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Math Problems
Algebra 1
Write and solve direct variation equations
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
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
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
42
42
42
when
x
x
x
is
6
6
6
, find
y
y
y
when
x
x
x
is
9
9
9
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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
4
4
4
, find
y
y
y
when
x
x
x
is
12
12
12
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
9
9
9
when
x
x
x
is
12
12
12
, find
y
y
y
when
x
x
x
is
4
4
4
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
4
4
4
when
x
x
x
is
8
8
8
, find
y
y
y
when
x
x
x
is
10
10
10
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
4
4
4
when
x
x
x
is
2
2
2
, find
y
y
y
when
x
x
x
is
5
5
5
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
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
10
10
10
, find
y
y
y
when
x
x
x
is
14
14
14
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
56
56
56
when
x
x
x
is
7
7
7
, find
y
y
y
when
x
x
x
is
6
6
6
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
8
8
8
when
x
x
x
is
12
12
12
, find
y
y
y
when
x
x
x
is
6
6
6
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
9
9
9
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
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
4
4
4
when
x
x
x
is
12
12
12
, find
y
y
y
when
x
x
x
is
15
15
15
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
2
2
2
when
x
x
x
is
4
4
4
, find
y
y
y
when
x
x
x
is
6
6
6
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
10
10
10
when
x
x
x
is
15
15
15
, find
y
y
y
when
x
x
x
is
9
9
9
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
7
7
7
when
x
x
x
is
14
14
14
, find
y
y
y
when
x
x
x
is
8
8
8
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
60
60
60
when
x
x
x
is
10
10
10
, find
y
y
y
when
x
x
x
is
15
15
15
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
1
1
1
when
x
x
x
is
4
4
4
, find
y
y
y
when
x
x
x
is
12
12
12
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
24
24
24
when
x
x
x
is
6
6
6
, find
y
y
y
when
x
x
x
is
3
3
3
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
are in direct proportion and
y
y
y
is
2
2
2
when
x
x
x
is
8
8
8
, find
y
y
y
when
x
x
x
is
12
12
12
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
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
4
4
4
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
If
x
x
x
and
y
y
y
vary directly and
y
y
y
is
25
25
25
when
x
x
x
is
5
5
5
, find
y
y
y
when
x
x
x
is
10
10
10
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
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
13
13
13
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
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
4
4
4
.
\newline
Answer:
y
=
y=
y
=
Get tutor help
The rate of change
d
P
d
t
\frac{d P}{d t}
d
t
d
P
of the number of fox at a national park is modeled by the following differential equation:
\newline
d
P
d
t
=
3277
16290
P
(
1
−
P
904
)
\frac{d P}{d t}=\frac{3277}{16290} P\left(1-\frac{P}{904}\right)
d
t
d
P
=
16290
3277
P
(
1
−
904
P
)
\newline
At
t
=
0
t=0
t
=
0
, the number of fox at the national park is
180
180
180
and is increasing at a rate of
29
29
29
fox per day. Find
lim
t
→
∞
P
′
(
t
)
\lim _{t \rightarrow \infty} P^{\prime}(t)
lim
t
→
∞
P
′
(
t
)
.
\newline
Answer:
Get tutor help
The rate of change
d
P
d
t
\frac{d P}{d t}
d
t
d
P
of the number of people on a beach is modeled by the following differential equation:
\newline
d
P
d
t
=
6154
21945
P
(
1
−
P
724
)
\frac{d P}{d t}=\frac{6154}{21945} P\left(1-\frac{P}{724}\right)
d
t
d
P
=
21945
6154
P
(
1
−
724
P
)
\newline
At
t
=
0
t=0
t
=
0
, the number of people on the beach is
154
154
154
and is increasing at a rate of
34
34
34
people per hour. Find
lim
t
→
∞
P
(
t
)
\lim _{t \rightarrow \infty} P(t)
lim
t
→
∞
P
(
t
)
.
\newline
Answer:
Get tutor help
D
=
[
−
1
0
2
−
2
1
3
]
\mathrm{D}=\left[\begin{array}{rr}-1 & 0 \\ 2 & -2 \\ 1 & 3\end{array}\right]
D
=
⎣
⎡
−
1
2
1
0
−
2
3
⎦
⎤
and
F
=
[
0
2
3
−
2
]
F=\left[\begin{array}{rr} 0 & 2 \\ 3 & -2 \end{array}\right]
F
=
[
0
3
2
−
2
]
\newline
Let
H
=
D
F
\mathrm{H}=\mathrm{DF}
H
=
DF
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
C
=
[
1
4
4
−
1
3
−
2
]
\mathrm{C}=\left[\begin{array}{rr}1 & 4 \\ 4 & -1 \\ 3 & -2\end{array}\right]
C
=
⎣
⎡
1
4
3
4
−
1
−
2
⎦
⎤
and
D
=
[
−
2
2
3
0
]
\mathrm{D}=\left[\begin{array}{rr} -2 & 2 \\ 3 & 0 \end{array}\right]
D
=
[
−
2
3
2
0
]
\newline
Let
H
=
C
D
\mathrm{H}=\mathrm{CD}
H
=
CD
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
E
=
[
1
−
1
5
5
5
0
]
\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]
E
=
[
1
5
−
1
5
5
0
]
and
F
=
[
−
2
−
1
5
2
5
−
2
]
F=\left[\begin{array}{rr}-2 & -1 \\ 5 & 2 \\ 5 & -2\end{array}\right]
F
=
⎣
⎡
−
2
5
5
−
1
2
−
2
⎦
⎤
\newline
Let
H
=
E
F
\mathrm{H}=\mathrm{EF}
H
=
EF
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
C
=
[
−
1
−
2
2
]
and
D
=
[
2
1
]
\mathrm{C}=\left[\begin{array}{r} -1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 1 \end{array}\right]
C
=
⎣
⎡
−
1
−
2
2
⎦
⎤
and
D
=
[
2
1
]
\newline
Let
H
=
C
D
\mathrm{H}=\mathrm{CD}
H
=
CD
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
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