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Math Problems
Algebra 2
Roots of rational numbers
Convert the fraction below into a decimal
\newline
5
11
\frac{5}{11}
11
5
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
2
5
\frac{2}{5}
5
2
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
7
8
\frac{7}{8}
8
7
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
17
20
\frac{17}{20}
20
17
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
4
15
\frac{4}{15}
15
4
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
1
11
\frac{1}{11}
11
1
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
29
40
\frac{29}{40}
40
29
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
Get tutor help
Convert the fraction below into a decimal
\newline
7
12
\frac{7}{12}
12
7
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
1
3
\frac{1}{3}
3
1
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
P
=
(
2
5
,
−
21
5
)
P=\left(\frac{2}{5},-\frac{\sqrt{21}}{5}\right)
P
=
(
5
2
,
−
5
21
)
\newline
Answer:
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
−
1
2
(
1
2
h
+
1
2
)
+
4
h
-\frac{1}{2}\left(\frac{1}{2} h+\frac{1}{2}\right)+4 h
−
2
1
(
2
1
h
+
2
1
)
+
4
h
\newline
Answer:
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
y
+
3
2
(
−
1
2
y
−
1
)
y+\frac{3}{2}\left(-\frac{1}{2} y-1\right)
y
+
2
3
(
−
2
1
y
−
1
)
\newline
Answer:
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
−
(
−
2
y
+
8
)
+
1
2
y
-(-2 y+8)+\frac{1}{2} y
−
(
−
2
y
+
8
)
+
2
1
y
\newline
Answer:
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Simplify the expression. Write your answers using integers or improper fractions.
\newline
−
1
5
(
−
25
q
+
25
)
−
q
-\frac{1}{5}(-25 q+25)-q
−
5
1
(
−
25
q
+
25
)
−
q
\newline
Answer:
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Probuct of atertion and a wi
\newline
Multiply. Write your answer as
\newline
5
8
×
3
\frac{5}{8} \times 3
8
5
×
3
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−
x
1
2
+
x
2
2
−
x
3
2
−
4
x
1
x
2
+
2
x
2
x
3
x
1
=
0
,
5
1
,
25
y
1
−
2
12
−
256
y
2
−
2
12
+
2
6
y
3
x
2
=
(
1
−
6
)
72
−
2
5
y
2
+
(
1
+
6
)
12
+
2
6
y
3
x
3
=
1
1
,
25
y
1
+
1
12
−
2
6
y
2
+
1
12
+
2
6
y
3
\begin{array}{l}-x_{1}^{2}+x_{2}^{2}-x_{3}^{2}-4 x_{1} x_{2}+2 x_{2} x_{3} \\ x_{1}=\frac{0,5}{\sqrt{1,25}} y_{1}-\frac{2}{\sqrt{12-256}} y_{2}-\frac{2}{\sqrt{12+2 \sqrt{6}}} y_{3} \\ x_{2}=\frac{(1-\sqrt{6})}{\sqrt{72-2 \sqrt{5}}} y_{2}+\frac{(1+\sqrt{6})}{\sqrt{12+2 \sqrt{6}}} y_{3} \\ x_{3}=\frac{1}{\sqrt{1,25}} y_{1}+\frac{1}{\sqrt{12-2 \sqrt{6}}} y_{2}+\frac{1}{\sqrt{12+2 \sqrt{6}}} y_{3} \\\end{array}
−
x
1
2
+
x
2
2
−
x
3
2
−
4
x
1
x
2
+
2
x
2
x
3
x
1
=
1
,
25
0
,
5
y
1
−
12
−
256
2
y
2
−
12
+
2
6
2
y
3
x
2
=
72
−
2
5
(
1
−
6
)
y
2
+
12
+
2
6
(
1
+
6
)
y
3
x
3
=
1
,
25
1
y
1
+
12
−
2
6
1
y
2
+
12
+
2
6
1
y
3
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
9
10
×
1
3
\frac{9}{10} \times \frac{1}{3}
10
9
×
3
1
\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
10
×
3
5
\frac{3}{10} \times \frac{3}{5}
10
3
×
5
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
1
2
÷
9
7
\frac{1}{2} \div \frac{9}{7}
2
1
÷
7
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
3
7
÷
9
10
\frac{3}{7} \div \frac{9}{10}
7
3
÷
10
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
3
7
×
1
4
\frac{3}{7} \times \frac{1}{4}
7
3
×
4
1
\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
2
5
×
1
4
\frac{2}{5} \times \frac{1}{4}
5
2
×
4
1
\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
8
×
7
4
\frac{1}{8} \times \frac{7}{4}
8
1
×
4
7
\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
5
÷
2
3
\frac{1}{5} \div \frac{2}{3}
5
1
÷
3
2
\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
5
÷
3
2
\frac{3}{5} \div \frac{3}{2}
5
3
÷
2
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
4
7
×
1
7
\frac{4}{7} \times \frac{1}{7}
7
4
×
7
1
\newline
Answer:
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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
7
+
3
8
\frac{3}{7}+\frac{3}{8}
7
3
+
8
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
14
19
−
10
19
\frac{14}{19}-\frac{10}{19}
19
14
−
19
10
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
11
16
−
3
20
\frac{11}{16}-\frac{3}{20}
16
11
−
20
3
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
1
8
−
1
12
\frac{1}{8}-\frac{1}{12}
8
1
−
12
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
5
13
+
2
13
\frac{5}{13}+\frac{2}{13}
13
5
+
13
2
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
4
9
+
1
15
\frac{4}{9}+\frac{1}{15}
9
4
+
15
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
−
1
4
\frac{1}{2}-\frac{1}{4}
2
1
−
4
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
+
1
18
\frac{1}{2}+\frac{1}{18}
2
1
+
18
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
5
8
+
2
7
\frac{5}{8}+\frac{2}{7}
8
5
+
7
2
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
7
12
−
1
7
\frac{7}{12}-\frac{1}{7}
12
7
−
7
1
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
1
15
+
5
6
\frac{1}{15}+\frac{5}{6}
15
1
+
6
5
\newline
Answer:
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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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19
19
19
.
27
3
\sqrt[3]{27}
3
27
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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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In this exercise we will use the Remainder Estimation Theorem to determine the number of terms that are required in Formula (
14
14
14
) to approximate
ln
2
\ln 2
ln
2
to five decimal-place accuracy. For this purpose let
\newline
f
(
x
)
=
ln
(
1
+
x
1
−
x
)
=
ln
(
1
+
x
)
−
ln
(
1
−
x
)
(
−
1
<
x
<
1
)
f(x)=\ln \left(\frac{1+x}{1-x}\right)=\ln(1+x)-\ln(1-x)\quad(-1 < x < 1)
f
(
x
)
=
ln
(
1
−
x
1
+
x
)
=
ln
(
1
+
x
)
−
ln
(
1
−
x
)
(
−
1
<
x
<
1
)
\newline
(a) Show that
\newline
f
(
n
+
1
)
(
x
)
=
n
!
[
(
−
1
)
n
(
1
+
x
)
n
+
1
+
1
(
1
−
x
)
n
+
1
]
f^{(n+1)}(x)=n!\left[\frac{(-1)^n}{(1+x)^{n+1}}+\frac{1}{(1-x)^{n+1}}\right]
f
(
n
+
1
)
(
x
)
=
n
!
[
(
1
+
x
)
n
+
1
(
−
1
)
n
+
(
1
−
x
)
n
+
1
1
]
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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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