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.0.4.6 | 14 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate using the given values: $x+6 z-4 y$; $x=6, y=4, z=4$ | $\boxed{14}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.55 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $i^{62}$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.3.34 | $-2 \sqrt[4]{3}-9 \sqrt[4]{5}-3 \sqrt[4]{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $2 \sqrt[4]{48}-3 \sqrt[4]{405}-3 \sqrt[4]{48}-\sqrt[4]{162}$ | $\boxed{-2 \sqrt[4]{3}-9 \sqrt[4]{5}-3 \sqrt[4]{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.25 | $9 b+5-\frac{5}{3 b+8}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{27 b^{2}+87 b+35}{3 b+8}$ | $\boxed{9 b+5-\frac{5}{3 b+8}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.3 | $5 \sqrt[3]{6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt[3]{750}$ | $\boxed{5 \sqrt[3]{6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.31 | $27 \mathrm{~min}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a tank in $45 \mathrm{~min}$ at the rate of $600 \mathrm{~kL} / \mathrm{min}$, how long will it take the pump to empty the same tank at the rate of $1000 \mathrm{~kL} / \mathrm{min}$ ? | $\boxed{27 \mathrm{~min}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.38 | -6 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(6)(-1)$ | $\boxed{-6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.7.5 | $2 x^{3}+4 x^{2}+\frac{x}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Divide: $\frac{12 x^{4}+24 x^{3}+3 x^{2}}{6 x}$ | $\boxed{2 x^{3}+4 x^{2}+\frac{x}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.15 | $15-11 \sqrt{5}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Multiply and simplify: $(\sqrt{5}-5)(2 \sqrt{5}-1)$ | $\boxed{15-11 \sqrt{5}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.3.14 | $1.76 \times 10^{-10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and write the answer in scientific notation: $\left(2 \times 10^{-6}\right)\left(8.8 \times 10^{-5}\right)$ | $\boxed{1.76 \times 10^{-10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.35 | $64 m^{12} n^{12}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\left(\frac{2 m n^{4} \cdot 2 m^{4} n^{4}}{m n^{4}}\right)^{3}$ | $\boxed{64 m^{12} n^{12}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.25 | $\frac{10}{2 p+1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{20}{4 p+2}$ | $\boxed{\frac{10}{2 p+1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.5.25 | $\frac{1}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $\log _{2} x=-2$ | $\boxed{\frac{1}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.32 | $\frac{9(x+6)}{10}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{9 x^{3}+54 x^{2}}{x^{2}+5 x-14} \cdot \frac{x^{2}+5 x-14}{10 x^{2}}$ | $\boxed{\frac{9(x+6)}{10}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.12 | $\frac{1}{1000}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate: $100^{-\frac{3}{2}}$ | $\boxed{\frac{1}{1000}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.5.32 | $\frac{a \sqrt{b}+b \sqrt{a}}{a-b}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{a b}{a \sqrt{b}-b \sqrt{a}}$ | $\boxed{\frac{a \sqrt{b}+b \sqrt{a}}{a-b}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.13 | $16 m^{2}-64 n^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $(4 m-8 n)(4 m+8 n)$ | $\boxed{16 m^{2}-64 n^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.3.11 | $(-2,-9)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following system of equations by elimination:
$2 x-y=5$
$5 x+2 y=-28$ | $\boxed{(-2,-9)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.38 | $\frac{4-6 i}{13}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{4}{4+6 i}$ | $\boxed{\frac{4-6 i}{13}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.10.19 | $45 \mathrm{mph}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | By going 15 miles per hour faster, a train would have required 1 hour less to travel 180 miles. How fast did it travel? | $\boxed{45 \mathrm{mph}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.35 | $\frac{(1-3 x)^{2}}{x^{2}(x+3)(x-3)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{x^{-2}-6 x^{-1}+9}{x^{2}-9}$ | $\boxed{\frac{(1-3 x)^{2}}{x^{2}(x+3)(x-3)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.23 | $25 x^{2}-1=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $\pm \frac{1}{5}$. | $\boxed{25 x^{2}-1=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.31 | $\frac{y-x}{x y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}$ | $\boxed{\frac{y-x}{x y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.5 | $\pm 1, \pm 7$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $a^{4}-50 a^{2}+49=0$ | $\boxed{\pm 1, \pm 7}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.16 | $v=-\frac{16}{7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{x+1}{9}=\frac{x+2}{2}$ | $\boxed{v=-\frac{16}{7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.21 | $-\frac{11}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(12,-19)$ and $(6,14)$. | $\boxed{-\frac{11}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.10.16 | 3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A long-distance runner started on a course running at an average speed of 6 mph. One hour later, a second runner began the same course at an average speed of $8 \mathrm{mph}$. How long after the second runner started will the second runner overtake the first runner? | $\boxed{3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.3.3 | 7 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $-5(-4+2 v)=-50$ | $\boxed{7}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.5.32 | $\$ 3000 @ 4.6 \%$ $\$ 4500$ @ 6.6\% | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Millicent earned $\$ 435$ last year in interest. If $\$ 3000$ was invested at a certain rate of return and $\$ 4500$ was invested in a fund with a rate that was $2 \%$ lower, find the two rates of interest. | $\boxed{\$ 3000 @ 4.6 \%$ $\$ 4500$ @ 6.6\%}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.35 | $2.5 \mathrm{~m}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The intensity of a light from a light bulb varies inversely as the square of the distance from the bulb. Suppose intensity is $90 \mathrm{~W} / \mathrm{m}^{2}$ (watts per square meter) when the distance is $5 \mathrm{~m}$. How much further would it be to a point where the intesity is $40 \mathrm{~W} / \mathrm{m}^{2}$ ? | $\boxed{2.5 \mathrm{~m}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.13 | $\frac{-2+i \sqrt{38}}{2}, \frac{-2-i \sqrt{38}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve each equation by completing the square: $6 x^{2}+12 x+63=0$ | $\boxed{\frac{-2+i \sqrt{38}}{2}, \frac{-2-i \sqrt{38}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.10.15 | 2 | 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 $8 \mathrm{mph}$ toward a small island. Two hours later a cabin cruiser leaves the same harbor and travels at an average speed of $16 \mathrm{mph}$ toward the same island. In how many hours after the cabin cruiser leaves will the cabin cruiser be alongside the motorboat? | $\boxed{2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.14 | $\frac{x^{7} y^{2}}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\frac{2 x y^{2} \cdot 4 x^{3} y^{-4}}{4 x^{-4} y^{-4} \cdot 4 x}$ | $\boxed{\frac{x^{7} y^{2}}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.57 | -1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $i^{154}$ | $\boxed{-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.1.13 | -108 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $-9=\frac{n}{12}$ | $\boxed{-108}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.34 | $10 x^{2}-55 x+60$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $5(x-4)(2 x-3)$ | $\boxed{10 x^{2}-55 x+60}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.34 | $-40 \sqrt[3]{6 x y}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $8 \sqrt[3]{-750 x y}$ | $\boxed{-40 \sqrt[3]{6 x y}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.40 | $-4 y z \sqrt{2 x z}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $-\sqrt{32 x y^{2} z^{3}}$ | $\boxed{-4 y z \sqrt{2 x z}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.4 | $5 \sqrt[3]{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt[3]{250}$ | $\boxed{5 \sqrt[3]{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.34 | $8.2 \mathrm{mph}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The drag force on a boat varies jointly as the wetted surface area and the square of the velocity of a boat. If a boat going $6.5 \mathrm{mph}$ experiences a drag force of $86 \mathrm{~N}$ when the wetted surface area is $41.2 \mathrm{ft}^{2}$, how fast must a boat with $28.5 \mathrm{ft}^{2}$ of wetted surface area go in order to experience a drag force of $94 \mathrm{~N} ?$ | $\boxed{8.2 \mathrm{mph}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.9 | $-8-2 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(i)-(2+3 i)-6$ | $\boxed{-8-2 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.6.28 | $n=-4,-1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the proportion: $\frac{1}{n+3}=\frac{n+2}{2}$ | $\boxed{n=-4,-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.8 | $\pm 6, \pm 2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $y^{4}-40 y^{2}+144=0$ | $\boxed{\pm 6, \pm 2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.8.1 | 11 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation: $x + 3 = 19$ | $\boxed{11}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.29 | 4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(8)\left(\frac{1}{2}\right)$ | $\boxed{4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.35 | $2\left|-3 n^{2}-1\right|+2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given $h(t)=2|-3 t-1|+2$, find $h\left(n^{2}\right)$ | $\boxed{2\left|-3 n^{2}-1\right|+2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.13 | $\frac{16}{3}, 5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $y$: $\frac{7}{y-3}-\frac{1}{2}=\frac{y-2}{y-4}$ | $\boxed{\frac{16}{3}, 5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.2.15 | $\frac{4}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and leave your answer as an improper fraction: $\frac{80}{60}$ | $\boxed{\frac{4}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.2.20 | $\frac{x+10}{x+4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression: $\frac{x^{2}-7 x+10}{x-2} \cdot \frac{x+10}{x^{2}-x-20}$ | $\boxed{\frac{x+10}{x+4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.28 | $\frac{-3 i-2}{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $\frac{-3+2 i}{-3 i}$ | $\boxed{\frac{-3 i-2}{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.6.44 | $-3,-1, \frac{3}{2},-\frac{1}{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following equation: $\left(2 x^{2}+3 x\right)^{2}=8\left(2 x^{2}+3 x\right)+9$ | $\boxed{-3,-1, \frac{3}{2},-\frac{1}{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.6.3 | 2868.41 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the principal that will amount to $\$ 3500$ if invested at $4 \%$ interest compounded quarterly for 5 years. | $\boxed{2868.41}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.27 | $\frac{4 \sqrt{3}}{9}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{2 \sqrt{4}}{3 \sqrt{3}}$ | $\boxed{\frac{4 \sqrt{3}}{9}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.9.11 | $(45,1),\left(-\frac{5}{3},-27\right)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$x y=45$
$(x-5)(y+3)=160$ | $\boxed{(45,1),\left(-\frac{5}{3},-27\right)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.29 | $\frac{8 x}{7(x+1)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{32 x^{2}}{28 x^{2}+28 x}$ | $\boxed{\frac{8 x}{7(x+1)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.2.39 | $18 x y \sqrt[4]{8 x y^{3} z^{2}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $6 \sqrt[4]{648 x^{5} y^{7} z^{2}}$ | $\boxed{18 x y \sqrt[4]{8 x y^{3} z^{2}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.8.20 | 3.6 hours | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A water tank is being filled by two inlet pipes. Pipe A can fill the tank in $4 \frac{1}{2}$ hrs, while both pipes together can fill the tank in 2 hours. How long does it take to fill the tank using only pipe B? | $\boxed{3.6 hours}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.31 | $\frac{5 x+12}{x^{2}+5 x+6}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{5 x}{x^{2}-x-6}-\frac{18}{x^{2}-9}$ | $\boxed{\frac{5 x+12}{x^{2}+5 x+6}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.2.6 | 1 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify. Your answer should contain only positive expontents: $\left(m^{0} n^{3} \cdot 2 m^{-3} n^{-3}\right)^{0}$ | $\boxed{1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.5.28 | $h=\frac{s-\pi r^{2}}{\pi r}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation $S=\pi \mathrm{rh}+\pi r^{2}$ for $\mathrm{h}$. | $\boxed{h=\frac{s-\pi r^{2}}{\pi r}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.8 | 0,2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | State the excluded values for $\frac{27 p}{18 p^{2}-36 p}$ | $\boxed{0,2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.37 | 1.2 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | How many ounces of dried apricots must be added to 18 oz of a snack mix that contains $20 \%$ dried apricots to make a mixture that is $25 \%$ dried apricots? | $\boxed{1.2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.1.16 | $16 x^{4} y^{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(2 x y)^{4}$ | $\boxed{16 x^{4} y^{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.7.36 | $\mathrm{V}=100.5 \mathrm{~cm}^{3}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The volume of a cone varies jointly as its height, and the square of its radius. If a cone with a height of 8 centimeters and a radius of 2 centimeters has a volume of $33.5 \mathrm{~cm}^{3}$, what is the volume of a cone with a height of 6 centimeters and a radius of 4 centimeters? | $\boxed{\mathrm{V}=100.5 \mathrm{~cm}^{3}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.7 | $\frac{1}{4} ;\left(y-\frac{1}{2}\right)^{2}$ | 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: $y^{2}-y+$ | $\boxed{\frac{1}{4} ;\left(y-\frac{1}{2}\right)^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.7.9 | $4 \mathrm{ft} \times 12 \mathrm{ft}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The area of a rectangle is $48 \mathrm{ft}^{2}$ and its perimeter is $32 \mathrm{ft}$. Find its length and width. | $\boxed{4 \mathrm{ft} \times 12 \mathrm{ft}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.7.31 | $\frac{13}{4}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the equation for $x$: $\frac{x-3}{x-6}+\frac{x+5}{x+3}=\frac{-2 x^{2}}{x^{2}-3 x-18}$ | $\boxed{\frac{13}{4}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.6.29 | 30 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | The manager of a garden shop mixes grass seed that is $60 \%$ rye grass with 70 lb of grass seed that is $80 \%$ rye grass to make a mixture that is $74 \%$ rye grass. How much of the $60 \%$ mixture is used? | $\boxed{30}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.6.30 | $64 x^{2}+80 x y+25 y^{2}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the square: $(8 x+5 y)^{2}$ | $\boxed{64 x^{2}+80 x y+25 y^{2}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.8.26 | 15 and $22.5 \mathrm{~min}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A takes $7 \frac{1}{2}$ minutes longer than $\mathrm{B}$ to do a job. Working together, they can do the job in 9 minutes. How long does it take each working alone? | $\boxed{15 and $22.5 \mathrm{~min}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.6.31 | $x y^{\frac{4}{3}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify and express with positive exponents: $\frac{\left(x^{-\frac{4}{3}} y^{-\frac{1}{3}} \cdot y\right)^{-1}}{x^{\frac{1}{3}} y^{-2}}$ | $\boxed{x y^{\frac{4}{3}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.3.11 | $f^{-1}(x)=\sqrt[5]{x-3}+2$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the inverse of the function: $f(x)=(x-2)^{5}+3$ | $\boxed{f^{-1}(x)=\sqrt[5]{x-3}+2}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.7 | $-4-11 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(3-3 i)+(-7-8 i)$ | $\boxed{-4-11 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.53 | $14 b+90$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $9(b+10)+5 b$ | $\boxed{14 b+90}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.18 | $-32-128 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find product: $(8 i)(-2 i)(-2-8 i)$ | $\boxed{-32-128 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.7.3 | $\sqrt[6]{8 x^{2} y^{3} z^{4}}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Reduce the following radical: $\sqrt[12]{64 x^{4} y^{6} z^{8}}$ | $\boxed{\sqrt[6]{8 x^{2} y^{3} z^{4}}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.5.16 | $\frac{x+2}{x-1}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\frac{1-\frac{1}{x}-\frac{6}{x^{2}}}{1-\frac{4}{x}+\frac{3}{x^{2}}}$ | $\boxed{\frac{x+2}{x-1}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.25 | $-\frac{26}{27}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the slope of the line through the points $(-17,19)$ and $(10,-7)$. | $\boxed{-\frac{26}{27}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.37 | -4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(x,-7)$ and $(-9,-9)$ and a slope of $\frac{2}{5}$, find the value of $x$. | $\boxed{-4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.8.2 | $-4 i$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(3 i)-(7 i)$ | $\boxed{-4 i}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.55 | 4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $\frac{-8}{-2}$ | $\boxed{4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.3.24 | $3,-1$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve each equation by completing the square: $6 n^{2}-12 n-14=4$ | $\boxed{3,-1}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.1.9 | 5 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve: $\sqrt{4 x+5}-\sqrt{x+4}=2$ | $\boxed{5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.46 | -3 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find quotient: $\frac{30}{-10}$ | $\boxed{-3}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.1 | 6,16 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each. | $\boxed{6,16}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.4.28 | $\frac{2 x+3}{(x-1)(x+4)}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Add or subtract the rational expressions and simplify: $\frac{2 x}{x^{2}-1}-\frac{3}{x^{2}+5 x+4}$ | $\boxed{\frac{2 x+3}{(x-1)(x+4)}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.19 | 9,18 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now? | $\boxed{9,18}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.2.2.33 | -8 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Given the points $(-3,-2)$ and $(x, 6)$ and a slope of $-\frac{8}{5}$, find the value of $x$. | $\boxed{-8}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.4.26 | $\frac{\sqrt{10}}{15}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{\sqrt{2}}{3 \sqrt{5}}$ | $\boxed{\frac{\sqrt{10}}{15}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.1.9.5 | 27,31 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Fred is 4 years older than Barney. Five years ago the sum of their ages was 48 . How old are they now? | $\boxed{27,31}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.9.5.25 | $x^{2}-11=0$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find a quadratic equation with the solutions $\pm \sqrt{11}$. | $\boxed{x^{2}-11=0}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.4.4 | -6 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify the expression $n^{3}-9 n^{2}+23 n-21$ when $n=5$. | $\boxed{-6}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.1.10 | $x \neq \pm 5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Specify the domain of the function: $y(x)=\frac{x}{x^{2}-25}$ | $\boxed{x \neq \pm 5}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.5.5.35 | $24 x^{2}-18 x-15$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the product: $3(2 x+1)(4 x-5)$ | $\boxed{24 x^{2}-18 x-15}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.4.4.29 | $(1,-3,-2,-1)$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Solve the following systems of equation:
$-2 w+2 x+2 y-2 z=-10$
$w+x+y+z=-5$
$3 w+2 x+2 y+4 z=-11$
$w+3 x-2 y+2 z=-6$ | $\boxed{(1,-3,-2,-1)}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.1.11 | 4 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Evaluate the expression: $3-(-1)$ | $\boxed{4}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.8.1.13 | $8 \sqrt{3 n}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\sqrt{192 n}$ | $\boxed{8 \sqrt{3 n}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.7.1.32 | $\frac{b+6}{b+7}$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $\frac{b^{2}+14 b+48}{b^{2}+15 b+56}$ | $\boxed{\frac{b+6}{b+7}}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.10.7.1 | 0.3256 | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Find the value: $\cos 71^{\circ}$ | $\boxed{0.3256}$ |
college_math.Beginning_and_Intermediate_Algebra | exercise.0.4.75 | $4 p-5$ | Creative Commons Attribution 3.0 Unported License (CC BY 3.0) | college_math.algebra | Simplify: $(5 p-6)+(1-p)$ | $\boxed{4 p-5}$ |
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