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Math Problems
Precalculus
Operations with rational exponents
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
−
2
10
x
2
−
60
x
+
80
⋅
x
2
−
10
x
+
24
x
5
−
9
x
4
+
18
x
3
\frac{x-2}{10 x^{2}-60 x+80} \cdot \frac{x^{2}-10 x+24}{x^{5}-9 x^{4}+18 x^{3}}
10
x
2
−
60
x
+
80
x
−
2
⋅
x
5
−
9
x
4
+
18
x
3
x
2
−
10
x
+
24
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
3
x
+
3
9
x
2
+
81
x
+
72
⋅
x
2
−
64
x
2
−
2
x
−
48
\frac{3 x+3}{9 x^{2}+81 x+72} \cdot \frac{x^{2}-64}{x^{2}-2 x-48}
9
x
2
+
81
x
+
72
3
x
+
3
⋅
x
2
−
2
x
−
48
x
2
−
64
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
−
25
x
x
2
+
12
x
+
35
⋅
x
+
7
x
4
+
9
x
3
\frac{x^{3}-25 x}{x^{2}+12 x+35} \cdot \frac{x+7}{x^{4}+9 x^{3}}
x
2
+
12
x
+
35
x
3
−
25
x
⋅
x
4
+
9
x
3
x
+
7
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
4
x
5
−
28
x
4
−
32
x
3
2
x
5
−
10
x
4
−
12
x
3
⋅
x
−
6
x
2
−
13
x
+
40
\frac{4 x^{5}-28 x^{4}-32 x^{3}}{2 x^{5}-10 x^{4}-12 x^{3}} \cdot \frac{x-6}{x^{2}-13 x+40}
2
x
5
−
10
x
4
−
12
x
3
4
x
5
−
28
x
4
−
32
x
3
⋅
x
2
−
13
x
+
40
x
−
6
\newline
Answer:
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Mildred has a bag of coins. The bag contains
10
10
10
dimes,
5
5
5
nickels, and
1
1
1
penny. She will randomly select
2
2
2
coins form the bag one at a time without replacement. What is the probability that Mildred will select a dime first and then a penny?
\newline
A.
83
120
\frac{83}{120}
120
83
\newline
B.
11
16
\frac{11}{16}
16
11
\newline
C.
5
128
\frac{5}{128}
128
5
\newline
D.
1
24
\frac{1}{24}
24
1
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Which pair of expressions below are equivalent?
\newline
5
p
+
9
p
5 p+9 p
5
p
+
9
p
and
14
p
2
14 p^{2}
14
p
2
\newline
5
(
9
p
)
5(9 p)
5
(
9
p
)
and
14
p
14 p
14
p
\newline
5
(
9
p
−
8
)
5(9 p-8)
5
(
9
p
−
8
)
and
45
p
−
8
45 p-8
45
p
−
8
\newline
5
p
+
9
q
5 p+9 q
5
p
+
9
q
and
9
q
+
5
p
9 q+5 p
9
q
+
5
p
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Which pair of expressions below are equivalent?
\newline
y
+
z
+
z
+
z
y+z+z+z
y
+
z
+
z
+
z
and
4
y
z
4 y z
4
yz
\newline
7
(
6
y
−
3
)
7(6 y-3)
7
(
6
y
−
3
)
and
42
y
−
3
42 y-3
42
y
−
3
\newline
7
(
6
y
−
3
)
7(6 y-3)
7
(
6
y
−
3
)
and
42
y
−
21
42 y-21
42
y
−
21
\newline
7
(
6
y
)
7(6 y)
7
(
6
y
)
and
13
y
13 y
13
y
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Prove the trigonometric identity.
\newline
cos
A
−
cos
B
=
−
2
sin
(
A
+
B
2
)
sin
(
A
−
B
2
)
\cos A - \cos B = -2 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)
cos
A
−
cos
B
=
−
2
sin
(
2
A
+
B
)
sin
(
2
A
−
B
)
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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
÷
7
5
\frac{2}{5} \div \frac{7}{5}
5
2
÷
5
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
7
8
÷
7
3
\frac{7}{8} \div \frac{7}{3}
8
7
÷
3
7
\newline
Answer:
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Solve.
\newline
tan
(
18
0
∘
−
x
)
⋅
sin
(
x
−
9
0
∘
)
4
sin
(
36
0
∘
+
x
)
\frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(x-90^{\circ}\right)}{4 \sin \left(360^{\circ}+x\right)}
4
s
i
n
(
36
0
∘
+
x
)
t
a
n
(
18
0
∘
−
x
)
⋅
s
i
n
(
x
−
9
0
∘
)
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Find the difference. Simplify your answer completely.
\newline
3
5
−
3
10
\frac{3}{5}-\frac{3}{10}
5
3
−
10
3
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3
g
2
+
12
g
g
+
7
⋅
4
8
g
2
\frac{3g^{2}+12g}{g+7}\cdot\frac{4}{8g^{2}}
g
+
7
3
g
2
+
12
g
⋅
8
g
2
4
\newline
Which expression is equivalent to the product for all
g
>
0
g > 0
g
>
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
g
+
48
g
2
+
56
g
\frac{3g+48}{g^{2}+56g}
g
2
+
56
g
3
g
+
48
\newline
(B)
12
g
+
12
8
g
2
+
7
g
\frac{12g+12}{8g^{2}+7g}
8
g
2
+
7
g
12
g
+
12
\newline
(C)
3
g
+
12
2
g
2
+
14
g
\frac{3g+12}{2g^{2}+14g}
2
g
2
+
14
g
3
g
+
12
\newline
(D)
3
+
12
g
2
g
+
14
\frac{3+12g}{2g+14}
2
g
+
14
3
+
12
g
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Simplify the expression.
sin
5
π
8
\sin \frac{5 \pi}{8}
sin
8
5
π
=
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x
2
5
−
x
x
9
+
1
3
\frac{\frac{x^{2}}{5}-x}{\frac{x}{9}+\frac{1}{3}}
9
x
+
3
1
5
x
2
−
x
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In the given equation,
k
k
k
is a constant. For what value of
k
k
k
does the equation have exactly one distinct real solution?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
25
8
-\frac{25}{8}
−
8
25
\newline
(B)
−
5
4
-\frac{5}{4}
−
4
5
\newline
(C)
5
4
\frac{5}{4}
4
5
\newline
(D)
25
8
\frac{25}{8}
8
25
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Divide:
\newline
17
12
÷
8
16
=
\frac{17}{12}\div\frac{8}{16}=
12
17
÷
16
8
=
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Divide:
\newline
5
3
÷
2
8
=
\frac{5}{3}\div\frac{2}{8}=
3
5
÷
8
2
=
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11
36
\sqrt{\frac{11}{36}}
36
11
=
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Evaluate:
4
10
×
6
10
\frac{4}{10}\times\frac{6}{10}
10
4
×
10
6
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b.
3
2
+
2
3
−
5
6
\frac{3}{2}+\frac{2}{3}-\frac{5}{6}
2
3
+
3
2
−
6
5
/
7
36
+
1
4
+
8
9
\frac{7}{36}+\frac{1}{4}+\frac{8}{9}
36
7
+
4
1
+
9
8
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Find the positive solution of the equation.
\newline
2
x
2
7
+
19
=
147
2 x^{\frac{2}{7}}+19=147
2
x
7
2
+
19
=
147
\newline
Answer:
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Find the positive solution of the equation.
\newline
8
x
3
2
+
25
=
4121
8 x^{\frac{3}{2}}+25=4121
8
x
2
3
+
25
=
4121
\newline
Answer:
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Find the positive solution of the equation.
\newline
6
x
6
7
+
24
=
3188670
6 x^{\frac{6}{7}}+24=3188670
6
x
7
6
+
24
=
3188670
\newline
Answer:
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Find the positive solution of the equation.
\newline
6
x
6
7
+
23
=
24599
6 x^{\frac{6}{7}}+23=24599
6
x
7
6
+
23
=
24599
\newline
Answer:
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Find the positive solution of the equation.
\newline
4
x
4
3
+
22
=
1046
4 x^{\frac{4}{3}}+22=1046
4
x
3
4
+
22
=
1046
\newline
Answer:
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Find the positive solution of the equation.
\newline
3
x
6
5
+
29
=
12317
3 x^{\frac{6}{5}}+29=12317
3
x
5
6
+
29
=
12317
\newline
Answer:
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Find the positive solution of the equation.
\newline
7
x
2
5
+
3
=
66
7 x^{\frac{2}{5}}+3=66
7
x
5
2
+
3
=
66
\newline
Answer:
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Find the positive solution of the equation.
\newline
6
x
8
5
−
28
=
100663268
6 x^{\frac{8}{5}}-28=100663268
6
x
5
8
−
28
=
100663268
\newline
Answer:
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Find the positive solution of the equation.
\newline
4
x
7
2
+
15
=
527
4 x^{\frac{7}{2}}+15=527
4
x
2
7
+
15
=
527
\newline
Answer:
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Find the positive solution of the equation.
\newline
6
x
7
8
+
19
=
787
6 x^{\frac{7}{8}}+19=787
6
x
8
7
+
19
=
787
\newline
Answer:
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Find the positive solution of the equation.
\newline
8
x
8
5
−
22
=
52466
8 x^{\frac{8}{5}}-22=52466
8
x
5
8
−
22
=
52466
\newline
Answer:
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Find the positive solution of the equation.
\newline
8
x
7
6
−
8
=
2239480
8 x^{\frac{7}{6}}-8=2239480
8
x
6
7
−
8
=
2239480
\newline
Answer:
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Find the positive solution of the equation.
\newline
3
x
2
5
+
8
=
200
3 x^{\frac{2}{5}}+8=200
3
x
5
2
+
8
=
200
\newline
Answer:
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Find the positive solution of the equation.
\newline
8
x
5
8
+
27
=
283
8 x^{\frac{5}{8}}+27=283
8
x
8
5
+
27
=
283
\newline
Answer:
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Find the positive solution of the equation.
\newline
2
x
6
7
−
7
=
93305
2 x^{\frac{6}{7}}-7=93305
2
x
7
6
−
7
=
93305
\newline
Answer:
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Find the positive solution of the equation.
\newline
4
x
5
6
+
6
=
4102
4 x^{\frac{5}{6}}+6=4102
4
x
6
5
+
6
=
4102
\newline
Answer:
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Find the positive solution of the equation.
\newline
3
x
9
8
+
24
=
5859399
3 x^{\frac{9}{8}}+24=5859399
3
x
8
9
+
24
=
5859399
\newline
Answer:
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Find the positive solution of the equation.
\newline
4
x
7
9
+
28
=
65564
4 x^{\frac{7}{9}}+28=65564
4
x
9
7
+
28
=
65564
\newline
Answer:
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Find the positive solution of the equation.
\newline
8
x
3
4
+
16
=
232
8 x^{\frac{3}{4}}+16=232
8
x
4
3
+
16
=
232
\newline
Answer:
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Find the positive solution of the equation.
\newline
2
x
6
7
+
28
=
156
2 x^{\frac{6}{7}}+28=156
2
x
7
6
+
28
=
156
\newline
Answer:
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Find the positive solution of the equation.
\newline
7
x
3
7
+
19
=
1531
7 x^{\frac{3}{7}}+19=1531
7
x
7
3
+
19
=
1531
\newline
Answer:
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Find the positive solution of the equation.
\newline
4
x
6
7
−
26
=
230
4 x^{\frac{6}{7}}-26=230
4
x
7
6
−
26
=
230
\newline
Answer:
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Select the answer which is equivalent to the given expression using your calculator.
\newline
cos
A
=
30
50
\cos A=\frac{30}{50}
cos
A
=
50
30
and A is in Quadrant I.
\newline
Find
cos
2
A
\cos 2 A
cos
2
A
.
\newline
2400
2500
\frac{2400}{2500}
2500
2400
\newline
−
350
2500
\frac{-350}{2500}
2500
−
350
\newline
−
700
2500
\frac{-700}{2500}
2500
−
700
\newline
1200
2500
\frac{1200}{2500}
2500
1200
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Select the answer which is equivalent to the given expression using your calculator.
cos
A
=
52
65
\cos A=\frac{52}{65}
cos
A
=
65
52
and A is in Quadrant I.
\newline
Find
cos
2
A
\cos 2 A
cos
2
A
.
\newline
2366
4225
\frac{2366}{4225}
4225
2366
\newline
4056
4225
\frac{4056}{4225}
4225
4056
\newline
2028
4225
\frac{2028}{4225}
4225
2028
\newline
1183
4225
\frac{1183}{4225}
4225
1183
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Select the answer which is equivalent to the given expression using your calculator.
sin
A
=
55
73
\sin A=\frac{55}{73}
sin
A
=
73
55
and
A
\mathrm{A}
A
is in Quadrant I.
\newline
Find
cos
2
A
\cos 2 A
cos
2
A
.
\newline
2640
5329
\frac{2640}{5329}
5329
2640
\newline
5280
5329
\frac{5280}{5329}
5329
5280
\newline
−
721
5329
\frac{-721}{5329}
5329
−
721
\newline
−
1442
5329
\frac{-1442}{5329}
5329
−
1442
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Select the answer which is equivalent to the given expression using your calculator.
tan
A
=
9
40
\tan A=\frac{9}{40}
tan
A
=
40
9
and A is in Quadrant I.
\newline
Find
sin
2
A
\sin 2 A
sin
2
A
.
\newline
360
1681
\frac{360}{1681}
1681
360
\newline
720
1681
\frac{720}{1681}
1681
720
\newline
3038
1681
\frac{3038}{1681}
1681
3038
\newline
1519
1681
\frac{1519}{1681}
1681
1519
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Select the answer which is equivalent to the given expression using your calculator.
cos
A
=
11
61
\cos A=\frac{11}{61}
cos
A
=
61
11
and A is in Quadrant I.
\newline
Find
cos
2
A
\cos 2 A
cos
2
A
.
\newline
660
3721
\frac{660}{3721}
3721
660
\newline
−
6958
3721
\frac{-6958}{3721}
3721
−
6958
\newline
−
3479
3721
\frac{-3479}{3721}
3721
−
3479
\newline
1320
3721
\frac{1320}{3721}
3721
1320
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Select the answer which is equivalent to the given expression using your calculator.
cos
A
=
63
65
\cos A=\frac{63}{65}
cos
A
=
65
63
and A is in Quadrant I.
\newline
Find
cos
2
A
\cos 2 A
cos
2
A
.
\newline
1008
4225
\frac{1008}{4225}
4225
1008
\newline
7426
4225
\frac{7426}{4225}
4225
7426
\newline
3713
4225
\frac{3713}{4225}
4225
3713
\newline
2016
4225
\frac{2016}{4225}
4225
2016
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
sin
(
arctan
7
51
)
\sin \left(\arctan \frac{7}{\sqrt{51}}\right)
sin
(
arctan
51
7
)
\newline
7
51
\frac{7}{\sqrt{51}}
51
7
\newline
10
7
\frac{10}{7}
7
10
\newline
51
7
\frac{\sqrt{51}}{7}
7
51
\newline
7
10
\frac{7}{10}
10
7
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