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Math Problems
Precalculus
Operations with rational exponents
2
2
2
. What is the solution to the equation
1
2
x
+
3
2
(
x
+
1
)
−
1
4
=
5
\frac{1}{2} x+\frac{3}{2}(x+1)-\frac{1}{4}=5
2
1
x
+
2
3
(
x
+
1
)
−
4
1
=
5
?
\newline
A.
5
2
\frac{5}{2}
2
5
\newline
B.
13
8
\frac{13}{8}
8
13
\newline
C.
15
8
\frac{15}{8}
8
15
\newline
D.
17
8
\frac{17}{8}
8
17
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20
20
20
(
1
1
1
point)
\newline
of the expression
(
(
2
−
3
)
(
2
5
)
2
8
)
−
1
3
\left(\frac{\left(2^{-3}\right)\left(2^{5}\right)}{2^{8}}\right)^{-\frac{1}{3}}
(
2
8
(
2
−
3
)
(
2
5
)
)
−
3
1
is
\newline
age
\newline
Next Page
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900
−
(
8
2
+
(
6
2
÷
4
)
−
58
)
2
×
3
=
900-\left(8^{2}+\left(6^{2} \div 4\right)-58\right)^{2} \times 3=
900
−
(
8
2
+
(
6
2
÷
4
)
−
58
)
2
×
3
=
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A
1
1
1
A
19
19
19
- Graphing Quadratics Guestion
6
6
6
of
12
12
12
(
1
1
1
point) I Que
\newline
y
=
x
2
−
2
x
+
4
y=x^{2}-2 x+4
y
=
x
2
−
2
x
+
4
\newline
Plot five points on the parabola: button.
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Find the area of ACDE. Round the final answer to the nearest whole number. Choose the correct answer.
\newline
83
c
m
2
83 \mathrm{~cm}^{2}
83
cm
2
\newline
70
c
m
2
70 \mathrm{~cm}^{2}
70
cm
2
\newline
153
c
m
2
153 \mathrm{~cm}^{2}
153
cm
2
\newline
140
c
m
2
140 \mathrm{~cm}^{2}
140
cm
2
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Select all the expressions that are equivalent to
5
4
⋅
7
4
5^{4} \cdot 7^{4}
5
4
⋅
7
4
.
\newline
3
5
−
3
3
5
−
7
\frac{35^{-3}}{35^{-7}}
3
5
−
7
3
5
−
3
\newline
3
5
16
35^{16}
3
5
16
\newline
1
3
5
4
\frac{1}{35^{4}}
3
5
4
1
\newline
(
3
5
−
4
)
−
1
\left(35^{-4}\right)^{-1}
(
3
5
−
4
)
−
1
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5
5
5
)
y
=
7
ln
(
arctg
3
x
)
5
y=\frac{7}{\sqrt[5]{\ln \left(\operatorname{arctg} \frac{3}{x}\right)}}
y
=
5
l
n
(
arctg
x
3
)
7
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5
16
\frac{5}{16}
16
5
meters
\newline
3
21
24
−
3
3
=
7
8
3 \frac{21}{24}-\frac{3}{3}=\frac{7}{8}
3
24
21
−
3
3
=
8
7
\newline
3
7
8
3 \frac{7}{8}
3
8
7
length
\newline
12
12
12
) Jodie spent the weekend studying for her chemistry final. She spent
3
13
15
3 \frac{13}{15}
3
15
13
hours studying on Saturday and
2
5
12
2 \frac{5}{12}
2
12
5
studying on Sunday. How muc longer did Jodie study on Saturday than on Sunday?
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(
7
x
3
5
)
1
2
\left(\frac{7 x^{3}}{5}\right)^{\frac{1}{2}}
(
5
7
x
3
)
2
1
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6
6
6
)
{
9
16
×
4
12
}
+
{
9
16
×
−
3
9
}
\left\{\frac{9}{16} \times \frac{4}{12}\right\}+\left\{\frac{9}{16} \times-\frac{3}{9}\right\}
{
16
9
×
12
4
}
+
{
16
9
×
−
9
3
}
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{
9
16
×
4
12
}
+
{
9
16
x
−
3
9
}
\left\{\frac{9}{16} \times \frac{4}{12}\right\}+\left\{\frac{9}{16} x-\frac{3}{9}\right\}
{
16
9
×
12
4
}
+
{
16
9
x
−
9
3
}
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5
5
5
)
(
2
5
×
(
−
3
7
)
−
(
1
6
×
3
2
)
+
(
1
14
×
2
5
)
\left(\frac{2}{5} \times\left(\frac{-3}{7}\right)-\left(\frac{1}{6} \times \frac{3}{2}\right)+\left(\frac{1}{14} \times \frac{2}{5}\right)\right.
(
5
2
×
(
7
−
3
)
−
(
6
1
×
2
3
)
+
(
14
1
×
5
2
)
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(
13
9
×
−
15
2
)
+
(
7
3
×
8
5
)
+
(
3
5
×
1
2
)
\left(\frac{13}{9} \times-\frac{15}{2}\right)+\left(\frac{7}{3} \times \frac{8}{5}\right)+\left(\frac{3}{5} \times \frac{1}{2}\right)
(
9
13
×
−
2
15
)
+
(
3
7
×
5
8
)
+
(
5
3
×
2
1
)
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5
6
=
20
x
\frac{5}{6}=\frac{20}{x}
6
5
=
x
20
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Rewrite the following equation in standard form.
\newline
7
2
y
=
−
8
3
x
+
5
6
\frac{7}{2} y=\frac{-8}{3} x+\frac{5}{6}
2
7
y
=
3
−
8
x
+
6
5
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13.
5
8
(
7
)
4
8
14.
3
5
O
1
5
\begin{array}{l}\text { 13. } \frac{5}{8}(7)^{\frac{4}{8}} \\ 14 . \frac{3}{5} O^{\frac{1}{5}}\end{array}
13.
8
5
(
7
)
8
4
14.
5
3
O
5
1
\newline
15
⋅
3
8
O
6
8
15 \cdot \frac{3}{8} O^{\frac{6}{8}}
15
⋅
8
3
O
8
6
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(d)
8
c
3
6
(
c
+
d
)
÷
2
c
2
3
c
+
3
d
\frac{8 c^{3}}{6(c+d)} \div \frac{2 c^{2}}{3 c+3 d}
6
(
c
+
d
)
8
c
3
÷
3
c
+
3
d
2
c
2
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Calculate.
\newline
5
⋅
10
−
(
6
⋅
4
−
10
)
+
20
÷
2
5 \cdot 10-(6 \cdot 4-10)+20 \div 2
5
⋅
10
−
(
6
⋅
4
−
10
)
+
20
÷
2
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Solve
(
8
20
)
(
7
19
)
(
6
18
)
\left(\frac{8}{20}\right)\left(\frac{7}{19}\right)\left(\frac{6}{18}\right)
(
20
8
)
(
19
7
)
(
18
6
)
=
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Find the sum of the first
9
9
9
terms of the following geometric series.
\newline
1
48
−
1
12
+
1
3
−
…
\frac{1}{48}-\frac{1}{12}+\frac{1}{3}-\ldots
48
1
−
12
1
+
3
1
−
…
\newline
The sum is
□
\square
□
.
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Find the value of
⋄
\diamond
⋄
:
\newline
(
7
⋄
)
6
)
2
=
7
−
36
(7^{\diamond})^{6})^{2}=7^{-36}
(
7
⋄
)
6
)
2
=
7
−
36
\newline
⋄
=
□
\diamond = \square
⋄
=
□
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Evaluate.
\newline
9
(
11
−
7
)
−
6
5
2
−
10
\frac{9(11-7)-6}{5^{2}-10}
5
2
−
10
9
(
11
−
7
)
−
6
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Divide.
\newline
2
5
6
÷
2
3
7
=
_
_
_
_
_
2 \frac{5}{6} \div 2 \frac{3}{7}= \_\_\_\_\_
2
6
5
÷
2
7
3
=
_____
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Solve the equation
1
2
(
16
x
−
6
)
=
2
\frac{1}{2}(16 x-6)=2
2
1
(
16
x
−
6
)
=
2
\newline
A.
1
2
\frac{1}{2}
2
1
\newline
B.
3
5
\frac{3}{5}
5
3
\newline
C.
5
8
\frac{5}{8}
8
5
\newline
D.
7
10
\frac{7}{10}
10
7
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(
9
5
×
4
3
)
+
(
6
5
×
4
3
)
+
(
4
5
×
1
3
)
+
[
(
−
2
5
)
×
(
4
3
)
]
\left(\frac{9}{5} \times \frac{4}{3}\right)+\left(\frac{6}{5} \times \frac{4}{3}\right)+\left(\frac{4}{5} \times \frac{1}{3}\right)+\left[\left(\frac{-2}{5}\right) \times\left(\frac{4}{3}\right)\right]
(
5
9
×
3
4
)
+
(
5
6
×
3
4
)
+
(
5
4
×
3
1
)
+
[
(
5
−
2
)
×
(
3
4
)
]
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Which fraction, when converted, is a repeating decimal?
\newline
(A)
3
8
\frac{3}{8}
8
3
\newline
(B)
11
25
\frac{11}{25}
25
11
\newline
(C)
2
5
\frac{2}{5}
5
2
\newline
(D)
5
7
\frac{5}{7}
7
5
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(
7
4
×
5
8
)
+
(
7
4
×
1
2
)
=
\left.\left(\frac{7}{4} \times \frac{5}{8}\right)+(\frac{7}{4} \times \frac{1}{2}\right)=
(
4
7
×
8
5
)
+
(
4
7
×
2
1
)
=
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36
t
7
÷
9
t
3
=
36 t^{7} \div 9 t^{3} =
36
t
7
÷
9
t
3
=
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Find
3
7
+
(
−
6
11
)
+
(
−
8
21
)
+
(
5
22
)
\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)
7
3
+
(
11
−
6
)
+
(
21
−
8
)
+
(
22
5
)
.
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Simplify to eliminate all unnecessary exponents.
8
2
⋅
5
−
4
⋅
8
5
8
8
\frac{8^{2} \cdot 5^{-4} \cdot 8^{5}}{8^{8}}
8
8
8
2
⋅
5
−
4
⋅
8
5
Get tutor help
Find the value of
⋄
\diamond
⋄
:
\newline
(
5
2
5
⋄
)
3
=
5
24
\left(\frac{5^{2}}{5^{\diamond}}\right)^{3}=5^{24}
(
5
⋄
5
2
)
3
=
5
24
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792
7
=
4
3
×
22
7
×
r
3
\frac{792}{7}=\frac{4}{3} \times \frac{22}{7} \times r^{3}
7
792
=
3
4
×
7
22
×
r
3
.
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35
x
12
y
4
z
7
7
x
6
y
8
z
6
\frac{35 x^{12} y^{4} z^{7}}{7 x^{6} y^{8} z^{6}}
7
x
6
y
8
z
6
35
x
12
y
4
z
7
Get tutor help
12
g
3
v
4
×
4
g
2
v
7
12 g^{3} v^{4} \times 4 g^{2} v^{7}
12
g
3
v
4
×
4
g
2
v
7
Get tutor help
18
x
7
y
4
12
x
9
y
4
\frac{18 x^{7} y^{4}}{12 x^{9} y^{4}}
12
x
9
y
4
18
x
7
y
4
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8
3
⋅
8
−
5
⋅
8
y
=
8
−
2
=
1
8
2
8^{3} \cdot 8^{-5} \cdot 8^{y}=8^{-2}=\frac{1}{8^{2}}
8
3
⋅
8
−
5
⋅
8
y
=
8
−
2
=
8
2
1
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Simplify:
4
3
−
1
2
n
=
5
8
\frac{4}{3}-\frac{1}{2} n=\frac{5}{8}
3
4
−
2
1
n
=
8
5
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3
3
3
.
(
16
÷
4
)
+
(
10
−
3
)
(16 \div 4)+(10-3)
(
16
÷
4
)
+
(
10
−
3
)
Get tutor help
(iii)
−
2
5
×
(
3
8
−
25
)
\frac{-2}{5} \times\left(\frac{3}{8}-25\right)
5
−
2
×
(
8
3
−
25
)
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Write the expression as a single power of
x
x
x
.
\newline
x
4
3
x
2
3
\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}
x
3
2
x
3
4
Get tutor help
Integrate
\newline
ln
(
5
12
a
)
da
\ln \left(\frac{5}{12} a\right) \text { da }
ln
(
12
5
a
)
da
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If
8
5
6
−
8
1
2
=
8
m
8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m}
8
6
5
−
8
2
1
=
8
m
for some value of
m
m
m
, what is the value of
m
m
m
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
\frac{1}{3}
3
1
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
1
1
1
\newline
(D)
5
3
\frac{5}{3}
3
5
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(
2
3
)
4
⋅
(
2
34
)
(
2
5
)
8
\frac{\left(2^{3}\right)^{4} \cdot\left(2^{34}\right)}{\left(2^{5}\right)^{8}}
(
2
5
)
8
(
2
3
)
4
⋅
(
2
34
)
Get tutor help
Write the answer in proper scientific notation:
\newline
2
8
x
1
0
−
5
\frac{2}{8x10^{-5}}
8
x
1
0
−
5
2
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11
10
÷
5
3
=
\frac{11}{10} \div \frac{5}{3}=
10
11
÷
3
5
=
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18
18
18
.
5
9
5
x
=
625
\frac{5^{9}}{5^{x}}=625
5
x
5
9
=
625
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(D)
12
12
12
square units
\newline
3
3
3
. Ramon has
6
6
6
whole oranges. He cut each whole into halves. Ramon gave away
2
2
2
halves. Which fraction shows the pieces Ramon gave away?
\newline
(A)
1
2
\frac{1}{2}
2
1
\newline
(B)
2
2
\frac{2}{2}
2
2
\newline
(C)
2
6
\frac{2}{6}
6
2
\newline
(D)
12
2
\frac{12}{2}
2
12
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3
7
=
15
x
\frac{3}{7}=\frac{15}{x}
7
3
=
x
15
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24
x
5
z
2
12
x
7
z
\frac{24 x^{5} z^{2}}{12 x^{7} z}
12
x
7
z
24
x
5
z
2
Get tutor help
(
12
12
12
) Hasil dari
2
2
5
×
1
,
75
−
4
5
2 \frac{2}{5} \times 1,75-\frac{4}{5}
2
5
2
×
1
,
75
−
5
4
adalah ....
\newline
A.
9
5
\frac{9}{5}
5
9
\newline
B.
8
5
\frac{8}{5}
5
8
\newline
c.
6
5
\frac{6}{5}
5
6
\newline
D.
3
5
\frac{3}{5}
5
3
\newline
E.
2
5
\frac{2}{5}
5
2
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