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Math Problems
Algebra 2
Solve multi-variable equations
Solve for
u
u
u
in terms of
q
q
q
,
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
s
r
=
−
u
t
q
sr = -utq
sr
=
−
u
tq
\newline
u
=
u =
u
=
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Solve for
s
s
s
in terms of
p
p
p
,
q
q
q
,
r
r
r
, and
t
t
t
.
\newline
s
p
=
r
t
q
sp = rtq
s
p
=
r
tq
\newline
s
=
s =
s
=
_____
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Solve for
y
y
y
in terms of
x
x
x
and
z
z
z
.
\newline
x
=
z
+
y
x = z + y
x
=
z
+
y
\newline
y
=
y =
y
=
______
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Solve for
c
c
c
in terms of
a
a
a
and
b
b
b
.
\newline
a
=
b
+
c
a = b + c
a
=
b
+
c
\newline
c
=
c =
c
=
______
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Solve for
s
s
s
in terms of
r
r
r
and
t
t
t
.
\newline
r
=
t
+
s
r = t + s
r
=
t
+
s
\newline
s
=
s =
s
=
______
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Solve for
p
p
p
in terms of
q
q
q
,
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
s
q
=
−
t
p
r
sq = -tpr
s
q
=
−
tp
r
\newline
p
=
p =
p
=
______
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Solve for
t
t
t
in terms of
r
r
r
,
s
s
s
,
u
u
u
, and
v
v
v
.
\newline
r
v
=
−
u
s
t
rv = -ust
r
v
=
−
u
s
t
\newline
t
=
t =
t
=
______
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Solve for
a
a
a
in terms of
b
b
b
and
c
c
c
.
\newline
c
=
a
−
b
c = a - b
c
=
a
−
b
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Solve for
t
t
t
in terms of
r
r
r
and
s
s
s
.
\newline
s
=
−
t
r
s = -\frac{t}{r}
s
=
−
r
t
\newline
t
=
t =
t
=
______
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Solve for
s
s
s
in terms of
r
r
r
,
t
t
t
, and
u
u
u
.
\newline
t
=
s
+
r
−
u
t = s + r - u
t
=
s
+
r
−
u
\newline
s
=
s =
s
=
______
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Solve for
t
t
t
in terms of
r
r
r
and
s
s
s
.
\newline
s
=
t
r
s = \frac{t}{r}
s
=
r
t
\newline
t
=
t =
t
=
______
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Solve for
v
v
v
in terms of
r
r
r
,
s
s
s
,
t
t
t
, and
u
u
u
.
\newline
s
u
=
v
t
r
su = vtr
s
u
=
v
t
r
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Solve for
s
s
s
in terms of
t
t
t
,
u
u
u
,
v
v
v
, and
w
w
w
.
\newline
w
t
=
−
s
u
v
wt = -suv
wt
=
−
s
uv
\newline
s
=
s =
s
=
______
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Solve for
x
x
x
in terms of
t
t
t
,
u
u
u
,
v
v
v
, and
w
w
w
.
\newline
x
t
=
v
u
w
xt = vuw
x
t
=
vu
w
\newline
x
=
x =
x
=
______
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Solve for
p
p
p
in terms of
q
q
q
and
r
r
r
.
\newline
q
=
r
+
p
q = r + p
q
=
r
+
p
\newline
p
=
p =
p
=
______
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Solve for
w
w
w
in terms of
u
u
u
and
v
v
v
.
\newline
u
=
v
+
w
u = v + w
u
=
v
+
w
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Solve for
b
b
b
in terms of
a
a
a
and
c
c
c
.
\newline
c
=
b
a
c = \frac{b}{a}
c
=
a
b
\newline
b
=
b =
b
=
______
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Solve for
u
u
u
in terms of
q
q
q
,
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
s
r
=
−
u
t
q
sr = -utq
sr
=
−
u
tq
\newline
u
=
u =
u
=
______
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Solve for
c
c
c
in terms of
a
a
a
,
b
b
b
, and
d
d
d
.
\newline
a
=
c
−
b
−
d
a = c - b - d
a
=
c
−
b
−
d
\newline
c
=
c =
c
=
______
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Solve for
w
w
w
in terms of
v
v
v
and
x
x
x
.
\newline
x
=
v
+
w
x = v + w
x
=
v
+
w
\newline
w
=
w =
w
=
______
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Solve for
v
v
v
in terms of
s
s
s
,
t
t
t
,
u
u
u
, and
w
w
w
.
\newline
v
w
=
−
u
s
t
vw = -ust
v
w
=
−
u
s
t
\newline
v
=
v =
v
=
______
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Solve for
v
v
v
in terms of
u
u
u
,
w
w
w
,
x
x
x
, and
y
y
y
.
\newline
u
x
=
−
y
w
v
ux = -ywv
ux
=
−
y
w
v
\newline
v = ______
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Solve for
x
x
x
in terms of
v
v
v
,
w
w
w
,
y
y
y
, and
z
z
z
.
\newline
z
v
=
−
x
y
w
zv = -xyw
z
v
=
−
x
y
w
\newline
x
=
x =
x
=
______
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Solve for
t
t
t
in terms of
q
q
q
,
r
r
r
, and
s
s
s
.
\newline
r
=
−
s
t
q
r = -stq
r
=
−
s
tq
\newline
t
=
t =
t
=
______
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Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
19
)
(0,19)
(
0
,
19
)
and
(
3
,
6517
)
(3,6517)
(
3
,
6517
)
.
\newline
Answer:
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Solve for
b
b
b
.
\newline
49
=
16
+
3
7
b
49=16+\frac{3}{7} b
49
=
16
+
7
3
b
\newline
Answer:
b
=
b=
b
=
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1
2
c
2
+
3
c
=
1
\frac{1}{2} c^{2}+3 c=1
2
1
c
2
+
3
c
=
1
\newline
Let
c
=
f
c=f
c
=
f
and
c
=
g
c=g
c
=
g
be the solutions to the given equation. If
f
>
g
f>g
f
>
g
, which of the following is the value of
f
f
f
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
+
2
-3+\sqrt{2}
−
3
+
2
\newline
(B)
−
3
+
11
-3+\sqrt{11}
−
3
+
11
\newline
(C)
3
+
2
3+\sqrt{2}
3
+
2
\newline
(D)
3
+
11
3+\sqrt{11}
3
+
11
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3
n
2
=
27
3 n^{2}=27
3
n
2
=
27
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
n
=
3
n=\sqrt{3}
n
=
3
\newline
(B)
n
=
3
n=3
n
=
3
\newline
(C)
n
=
−
3
n=-\sqrt{3}
n
=
−
3
and
n
=
3
n=\sqrt{3}
n
=
3
\newline
(D)
n
=
−
3
n=-3
n
=
−
3
and
n
=
3
n=3
n
=
3
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