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.8.1.1 | $7 \sqrt{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt{245}$ | $\boxed{7 \sqrt{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.27 | $-\frac{5}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{3}{2}\left(v+\frac{3}{2}\right)=-\frac{7}{4} v-\frac{19}{6}$ | $\boxed{-\frac{5}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.8.25 | $\mathrm{P}=7, \mathrm{~S}=17 \frac{1}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | It takes Sally $10 \frac{1}{2}$ minutes longer than Patricia to clean up their dorm room. If they work together, they can clean it in 5 minutes. How long will it take each of them if they work alone? | $\boxed{\mathrm{P}=7, \mathrm{~S}=17 \frac{1}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.2 | $7.44 \times 10^{-4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Write the number in scientific notation: 0.000744 | $\boxed{7.44 \times 10^{-4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.7.5 | $6 \times 10$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The length of a rectangular lot is 4 rods greater than its width, and its area is 60 square rods. Find the dimensions of the lot. | $\boxed{6 \times 10}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.1 | $b=\frac{c}{a}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $a b=c$ for $b$. | $\boxed{b=\frac{c}{a}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.2 | No | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State if the given functions are inverses:
$g(x)=\frac{4-x}{x}$
$f(x)=\frac{4}{x}$ | $\boxed{No}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.23 | $\frac{x-3}{x+4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{x-4+\frac{9}{2 x+3}}{x+3-\frac{5}{2 x+3}}$ | $\boxed{\frac{x-3}{x+4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.10 | $-\frac{1}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{\frac{-5}{b-5}-3}{\frac{10}{b-5}+6}$ | $\boxed{-\frac{1}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.5 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $66=6(6+5 x)$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.25 | $-3+11 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(1+5 i)(2+i)$ | $\boxed{-3+11 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.7 | $25 n^{2}-64$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(5 n-8)(5 n+8)$ | $\boxed{25 n^{2}-64}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.2 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $4-(-1)$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.3.17 | -40 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $[6 \cdot 2+2-(-6)]\left(-5+\left|\frac{-18}{6}\right|\right)$ | $\boxed{-40}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.55 | $\frac{2}{7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{3}{7}-\frac{1}{7}$ | $\boxed{\frac{2}{7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.54 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $i^{68}$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.8.20 | $6.608 \mathrm{mi} / \mathrm{hr}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A chair lift at the Divide ski resort in Cold Springs, WY is 4806 feet long and takes 9 minutes. What is the average speed in miles per hour? How many feet per second does the lift travel? | $\boxed{6.608 \mathrm{mi} / \mathrm{hr}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.26 | $\frac{5 x+1}{(x-5)(x+2)}, \frac{4 x+8}{(x-5)(x+2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{5 x+1}{x^{2}-3 x-10}, \frac{4}{x-5}$ | $\boxed{\frac{5 x+1}{(x-5)(x+2)}, \frac{4 x+8}{(x-5)(x+2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.27 | $\frac{x-3}{(x+3)(x+1)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{x}{x^{2}+5 x+6}-\frac{2}{x^{2}+3 x+2}$ | $\boxed{\frac{x-3}{(x+3)(x+1)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.37 | $-\frac{621}{10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\log _{5}(-10 x+4)=4$ | $\boxed{-\frac{621}{10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.37 | $-18 m^{2} n p^{2} \sqrt[3]{2 m^{2} p}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $6 \sqrt[3]{-54 m^{8} n^{3} p^{7}}$ | $\boxed{-18 m^{2} n p^{2} \sqrt[3]{2 m^{2} p}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.34 | $\frac{2 x+7}{x^{2}+5 x+6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{x-1}{x^{2}+3 x+2}+\frac{x+5}{x^{2}+4 x+3}$ | $\boxed{\frac{2 x+7}{x^{2}+5 x+6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.33 | $\frac{1}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $4^{3 k-3} \cdot 4^{2-2 k}=16^{-k}$ | $\boxed{\frac{1}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.32 | $\frac{2 \sqrt{5 n}}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\sqrt{8 n^{2}}}{\sqrt{10 n}}$ | $\boxed{\frac{2 \sqrt{5 n}}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.10 | $13-8 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(5-4 i)+(8-4 i)$ | $\boxed{13-8 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.16 | 2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x+2}{3 x-1}-\frac{1}{x}=\frac{3 x-3}{3 x^{2}-x}$ | $\boxed{2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.37 | $p^{2}+4 p-1+\frac{4}{9 p+9}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{9 p^{3}+45 p^{2}+27 p-5}{9 p+9}$ | $\boxed{p^{2}+4 p-1+\frac{4}{9 p+9}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.28 | $-\frac{2 x}{x^{2}+1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{\frac{x-1}{x+1}-\frac{x+1}{x-1}}{\frac{x-1}{x+1}+\frac{x+1}{x-1}}$ | $\boxed{-\frac{2 x}{x^{2}+1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.6 | $6 a^{2} \sqrt[3]{5 a}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Multiply and simplify: $3 \sqrt[3]{4 a^{4}} \cdot \sqrt[3]{10 a^{3}}$ | $\boxed{6 a^{2} \sqrt[3]{5 a}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.56 | $3,-\frac{3}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $10 v^{2}-15 v=27+4 v^{2}-6 v$ | $\boxed{3,-\frac{3}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.29 | $k+5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine Like Terms: $k-2+7$ | $\boxed{k+5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.11 | 2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Write the number in standard notation: $2 \times 10^{0}$ | $\boxed{2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.35 | -5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(-8, y)$ and $(-1,1)$ and a slope of $\frac{6}{7}$, find the value of $y$. | $\boxed{-5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.30 | 16,32 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Chelsea's age is double Daniel's age. Eight years ago the sum of their ages was 32 . How old are they now? | $\boxed{16,32}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.15 | $9,11,13$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70. | $\boxed{9,11,13}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.21 | 0,5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x-2}{x+3}-\frac{1}{x-2}=\frac{1}{x^{2}+x-6}$ | $\boxed{0,5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.10.1 | $1 \frac{1}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A is 60 miles from B. An automobile at A starts for B at the rate of 20 miles an hour at the same time that an automobile at B starts for A at the rate of 25 miles an hour. How long will it be before the automobiles meet? | $\boxed{1 \frac{1}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.23 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-4 n+11=2(1-8 n)+3 n$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.20 | $\sqrt[10]{4 a^{9} b^{9}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine the following radicals: $\sqrt{a b} \sqrt[5]{2 a^{2} b^{2}}$ | $\boxed{\sqrt[10]{4 a^{9} b^{9}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.1 | $\frac{7}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{42}{12}$ | $\boxed{\frac{7}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.27 | $-\frac{1}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(7,-14)$ and $(-8,-9)$. | $\boxed{-\frac{1}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.14 | $-\frac{5}{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $27^{-2 n-1}=9$ | $\boxed{-\frac{5}{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.34 | $8.404 \times 10^{1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\frac{9.58 \times 10^{-2}}{1.14 \times 10^{-3}}$ | $\boxed{8.404 \times 10^{1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.27 | $16 x^{2}-3=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $\pm \frac{\sqrt{3}}{4}$. | $\boxed{16 x^{2}-3=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.29 | 8,4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The sum of the ages of two ships is 12 years. Two years ago, the age of the older ship was three times the age of the newer ship. Find the present age of each ship. | $\boxed{8,4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.50 | $\frac{3+2 i \sqrt{2}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{6+\sqrt{-32}}{4}$ | $\boxed{\frac{3+2 i \sqrt{2}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.27 | $-2 x y \sqrt[3]{4 x y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt[3]{-32 x^{4} y^{4}}$ | $\boxed{-2 x y \sqrt[3]{4 x y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.9 | $\frac{2}{9 y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\frac{2 x^{-3} y^{2}}{3 x^{-3} y^{3} \cdot 3 x^{0}}$ | $\boxed{\frac{2}{9 y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.10 | $\frac{3}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{3}{2}-\frac{7}{4} v=-\frac{9}{8}$ | $\boxed{\frac{3}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.32 | $-8 y^{2} \sqrt[3]{7 x^{2} y^{2}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-4 \sqrt[3]{56 x^{2} y^{8}}$ | $\boxed{-8 y^{2} \sqrt[3]{7 x^{2} y^{2}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.42 | $6 b^{2}+b+9+\frac{3}{4 b-7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{24 b^{3}-38 b^{2}+29 b-60}{4 b-7}$ | $\boxed{6 b^{2}+b+9+\frac{3}{4 b-7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.18 | $2 x \sqrt[6]{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt[6]{256 x^{6}}$ | $\boxed{2 x \sqrt[6]{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.2 | $(2,4)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$-7 x+y=-10$
$-9 x-y=-22$ | $\boxed{(2,4)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.21 | $\frac{1}{8 m^{4} n^{7}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\frac{2 n m^{4}}{\left(2 m^{2} n^{2}\right)^{4}}$ | $\boxed{\frac{1}{8 m^{4} n^{7}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.24 | 9 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $8-(-1)$ | $\boxed{9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.45 | $\frac{7+i \sqrt{139}}{2}, \frac{7-i \sqrt{139}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $k^{2}-7 k+50=3$ | $\boxed{\frac{7+i \sqrt{139}}{2}, \frac{7-i \sqrt{139}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.2 | $\mathrm{h}=\mathrm{gi}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $\mathrm{g}=\frac{h}{i}$ for $\mathrm{h}$. | $\boxed{\mathrm{h}=\mathrm{gi}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.6 | $6 \sqrt{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt{72}$ | $\boxed{6 \sqrt{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.30 | $a \sqrt[10]{a b^{7}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine the following radicals: $\sqrt[5]{a^{3} b} \sqrt{a b}$ | $\boxed{a \sqrt[10]{a b^{7}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.33 | 14 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $10=x-4$ | $\boxed{14}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.26 | $12 v^{3}+3 v+3$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate $\left(6 v+8 v^{3}\right)+\left(3+4 v^{3}-3 v\right)$. | $\boxed{12 v^{3}+3 v+3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.17 | $-3 \sqrt{6}-\sqrt{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-3 \sqrt{6}-3 \sqrt{6}-\sqrt{3}+3 \sqrt{6}$ | $\boxed{-3 \sqrt{6}-\sqrt{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.18 | $(x-3)^{2}(x+3)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the Least Common Denominator: $x^{2}-9, x^{2}-6 x+9$ | $\boxed{(x-3)^{2}(x+3)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.1.1 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\sqrt{2 x+3}-3=0$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.20 | 15,20 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The sum of Jason and Mandy's age is 35. Ten years ago Jason was double Mandy's age. How old are they now? | $\boxed{15,20}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.47 | $\frac{(n-1)^{2}}{6(n+1)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State the excluded values for $\frac{n^{2}-2 n+1}{6 n+6}$ | $\boxed{\frac{(n-1)^{2}}{6(n+1)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.6 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $32=2-5(-4 n+6)$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.38 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $3^{2-x} \cdot 3^{3 m}=1$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.7.24 | $25 \mathrm{ft}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A third farmer has a field that is $500 \mathrm{ft}$ by $550 \mathrm{ft}$. He wants to increase his field by $20 \%$. How wide a ring should he cultivate around the outside of his field? | $\boxed{25 \mathrm{ft}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.31 | 75,25 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A caterer made an ice cream punch by combining fruit juice that cost $\$ 2.25$ per gallon with ice cream that costs $\$ 3.25$ per gallon. How many gallons of each were used to make 100 gal of punch costing $\$ 2.50$ per pound? | $\boxed{75,25}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.26 | $8 u^{18} v^{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(u^{2} v^{2} \cdot 2 u^{4}\right)^{3}$ | $\boxed{8 u^{18} v^{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.9.8 | $(16,3),(-6,-8)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$x y=48$
$(x-6)(y+3)=60$ | $\boxed{(16,3),(-6,-8)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.30 | $(1,2)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$-7 x+10 y=13$
$4 x+9 y=22$ | $\boxed{(1,2)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.44 | $\frac{-1+2 i \sqrt{6}}{2}, \frac{-1-2 i \sqrt{6}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $4 x^{2}+4 x+25=0$ | $\boxed{\frac{-1+2 i \sqrt{6}}{2}, \frac{-1-2 i \sqrt{6}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.39 | $8 n^{2}+72 n$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Distribute: $8 n(n+9)$ | $\boxed{8 n^{2}+72 n}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.12 | All real numbers | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-3 n-27=-27-3 n$ | $\boxed{All real numbers}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.1 | 2666.7 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A tank contains 8000 liters of a solution that is $40 \%$ acid. How much water should be added to make a solution that is $30 \%$ acid? | $\boxed{2666.7}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.2 | $5 \sqrt[3]{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt[3]{375}$ | $\boxed{5 \sqrt[3]{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.9 | -2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $2 b+\frac{9}{5}=-\frac{11}{5}$ | $\boxed{-2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.18 | $L=S-2 B$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $S=L+2 B$ for $\mathrm{L}$. | $\boxed{L=S-2 B}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.25 | $2.887 \times 10^{-6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\left(7.8 \times 10^{-2}\right)^{5}$ | $\boxed{2.887 \times 10^{-6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.5.40 | $\$ 3000 @ 11 \%$; $\$ 24000 @ 7 \%$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | An investment portfolio earned $\$ 2010$ in interest last year. If $\$ 3000$ was invested at a certain rate of return and $\$ 24000$ was invested in a fund with a rate that was $4 \%$ lower, find the two rates of interest. | $\boxed{\$ 3000 @ 11 \%$; $\$ 24000 @ 7 \%}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.34 | $\frac{2 x-1}{2 x+1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{4-4 x^{-1}+x^{-2}}{4-x^{-2}}$ | $\boxed{\frac{2 x-1}{2 x+1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.19 | $80-10 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(-7-4 i)(-8+6 i)$ | $\boxed{80-10 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.7.16 | 1 in | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A picture 10 inches long by 8 inches wide has a frame whose area is one half the area of the picture. What are the outside dimensions of the frame? | $\boxed{1 in}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.5 | $x=\frac{a}{3 b}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $3 x=\frac{a}{b}$ for $x$. | $\boxed{x=\frac{a}{3 b}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.2.34 | -13 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-80=4 x-28$ | $\boxed{-13}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.58 | $-19-90 a$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-9-10(1+9 a)$ | $\boxed{-19-90 a}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.62 | $\frac{3}{7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{12}{7}-\frac{9}{7}$ | $\boxed{\frac{3}{7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.26 | $\frac{1}{9}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{n-9}{9 n-81}$ | $\boxed{\frac{1}{9}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.10.13 | 56,76 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Two drivers are testing the same model car at speeds that differ by $20 \mathrm{~km} / \mathrm{hr}$. The one driving at the slower rate drives 70 kilometers down a speedway and returns by the same route. The one driving at the faster rate drives 76 kilometers down the speedway and returns by the same route. Both drivers leave at the same time, and the faster car returns $\frac{1}{2}$ hour earlier than the slower car. At what rates were the cars driven? | $\boxed{56,76}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.8 | $\frac{289}{4} ;\left(p-\frac{17}{2}\right)^{2}$ | 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: $p^{2}-17 p+$ | $\boxed{\frac{289}{4} ;\left(p-\frac{17}{2}\right)^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.19 | -3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-32-24 v=34-2 v$ | $\boxed{-3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.13 | 40 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(-5 i)(8 i)$ | $\boxed{40}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.34 | 20 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | How many pounds of coffee that is $40 \%$ java beans must be mixed with $80 \mathrm{lb}$ of coffee that is $30 \%$ java beans to make a coffee blend that is $32 \%$ java beans? | $\boxed{20}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.9 | $3^{12}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(3^{3}\right)^{4}$ | $\boxed{3^{12}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.26 | $(-3,0)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$-4 x-5 y=12$
$-10 x+6 y=30$ | $\boxed{(-3,0)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.18 | $36,36,108$ | 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. | $\boxed{36,36,108}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.37 | $\frac{5 \sqrt[4]{10 r^{2}}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{5 \sqrt[4]{5 r^{4}}}{\sqrt[4]{8 r^{2}}}$ | $\boxed{\frac{5 \sqrt[4]{10 r^{2}}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.13 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate using the given values: $q-p-(q-1-3)$; $p=3, q=6$ | $\boxed{1}$ |
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