline
7
=
J
f
7=J f
7
=
Jf
\newline
Answer:
f
=
f=
f
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
2
=
F
a
2=F a
2
=
F
a
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
h
h
h
. Be sure to take into account whether a letter is capitalized or not.
\newline
6
h
=
r
6 h=r
6
h
=
r
\newline
Answer:
h
=
h=
h
=
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Solve the following equation for
B
B
B
. Be sure to take into account whether a letter is capitalized or not.
\newline
Q
=
B
d
Q=B d
Q
=
B
d
\newline
Answer:
B
=
B=
B
=
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Solve the following equation for
D
D
D
. Be sure to take into account whether a letter is capitalized or not.
\newline
J
=
6
D
J=6 D
J
=
6
D
\newline
Answer:
D
=
D=
D
=
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
4
h
=
b
4
+
g
4 h=\frac{b}{4+g}
4
h
=
4
+
g
b
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
4
d
+
n
=
q
a
4 d+n=q a
4
d
+
n
=
q
a
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
3
r
a
=
g
3 r a=g
3
r
a
=
g
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
d
=
2
A
r
d=2 A r
d
=
2
A
r
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
d
d
d
. Be sure to take into account whether a letter is capitalized or not.
\newline
3
q
d
=
g
3 q d=g
3
q
d
=
g
\newline
Answer:
d
=
d=
d
=
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Solve the following equation for
G
G
G
. Be sure to take into account whether a letter is capitalized or not.
\newline
n
=
G
(
H
−
2
M
)
n=G(H-2 M)
n
=
G
(
H
−
2
M
)
\newline
Answer:
G
=
G=
G
=
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Solve the following equation for
d
d
d
. Be sure to take into account whether a letter is capitalized or not.
\newline
q
=
d
H
q=d H
q
=
d
H
\newline
Answer:
d
=
d=
d
=
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A formula for converting degrees Fahrenheit
(
F
)
(F)
(
F
)
to degrees Celsius
(
C
)
(C)
(
C
)
is given by the formula
C
=
5
9
(
F
−
32
)
C=\frac{5}{9}(F-32)
C
=
9
5
(
F
−
32
)
. Solve the formula for
F
F
F
in terms of
C
C
C
.
\newline
Answer:
F
=
F=
F
=
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Solve the following equation for
h
h
h
. Be sure to take into account whether a letter is capitalized or not.
\newline
−
M
+
h
=
q
-M+h=q
−
M
+
h
=
q
\newline
Answer:
h
=
h=
h
=
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Solve the following equation for
j
j
j
. Be sure to take into account whether a letter is capitalized or not.
\newline
−
n
+
j
=
q
-n+j=q
−
n
+
j
=
q
\newline
Answer:
j
=
j=
j
=
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If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
5
5
5
when
x
x
x
is
15
15
15
, find
y
y
y
when
x
x
x
is
6
6
6
.
\newline
Answer:
y
=
y=
y
=
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If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
14
14
14
when
x
x
x
is
2
2
2
, find
y
y
y
when
x
x
x
is
9
9
9
.
\newline
Answer:
y
=
y=
y
=
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If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
3
3
3
when
x
x
x
is
12
12
12
, find
y
y
y
when
x
x
x
is
8
8
8
.
\newline
Answer:
y
=
y=
y
=
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If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
55
55
55
when
x
x
x
is
11
11
11
, find
y
y
y
when
x
x
x
is
14
14
14
.
\newline
Answer:
y
=
y=
y
=
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