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Math Problems
Algebra 2
Roots of rational numbers
Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
7
10
+
1
8
\frac{7}{10}+\frac{1}{8}
10
7
+
8
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
3
8
+
1
8
\frac{3}{8}+\frac{1}{8}
8
3
+
8
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
1
2
+
3
16
\frac{1}{2}+\frac{3}{16}
2
1
+
16
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
7
10
−
3
8
\frac{7}{10}-\frac{3}{8}
10
7
−
8
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form
−
3
7
÷
6
11
×
3
5
-\frac{3}{7}\div\frac{6}{11}\times\frac{3}{5}
−
7
3
÷
11
6
×
5
3
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Write the sum or difference.
\newline
11
1
5
−
6
2
3
\begin{array}{r}11 \frac{1}{5} \\ -\quad 6 \frac{2}{3} \\ \hline \end{array}
11
5
1
−
6
3
2
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Simplify and find the differentiation.
y
=
1
−
sin
x
1
+
sin
x
y=\sqrt{\frac{1-\sin x}{1+\sin x}}
y
=
1
+
s
i
n
x
1
−
s
i
n
x
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81
a
5
b
4
3
\sqrt[3]{81 a^{5} b^{4}}
3
81
a
5
b
4
=
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1
3
x
+
3
4
=
5
12
\frac{1}{3}x + \frac{3}{4} = \frac{5}{12}
3
1
x
+
4
3
=
12
5
Find
x
x
x
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Use the reference angle to find the exact value of the given expression.
\newline
cos
(
7
π
6
)
\cos \left(\frac{7\pi}{6}\right)
cos
(
6
7
π
)
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(a) Write as a single fraction:
\newline
2
x
+
3
3
+
x
−
4
4
\frac{2x+3}{3}+\frac{x-4}{4}
3
2
x
+
3
+
4
x
−
4
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Select the answer which is equivalent to the given expression using your calculator.
\newline
sec
(
arccos
156
16
)
\sec \left(\arccos \frac{\sqrt{156}}{16}\right)
sec
(
arccos
16
156
)
\newline
10
16
\frac{10}{16}
16
10
\newline
16
10
\frac{16}{10}
10
16
\newline
10
156
\frac{10}{\sqrt{156}}
156
10
\newline
16
156
\frac{16}{\sqrt{156}}
156
16
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Select the answer which is equivalent to the given expression using your calculator.
\newline
cos
(
arccos
156
16
)
\cos \left(\arccos \frac{\sqrt{156}}{16}\right)
cos
(
arccos
16
156
)
\newline
16
10
\frac{16}{10}
10
16
\newline
10
16
\frac{10}{16}
16
10
\newline
156
16
\frac{\sqrt{156}}{16}
16
156
\newline
156
10
\frac{\sqrt{156}}{10}
10
156
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19
n
3
=
□
\sqrt[3]{19n} = \square
3
19
n
=
□
\newline
(Use integers or fractions for any numbers in the expression. Type your answer using exponential notation.)
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
2
(
1
2
5
)
\log _{2}\left(\frac{1}{\sqrt[5]{2}}\right)
lo
g
2
(
5
2
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
ln
(
1
e
)
\ln \left(\frac{1}{\sqrt{e}}\right)
ln
(
e
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
4
log
4
10
−
log
4
4
)
\left(4^{\log _{4} 10-\log _{4} 4}\right)
(
4
l
o
g
4
10
−
l
o
g
4
4
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
12
(
1
12
4
)
\log _{12}\left(\frac{1}{\sqrt[4]{12}}\right)
lo
g
12
(
4
12
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
6
log
6
17
+
log
6
3
)
\left(6^{\log _{6} 17+\log _{6} 3}\right)
(
6
l
o
g
6
17
+
l
o
g
6
3
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
8
log
8
3
)
\left(8^{\log _{8} 3}\right)
(
8
l
o
g
8
3
)
\newline
Answer:
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
20
5
,
40
,
16
5
,
…
20 \sqrt{5}, \quad 40, \quad 16 \sqrt{5}, \quad \ldots
20
5
,
40
,
16
5
,
…
\newline
2
5
2 \sqrt{5}
2
5
\newline
2
5
5
\frac{2 \sqrt{5}}{5}
5
2
5
\newline
5
5
\frac{\sqrt{5}}{5}
5
5
\newline
5
\sqrt{5}
5
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(
45
5
)
4
4
\sqrt[4]{\left(\frac{45}{5}\right)^{4}}
4
(
5
45
)
4
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Simplify the expression completely.
\newline
4
64
3
−
4
+
−
729
3
4 \sqrt[3]{64}-\sqrt{4}+\sqrt[3]{-729}
4
3
64
−
4
+
3
−
729
\newline
Answer:
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Simplify the expression completely.
\newline
−
25
+
5
−
25
−
5
−
125
3
+
−
125
3
-\sqrt{25}+5 \sqrt{-25}-5 \sqrt[3]{-125}+\sqrt[3]{-125}
−
25
+
5
−
25
−
5
3
−
125
+
3
−
125
\newline
Answer:
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Simplify the expression completely.
\newline
−
5
−
1
3
+
5
−
100
+
36
+
343
3
-5 \sqrt[3]{-1}+5 \sqrt{-100}+\sqrt{36}+\sqrt[3]{343}
−
5
3
−
1
+
5
−
100
+
36
+
3
343
\newline
Answer:
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Simplify the expression completely.
\newline
49
+
4
−
1000
3
−
1
3
+
−
9
\sqrt{49}+4 \sqrt[3]{-1000}-\sqrt[3]{1}+\sqrt{-9}
49
+
4
3
−
1000
−
3
1
+
−
9
\newline
Answer:
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Simplify the expression completely.
\newline
−
4
729
3
+
4
216
3
+
4
−
81
−
729
3
-4 \sqrt[3]{729}+4 \sqrt[3]{216}+4 \sqrt{-81}-\sqrt[3]{729}
−
4
3
729
+
4
3
216
+
4
−
81
−
3
729
\newline
Answer:
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Simplify the expression completely.
\newline
3
−
8
3
−
5
−
49
−
−
216
3
3 \sqrt[3]{-8}-5 \sqrt{-49}-\sqrt[3]{-216}
3
3
−
8
−
5
−
49
−
3
−
216
\newline
Answer:
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Simplify the expression completely.
\newline
−
−
27
3
+
4
8
3
+
64
-\sqrt[3]{-27}+4 \sqrt[3]{8}+\sqrt{64}
−
3
−
27
+
4
3
8
+
64
\newline
Answer:
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Simplify the expression completely.
\newline
−
729
3
−
3
36
+
−
100
+
3
125
3
-\sqrt[3]{729}-3 \sqrt{36}+\sqrt{-100}+3 \sqrt[3]{125}
−
3
729
−
3
36
+
−
100
+
3
3
125
\newline
Answer:
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Simplify the expression completely.
\newline
−
4
−
100
−
−
1
+
−
125
3
-4 \sqrt{-100}-\sqrt{-1}+\sqrt[3]{-125}
−
4
−
100
−
−
1
+
3
−
125
\newline
Answer:
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Simplify the expression completely.
\newline
−
−
216
3
+
4
1
3
+
2
1000
3
−
3
1000
3
-\sqrt[3]{-216}+4 \sqrt[3]{1}+2 \sqrt[3]{1000}-3 \sqrt[3]{1000}
−
3
−
216
+
4
3
1
+
2
3
1000
−
3
3
1000
\newline
Answer:
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Simplify the expression completely.
\newline
100
+
64
3
+
5
−
729
3
\sqrt{100}+\sqrt[3]{64}+5 \sqrt[3]{-729}
100
+
3
64
+
5
3
−
729
\newline
Answer:
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Simplify the expression completely.
\newline
−
2
−
49
−
16
+
4
1000
3
−
216
3
-2 \sqrt{-49}-\sqrt{16}+4 \sqrt[3]{1000}-\sqrt[3]{216}
−
2
−
49
−
16
+
4
3
1000
−
3
216
\newline
Answer:
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Simplify the expression completely.
\newline
5
1
3
+
49
+
−
125
3
5 \sqrt[3]{1}+\sqrt{49}+\sqrt[3]{-125}
5
3
1
+
49
+
3
−
125
\newline
Answer:
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Simplify the expression completely.
\newline
8
3
−
−
9
−
16
−
2
−
125
3
\sqrt[3]{8}-\sqrt{-9}-\sqrt{16}-2 \sqrt[3]{-125}
3
8
−
−
9
−
16
−
2
3
−
125
\newline
Answer:
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Solve the equation using the multiplication property of equality. Be sure to check your solution.
\newline
15
=
−
5
3
x
15=-\frac{5}{3} x
15
=
−
3
5
x
\newline
The solution set is
□
\square
□
.
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Solve for
y
y
y
. Express your answer as a proper or improper fraction in simplest terms.
\newline
3
4
−
4
7
y
=
1
3
\frac{3}{4}-\frac{4}{7} y=\frac{1}{3}
4
3
−
7
4
y
=
3
1
\newline
Answer:
y
=
y=
y
=
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Find all vertical asymptotes of the following function.
\newline
f
(
x
)
=
x
2
−
16
2
x
2
+
8
x
f(x)=\frac{x^{2}-16}{2x^{2}+8x}
f
(
x
)
=
2
x
2
+
8
x
x
2
−
16
\newline
Answer
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
5
2
⋅
8
9
-\frac{5}{2} \cdot \frac{8}{9}
−
2
5
⋅
9
8
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
9
8
−
4
\frac{\frac{9}{8}}{-4}
−
4
8
9
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
2
÷
−
5
4
\frac{1}{2} \div-\frac{5}{4}
2
1
÷
−
4
5
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
3
7
4
5
\frac{\frac{3}{7}}{\frac{4}{5}}
5
4
7
3
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
10
3
⋅
2
7
-\frac{10}{3} \cdot \frac{2}{7}
−
3
10
⋅
7
2
\newline
Answer:
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Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
x
2
x
2
3
4
=
□
\sqrt[4]{\frac{x^{2}}{x^{\frac{2}{3}}}}=\square
4
x
3
2
x
2
=
□
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Solve for
x
\mathrm{x}
x
in simplest form.
\newline
5
=
1
4
(
3
x
−
8
)
5=\frac{1}{4}(3 x-8)
5
=
4
1
(
3
x
−
8
)
\newline
Answer:
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Solve for
u
u
u
and simplify your answer.
\newline
−
3
2
u
=
21
-\frac{3}{2} u=21
−
2
3
u
=
21
\newline
Answer:
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Solve for
s
s
s
and simplify your answer.
\newline
−
5
3
s
=
16
-\frac{5}{3} s=16
−
3
5
s
=
16
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
1
2
3
5
\frac{\frac{1}{2}}{\frac{3}{5}}
5
3
2
1
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
8
5
3
2
\frac{\frac{8}{5}}{\frac{3}{2}}
2
3
5
8
\newline
Answer:
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