data_source
stringclasses 9
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stringlengths 14
17
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stringlengths 14
1.32k
| answer
stringlengths 1
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stringclasses 8
values | data_topic
stringclasses 7
values | solution
stringlengths 1
991
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|---|---|---|---|---|---|---|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.7
|
Reduce the following radical: $\sqrt[12]{x^{6} y^{9}}$
|
$\sqrt[4]{x^{2} y^{3}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[4]{x^{2} y^{3}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.40
|
Add or subtract the rational expressions and simplify: $\frac{2 r}{r^{2}-s^{2}}+\frac{1}{r+s}-\frac{1}{r-s}$
|
$\frac{2}{r+s}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{2}{r+s}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.6.8
|
Solve the absolute value equation: $|3-x|=6$
|
$-3,9$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-3,9
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.82
|
Simplify: $\left(3-7 n^{2}\right)+\left(6 n^{2}+3\right)$
|
$-n^{2}+6$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-n^{2}+6
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.7
|
Add or subtract the rational expressions and simplify: $\frac{5}{6 r}-\frac{5}{8 r}$
|
$\frac{5}{24 r}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5}{24 r}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.10.4
|
A dealer bought a number of sheep for $\$ 440$. After 5 had died he sold the remainder at a profit of $\mathbb{\$} 2$ each making a profit of $\mathbb{\$} 60$ for the sheep. How many sheep did he originally purchase?
|
55
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
55
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.33
|
Combine the following radicals: $\sqrt[3]{3 x y^{2} z} \sqrt[4]{9 x^{3} y z^{2}}$
|
$x \sqrt[12]{59049 x y^{11} z^{10}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x \sqrt[12]{59049 x y^{11} z^{10}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.33
|
Solve the following equation: $(x-3)^{2}-2(x-3)=35$
|
$-2,10$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-2,10
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.6.17
|
Solve the proportion: $\frac{v-5}{v+6}=\frac{4}{9}$
|
$v=\frac{69}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
v=\frac{69}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.40
|
Find the product: $(3 a-8)(3 a+8)$
|
$9 a^{2}-64$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
9 a^{2}-64
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.22
|
Simplify: $4 \sqrt[3]{250 a^{6}}$
|
$20 a^{2} \sqrt[3]{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
20 a^{2} \sqrt[3]{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.5.5
|
Find the slope of a line parallel to the given line: $x-y=4$
|
1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.10
|
You lend out $\$ 5500$ at $10 \%$ compounded monthly. If the debt is repaid in 18 months, what is the total owed at the time of repayment?
|
6386.12
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6386.12
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.33
|
Simplify: $\frac{9 v+54}{v^{2}-4 v-60}$
|
$\frac{9}{v-10}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{9}{v-10}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.18
|
Find the square: $(v+4)^{2}$
|
$v^{2}+8 v+16$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
v^{2}+8 v+16
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.7.11
|
Divide: $\frac{n^{2}+13 n+32}{n+5}$
|
$n+8-\frac{8}{n+5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
n+8-\frac{8}{n+5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.67
|
Evaluate the expression: $\left(-\frac{1}{2}\right)+\frac{3}{2}$
|
1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.16
|
Simplify the expression: $\frac{1}{a-6} \cdot \frac{8 a+80}{8}$
|
$\frac{a+10}{a-6}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{a+10}{a-6}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.2.8
|
Solve: $(5 x+1)^{4}=16$
|
$\frac{1}{5},-\frac{3}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{5},-\frac{3}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.3
|
Find the value that completes the square and then rewrite as a perfect square: $m^{2}-36 m+$
|
$324 ;(m-18)^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
324 ;(m-18)^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.4.17
|
Solve the equation: $\frac{16}{9}=-\frac{4}{3}\left(-\frac{4}{3} n-\frac{4}{3}\right)$
|
0
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.5.1
|
Find the slope of a line parallel to the given line: $y=2 x+4$
|
2
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.3.1
|
Solve the following system of equations by elimination:
$4 x+2 y=0$
$-4 x-9 y=-28$
|
$(-2,4)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
(-2,4)
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.3.2.23
|
Solve the compound inequality and give interval notation: $-5 b+10 \leqslant 30$ and $7 b+2 \leqslant-40$
|
No solution : $\oslash$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
No solution : $\oslash
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.3.23
|
Simplify: $3 \sqrt{24}-3 \sqrt{27}+2 \sqrt{6}+2 \sqrt{8}$
|
$8 \sqrt{6}-9 \sqrt{3}+4 \sqrt{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
8 \sqrt{6}-9 \sqrt{3}+4 \sqrt{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.4.24
|
Simplify: $\frac{\sqrt{12}}{\sqrt{3}}$
|
2
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.3.33
|
Simplify: $2 \sqrt[4]{2}+2 \sqrt[4]{3}+3 \sqrt[4]{64}-\sqrt[4]{3}$
|
$2 \sqrt[4]{2}+\sqrt[4]{3}+6 \sqrt[4]{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2 \sqrt[4]{2}+\sqrt[4]{3}+6 \sqrt[4]{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.21
|
Simplify: $\frac{3 n m^{2}}{3 n}$
|
$m^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
m^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.9
|
Simplify the expression: $\frac{7 r}{7 r(r+10)} \div \frac{r-6}{(r-6)^{2}}$
|
$\frac{r-6}{r+10}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{r-6}{r+10}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.10
|
Solve each equation by completing the square: $n^{2}-8 n-12=0$
|
$4+2 \sqrt{7}, 4-2 \sqrt{7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4+2 \sqrt{7}, 4-2 \sqrt{7}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.66
|
Simplify: $9(6 b+5)-4 b(b+3)$
|
$-42 b-45-4 b^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-42 b-45-4 b^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.2.15
|
Solve: $(2 x-3)^{\frac{2}{3}}=4$
|
$\frac{11}{2},-\frac{5}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{11}{2},-\frac{5}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.3.3
|
Solve: $3+(8) \div|4|$
|
5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.18
|
Simplify and leave your answer as an improper fraction: $\frac{126}{108}$
|
$\frac{7}{6}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{7}{6}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.6.5
|
Solve the absolute value equation: $|5+8 a|=53$
|
$6,-\frac{29}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6,-\frac{29}{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.45
|
Simplify the following expression: $\frac{\sqrt[3]{(2 x+1)^{2}}}{\sqrt[5]{(2 x+1)^{2}}}$
|
$\sqrt[15]{(2 x+1)^{4}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[15]{(2 x+1)^{4}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.6.27
|
Simplify and express with positive exponents: $\left(\frac{m^{\frac{3}{2}} n^{-2}}{\left(m n^{\frac{4}{3}}\right)^{-1}}\right)^{\frac{7}{4}}$
|
$\frac{m^{\frac{35}{8}}}{n^{\frac{7}{6}}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{m^{\frac{35}{8}}}{n^{\frac{7}{6}}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.30
|
Simplify: $\frac{2 b a^{7} \cdot 2 b^{4}}{b a^{2} \cdot 3 a^{3} b^{4}}$
|
$\frac{4 a^{2}}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{4 a^{2}}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.8.3
|
Convert $11.2 \mathrm{mg}$ to grams.
|
$0.0112 \mathrm{~g}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
0.0112 \mathrm{~g}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.3.2.32
|
Solve the compound inequality and give interval notation: $-9 m+2<-10-6 m$ or $-m+5 \geqslant 10+4 m$
|
$m>4$ or $m \leqslant-1:(-\infty,-1] \cup(4, \infty)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
m>4$ or $m \leqslant-1:(-\infty,-1] \cup(4, \infty)
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.3.2.1
|
Solve the compound inequality and give interval notation: $\frac{n}{3} \leqslant-3$ or $-5 n \leqslant-10$
|
$n \leqslant-9$ or $n \geqslant 2:(-\infty,-9] \cup[2, \infty)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
n \leqslant-9$ or $n \geqslant 2:(-\infty,-9] \cup[2, \infty)
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.2
|
Find a quadratic equation with the solutions 3 and 6.
|
$x^{2}-9 x+18=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x^{2}-9 x+18=0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.1.24
|
Solve the equation: $m-4=-13$
|
-9
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-9
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.5
|
Evaluate using the given values: $c^{2}-(a-1)$; $a=3$ and $c=5$
|
23
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
23
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.30
|
Solve: $5 x^{2}=-26+10 x$
|
$\frac{5+i \sqrt{105}}{5}, \frac{5-i \sqrt{105}}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5+i \sqrt{105}}{5}, \frac{5-i \sqrt{105}}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.7.21
|
Hooke's law states that the distance that a spring is stretched by hanging object varies directly as the mass of the object. If the distance is $20 \mathrm{~cm}$ when the mass is $3 \mathrm{~kg}$, what is the distance when the mass is $5 \mathrm{~kg}$ ?
|
$33.3 \mathrm{~cm}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
33.3 \mathrm{~cm}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.6.12
|
How many kilograms of soil supplement that costs $\$ 7.00$ per kilogram must be mixed with $20 \mathrm{~kg}$ of aluminum nitrate that costs $\$ 3.50$ per kilogram to make a fertilizer that costs $\$ 4.50$ per kilogram?
|
8
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
8
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.3.29
|
Solve: $-a-5(8 a-1)=39-7 a$
|
-1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.8.22
|
Let the first angle of a triangle be $x$ degrees. Find the measures of the second and third angles.
|
$28,84,68$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
28,84,68
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.34
|
Given the points $(-2,y)$ and $(2,4)$ and a slope of $\frac{1}{4}$, find the value of $y$.
|
3
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
3
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.76
|
Evaluate the expression: $(-1)-\left(-\frac{1}{3}\right)$
|
$-\frac{2}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{2}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.3.25
|
Simplify: $-2 \sqrt[3]{16}+2 \sqrt[3]{16}+2 \sqrt[3]{2}$
|
$2 \sqrt[3]{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2 \sqrt[3]{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.24
|
Simplify the expression: $\frac{2 n^{2}-12 n-54}{n+7} \div(2 n+6)$
|
$\frac{n-9}{n+7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{n-9}{n+7}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.5.38
|
Find the product: $5(2 x-1)(4 x+1)$
|
$40 x^{2}-10 x-5$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
40 x^{2}-10 x-5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.9
|
$\$ 1750$ is invested in an account earning $13.5 \%$ interest compounded monthly for a 2 year period. What is the balance at the end of 9 years?
|
2288.98
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2288.98
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.2.18
|
Solve the equation: $-8+\frac{n}{12}=-7$
|
12
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
12
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.52
|
Evaluate the expression: $i^{251}$
|
$-i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-i
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.20
|
Solve each equation by completing the square: $m^{2}-8 m-3=6$
|
$9,-1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
9,-1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.75
|
Evaluate the expression: $\frac{3}{2}-\frac{15}{8}$
|
$-\frac{3}{8}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{3}{8}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.5.32
|
Solve the equation: $\log _{2}-8 r=1$
|
$-\frac{1}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{1}{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.3.28
|
Solve: $-8 n-19=-2(8 n-3)+3 n$
|
5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.18
|
A pitcher is 30 years old, and a vase is 22 years old. How many years ago was the pitcher twice as old as the vase?
|
14
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
14
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.35
|
Find product: $(-4)(-2)$
|
8
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
8
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.4
|
Simplify: $5+(-6-6 i)$
|
$-1-6 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-1-6 i
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.38
|
Given the points $(2,-5)$ and $(3, y)$ and a slope of 6, find the value of $y$.
|
1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.34
|
Simplify: $\frac{y x^{2} \cdot\left(y^{4}\right)^{2}}{2 y^{4}}$
|
$\frac{y^{5} x^{2}}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{y^{5} x^{2}}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.9
|
Solve: $\frac{\frac{3}{2 a-3}+2}{\frac{-6}{2 a-3}-4}$
|
$-\frac{1}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{1}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.18
|
Find a quadratic equation with the solutions $\frac{5}{3}$ and $-\frac{1}{2}$.
|
$6 x^{2}-7 x-5=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6 x^{2}-7 x-5=0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.22
|
Simplify: $-2 \sqrt{128 n}$
|
$-16 \sqrt{2 n}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-16 \sqrt{2 n}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.40
|
Find quotient: $-2 \div \frac{-3}{2}$
|
$\frac{4}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{4}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.6
|
Reduce the following radical: $\sqrt[15]{x^{9} y^{12} z^{6}}$
|
$\sqrt[5]{x^{3} y^{4} z^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[5]{x^{3} y^{4} z^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.3.21
|
Build up each fraction by finding the Least Common Denominator: $\frac{3 a}{5 b^{2}}, \frac{2}{10 a^{3} b}$
|
$\frac{6 a^{4}}{10 a^{3} b^{2}}, \frac{2 b}{10 a^{3} b^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{6 a^{4}}{10 a^{3} b^{2}}, \frac{2 b}{10 a^{3} b^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.1
|
Solve: $\frac{1+\frac{1}{x}}{1-\frac{1}{x^{2}}}$
|
$\frac{x}{x-1}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{x}{x-1}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.21
|
Simplify: $-7 \sqrt{64 x^{4}}$
|
$-56 x^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-56 x^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.4.7
|
Simplify the expression $x^{2}+9 x+23$ when $x=-3$.
|
5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.2.36
|
Simplify. Your answer should contain only positive expontents: $\left(\frac{\left(2 x^{-3} y^{0} z^{-1}\right)^{3} \cdot x^{-3} y^{2}}{2 x^{3}}\right)^{-2}$
|
$\frac{x^{30} z^{6}}{16 y^{4}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{x^{30} z^{6}}{16 y^{4}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.5.21
|
Evaluate the expression: $\log _{2} 64$
|
6
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.7.3
|
Find the value: $\sin 75^{\circ}$
|
0.9659
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
0.9659
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.1.12
|
Solve: $\sqrt{7 x+2}-\sqrt{3 x+6}=6$
|
46
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
46
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.6.34
|
Simplify and express with positive exponents: $\left(\frac{y^{\frac{1}{3}} y^{-2}}{\left(x^{\frac{5}{3}} y^{3}\right)^{-\frac{3}{2}}}\right)^{\frac{3}{2}}$
|
$x^{\frac{15}{4}} y^{\frac{17}{4}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x^{\frac{15}{4}} y^{\frac{17}{4}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.7.28
|
Solve the equation for $x$: $\frac{x}{x+1}-\frac{3}{x+3}=\frac{-2 x^{2}}{x^{2}+4 x+3}$
|
1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.37
|
Distribute: $-8(x-4)$
|
$-8 x+32$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-8 x+32
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.51
|
Evaluate the expression: $i^{73}$
|
$i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
i
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.52
|
Distribute: $2 x(8 x-10)$
|
$16 x^{2}-20 x$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
16 x^{2}-20 x
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.4
|
Simplify the expression: $\frac{9 m}{5 m^{2}} \cdot \frac{7}{2}$
|
$\frac{63}{10 m}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{63}{10 m}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.30
|
Evaluate the expression: $\frac{-4+2 i}{3 i}$
|
$\frac{4 i+2}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{4 i+2}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.8
|
Specify the domain of the function: $f(x)=\frac{-2}{x^{2}-3 x-4}$
|
$x \neq-1,4$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x \neq-1,4
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.5.13
|
Find the product: $(3 v-4)(5 v-2)$
|
$15 v^{2}-26 v+8$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
15 v^{2}-26 v+8
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.7.9
|
Solve the equation for $m$: $\frac{3 m}{2 m-5}-\frac{7}{3 m+1}=\frac{3}{2}$
|
-5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.26
|
Find the slope of the line through the points $(11,-2)$ and $(1,17)$.
|
$-\frac{19}{10}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{19}{10}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.10.21
|
A motorboat leaves a harbor and travels at an average speed of $18 \mathrm{mph}$ to an island. The average speed on the return trip was $12 \mathrm{mph}$. How far was the island from the harbor if the total trip took $5 \mathrm{~h}$?
|
36
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
36
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.19
|
Find the square: $(x-8)^{2}$
|
$x^{2}-16 x+64$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x^{2}-16 x+64
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.31
|
Simplify the expression: $\frac{x^{2}-12 x+32}{x^{2}-6 x-16} \cdot \frac{7 x^{2}+14 x}{7 x^{2}+21 x}$
|
$\frac{x-4}{x+3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{x-4}{x+3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.7
|
A thousand dollars is left in a bank savings account drawing $7 \%$ interest, compounded quarterly for 10 years. What is the balance at the end of that time?
|
2001.60
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2001.60
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.7
|
Specify the domain of the function: $f(x)=\sqrt{x-16}$
|
$x \geqslant 16$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x \geqslant 16
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.7.24
|
Solve the equation for $x$: $\frac{x}{x+3}-\frac{4}{x-2}=\frac{-5 x^{2}}{x^{2}+x-6}$
|
-1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.6
|
Find the principal that will amount to $\$ 1750$ if invested at $3 \%$ interest compounded quarterly for 5 years.
|
1507.08
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1507.08
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.24
|
Add or subtract the rational expressions and simplify: $\frac{3 a}{4 a-20}+\frac{9 a}{6 a-30}$
|
$\frac{9 a}{4(a-5)}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{9 a}{4(a-5)}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.2.18
|
Solve: $(x-1)^{-\frac{5}{3}}=32$
|
$\frac{9}{8}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{9}{8}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.3.24
|
Solve the following system of equations by elimination:
$3 x+7 y=-8$
$4 x+6 y=-4$
|
$(2,-2)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
(2,-2)
|
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