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Math Problems
Grade 8
Negative Exponents
Solve for
x
\mathrm{x}
x
.
\newline
4
x
+
2
3
=
x
+
3
2
\frac{4 x+2}{3}=\frac{x+3}{2}
3
4
x
+
2
=
2
x
+
3
\newline
Answer:
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P
(
t
)
=
30
(
2
)
(
t
18
)
P(t)=30(2)^{\left(\frac{t}{18}\right)}
P
(
t
)
=
30
(
2
)
(
18
t
)
\newline
The function models
P
P
P
, the amount of bacteria, in colony-forming units, in a bacteria culture after
t
t
t
minutes of growth. How many colony-forming units of bacteria are in the bacteria culture after
90
90
90
minutes?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
×
1
0
2
3\times10^{2}
3
×
1
0
2
\newline
(B)
9.6
×
1
0
2
9.6 \times10^{2}
9.6
×
1
0
2
\newline
(C)
5.4
×
1
0
3
5.4 \times10^{3}
5.4
×
1
0
3
\newline
(D)
2.43
×
1
0
7
2.43 \times10^{7}
2.43
×
1
0
7
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
4
÷
1
2
\frac{1}{4} \div \frac{1}{2}
4
1
÷
2
1
\newline
Answer:
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Use the distributive property to write an equivalent expression.
\newline
3
(
9
q
+
4
r
−
1
)
3(9 q+4 r-1)
3
(
9
q
+
4
r
−
1
)
\newline
Answer:
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Use the distributive property to write an equivalent expression.
\newline
3
(
5
v
−
8
w
+
10
)
3(5 v-8 w+10)
3
(
5
v
−
8
w
+
10
)
\newline
Answer:
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Convert the decimal below to a fraction in simplest form.
\newline
0.365
0.365
0.365
\newline
Answer:
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Convert the decimal below to a fraction in simplest form.
\newline
0.515
0.515
0.515
\newline
Answer:
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Suppose the diameter of a circle is
6
6
6
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Suppose the radius of a circle is
8
8
8
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Find the area of a circle with a circumference of
50
50
50
.
24
24
24
units.
\newline
□
\square
□
units
2
^{2}
2
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Rewrite the fraction as a decimal.
\newline
13
10
=
\frac{13}{10}=
10
13
=
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Rewrite the fraction as a decimal.
\newline
82
5
=
\frac{82}{5}=
5
82
=
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Rewrite the fraction as a decimal.
\newline
57
5
=
\frac{57}{5}=
5
57
=
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Rewrite the fraction as a decimal.
\newline
69
4
=
\frac{69}{4}=
4
69
=
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Rewrite the fraction as a decimal.
\newline
7
4
=
\frac{7}{4}=
4
7
=
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Rewrite the fraction as a decimal.
\newline
19
50
=
\frac{19}{50}=
50
19
=
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Rewrite the fraction as a decimal.
\newline
33
25
=
\frac{33}{25}=
25
33
=
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Rewrite the fraction as a decimal.
\newline
15
4
=
\frac{15}{4}=
4
15
=
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Rewrite the fraction as a decimal.
\newline
94
5
=
\frac{94}{5}=
5
94
=
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lim
x
→
−
3
x
3
+
x
2
−
6
x
x
2
+
3
x
=
\lim _{x \rightarrow-3} \frac{x^{3}+x^{2}-6 x}{x^{2}+3 x}=
lim
x
→
−
3
x
2
+
3
x
x
3
+
x
2
−
6
x
=
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lim
x
→
−
5
10
x
2
+
50
x
x
2
−
25
=
\lim _{x \rightarrow-5} \frac{10 x^{2}+50 x}{x^{2}-25}=
lim
x
→
−
5
x
2
−
25
10
x
2
+
50
x
=
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lim
x
→
−
1
x
4
+
2
x
3
+
x
2
x
+
1
=
\lim _{x \rightarrow-1} \frac{x^{4}+2 x^{3}+x^{2}}{x+1}=
lim
x
→
−
1
x
+
1
x
4
+
2
x
3
+
x
2
=
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lim
x
→
4
−
5
x
2
+
20
x
x
3
−
3
x
2
−
4
x
=
\lim _{x \rightarrow 4} \frac{-5 x^{2}+20 x}{x^{3}-3 x^{2}-4 x}=
lim
x
→
4
x
3
−
3
x
2
−
4
x
−
5
x
2
+
20
x
=
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lim
x
→
2
x
4
+
3
x
3
−
10
x
2
x
2
−
2
x
=
\lim _{x \rightarrow 2} \frac{x^{4}+3 x^{3}-10 x^{2}}{x^{2}-2 x}=
lim
x
→
2
x
2
−
2
x
x
4
+
3
x
3
−
10
x
2
=
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Apply the distributive property to create an equivalent expression.
\newline
5
×
(
−
2
w
−
4
)
=
5 \times(-2 w-4)=
5
×
(
−
2
w
−
4
)
=
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Apply the distributive property to create an equivalent expression.
\newline
(
3
−
8
y
)
⋅
(
−
2.5
)
=
(3-8 y) \cdot(-2.5)=
(
3
−
8
y
)
⋅
(
−
2.5
)
=
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Apply the distributive property to create an equivalent expression.
\newline
(
−
7
c
+
8
d
)
0.6
=
(-7 c+8 d) 0.6=
(
−
7
c
+
8
d
)
0.6
=
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−
100
%
+
0.58
=
-100 \%+0.58=
−
100%
+
0.58
=
\newline
Enter the answer as an exact decimal or simplified fraction.
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−
2
+
12
25
=
-2+\frac{12}{25}=
−
2
+
25
12
=
\newline
Enter the answer as an exact decimal or simplified fraction.
Get tutor help
Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
+
3
p(x)+\frac{k}{x+3}
p
(
x
)
+
x
+
3
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
7
x
+
3
=
\frac{x^{2}-7}{x+3}=
x
+
3
x
2
−
7
=
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Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
−
1
p(x)+\frac{k}{x-1}
p
(
x
)
+
x
−
1
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
2
x
−
1
=
\frac{x^{2}+2}{x-1}=
x
−
1
x
2
+
2
=
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Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
+
4
p(x)+\frac{k}{x+4}
p
(
x
)
+
x
+
4
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
1
x
+
4
=
\frac{x^{2}+1}{x+4}=
x
+
4
x
2
+
1
=
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Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
−
2
p(x)+\frac{k}{x-2}
p
(
x
)
+
x
−
2
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
5
x
−
2
=
\frac{x^{2}-5}{x-2}=
x
−
2
x
2
−
5
=
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Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
−
3
p(x)+\frac{k}{x-3}
p
(
x
)
+
x
−
3
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
4
x
−
3
=
\frac{x^{2}+4}{x-3}=
x
−
3
x
2
+
4
=
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Evaluate.
\newline
2
−
4
3
5
4
−
4
3
=
\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=
5
4
−
3
4
2
−
3
4
=
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lim
x
→
−
1
(
6
x
2
+
5
x
−
1
)
=
\lim _{x \rightarrow-1}\left(6 x^{2}+5 x-1\right)=
lim
x
→
−
1
(
6
x
2
+
5
x
−
1
)
=
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lim
x
→
5
3
−
x
2
2
x
+
1
=
\lim _{x \rightarrow 5} \frac{3-x^{2}}{2 x+1}=
lim
x
→
5
2
x
+
1
3
−
x
2
=
Get tutor help
Find the sum.
\newline
∑
k
=
1
40
(
25
−
2
k
)
=
\sum_{k=1}^{40}(25-2 k)=
k
=
1
∑
40
(
25
−
2
k
)
=
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Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
2
x
x
2
−
3
x
−
4
+
3
5
x
2
−
20
x
=
\frac{2 x}{x^{2}-3 x-4}+\frac{3}{5 x^{2}-20 x}=
x
2
−
3
x
−
4
2
x
+
5
x
2
−
20
x
3
=
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Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
4
x
−
1
−
9
x
−
7
=
\frac{4}{x-1}-\frac{9}{x-7}=
x
−
1
4
−
x
−
7
9
=
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Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
9
x
−
3
−
3
x
=
□
\frac{9}{x-3}-\frac{3}{x}=\square
x
−
3
9
−
x
3
=
□
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Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
8
x
+
3
−
2
x
+
8
=
\frac{8}{x+3}-\frac{2}{x+8}=
x
+
3
8
−
x
+
8
2
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
5
x
−
9
+
4
x
−
6
=
\frac{5}{x-9}+\frac{4}{x-6}=
x
−
9
5
+
x
−
6
4
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
8
x
+
2
−
6
x
+
5
=
\frac{8}{x+2}-\frac{6}{x+5}=
x
+
2
8
−
x
+
5
6
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
5
x
−
6
−
1
x
+
5
=
\frac{5}{x-6}-\frac{1}{x+5}=
x
−
6
5
−
x
+
5
1
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
3
x
+
7
−
6
x
−
2
=
\frac{3}{x+7}-\frac{6}{x-2}=
x
+
7
3
−
x
−
2
6
=
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Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
6
x
−
5
+
1
x
−
2
=
\frac{6}{x-5}+\frac{1}{x-2}=
x
−
5
6
+
x
−
2
1
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
2
x
−
4
+
9
x
+
3
=
\frac{2}{x-4}+\frac{9}{x+3}=
x
−
4
2
+
x
+
3
9
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
1
x
+
9
+
7
x
−
8
=
\frac{1}{x+9}+\frac{7}{x-8}=
x
+
9
1
+
x
−
8
7
=
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Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
7
x
+
4
+
3
x
+
6
=
\frac{7}{x+4}+\frac{3}{x+6}=
x
+
4
7
+
x
+
6
3
=
Get tutor help
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