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Math Problems
Algebra 2
Simplify variable expressions using properties
Simplify the expression:
\newline
(
2
n
)
(
2
)
=
(2n)(2) =
(
2
n
)
(
2
)
=
_____
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Simplify the expression:
\newline
4
(
4
x
)
=
4(4x) =
4
(
4
x
)
=
_____
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Simplify the expression:
\newline
2
(
2
n
)
=
2(2n) =
2
(
2
n
)
=
_____
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Simplify the expression:
\newline
4
(
2
z
)
4(2z)
4
(
2
z
)
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Simplify the expression:
\newline
4
(
2
v
)
=
4(2v) =
4
(
2
v
)
=
_____
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Simplify the expression:
\newline
(
2
t
)
(
4
)
=
(2t)(4) =
(
2
t
)
(
4
)
=
_____
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Simplify the expression:
\newline
(
2
m
)
(
2
)
=
(2m)(2) =
(
2
m
)
(
2
)
=
_____
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Simplify the expression:
\newline
3
(
3
v
)
=
3(3v) =
3
(
3
v
)
=
_____
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Which of the following are natural numbers?
\newline
Multi-select Choices:
\newline
(A)
5
5
5
\newline
(B)
8
\sqrt{8}
8
\newline
(C)
8
8
8
\newline
(D)
π
\pi
π
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2
log
4
3
+
2
log
4
5
=
2\log_{4}3+2\log_{4}5=
2
lo
g
4
3
+
2
lo
g
4
5
=
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Find the sum of the first
9
9
9
terms of the following series, to the nearest integer.
\newline
6
,
2
,
2
3
,
…
6,2, \frac{2}{3}, \ldots
6
,
2
,
3
2
,
…
\newline
Answer:
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Evaluate:
\newline
∑
n
=
2
6
(
n
x
−
1
)
\sum_{n=2}^{6}(n x-1)
n
=
2
∑
6
(
n
x
−
1
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
0
2
(
n
x
+
1
)
\sum_{n=0}^{2}(n x+1)
n
=
0
∑
2
(
n
x
+
1
)
\newline
Answer:
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Evaluate the summation below.
\newline
3
∑
m
=
0
4
(
2
m
2
−
6
)
3 \sum_{m=0}^{4}\left(2 m^{2}-6\right)
3
m
=
0
∑
4
(
2
m
2
−
6
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
2
4
(
3
x
+
3
n
)
\sum_{n=2}^{4}(3 x+3 n)
n
=
2
∑
4
(
3
x
+
3
n
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
2
6
(
n
x
−
3
)
\sum_{n=2}^{6}(n x-3)
n
=
2
∑
6
(
n
x
−
3
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
2
6
(
n
x
+
3
)
\sum_{n=2}^{6}(n x+3)
n
=
2
∑
6
(
n
x
+
3
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
1
3
(
n
x
+
1
)
\sum_{n=1}^{3}(n x+1)
n
=
1
∑
3
(
n
x
+
1
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
0
2
(
3
x
+
3
n
)
\sum_{n=0}^{2}(3 x+3 n)
n
=
0
∑
2
(
3
x
+
3
n
)
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
5
x
8
y
7
15
x
6
y
7
\frac{5 x^{8} y^{7}}{15 x^{6} y^{7}}
15
x
6
y
7
5
x
8
y
7
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
15
x
7
y
10
x
6
y
6
\frac{15 x^{7} y}{10 x^{6} y^{6}}
10
x
6
y
6
15
x
7
y
\newline
Answer:
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Fully simplify using only positive exponents.
\newline
8
x
6
y
3
4
x
3
y
7
\frac{8 x^{6} y^{3}}{4 x^{3} y^{7}}
4
x
3
y
7
8
x
6
y
3
\newline
Answer:
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Simplify:
\newline
(
3
c
2
)
3
\left(3 c^{2}\right)^{3}
(
3
c
2
)
3
\newline
Answer:
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Simplify:
\newline
(
−
3
x
2
)
3
\left(-3 x^{2}\right)^{3}
(
−
3
x
2
)
3
\newline
Answer:
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Simplify:
\newline
(
−
3
c
)
3
(-3 c)^{3}
(
−
3
c
)
3
\newline
Answer:
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Simplify:
\newline
(
2
c
3
)
(
7
c
2
)
\left(2 c^{3}\right)\left(7 c^{2}\right)
(
2
c
3
)
(
7
c
2
)
\newline
Answer:
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Simplify:
\newline
(
6
z
3
)
(
2
z
4
)
\left(6 z^{3}\right)\left(2 z^{4}\right)
(
6
z
3
)
(
2
z
4
)
\newline
Answer:
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Simplify:
\newline
(
−
6
q
5
)
2
\left(-6 q^{5}\right)^{2}
(
−
6
q
5
)
2
\newline
Answer:
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Simplify:
\newline
(
−
5
x
4
)
2
\left(-5 x^{4}\right)^{2}
(
−
5
x
4
)
2
\newline
Answer:
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Simplify:
\newline
(
−
6
r
2
)
(
3
r
)
\left(-6 r^{2}\right)(3 r)
(
−
6
r
2
)
(
3
r
)
\newline
Answer:
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Simplify:
\newline
(
2
r
5
)
3
\left(2 r^{5}\right)^{3}
(
2
r
5
)
3
\newline
Answer:
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Simplify:
\newline
(
5
z
)
3
(5 z)^{3}
(
5
z
)
3
\newline
Answer:
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Simplify:
\newline
(
−
2
s
5
)
(
4
s
3
)
\left(-2 s^{5}\right)\left(4 s^{3}\right)
(
−
2
s
5
)
(
4
s
3
)
\newline
Answer:
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Simplify:
\newline
(
−
3
x
)
3
(-3 x)^{3}
(
−
3
x
)
3
\newline
Answer:
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Simplify the expression completely.
\newline
2
36
−
5
−
25
−
4
125
3
2 \sqrt{36}-5 \sqrt{-25}-4 \sqrt[3]{125}
2
36
−
5
−
25
−
4
3
125
\newline
Answer:
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Solve for
x
x
x
.
\newline
2
−
6
x
=
1
2
2-\frac{6}{x}=\frac{1}{2}
2
−
x
6
=
2
1
\newline
Answer:
x
=
x=
x
=
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Simplify the following expression completely.
\newline
x
2
−
4
x
+
3
x
2
−
5
x
+
4
\frac{x^{2}-4 x+3}{x^{2}-5 x+4}
x
2
−
5
x
+
4
x
2
−
4
x
+
3
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
3
x
−
10
x
2
−
5
x
+
6
\frac{x^{2}+3 x-10}{x^{2}-5 x+6}
x
2
−
5
x
+
6
x
2
+
3
x
−
10
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
8
x
−
20
x
2
−
12
x
+
20
\frac{x^{2}+8 x-20}{x^{2}-12 x+20}
x
2
−
12
x
+
20
x
2
+
8
x
−
20
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
4
x
+
4
x
2
+
6
x
+
8
\frac{x^{2}+4 x+4}{x^{2}+6 x+8}
x
2
+
6
x
+
8
x
2
+
4
x
+
4
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
8
x
+
15
x
2
−
2
x
−
3
\frac{x^{2}-8 x+15}{x^{2}-2 x-3}
x
2
−
2
x
−
3
x
2
−
8
x
+
15
\newline
Answer:
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For the function
f
(
x
)
=
9
−
5
x
3
+
x
f(x)=\frac{9-5 x}{3+x}
f
(
x
)
=
3
+
x
9
−
5
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
5
7
−
2
x
f(x)=\frac{5}{7-2 x}
f
(
x
)
=
7
−
2
x
5
, 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
)
=
−
1
9
−
x
f(x)=\frac{-1}{9-x}
f
(
x
)
=
9
−
x
−
1
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
2
x
+
3
2
x
f(x)=\frac{2 x+3}{2 x}
f
(
x
)
=
2
x
2
x
+
3
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
2
x
9
−
4
x
f(x)=\frac{2 x}{9-4 x}
f
(
x
)
=
9
−
4
x
2
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
9
−
2
x
3
+
4
x
f(x)=\frac{9-2 x}{3+4 x}
f
(
x
)
=
3
+
4
x
9
−
2
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
−
3
x
−
2
f(x)=\frac{-3}{x-2}
f
(
x
)
=
x
−
2
−
3
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
x
−
9
7
−
2
x
f(x)=\frac{x-9}{7-2 x}
f
(
x
)
=
7
−
2
x
x
−
9
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
7
−
4
x
10
+
3
x
f(x)=\frac{7-4 x}{10+3 x}
f
(
x
)
=
10
+
3
x
7
−
4
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
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