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Math Problems
Algebra 2
Simplify variable expressions using properties
For the function
f
(
x
)
=
3
+
x
4
x
−
9
f(x)=\frac{3+x}{4 x-9}
f
(
x
)
=
4
x
−
9
3
+
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
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For the function
f
(
x
)
=
3
9
−
2
x
f(x)=\frac{3}{9-2 x}
f
(
x
)
=
9
−
2
x
3
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
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For the function
f
(
x
)
=
2
x
−
9
x
+
10
f(x)=\frac{2 x-9}{x+10}
f
(
x
)
=
x
+
10
2
x
−
9
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
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Solve for all values of
x
x
x
.
\newline
3
x
11
=
3
11
x
\frac{3 x}{11}=\frac{3}{11 x}
11
3
x
=
11
x
3
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
10
=
8
5
x
\frac{x}{10}=\frac{8}{5 x}
10
x
=
5
x
8
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
+
2
x
−
2
=
−
3
x
\frac{x+2}{x-2}=\frac{-3}{x}
x
−
2
x
+
2
=
x
−
3
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
+
2
x
+
6
=
1
x
\frac{x+2}{x+6}=\frac{1}{x}
x
+
6
x
+
2
=
x
1
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
+
3
x
+
9
=
6
x
\frac{x+3}{x+9}=\frac{6}{x}
x
+
9
x
+
3
=
x
6
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
9
7
x
=
9
x
7
\frac{9}{7 x}=\frac{9 x}{7}
7
x
9
=
7
9
x
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
+
1
x
−
5
=
−
2
x
\frac{x+1}{x-5}=\frac{-2}{x}
x
−
5
x
+
1
=
x
−
2
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
−
1
x
−
2
=
6
x
\frac{x-1}{x-2}=\frac{6}{x}
x
−
2
x
−
1
=
x
6
\newline
Answer:
x
=
x=
x
=
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
8
x
18
y
6
)
−
2
3
\left(8 x^{18} y^{6}\right)^{-\frac{2}{3}}
(
8
x
18
y
6
)
−
3
2
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
8
x
−
3
y
−
21
)
2
3
\left(8 x^{-3} y^{-21}\right)^{\frac{2}{3}}
(
8
x
−
3
y
−
21
)
3
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
20
w
7
−
4
(
w
2
b
)
4
\frac{20 w^{7}}{-4\left(w^{2} b\right)^{4}}
−
4
(
w
2
b
)
4
20
w
7
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
3
w
9
3
(
w
3
)
5
\frac{3 w^{9}}{3\left(w^{3}\right)^{5}}
3
(
w
3
)
5
3
w
9
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
20
z
4
4
(
z
2
)
3
\frac{20 z^{4}}{4\left(z^{2}\right)^{3}}
4
(
z
2
)
3
20
z
4
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
12
t
8
4
(
t
2
)
3
\frac{12 t^{8}}{4\left(t^{2}\right)^{3}}
4
(
t
2
)
3
12
t
8
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
15
w
3
(
3
w
)
2
\frac{15 w^{3}}{(3 w)^{2}}
(
3
w
)
2
15
w
3
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
20
z
3
(
4
z
5
)
4
\frac{20 z^{3}}{\left(4 z^{5}\right)^{4}}
(
4
z
5
)
4
20
z
3
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
20
a
7
−
4
(
a
−
2
)
2
\frac{20 a^{7}}{-4\left(a^{-2}\right)^{2}}
−
4
(
a
−
2
)
2
20
a
7
\newline
Answer:
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2
x
+
4
y
+
8
z
=
328
#
x
,
y
,
z
=
?
?
(
x
,
y
,
z
)
∈
+
z
\begin{array}{c}\frac{2^{x}+4^{y}+8^{z}=328}{\text { \# }} \\ x, y, z=? ? \\ (x, y, z) \in+z\end{array}
#
2
x
+
4
y
+
8
z
=
328
x
,
y
,
z
=
??
(
x
,
y
,
z
)
∈
+
z
Get tutor help
g
(
x
)
=
2
x
+
5
n
(
x
)
=
5
x
−
1
x
+
2
\begin{array}{r}g(x)=\sqrt{2 x+5} \\ n(x)=\frac{5 x-1}{x+2}\end{array}
g
(
x
)
=
2
x
+
5
n
(
x
)
=
x
+
2
5
x
−
1
\newline
n
(
g
(
x
)
)
=
?
n(g(x))=?
n
(
g
(
x
))
=
?
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y
=
3
x
2
−
1
1
−
4
x
y=\frac{3 x^{2}-1}{\sqrt{1-4 x}}
y
=
1
−
4
x
3
x
2
−
1
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Fully simplify using only positive exponents.
\newline
27
x
2
y
6
3
x
3
y
7
\frac{27 x^{2} y^{6}}{3 x^{3} y^{7}}
3
x
3
y
7
27
x
2
y
6
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
40
x
7
y
6
16
x
2
y
7
\frac{40 x^{7} y^{6}}{16 x^{2} y^{7}}
16
x
2
y
7
40
x
7
y
6
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
4
x
6
y
6
8
x
3
y
7
\frac{4 x^{6} y^{6}}{8 x^{3} y^{7}}
8
x
3
y
7
4
x
6
y
6
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
24
x
4
y
6
8
x
y
\frac{24 x^{4} y^{6}}{8 x y}
8
x
y
24
x
4
y
6
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
24
x
3
y
5
16
x
8
y
8
\frac{24 x^{3} y^{5}}{16 x^{8} y^{8}}
16
x
8
y
8
24
x
3
y
5
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
27
x
4
y
2
9
x
4
y
\frac{27 x^{4} y^{2}}{9 x^{4} y}
9
x
4
y
27
x
4
y
2
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
5
x
y
6
125
x
2
y
6
\frac{5 x y^{6}}{125 x^{2} y^{6}}
125
x
2
y
6
5
x
y
6
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
2
x
7
y
5
10
x
7
y
\frac{2 x^{7} y^{5}}{10 x^{7} y}
10
x
7
y
2
x
7
y
5
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
12
x
8
y
3
18
x
6
y
5
\frac{12 x^{8} y^{3}}{18 x^{6} y^{5}}
18
x
6
y
5
12
x
8
y
3
\newline
Answer:
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Solve for
x
x
x
and write your answer in simplest form.
\newline
6
x
−
(
9
x
−
3
2
)
=
−
2
(
3
x
−
5
4
)
+
2
6 x-\left(9 x-\frac{3}{2}\right)=-2\left(3 x-\frac{5}{4}\right)+2
6
x
−
(
9
x
−
2
3
)
=
−
2
(
3
x
−
4
5
)
+
2
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
and write your answer in simplest form.
\newline
−
9
−
2
x
=
4
(
1
2
x
+
1
)
+
3
2
-9-2 x=4\left(\frac{1}{2} x+1\right)+\frac{3}{2}
−
9
−
2
x
=
4
(
2
1
x
+
1
)
+
2
3
\newline
Answer:
x
=
x=
x
=
Get tutor help
Decompose the function
f
(
g
(
x
)
)
=
(
6
x
)
8
f(g(x))=(6 x)^{8}
f
(
g
(
x
))
=
(
6
x
)
8
into
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
.
\newline
g
(
x
)
=
g(x)=
g
(
x
)
=
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
Get tutor help
Factor the expression completely.
\newline
−
5
x
3
+
6
x
2
-5 x^{3}+6 x^{2}
−
5
x
3
+
6
x
2
\newline
Answer:
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lim
x
→
0
2
−
cos
x
−
1
3
x
2
=
□
\lim_{x \to 0}\frac{\sqrt{2-\cos x}-1}{3x^{2}}=\square
x
→
0
lim
3
x
2
2
−
cos
x
−
1
=
□
Get tutor help
Solve for
x
\mathrm{x}
x
in simplest form.
\newline
5
=
1
2
(
7
x
+
2
)
5=\frac{1}{2}(7 x+2)
5
=
2
1
(
7
x
+
2
)
\newline
Answer:
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Solve for
t
t
t
and simplify your answer.
\newline
16
=
−
2
3
t
16=-\frac{2}{3} t
16
=
−
3
2
t
\newline
Answer:
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Solve for
y
y
y
and simplify your answer.
\newline
−
11
=
−
6
5
y
-11=-\frac{6}{5} y
−
11
=
−
5
6
y
\newline
Answer:
Get tutor help
Rewrite in simplest terms:
4
(
7
s
−
8
t
)
+
5
t
−
5
(
−
4
t
−
9
s
)
4(7 s-8 t)+5 t-5(-4 t-9 s)
4
(
7
s
−
8
t
)
+
5
t
−
5
(
−
4
t
−
9
s
)
\newline
Answer:
Get tutor help
Rewrite in simplest terms:
9
(
−
8
f
+
7
)
+
2
f
9(-8 f+7)+2 f
9
(
−
8
f
+
7
)
+
2
f
\newline
Answer:
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Rewrite in simplest terms:
(
x
+
4
y
)
−
(
8
x
+
7
y
)
(x+4 y)-(8 x+7 y)
(
x
+
4
y
)
−
(
8
x
+
7
y
)
\newline
Answer:
Get tutor help
Rewrite in simplest terms:
(
7
x
−
8
)
+
(
5
x
+
8
)
(7 x-8)+(5 x+8)
(
7
x
−
8
)
+
(
5
x
+
8
)
\newline
Answer:
Get tutor help
Simplify to a single power of
3
3
3
:
\newline
3
5
3
2
\frac{3^{5}}{3^{2}}
3
2
3
5
\newline
Answer:
3
□
3 ^\square
3
□
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Simplify to a single power of
4
4
4
:
\newline
4
4
4
3
\frac{4^{4}}{4^{3}}
4
3
4
4
\newline
Answer:
4
□
4 ^\square
4
□
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Simplify to a single power of
6
6
6
:
\newline
6
6
×
6
2
6^{6} \times 6^{2}
6
6
×
6
2
\newline
Answer:
6
□
6 ^\square
6
□
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Rewrite in simplest terms:
(
−
2
x
−
3
y
)
−
(
−
4
x
−
2
y
)
(-2 x-3 y)-(-4 x-2 y)
(
−
2
x
−
3
y
)
−
(
−
4
x
−
2
y
)
\newline
Answer:
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cos
(
13
π
12
)
=
\cos\left(\frac{13\pi}{12}\right)=
cos
(
12
13
π
)
=
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(
−
t
7
)
(
−
t
5
)
=
□
(-t^7)(-t^5)=\Box
(
−
t
7
)
(
−
t
5
)
=
□
Get tutor help
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