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.5.1.14 | $x^{3} y^{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(x y)^{3}$ | $\boxed{x^{3} y^{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.27 | $40 \mathrm{~kg}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The number of kilograms of water in a human body varies directly as the mass of the body. A 96-kg person contains $64 \mathrm{~kg}$ of water. How many kilo grams of water are in a $60-\mathrm{kg}$ person? | $\boxed{40 \mathrm{~kg}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.3 | $12 x+6$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $2(6 x+3)$ | $\boxed{12 x+6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.25 | $\frac{x^{2}-4 x}{(x-4)^{2}(x+4)}, \frac{3 x^{2}+12 x}{(x-4)^{2}(x+4)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{x}{x^{2}-16}, \frac{3 x}{x^{2}-8 x+16}$ | $\boxed{\frac{x^{2}-4 x}{(x-4)^{2}(x+4)}, \frac{3 x^{2}+12 x}{(x-4)^{2}(x+4)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.32 | $-6 x^{4}+13 x^{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate $\left(7 x^{2}+2 x^{4}+7 x^{3}\right)+\left(6 x^{3}-8 x^{4}-7 x^{2}\right)$. | $\boxed{-6 x^{4}+13 x^{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.2.27 | -9 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-2 x+4=22$ | $\boxed{-9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.38 | $2 y^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\left(2 y^{3} x^{2}\right)^{2}}{2 x^{2} y^{4} \cdot x^{2}}$ | $\boxed{2 y^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.7 | $x^{2}=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions 0 and 0. | $\boxed{x^{2}=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.13 | $\frac{-7 x-13}{4 x}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{x-1}{4 x}-\frac{2 x+3}{x}$ | $\boxed{\frac{-7 x-13}{4 x}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.6 | $-3 \sqrt{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-3 \sqrt{3}+2 \sqrt{3}-2 \sqrt{3}$ | $\boxed{-3 \sqrt{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.20 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{1}{12}=\frac{4}{3} x+\frac{5}{3}\left(x-\frac{7}{4}\right)$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.35 | $\frac{2 x-7}{5 x-7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{12 x^{2}-42 x}{30 x^{2}-42 x}$ | $\boxed{\frac{2 x-7}{5 x-7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.27 | $9 i+5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{-9+5 i}{i}$ | $\boxed{9 i+5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.33 | $\frac{u^{\frac{1}{2}}}{v^{\frac{3}{4}}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\frac{\left(u v^{2}\right)^{\frac{1}{2}}}{v^{-\frac{1}{4}} v^{2}}$ | $\boxed{\frac{u^{\frac{1}{2}}}{v^{\frac{3}{4}}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.45 | 325,950 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The cost of a private pilot course is $\$1,275$. The flight portion costs $\$625$ more than the ground school portion. What is the cost of each? | $\boxed{325,950}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.32 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{216}{6^{-2 a}}=6^{3 a}$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.2 | $\frac{5}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{25}{20}$ | $\boxed{\frac{5}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.19 | $3 n^{3}+8$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate $\left(5 n^{4}+6 n^{3}\right)+\left(8-3 n^{3}-5 n^{4}\right)$. | $\boxed{3 n^{3}+8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.31 | $15 k^{4}+24 k^{3}+48 k^{2}+27 k+18$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $\left(5 k^{2}+3 k+3\right)\left(3 k^{2}+3 k+6\right)$ | $\boxed{15 k^{4}+24 k^{3}+48 k^{2}+27 k+18}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.36 | -2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-8(6+6 x)+4(-3+6 x)=-12$ | $\boxed{-2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.39 | $\frac{2}{9}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $\frac{-1}{9} \div \frac{-1}{2}$ | $\boxed{\frac{2}{9}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.35 | $w=\frac{V}{\ell h}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation lwh $=\mathrm{V}$ for $\mathrm{w}$. | $\boxed{w=\frac{V}{\ell h}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.36 | $\frac{5}{14}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $\left(\frac{1}{2}\right)\left(\frac{5}{7}\right)$ | $\boxed{\frac{5}{14}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.28 | $\frac{33}{56}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $\left(-\frac{3}{7}\right)\left(-\frac{11}{8}\right)$ | $\boxed{\frac{33}{56}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.20 | $\frac{1}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\log _{36} 6$ | $\boxed{\frac{1}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.9 | $\frac{3}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{27}{18}$ | $\boxed{\frac{3}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.11 | $7,-\frac{29}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $|8+6 m|=50$ | $\boxed{7,-\frac{29}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.3.16 | 28 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-4-\left[2+4(-6)-4-\left|2^{2}-5 \cdot 2\right|\right]$ | $\boxed{28}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.17 | 40,20 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A farmer has some cream which is $21 \%$ butterfat and some which is $15 \%$ butter fat. How many gallons of each must be mixed to produce 60 gallons of cream which is $19 \%$ butterfat? | $\boxed{40,20}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.50 | $\frac{1+i \sqrt{163}}{2}, \frac{1-i \sqrt{163}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $n^{2}-n=-41$ | $\boxed{\frac{1+i \sqrt{163}}{2}, \frac{1-i \sqrt{163}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.23 | $\frac{1}{20}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\sqrt{5}}{4 \sqrt{125}}$ | $\boxed{\frac{1}{20}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.8.11 | $0.0072 \mathrm{yd}^{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Convert $5,500 \mathrm{~cm}^{3}$ to cubic yards. | $\boxed{0.0072 \mathrm{yd}^{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.29 | $48 n^{4}-16 n^{3}+64 n^{2}-6 n+36$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $\left(8 n^{2}+4 n+6\right)\left(6 n^{2}-5 n+6\right)$ | $\boxed{48 n^{4}-16 n^{3}+64 n^{2}-6 n+36}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.38 | $\frac{20}{21}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $\frac{-12}{7} \div \frac{-9}{5}$ | $\boxed{\frac{20}{21}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.29 | $k \geqslant 2$ or $k<-20:(-\infty,-20) \cup[2, \infty)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the compound inequality and give interval notation: $1+5 k \leqslant 7 k-3$ or $k-10>2 k+10$ | $\boxed{k \geqslant 2$ or $k<-20:(-\infty,-20) \cup[2, \infty)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.16 | $x(x-7)(x+1)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the Least Common Denominator: $x, x-7, x+1$ | $\boxed{x(x-7)(x+1)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.31 | $24 y \sqrt{5 x}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $6 \sqrt{80 x y^{2}}$ | $\boxed{24 y \sqrt{5 x}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.8.7 | $0.435 \mathrm{~km}^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Convert $435,000 \mathrm{~m}^{2}$ to sqaure kilometers. | $\boxed{0.435 \mathrm{~km}^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.14 | $3 x+2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{\frac{x}{3 x-2}}{\frac{x}{9 x^{2}-4}}$ | $\boxed{3 x+2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.10 | $b^{2}-49$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(b-7)(b+7)$ | $\boxed{b^{2}-49}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.28 | $g^{-1}(x)=-3 x+2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the inverse of the function: $g(x)=\frac{-x+2}{3}$ | $\boxed{g^{-1}(x)=-3 x+2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.11 | 48 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(6 i)(-8 i)$ | $\boxed{48}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.44 | $-2 n-2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-2(n+1)$ | $\boxed{-2 n-2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.34 | 60,180 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Harry and his sister collected $240$ stamps in total. Harry collected $3$ times as many stamps as his sister. How many stamps did each of them collect? | $\boxed{60,180}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.13 | $1.4 \times 10^{-3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\left(7 \times 10^{-1}\right)\left(2 \times 10^{-3}\right)$ | $\boxed{1.4 \times 10^{-3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.5 | No solution | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$-6 x+9 y=3$
$6 x-9 y=-9$ | $\boxed{No solution}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.29 | $Q_{2}=\frac{Q_{1}+\mathrm{PQ}_{1}}{P}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $Q_{1}=P\left(Q_{2}-Q_{1}\right)$ for $Q_{2}$. | $\boxed{Q_{2}=\frac{Q_{1}+\mathrm{PQ}_{1}}{P}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.8 | $\frac{m^{2}}{3}+2 m+3$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{3 m^{4}+18 m^{3}+27 m^{2}}{9 m^{2}}$ | $\boxed{\frac{m^{2}}{3}+2 m+3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.16 | $9 x^{2}-20 x+4=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions 2 and $\frac{2}{9}$. | $\boxed{9 x^{2}-20 x+4=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.8.1 | $29^{\circ}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the angle measure to the nearest degree given $\sin Z=0.4848$ | $\boxed{29^{\circ}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.25 | $\frac{2}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x}{x-1}-\frac{2}{x+1}=\frac{4 x^{2}}{x^{2}-1}$ | $\boxed{\frac{2}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.33 | $1.715 \times 10^{14}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\left(1.8 \times 10^{-5}\right)^{-3}$ | $\boxed{1.715 \times 10^{14}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.1 | $-48 \sqrt{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Multiply and simplify: $3 \sqrt{5} \cdot-4 \sqrt{16}$ | $\boxed{-48 \sqrt{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.40 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(6,2)$ and $(x, 6)$ and a slope of $-\frac{4}{5}$, find the value of $x$. | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.24 | No Solution | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $(3-2 x)^{\frac{4}{3}}=-81$ | $\boxed{No Solution}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.44 | $\frac{3(x-2)}{4(x+2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{x^{2}+3 x-10}{x^{2}+6 x+5} \cdot \frac{2 x^{2}-x-3}{2 x^{2}+x-6} \div \frac{8 x+20}{6 x+15}$ | $\boxed{\frac{3(x-2)}{4(x+2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.25 | 37,46 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Brandon is 9 years older than Ronda. In four years the sum of their ages will be 91 . How old are they now? | $\boxed{37,46}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.36 | 3,2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A tea that is $20 \%$ jasmine is blended with a tea that is $15 \%$ jasmine. How many pounds of each tea are used to make $5 \mathrm{lb}$ of tea that is $18 \%$ jasmine? | $\boxed{3,2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.28 | -32 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given $k(x)=-2 \cdot 4^{2 x-2}$, find $k(2)$ | $\boxed{-32}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.22 | $49 k^{2}-98 k+49$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(7 k-7)^{2}$ | $\boxed{49 k^{2}-98 k+49}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.6 | $-\frac{5}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $625^{-n-2}=\frac{1}{125}$ | $\boxed{-\frac{5}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.8 | $\frac{4}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{36}{27}$ | $\boxed{\frac{4}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.23 | Undefined | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(-5,-10)$ and $(-5,20)$. | $\boxed{Undefined}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.41 | $2 x^{4}-x^{3}-4 x+2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate $\left(8 x^{4}+2 x^{3}+2 x\right)+\left(2 x+2-2 x^{3}-x^{4}\right)-\left(x^{3}+5 x^{4}+8 x\right)$. | $\boxed{2 x^{4}-x^{3}-4 x+2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.39 | $\frac{5+i \sqrt{130}}{5}, \frac{5-i \sqrt{130}}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $5 x^{2}+5 x=-31-5 x$ | $\boxed{\frac{5+i \sqrt{130}}{5}, \frac{5-i \sqrt{130}}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.25 | $4 x^{10} y^{14}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(x^{3} y^{4} \cdot 2 x^{2} y^{3}\right)^{2}$ | $\boxed{4 x^{10} y^{14}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.42 | $\frac{5 x+5}{x^{2}+2 x-15}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{x+2}{x^{2}-4 x+3}+\frac{4 x+5}{x^{2}+4 x-5}$ | $\boxed{\frac{5 x+5}{x^{2}+2 x-15}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.36 | $-\frac{1}{11}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\log _{11}(10 v+1)=-1$ | $\boxed{-\frac{1}{11}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.42 | $\frac{9 r}{5(r+1)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State the excluded values for $\frac{56 x-48}{24 x^{2}+56 x+32}$ | $\boxed{\frac{9 r}{5(r+1)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.22 | $\frac{3 x^{2}+6 x}{(x-4)(x+2)}, \frac{2 x-8}{(x-4)(x+2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{3 x}{x-4}, \frac{2}{x+2}$ | $\boxed{\frac{3 x^{2}+6 x}{(x-4)(x+2)}, \frac{2 x-8}{(x-4)(x+2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.1 | $x^{2}-7 x+10=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions 2 and 5. | $\boxed{x^{2}-7 x+10=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.25 | $-5+2 i,-5-2 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $x^{2}=-10 x-29$ | $\boxed{-5+2 i,-5-2 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.34 | $x^{2}+4 x+20=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $-2 \pm 4 i$. | $\boxed{x^{2}+4 x+20=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.10 | $x^{2}-2 x-3=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions 3 and $-1$. | $\boxed{x^{2}-2 x-3=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.41 | $\sqrt[10]{a b^{9} c^{7}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the following expression: $\frac{\sqrt{a b^{3} c}}{\sqrt[5]{a^{2} b^{3} c^{-1}}}$ | $\boxed{\sqrt[10]{a b^{9} c^{7}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.15 | $f^{-1}(x)=\frac{-2 x-2}{x+2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the inverse of the function: $f(x)=\frac{-2 x-2}{x+2}$ | $\boxed{f^{-1}(x)=\frac{-2 x-2}{x+2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.35 | $x^{2}-12 x+39=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $6 \pm i \sqrt{3}$. | $\boxed{x^{2}-12 x+39=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.29 | $-\frac{2}{y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{\frac{y}{y+2}-\frac{y}{y-2}}{\frac{y}{y+2}+\frac{y}{y-2}}$ | $\boxed{-\frac{2}{y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.3 | -4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $6x - 18 = -42$ | $\boxed{-4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.8.14 | $104.32 \mathrm{mi} / \mathrm{hr}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Convert $153 \mathrm{ft} / \mathrm{s}$ (feet per second) to miles per hour. | $\boxed{104.32 \mathrm{mi} / \mathrm{hr}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.45 | -24 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(4)(-6)$ | $\boxed{-24}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.4 | $18 n^{3}+21 n^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $3 n^{2}(6 n+7)$ | $\boxed{18 n^{3}+21 n^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.6 | $\pm 3, \pm 1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $b^{4}-10 b^{2}+9=0$ | $\boxed{\pm 3, \pm 1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.23 | $241,920,000$ cans | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The number of aluminum cans used each year varies directly as the number of people using the cans. If 250 people use 60,000 cans in one year, how many cans are used each year in Dallas, which has a population of $1,008,000$ ? | $\boxed{241,920,000$ cans}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.17 | $a^{2}+10 a+25$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(a+5)^{2}$ | $\boxed{a^{2}+10 a+25}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.44 | $3 i \sqrt{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the square root of $-45$ | $\boxed{3 i \sqrt{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.8 | $-3-6 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(-4-i)+(1-5 i)$ | $\boxed{-3-6 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.33 | $\mathrm{r}=36$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The stopping distance of a car after the brakes have been applied varies directly as the square of the speed $\mathrm{r}$. If a car, traveling $60 \mathrm{mph}$ can stop in 200 $\mathrm{ft}$, how fast can a car go and still stop in $72 \mathrm{ft}$ ? | $\boxed{\mathrm{r}=36}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.25 | 8 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-6 v-29=-4 v-5(v+1)$ | $\boxed{8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.23 | $\frac{x^{2}+4 x+4}{(x-3)(x+2)}, \frac{x^{2}-6 x+9}{(x-3)(x+2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{x+2}{x-3}, \frac{x-3}{x+2}$ | $\boxed{\frac{x^{2}+4 x+4}{(x-3)(x+2)}, \frac{x^{2}-6 x+9}{(x-3)(x+2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.14 | $-\frac{11}{2}, \frac{5}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $(2 x+3)^{\frac{4}{3}}=16$ | $\boxed{-\frac{11}{2}, \frac{5}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.6 | $\frac{5}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{30}{24}$ | $\boxed{\frac{5}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.29 | $\frac{10 i-9}{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{-10-9 i}{6 i}$ | $\boxed{\frac{10 i-9}{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.8 | $\frac{17}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $8x - 14 = 4x + 3$ | $\boxed{\frac{17}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.5.27 | $4-2 \sqrt{3}+2 \sqrt{6}-3 \sqrt{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{2+\sqrt{6}}{2+\sqrt{3}}$ | $\boxed{4-2 \sqrt{3}+2 \sqrt{6}-3 \sqrt{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.70 | $-\frac{2}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{6}{5}-\frac{8}{5}$ | $\boxed{-\frac{2}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.54 | -10 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $\frac{80}{-8}$ | $\boxed{-10}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.18 | $\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\frac{2 x^{\frac{1}{2}} y^{\frac{1}{3}}}{2 x^{\frac{4}{3}} y^{-\frac{7}{4}}}$ | $\boxed{\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.6 | $1.5 \times 10^{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Write the number in scientific notation: 15000 | $\boxed{1.5 \times 10^{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.5.26 | $\frac{1}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{a+\sqrt{\mathrm{ab}}}{\sqrt{a}+\sqrt{b}}$ | $\boxed{\frac{1}{3}}$ |
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