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college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.61 | $10-4 n$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-10-4(n-5)$ | $\boxed{10-4 n}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.9.7 | $(45,2),(-10,-9)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$x y=90$
$(x-5)(y+1)=120$ | $\boxed{(45,2),(-10,-9)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.42 | $\frac{48 i-56}{85}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{8 i}{6-7 i}$ | $\boxed{\frac{48 i-56}{85}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.9 | $35,36,37$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find three consecutive integers such that their sum is 108. | $\boxed{35,36,37}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.31 | $x^{2}-4 x-2=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $2 \pm \sqrt{6}$. | $\boxed{x^{2}-4 x-2=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.5 | all real numbers | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Specify the domain of the function: $f(x)=x^{2}-3 x-4$ | $\boxed{all real numbers}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.21 | $p^{2}+14 p+49$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(p+7)^{2}$ | $\boxed{p^{2}+14 p+49}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.36 | $\frac{k-8}{k+4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{k^{2}-12 k+32}{k^{2}-64}$ | $\boxed{\frac{k-8}{k+4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.47 | $-36 x+9 x^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Distribute: $-9 x(4-x)$ | $\boxed{-36 x+9 x^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.4 | $1.09 \times 10^{0}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Write the number in scientific notation: 1.09 | $\boxed{1.09 \times 10^{0}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.15 | $a=\frac{6}{7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{3}{10}=\frac{a}{a+2}$ | $\boxed{a=\frac{6}{7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.31 | $-1<x \leqslant 1:(-1,1]$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the compound inequality and give interval notation: $2 x+9 \geqslant 10 x+1$ and $3 x-2<7 x+2$ | $\boxed{-1<x \leqslant 1:(-1,1]}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.31 | $\frac{\sqrt{6 p}}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\sqrt{2 p^{2}}}{\sqrt{3 p}}$ | $\boxed{\frac{\sqrt{6 p}}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.28 | $3 m^{4}-2 m+6$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate $\left(7+4 m+8 m^{4}\right)-\left(5 m^{4}+1+6 m\right)$. | $\boxed{3 m^{4}-2 m+6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.10.1 | 12 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A merchant bought some pieces of silk for $\$ 900$. Had he bought 3 pieces more for the same money, he would have paid $\$ 15$ less for each piece. Find the number of pieces purchased. | $\boxed{12}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.19 | $-\frac{1}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $9^{2 n+3}=243$ | $\boxed{-\frac{1}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.5.11 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of a line perpendicular to the given line: $y=-\frac{1}{3} x$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.19 | -3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $(-8)-(-5)$ | $\boxed{-3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.11 | 0 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{3}{2}\left(\frac{7}{3} n+1\right)=\frac{3}{2}$ | $\boxed{0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.28 | 4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $7-3$ | $\boxed{4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.2.4 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $4 x^{3}-2=106$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.35 | -11 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $13 a=-143$ | $\boxed{-11}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.77 | $-\frac{5}{24}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\left(-\frac{15}{8}\right)+\frac{5}{3}$ | $\boxed{-\frac{5}{24}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.34 | $\frac{10}{9(n+6)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{n-7}{n^{2}-2 n-35} \div \frac{9 n+54}{10 n+50}$ | $\boxed{\frac{10}{9(n+6)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.43 | 14,16 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | An electrician cuts a $30$ ft piece of wire into two pieces. One piece is $2$ ft longer than the other. Find the lengths of the two pieces. | $\boxed{14,16}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.29 | $\frac{4 x}{(x-3)(x+2)}, \frac{x^{2}+4 x+4}{(x-3)(x+2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Build up each fraction by finding the Least Common Denominator: $\frac{4 x}{x^{2}-x-6}, \frac{x+2}{x-3}$ | $\boxed{\frac{4 x}{(x-3)(x+2)}, \frac{x^{2}+4 x+4}{(x-3)(x+2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.17 | 36 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate using the given values: $k \times 3^{2}-(j+k)-5$; $j=4, k=5$ | $\boxed{36}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.37 | $-48 x^{2} z^{2} y \sqrt{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-8 \sqrt{180 x^{4} y^{2} z^{4}}$ | $\boxed{-48 x^{2} z^{2} y \sqrt{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.4.18 | $(-1,2,-2)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$x+2 y-3 z=9$
$2 x-y+2 z=-8$
$3 x-y-4 z=3$ | $\boxed{(-1,2,-2)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.3 | $1-9 p^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(1+3 p)(1-3 p)$ | $\boxed{1-9 p^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.13 | $-2-4 \sqrt{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Multiply and simplify: $(2+2 \sqrt{2})(-3+\sqrt{2})$ | $\boxed{-2-4 \sqrt{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.3 | $x=\frac{\mathrm{gb}}{f}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $\frac{f}{g} x=b$ for $\mathrm{x}$. | $\boxed{x=\frac{\mathrm{gb}}{f}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.20 | $9.836 \times 10^{-1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\frac{7.2 \times 10^{-1}}{7.32 \times 10^{-1}}$ | $\boxed{9.836 \times 10^{-1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.19 | $x-3+\frac{3}{10 x-2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{10 x^{2}-32 x+9}{10 x-2}$ | $\boxed{x-3+\frac{3}{10 x-2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.12 | $-\frac{1}{3},-1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $|9 p+6|=3$ | $\boxed{-\frac{1}{3},-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.32 | $\frac{4 x+1}{(x+1)(x-2)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{4 x}{x^{2}-2 x-3}-\frac{3}{x^{2}-5 x+6}$ | $\boxed{\frac{4 x+1}{(x+1)(x-2)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.5 | 1726.16 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the principal that will amount to $\$ 2500$ if invested at $5 \%$ interest compounded semiannually for 7.5 years. | $\boxed{1726.16}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.3.2.18 | 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: $1 \leqslant \frac{p}{8} \leqslant 0$ | $\boxed{No solution : $\oslash}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.25 | $\frac{3 y^{\frac{1}{12}}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\frac{3 y^{-\frac{5}{4}}}{y^{-1} \cdot 2 y^{-\frac{1}{3}}}$ | $\boxed{\frac{3 y^{\frac{1}{12}}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.25 | $p=-7,-2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{2}{p+4}=\frac{p+5}{3}$ | $\boxed{p=-7,-2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.23 | 4,7 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{3}{x+2}+\frac{x-1}{x+5}=\frac{5 x+20}{6 x+24}$ | $\boxed{4,7}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.27 | $-9 x$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine Like Terms: $-7 x-2 x$ | $\boxed{-9 x}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.6 | Yes | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State if the given functions are inverses:
$f(x)=\frac{x-5}{10}$
$h(x)=10 x+5$ | $\boxed{Yes}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.24 | $L=\frac{q+6 p}{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $\mathrm{q}=6(L-p)$ for $\mathrm{L}$. | $\boxed{L=\frac{q+6 p}{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.6 | $\frac{5 p^{3}}{4}+4 p^{2}+4 p$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{5 p^{4}+16 p^{3}+16 p^{2}}{4 p}$ | $\boxed{\frac{5 p^{3}}{4}+4 p^{2}+4 p}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.9 | $56 b^{2}-19 b-15$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(8 b+3)(7 b-5)$ | $\boxed{56 b^{2}-19 b-15}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.4.26 | $(1,2,4)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$2 x+y=z$
$4 x+z=4 y$
$y=x+1$ | $\boxed{(1,2,4)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.2.40 | -9 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $4+\frac{a}{3}=1$ | $\boxed{-9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.27 | 7,3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $n^{2}=-21+10 n$ | $\boxed{7,3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.34 | $-\frac{2401}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\log _{7}-3 n=4$ | $\boxed{-\frac{2401}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.27 | $\pm 1, \pm i, \pm 2, \pm 2 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $x^{8}-17 x^{4}+16=0$ | $\boxed{\pm 1, \pm i, \pm 2, \pm 2 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.10.17 | $\mathrm{r}=5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The rate of a stream is 3 miles an hour. If a crew rows downstream for a distance of 8 miles and then back again, the round trip occupying 5 hours, what is the rate of the crew in still water? | $\boxed{\mathrm{r}=5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.15 | $\frac{u^{2}}{12 v^{5}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\frac{u^{2}}{4 u^{0} v^{3} \cdot 3 v^{2}}$ | $\boxed{\frac{u^{2}}{12 v^{5}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.40 | $4 x^{2} y^{4} z^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{2 x^{4} y^{5} \cdot 2 z^{10} x^{2} y^{7}}{\left(x y^{2} z^{2}\right)^{4}}$ | $\boxed{4 x^{2} y^{4} z^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.26 | $\frac{1}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $625^{2 x}=25$ | $\boxed{\frac{1}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.22 | 7 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{2 r}{r+6} \div \frac{2 r}{7 r+42}$ | $\boxed{7}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.3 | Yes | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State if the given functions are inverses:
$f(x)=\frac{-x-1}{x-2}$
$g(x)=\frac{-2 x+1}{-x-1}$ | $\boxed{Yes}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.26 | $n=-6,9$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{5}{n+1}=\frac{n-4}{10}$ | $\boxed{n=-6,9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.22 | $6,-\frac{25}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $3-|6 n+7|=-40$ | $\boxed{6,-\frac{25}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.12 | $\frac{5 a^{2}+7 a-3}{9 a^{2}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{2 a-1}{3 a^{2}}+\frac{5 a+1}{9 a}$ | $\boxed{\frac{5 a^{2}+7 a-3}{9 a^{2}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.11 | 10,6 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The sum of the ages of a china plate and a glass plate is 16 years. Four years ago the china plate was three times the age of the glass plate. Find the present age of each plate. | $\boxed{10,6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.14 | $-\frac{3}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(13,-2)$ and $(7,7)$. | $\boxed{-\frac{3}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.11 | $-5,0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{4-x}{1-x}=\frac{12}{3-x}$ | $\boxed{-5,0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.71 | $-75-20 k$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $5(1-6 k)+10(k-8)$ | $\boxed{-75-20 k}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.12 | $3^{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(3^{2}\right)^{3}$ | $\boxed{3^{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.46 | $-2 \sqrt{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\sqrt{-12} \sqrt{-2}$ | $\boxed{-2 \sqrt{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.4.24 | $-\frac{9}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-\frac{149}{16}-\frac{11}{3} r=-\frac{7}{4} r-\frac{5}{4}\left(-\frac{4}{3} r+1\right)$ | $\boxed{-\frac{9}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.1 | $\sqrt[4]{4 x^{2} y^{3}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Reduce the following radical: $\sqrt[8]{16 x^{4} y^{6}}$ | $\boxed{\sqrt[4]{4 x^{2} y^{3}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.3 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $x+\frac{20}{x-4}=\frac{5 x}{x-4}-2$ | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.7.15 | $7 \times 9$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A page is to have a margin of 1 inch and is to contain $35 \mathrm{in}^{2}$ of painting. How large must the page be if the length is to exceed the width by 2 inches? | $\boxed{7 \times 9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.4.39 | -3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $5^{-3 n-3} \cdot 5^{2 n}=1$ | $\boxed{-3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.33 | $x^{2}-2 x+10=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $1 \pm 3 i$. | $\boxed{x^{2}-2 x+10=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.11 | 0 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State the excluded values for $\frac{10 m^{2}+8 m}{10 m}$ | $\boxed{0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.31 | $-5 x-9$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Combine Like Terms: $x-10-6 x+1$ | $\boxed{-5 x-9}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.14 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\frac{5}{9}=\frac{b}{9}$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.7 | 25 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate using the given values: $5 j+\frac{k h}{2}$; $h=5, j=4, k=2$ | $\boxed{25}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.5.12 | $\frac{2 \sqrt{3}+\sqrt{2}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{5}{2 \sqrt{3}-\sqrt{2}}$ | $\boxed{\frac{2 \sqrt{3}+\sqrt{2}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.3.12 | $25 x^{3} y^{5} z$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the Least Common Denominator: $5 x^{2} y, 25 x^{3} y^{5} z$ | $\boxed{25 x^{3} y^{5} z}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.7 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $0=-8(p-5)$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.6.29 | $-\frac{13}{7}, 1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the absolute value equation: $-7+8|-7 x-3|=73$ | $\boxed{-\frac{13}{7}, 1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.30 | $f^{-1}(x)=\frac{5+4 x}{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the inverse of the function: $f(x)=\frac{5 x-5}{4}$ | $\boxed{f^{-1}(x)=\frac{5+4 x}{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.33 | $3 n^{2}-9 n-10-\frac{8}{n+6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{3 n^{3}+9 n^{2}-64 n-68}{n+6}$ | $\boxed{3 n^{2}-9 n-10-\frac{8}{n+6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.43 | $\frac{-(x-29)}{(x-3)(x+5)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{2 x+7}{x^{2}-2 x-3}-\frac{3 x-2}{x^{2}+6 x+5}$ | $\boxed{\frac{-(x-29)}{(x-3)(x+5)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.26 | $\frac{1}{2},-1, \frac{-1 \pm i \sqrt{3}}{4}, \frac{1 \pm i \sqrt{3}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $8 x^{6}+7 x^{3}-1=0$ | $\boxed{\frac{1}{2},-1, \frac{-1 \pm i \sqrt{3}}{4}, \frac{1 \pm i \sqrt{3}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.9 | $-8 \sqrt{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $2 \sqrt{2}-3 \sqrt{18}-\sqrt{2}$ | $\boxed{-8 \sqrt{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.40 | $36 x^{2}+108 x+81$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $3(2 x+3)(6 x+9)$ | $\boxed{36 x^{2}+108 x+81}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.26 | 8 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $3 n=24$ | $\boxed{8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.8.12 | $4 \frac{4}{9}$ days | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Tim can finish a certain job in 10 hours. It takes his wife JoAnn only 8 hours to do the same job. If they work together, how long will it take them to complete the job? | $\boxed{4 \frac{4}{9}$ days}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.5.25 | $\sqrt{a}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{a+\sqrt{\mathrm{ab}}}{\sqrt{a}+\sqrt{b}}$ | $\boxed{\sqrt{a}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.5.15 | $13 \mathrm{n}, 5 \mathrm{~d}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A coin purse contains 18 coins in nickels and dimes. The coins have a total value of $\$ 1.15$. Find the number of nickels and dimes in the coin purse. | $\boxed{13 \mathrm{n}, 5 \mathrm{~d}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.36 | $\frac{x+y}{x y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{x^{-3}+y^{-3}}{x^{-2}-x^{-1} y^{-1}+y^{-2}}$ | $\boxed{\frac{x+y}{x y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.3.22 | -3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{-9 \cdot 2-(3-6)}{1-(-2+1)-(-3)}$ | $\boxed{-3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.1.3 | 1,5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\sqrt{6 x-5}-x=0$ | $\boxed{1,5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.10 | $45 \sqrt{5}+10 \sqrt{15}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Multiply and simplify: $5 \sqrt{15}(3 \sqrt{3}+2)$ | $\boxed{45 \sqrt{5}+10 \sqrt{15}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.9 | $x^{2}-7 x-44=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $-4$ and 11. | $\boxed{x^{2}-7 x-44=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.16 | $10 n \sqrt{n}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt{100 n^{3}}$ | $\boxed{10 n \sqrt{n}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.23 | $\frac{b^{\frac{7}{4}} a^{\frac{3}{4}}}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\frac{a^{\frac{3}{4}} b^{-1} \cdot b^{\frac{7}{4}}}{3 b^{-1}}$ | $\boxed{\frac{b^{\frac{7}{4}} a^{\frac{3}{4}}}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.8 | $x^{2}+7 x+10=0$ | 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.5.5.1 | $6 p-42$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $6(p-7)$ | $\boxed{6 p-42}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.2.6 | -12 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-4-b=8$ | $\boxed{-12}$ |
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