data_source stringclasses 9 values | question_number stringlengths 14 17 | answer stringlengths 1 993 | license stringclasses 8 values | data_topic stringclasses 7 values | problem stringlengths 14 1.32k | solution stringlengths 11 1k |
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college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.7 | $\sqrt[4]{x^{2} y^{3}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Reduce the following radical: $\sqrt[12]{x^{6} y^{9}}$ | $\boxed{\sqrt[4]{x^{2} y^{3}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.40 | $\frac{2}{r+s}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{2 r}{r^{2}-s^{2}}+\frac{1}{r+s}-\frac{1}{r-s}$ | $\boxed{\frac{2}{r+s}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.8 | $-3,9$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $|3-x|=6$ | $\boxed{-3,9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.82 | $-n^{2}+6$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(3-7 n^{2}\right)+\left(6 n^{2}+3\right)$ | $\boxed{-n^{2}+6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.7 | $\frac{5}{24 r}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{5}{6 r}-\frac{5}{8 r}$ | $\boxed{\frac{5}{24 r}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.10.4 | 55 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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? | $\boxed{55}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.33 | $x \sqrt[12]{59049 x y^{11} z^{10}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine the following radicals: $\sqrt[3]{3 x y^{2} z} \sqrt[4]{9 x^{3} y z^{2}}$ | $\boxed{x \sqrt[12]{59049 x y^{11} z^{10}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.33 | $-2,10$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $(x-3)^{2}-2(x-3)=35$ | $\boxed{-2,10}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.17 | $v=\frac{69}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{v-5}{v+6}=\frac{4}{9}$ | $\boxed{v=\frac{69}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.40 | $9 a^{2}-64$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(3 a-8)(3 a+8)$ | $\boxed{9 a^{2}-64}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.22 | $20 a^{2} \sqrt[3]{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $4 \sqrt[3]{250 a^{6}}$ | $\boxed{20 a^{2} \sqrt[3]{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.5.5 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of a line parallel to the given line: $x-y=4$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.10 | 6386.12 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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? | $\boxed{6386.12}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.33 | $\frac{9}{v-10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{9 v+54}{v^{2}-4 v-60}$ | $\boxed{\frac{9}{v-10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.18 | $v^{2}+8 v+16$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(v+4)^{2}$ | $\boxed{v^{2}+8 v+16}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.11 | $n+8-\frac{8}{n+5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{n^{2}+13 n+32}{n+5}$ | $\boxed{n+8-\frac{8}{n+5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.67 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\left(-\frac{1}{2}\right)+\frac{3}{2}$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.16 | $\frac{a+10}{a-6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{1}{a-6} \cdot \frac{8 a+80}{8}$ | $\boxed{\frac{a+10}{a-6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.8 | $\frac{1}{5},-\frac{3}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $(5 x+1)^{4}=16$ | $\boxed{\frac{1}{5},-\frac{3}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.3 | $324 ;(m-18)^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the value that completes the square and then rewrite as a perfect square: $m^{2}-36 m+$ | $\boxed{324 ;(m-18)^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.17 | 0 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{16}{9}=-\frac{4}{3}\left(-\frac{4}{3} n-\frac{4}{3}\right)$ | $\boxed{0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.5.1 | 2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of a line parallel to the given line: $y=2 x+4$ | $\boxed{2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.1 | $(-2,4)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$4 x+2 y=0$
$-4 x-9 y=-28$ | $\boxed{(-2,4)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.23 | No solution : $\oslash$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the compound inequality and give interval notation: $-5 b+10 \leqslant 30$ and $7 b+2 \leqslant-40$ | $\boxed{No solution : $\oslash}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.23 | $8 \sqrt{6}-9 \sqrt{3}+4 \sqrt{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $3 \sqrt{24}-3 \sqrt{27}+2 \sqrt{6}+2 \sqrt{8}$ | $\boxed{8 \sqrt{6}-9 \sqrt{3}+4 \sqrt{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.24 | 2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\sqrt{12}}{\sqrt{3}}$ | $\boxed{2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.33 | $2 \sqrt[4]{2}+\sqrt[4]{3}+6 \sqrt[4]{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $2 \sqrt[4]{2}+2 \sqrt[4]{3}+3 \sqrt[4]{64}-\sqrt[4]{3}$ | $\boxed{2 \sqrt[4]{2}+\sqrt[4]{3}+6 \sqrt[4]{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.21 | $m^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{3 n m^{2}}{3 n}$ | $\boxed{m^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.9 | $\frac{r-6}{r+10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{7 r}{7 r(r+10)} \div \frac{r-6}{(r-6)^{2}}$ | $\boxed{\frac{r-6}{r+10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.10 | $4+2 \sqrt{7}, 4-2 \sqrt{7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve each equation by completing the square: $n^{2}-8 n-12=0$ | $\boxed{4+2 \sqrt{7}, 4-2 \sqrt{7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.66 | $-42 b-45-4 b^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $9(6 b+5)-4 b(b+3)$ | $\boxed{-42 b-45-4 b^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.15 | $\frac{11}{2},-\frac{5}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $(2 x-3)^{\frac{2}{3}}=4$ | $\boxed{\frac{11}{2},-\frac{5}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.3.3 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $3+(8) \div|4|$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.18 | $\frac{7}{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{126}{108}$ | $\boxed{\frac{7}{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.5 | $6,-\frac{29}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $|5+8 a|=53$ | $\boxed{6,-\frac{29}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.45 | $\sqrt[15]{(2 x+1)^{4}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the following expression: $\frac{\sqrt[3]{(2 x+1)^{2}}}{\sqrt[5]{(2 x+1)^{2}}}$ | $\boxed{\sqrt[15]{(2 x+1)^{4}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.27 | $\frac{m^{\frac{35}{8}}}{n^{\frac{7}{6}}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\left(\frac{m^{\frac{3}{2}} n^{-2}}{\left(m n^{\frac{4}{3}}\right)^{-1}}\right)^{\frac{7}{4}}$ | $\boxed{\frac{m^{\frac{35}{8}}}{n^{\frac{7}{6}}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.30 | $\frac{4 a^{2}}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{2 b a^{7} \cdot 2 b^{4}}{b a^{2} \cdot 3 a^{3} b^{4}}$ | $\boxed{\frac{4 a^{2}}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.8.3 | $0.0112 \mathrm{~g}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Convert $11.2 \mathrm{mg}$ to grams. | $\boxed{0.0112 \mathrm{~g}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.32 | $m>4$ or $m \leqslant-1:(-\infty,-1] \cup(4, \infty)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the compound inequality and give interval notation: $-9 m+2<-10-6 m$ or $-m+5 \geqslant 10+4 m$ | $\boxed{m>4$ or $m \leqslant-1:(-\infty,-1] \cup(4, \infty)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.1 | $n \leqslant-9$ or $n \geqslant 2:(-\infty,-9] \cup[2, \infty)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the compound inequality and give interval notation: $\frac{n}{3} \leqslant-3$ or $-5 n \leqslant-10$ | $\boxed{n \leqslant-9$ or $n \geqslant 2:(-\infty,-9] \cup[2, \infty)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.2 | $x^{2}-9 x+18=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions 3 and 6. | $\boxed{x^{2}-9 x+18=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.24 | -9 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $m-4=-13$ | $\boxed{-9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.5 | 23 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate using the given values: $c^{2}-(a-1)$; $a=3$ and $c=5$ | $\boxed{23}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.30 | $\frac{5+i \sqrt{105}}{5}, \frac{5-i \sqrt{105}}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $5 x^{2}=-26+10 x$ | $\boxed{\frac{5+i \sqrt{105}}{5}, \frac{5-i \sqrt{105}}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.21 | $33.3 \mathrm{~cm}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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 $5 \mathrm{~kg}$ ? | $\boxed{33.3 \mathrm{~cm}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.12 | 8 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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? | $\boxed{8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.29 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-a-5(8 a-1)=39-7 a$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.22 | $28,84,68$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Let the first angle of a triangle be $x$ degrees. Find the measures of the second and third angles. | $\boxed{28,84,68}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.34 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(-2,y)$ and $(2,4)$ and a slope of $\frac{1}{4}$, find the value of $y$. | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.76 | $-\frac{2}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $(-1)-\left(-\frac{1}{3}\right)$ | $\boxed{-\frac{2}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.25 | $2 \sqrt[3]{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-2 \sqrt[3]{16}+2 \sqrt[3]{16}+2 \sqrt[3]{2}$ | $\boxed{2 \sqrt[3]{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.24 | $\frac{n-9}{n+7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{2 n^{2}-12 n-54}{n+7} \div(2 n+6)$ | $\boxed{\frac{n-9}{n+7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.38 | $40 x^{2}-10 x-5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $5(2 x-1)(4 x+1)$ | $\boxed{40 x^{2}-10 x-5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.9 | 2288.98 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | $\$ 1750$ 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? | $\boxed{2288.98}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.2.18 | 12 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-8+\frac{n}{12}=-7$ | $\boxed{12}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.52 | $-i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $i^{251}$ | $\boxed{-i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.20 | $9,-1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve each equation by completing the square: $m^{2}-8 m-3=6$ | $\boxed{9,-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.75 | $-\frac{3}{8}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{3}{2}-\frac{15}{8}$ | $\boxed{-\frac{3}{8}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.32 | $-\frac{1}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\log _{2}-8 r=1$ | $\boxed{-\frac{1}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.28 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-8 n-19=-2(8 n-3)+3 n$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.18 | 14 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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? | $\boxed{14}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.35 | 8 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(-4)(-2)$ | $\boxed{8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.4 | $-1-6 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $5+(-6-6 i)$ | $\boxed{-1-6 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.38 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(2,-5)$ and $(3, y)$ and a slope of 6, find the value of $y$. | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.34 | $\frac{y^{5} x^{2}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{y x^{2} \cdot\left(y^{4}\right)^{2}}{2 y^{4}}$ | $\boxed{\frac{y^{5} x^{2}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.9 | $-\frac{1}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{\frac{3}{2 a-3}+2}{\frac{-6}{2 a-3}-4}$ | $\boxed{-\frac{1}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.18 | $6 x^{2}-7 x-5=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $\frac{5}{3}$ and $-\frac{1}{2}$. | $\boxed{6 x^{2}-7 x-5=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.22 | $-16 \sqrt{2 n}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-2 \sqrt{128 n}$ | $\boxed{-16 \sqrt{2 n}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.40 | $\frac{4}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $-2 \div \frac{-3}{2}$ | $\boxed{\frac{4}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.6 | $\sqrt[5]{x^{3} y^{4} z^{2}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Reduce the following radical: $\sqrt[15]{x^{9} y^{12} z^{6}}$ | $\boxed{\sqrt[5]{x^{3} y^{4} z^{2}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.21 | $\frac{6 a^{4}}{10 a^{3} b^{2}}, \frac{2 b}{10 a^{3} b^{2}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{3 a}{5 b^{2}}, \frac{2}{10 a^{3} b}$ | $\boxed{\frac{6 a^{4}}{10 a^{3} b^{2}}, \frac{2 b}{10 a^{3} b^{2}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.1 | $\frac{x}{x-1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{1+\frac{1}{x}}{1-\frac{1}{x^{2}}}$ | $\boxed{\frac{x}{x-1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.21 | $-56 x^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-7 \sqrt{64 x^{4}}$ | $\boxed{-56 x^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.7 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression $x^{2}+9 x+23$ when $x=-3$. | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.36 | $\frac{x^{30} z^{6}}{16 y^{4}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\left(\frac{\left(2 x^{-3} y^{0} z^{-1}\right)^{3} \cdot x^{-3} y^{2}}{2 x^{3}}\right)^{-2}$ | $\boxed{\frac{x^{30} z^{6}}{16 y^{4}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.21 | 6 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\log _{2} 64$ | $\boxed{6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.7.3 | 0.9659 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the value: $\sin 75^{\circ}$ | $\boxed{0.9659}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.1.12 | 46 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\sqrt{7 x+2}-\sqrt{3 x+6}=6$ | $\boxed{46}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.34 | $x^{\frac{15}{4}} y^{\frac{17}{4}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\left(\frac{y^{\frac{1}{3}} y^{-2}}{\left(x^{\frac{5}{3}} y^{3}\right)^{-\frac{3}{2}}}\right)^{\frac{3}{2}}$ | $\boxed{x^{\frac{15}{4}} y^{\frac{17}{4}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.28 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x}{x+1}-\frac{3}{x+3}=\frac{-2 x^{2}}{x^{2}+4 x+3}$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.37 | $-8 x+32$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Distribute: $-8(x-4)$ | $\boxed{-8 x+32}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.51 | $i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $i^{73}$ | $\boxed{i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.52 | $16 x^{2}-20 x$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Distribute: $2 x(8 x-10)$ | $\boxed{16 x^{2}-20 x}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.4 | $\frac{63}{10 m}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{9 m}{5 m^{2}} \cdot \frac{7}{2}$ | $\boxed{\frac{63}{10 m}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.30 | $\frac{4 i+2}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{-4+2 i}{3 i}$ | $\boxed{\frac{4 i+2}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.8 | $x \neq-1,4$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Specify the domain of the function: $f(x)=\frac{-2}{x^{2}-3 x-4}$ | $\boxed{x \neq-1,4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.13 | $15 v^{2}-26 v+8$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(3 v-4)(5 v-2)$ | $\boxed{15 v^{2}-26 v+8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.9 | -5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $m$: $\frac{3 m}{2 m-5}-\frac{7}{3 m+1}=\frac{3}{2}$ | $\boxed{-5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.26 | $-\frac{19}{10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(11,-2)$ and $(1,17)$. | $\boxed{-\frac{19}{10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.10.21 | 36 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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 $5 \mathrm{~h}$? | $\boxed{36}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.19 | $x^{2}-16 x+64$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(x-8)^{2}$ | $\boxed{x^{2}-16 x+64}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.31 | $\frac{x-4}{x+3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{x^{2}-12 x+32}{x^{2}-6 x-16} \cdot \frac{7 x^{2}+14 x}{7 x^{2}+21 x}$ | $\boxed{\frac{x-4}{x+3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.7 | 2001.60 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | 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? | $\boxed{2001.60}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.7 | $x \geqslant 16$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Specify the domain of the function: $f(x)=\sqrt{x-16}$ | $\boxed{x \geqslant 16}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.24 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x}{x+3}-\frac{4}{x-2}=\frac{-5 x^{2}}{x^{2}+x-6}$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.6 | 1507.08 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the principal that will amount to $\$ 1750$ if invested at $3 \%$ interest compounded quarterly for 5 years. | $\boxed{1507.08}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.24 | $\frac{9 a}{4(a-5)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{3 a}{4 a-20}+\frac{9 a}{6 a-30}$ | $\boxed{\frac{9 a}{4(a-5)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.18 | $\frac{9}{8}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $(x-1)^{-\frac{5}{3}}=32$ | $\boxed{\frac{9}{8}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.24 | $(2,-2)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$3 x+7 y=-8$
$4 x+6 y=-4$ | $\boxed{(2,-2)}$ |
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