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Math Problems
Algebra 1
Multiplication with rational exponents
3
4
x
−
3
4
≥
−
6
\frac{3}{4}x-\frac{3}{4} \geq -6
4
3
x
−
4
3
≥
−
6
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Dante took
5
1
2
5 \frac{1}{2}
5
2
1
hours to clean the bathroom. He took
3
2
5
3 \frac{2}{5}
3
5
2
hours to clean the bedroom. How much longer did it take Dante to clean the bathroom?
\newline
Write your answer as a mixed number in simplest form.
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A farmer's land is separated into sections of size
2
3
7
2 \frac{3}{7}
2
7
3
acres. Suppose there are
2
4
5
2 \frac{4}{5}
2
5
4
such sections. How many acres of land does the farmer own?
\newline
Write your answer as a mixed number in simplest form.
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5
w
7
w
4
\frac{5w}{7w^{4}}
7
w
4
5
w
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Select the expressions that are equivalent to
6
(
r
+
8
)
6(r + 8)
6
(
r
+
8
)
.
\newline
Multi-select Choices:
\newline
(A)
48
r
+
6
48r + 6
48
r
+
6
\newline
(B)
8
(
6
+
r
)
8(6 + r)
8
(
6
+
r
)
\newline
(C)
(
r
×
8
)
6
(r \times 8)6
(
r
×
8
)
6
\newline
(D)
6
r
+
48
6r + 48
6
r
+
48
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(
2
3
)
−
4
÷
(
6
4
)
−
2
\left(\frac{2}{3}\right)^{-4} \div\left(\frac{6}{4}\right)^{-2}
(
3
2
)
−
4
÷
(
4
6
)
−
2
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5
2
∗
5
6
5^{2} * 5^{6}
5
2
∗
5
6
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Simplify:
1
9
x
9
8
x
3
\frac{\frac{1}{9x}}{\frac{9}{8x^{3}}}
8
x
3
9
9
x
1
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Multiply the expression:
(
10
)
(
1
)
∗
(
10
)
(
3
)
∗
(
10
)
(
5
)
(10)^{(1)}*(10)^{(3)}*(10)^{(5)}
(
10
)
(
1
)
∗
(
10
)
(
3
)
∗
(
10
)
(
5
)
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(
y
−
2
)
−
6
−
x
4
y
−
4
⋅
−
x
y
4
\frac{\left(y^{-2}\right)^{-6}}{-x^{4} y^{-4} \cdot-x y^{4}}
−
x
4
y
−
4
⋅−
x
y
4
(
y
−
2
)
−
6
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4
x
y
−
2
−
3
y
x
2
⋅
−
2
y
0
\frac{4 x y^{-2}}{-3 y x^{2} \cdot-2 y^{0}}
−
3
y
x
2
⋅−
2
y
0
4
x
y
−
2
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(
b
2
−
2
b
5
⋅
a
b
2
)
0
\left(\frac{b^{2}}{-2 b^{5} \cdot a b^{2}}\right)^{0}
(
−
2
b
5
⋅
a
b
2
b
2
)
0
=
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−
4
x
3
⋅
x
2
y
4
−
2
x
3
y
4
\frac{-4 x^{3} \cdot x^{2} y^{4}}{-2 x^{3} y^{4}}
−
2
x
3
y
4
−
4
x
3
⋅
x
2
y
4
=
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Which expressions are equivalent to
\newline
5
2
5
8
\frac{5^{2}}{5^{8}}
5
8
5
2
?
\newline
Choose
2
2
2
answers:
\newline
A
1
5
6
\frac{1}{5^{6}}
5
6
1
\newline
B
1
−
6
1^{-6}
1
−
6
\newline
C.
(
5
2
)
−
3
(5^{2})^{-3}
(
5
2
)
−
3
\newline
D
(
5
2
)
−
8
(5^{2})^{-8}
(
5
2
)
−
8
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What is the slope of the line?
\newline
2
x
−
5
y
=
9
2x-5y=9
2
x
−
5
y
=
9
\newline
Choose
1
1
1
answer:
\newline
(A)
5
2
\frac{5}{2}
2
5
\newline
(B)
2
5
\frac{2}{5}
5
2
\newline
(C)
−
5
2
-\frac{5}{2}
−
2
5
\newline
(D)
−
2
5
-\frac{2}{5}
−
5
2
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Select the equivalent expression.
\newline
(
3
−
8
⋅
7
3
)
−
2
=
(3^{-8}\cdot7^{3})^{-2}=
(
3
−
8
⋅
7
3
)
−
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
7
6
3
16
\frac{7^{6}}{3^{16}}
3
16
7
6
\newline
(B)
\newline
2
1
10
21^{10}
2
1
10
\newline
(C)
\newline
3
16
⋅
7
−
6
3^{16}\cdot7^{-6}
3
16
⋅
7
−
6
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(
2
y
4
)
3
(
5
y
6
)
2
=
\left(2 y^{4}\right)^{3}\left(5 y^{6}\right)^{2}=
(
2
y
4
)
3
(
5
y
6
)
2
=
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Determine the convergence or divergence of the series.
\newline
1
+
1
4
3
+
1
9
3
+
1
16
3
+
1
25
3
+
…
1+\frac{1}{\sqrt[3]{4}}+\frac{1}{\sqrt[3]{9}}+\frac{1}{\sqrt[3]{16}}+\frac{1}{\sqrt[3]{25}}+\dots
1
+
3
4
1
+
3
9
1
+
3
16
1
+
3
25
1
+
…
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6
6
6
. Which expression is equivalent to
\newline
3
2
8
y
16
4
⋅
2
2
6
y
12
6
⋅
2
24
y
16
8
where
y
>
0
?
3 \sqrt[4]{2^{8} y^{16}} \cdot 2 \sqrt[6]{2^{6} y^{12}} \cdot \sqrt[8]{2^{24} y^{16}} \text { where } y>0 ?
3
4
2
8
y
16
⋅
2
6
2
6
y
12
⋅
8
2
24
y
16
where
y
>
0
?
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(
1
3
)
−
2
÷
(
3
5
)
−
3
\left(\frac{1}{3}\right)^{-2} \div\left(\frac{3}{5}\right)^{-3}
(
3
1
)
−
2
÷
(
5
3
)
−
3
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x
=
1
2
2
+
2
2
+
2
+
2
2
+
2
+
2
2
x=\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2}}}
x
=
2
2
+
2
+
2
2
+
2
+
2
2
+
2
2
1
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1
2
2
+
2
2
+
2
+
2
2
+
2
+
2
2
+
2
\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2+2}}}
2
+
2
2
+
2
+
2
2
+
2
+
2
2
+
2
2
1
Get tutor help
A bowl contains
12
12
12
green candies,
4
4
4
yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?
\newline
E.
\newline
(
2
)
/
(
11
)
(2)/(11)
(
2
)
/
(
11
)
\newline
F.
\newline
(
2
)
/
(
9
)
(2)/(9)
(
2
)
/
(
9
)
\newline
G.
\newline
(
1
)
/
(
4
)
(1)/(4)
(
1
)
/
(
4
)
\newline
H.
\newline
(
3
)
/
(
11
)
(3)/(11)
(
3
)
/
(
11
)
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Complete the equation. Write the sum as a mixed number.
\newline
4
3
+
2
7
=
28
21
+
14
21
=
□
42
21
\frac{4}{3}+\frac{2}{7}=\frac{28}{21}+\frac{14}{21}=\square \frac{42}{21}
3
4
+
7
2
=
21
28
+
21
14
=
□
21
42
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Complete the equation. Write the sum as a mixed number.
\newline
2
2
3
+
4
5
=
40
□
+
12
□
=
□
□
□
2 \frac{2}{3}+\frac{4}{5}=\frac{40}{\square}+\frac{12}{\square}=\square \frac{\square}{\square}
2
3
2
+
5
4
=
□
40
+
□
12
=
□
□
□
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Complete the equation. Write the sum as a mixed number.
\newline
4
3
+
2
7
=
□
21
+
□
21
=
□
□
□
\frac{4}{3}+\frac{2}{7}=\frac{\square}{21}+\frac{\square}{21}=\square \frac{\square}{\square}
3
4
+
7
2
=
21
□
+
21
□
=
□
□
□
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2
1
2
×
2
3
4
×
3
×
3
3
2
2
1
2
×
3
−
1
2
\frac{2^{\frac{1}{2}}\times2^{\frac{3}{4}}\times3\times3^{\frac{3}{2}}}{2^{\frac{1}{2}}\times3^{-\frac{1}{2}}}
2
2
1
×
3
−
2
1
2
2
1
×
2
4
3
×
3
×
3
2
3
Get tutor help
2
−
1
+
5
×
4
−
(
5
−
1
)
2-1+5\times 4-(5-1)
2
−
1
+
5
×
4
−
(
5
−
1
)
Get tutor help
x
8
3
x
⋅
x
1
2
\frac{x^{\frac{8}{3}}}{x \cdot x^{\frac{1}{2}}}
x
⋅
x
2
1
x
3
8
Get tutor help
Question
\newline
Perform the operation and combine to one fraction.
\newline
3
x
+
5
x
+
7
+
3
x
+
5
\frac{3 x+5}{x+7}+\frac{3}{x+5}
x
+
7
3
x
+
5
+
x
+
5
3
Get tutor help
Solve for
x
x
x
.
\newline
6
=
−
3
x
6=-\frac{3}{x}
6
=
−
x
3
\newline
Simplify your answer as much as possible.
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2
2
2
. Select all the expressions that equal
6
−
10
6^{-10}
6
−
10
.
\newline
A.
6
−
5
⋅
6
2
6^{-5} \cdot 6^{2}
6
−
5
⋅
6
2
\newline
B.
(
1
6
2
)
5
\left(\frac{1}{6^{2}}\right)^{5}
(
6
2
1
)
5
\newline
C.
(
6
−
5
)
2
\left(6^{-5}\right)^{2}
(
6
−
5
)
2
\newline
D.
6
−
3
6
7
\frac{6^{-3}}{6^{7}}
6
7
6
−
3
\newline
E.
6
5
⋅
6
−
3
6
−
8
\frac{6^{5} \cdot 6^{-3}}{6^{-8}}
6
−
8
6
5
⋅
6
−
3
Get tutor help
(
t
+
8
3
)
(
t
+
b
)
=
0
(t+\frac{8}{3})(t+b)=0
(
t
+
3
8
)
(
t
+
b
)
=
0
\newline
In the given equation,
b
b
b
is a constant.
\newline
If
−
8
3
-\frac{8}{3}
−
3
8
and
13
3
\frac{13}{3}
3
13
are solutions to the equation, then what is the value of
b
b
b
?
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Mathematics
\newline
1
1
1
Which expression is equivalent to
8
−
4
⋅
8
3
8^{-4} \cdot 8^{3}
8
−
4
⋅
8
3
?
\newline
Select one answer.
\newline
A
−
8
-8
−
8
\newline
B
−
1
8
-\frac{1}{8}
−
8
1
\newline
c
1
8
\frac{1}{8}
8
1
\newline
D
8
8
8
Get tutor help
cos
(
π
20
)
cos
(
π
5
)
−
sin
(
π
20
)
sin
(
π
5
)
\cos \left(\frac{\pi}{20}\right) \cos \left(\frac{\pi}{5}\right)-\sin \left(\frac{\pi}{20}\right) \sin \left(\frac{\pi}{5}\right)
cos
(
20
π
)
cos
(
5
π
)
−
sin
(
20
π
)
sin
(
5
π
)
Get tutor help
3
3
3
The fourth term of a sequence is
13
2
\frac{13}{2}
2
13
. Which recursive formula could be used to find this term?
\newline
f
(
1
)
=
1
2
,
f
(
n
)
=
f
(
n
−
1
)
+
2
y
=
1
2
=
f
+
2
\begin{aligned} f(1)=\frac{1}{2}, f(n) & =f(n-1)+2 \\ y & =\frac{1}{2}=f+2 \end{aligned}
f
(
1
)
=
2
1
,
f
(
n
)
y
=
f
(
n
−
1
)
+
2
=
2
1
=
f
+
2
\newline
f
(
1
)
=
4
,
f
(
n
)
=
f
(
n
−
1
)
f(1)=4, f(n)=f(n-1)
f
(
1
)
=
4
,
f
(
n
)
=
f
(
n
−
1
)
\newline
B
f
(
1
)
=
1
2
,
f
(
n
)
=
13
f
(
n
−
1
)
f(1)=\frac{1}{2}, f(n)=13 f(n-1)
f
(
1
)
=
2
1
,
f
(
n
)
=
13
f
(
n
−
1
)
\newline
D
f
(
1
)
=
13
2
f
(
n
)
=
4
f
(
n
−
1
)
D f(1)=\frac{13}{2} f(n)=4 f(n-1)
D
f
(
1
)
=
2
13
f
(
n
)
=
4
f
(
n
−
1
)
Get tutor help
−
1
5
f
+
8
=
3
5
(
5
3
f
+
15
)
−
1
5
f
-\frac{1}{5} f+8=\frac{3}{5}\left(\frac{5}{3} f+15\right)-\frac{1}{5} f
−
5
1
f
+
8
=
5
3
(
3
5
f
+
15
)
−
5
1
f
Get tutor help
2
2
2
) Solve for
x
x
x
:
x
3
=
12
6
\frac{x}{3}=\frac{12}{6}
3
x
=
6
12
Get tutor help
A symbol, such as
2
3
,
5
1
\frac{2}{3}, \frac{5}{1}
3
2
,
1
5
, or
8
5
\frac{8}{5}
5
8
, used to name part of a whole, part of a set, or a location on a number line is called a
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
8
n
8^{n}
8
n
.
\newline
8
6
⋅
8
4
=
8^{6} \cdot 8^{4}=
8
6
⋅
8
4
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
x
3
⋅
x
4
=
x^{3} \cdot x^{4}=
x
3
⋅
x
4
=
Get tutor help
Select the equivalent expression.
\newline
(
z
4
6
2
)
−
3
=
?
\left(\frac{z^{4}}{6^{2}}\right)^{-3}=?
(
6
2
z
4
)
−
3
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
6
−
1
\frac{z}{6^{-1}}
6
−
1
z
\newline
(B)
6
6
z
12
\frac{6^{6}}{z^{12}}
z
12
6
6
\newline
(C)
z
12
⋅
6
6
z^{12} \cdot 6^{6}
z
12
⋅
6
6
Get tutor help
Select the equivalent expression.
\newline
(
a
−
2
⋅
8
7
)
2
=
?
\left(a^{-2} \cdot 8^{7}\right)^{2}=?
(
a
−
2
⋅
8
7
)
2
=
?
Get tutor help
(vii)
4
5
×
12
7
\frac{4}{5} \times \frac{12}{7}
5
4
×
7
12
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3
5
×
(
−
1
4
−
1
6
)
÷
(
−
2
1
3
+
1
1
4
)
\frac{3}{5} \times\left(-\frac{1}{4}-\frac{1}{6}\right) \div\left(-2 \frac{1}{3}+1 \frac{1}{4}\right)
5
3
×
(
−
4
1
−
6
1
)
÷
(
−
2
3
1
+
1
4
1
)
Get tutor help
2
m
−
1
n
3
p
\frac{\frac{2}{m}-\frac{1}{n}}{\frac{3}{p}}
p
3
m
2
−
n
1
Get tutor help
5
5
5
)
1
5
÷
1
4
=
1
5
×
4
1
=
\frac{1}{5} \div \frac{1}{4}=\frac{1}{5} \times \frac{4}{1}=
5
1
÷
4
1
=
5
1
×
1
4
=
\newline
6
6
6
)
2
5
÷
3
4
=
2
5
×
3
4
=
\frac{2}{5} \div \frac{3}{4}=\frac{2}{5} \times \frac{3}{4}=
5
2
÷
4
3
=
5
2
×
4
3
=
\newline
7
7
7
)
2
5
÷
1
2
=
2
5
×
2
1
=
\frac{2}{5} \div \frac{1}{2}=\frac{2}{5} \times \frac{2}{1}=
5
2
÷
2
1
=
5
2
×
1
2
=
\newline
8
8
8
)
2
5
÷
1
2
=
2
5
×
2
1
=
\frac{2}{5} \div \frac{1}{2}=\frac{2}{5} \times \frac{2}{1}=
5
2
÷
2
1
=
5
2
×
1
2
=
Get tutor help
ln
y
n
=
1
2
⋅
ln
(
x
2
+
1
)
+
c
\ln y_{n}=\frac{1}{2} \cdot \ln \left(x^{2}+1\right)+c
ln
y
n
=
2
1
⋅
ln
(
x
2
+
1
)
+
c
Get tutor help
For
j
(
x
)
=
(
x
2
−
4
)
(
−
4
x
2
−
2
x
)
j(x)=\left(x^{2}-4\right)\left(-4 x^{2}-2 x\right)
j
(
x
)
=
(
x
2
−
4
)
(
−
4
x
2
−
2
x
)
, find
j
′
(
x
)
j^{\prime}(x)
j
′
(
x
)
by applying the product rule.
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3
4
+
4
3
=
1
1
\frac{3}{4}+\frac{4}{3}=\frac{1}{1}
4
3
+
3
4
=
1
1
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