data_source
stringclasses 9
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stringlengths 14
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1.32k
| answer
stringlengths 1
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stringclasses 8
values | data_topic
stringclasses 7
values |
|---|---|---|---|---|---|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.6
|
Evaluate using the given values: $x+6 z-4 y$; $x=6, y=4, z=4$
|
14
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.55
|
Evaluate the expression: $i^{62}$
|
-1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.3.34
|
Simplify: $2 \sqrt[4]{48}-3 \sqrt[4]{405}-3 \sqrt[4]{48}-\sqrt[4]{162}$
|
$-2 \sqrt[4]{3}-9 \sqrt[4]{5}-3 \sqrt[4]{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.7.25
|
Divide: $\frac{27 b^{2}+87 b+35}{3 b+8}$
|
$9 b+5-\frac{5}{3 b+8}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.3
|
Simplify: $\sqrt[3]{750}$
|
$5 \sqrt[3]{6}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.7.31
|
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 $1000 \mathrm{~kL} / \mathrm{min}$ ?
|
$27 \mathrm{~min}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.38
|
Find product: $(6)(-1)$
|
-6
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.7.5
|
Divide: $\frac{12 x^{4}+24 x^{3}+3 x^{2}}{6 x}$
|
$2 x^{3}+4 x^{2}+\frac{x}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.4.15
|
Multiply and simplify: $(\sqrt{5}-5)(2 \sqrt{5}-1)$
|
$15-11 \sqrt{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.3.14
|
Simplify and write the answer in scientific notation: $\left(2 \times 10^{-6}\right)\left(8.8 \times 10^{-5}\right)$
|
$1.76 \times 10^{-10}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.35
|
Simplify: $\left(\frac{2 m n^{4} \cdot 2 m^{4} n^{4}}{m n^{4}}\right)^{3}$
|
$64 m^{12} n^{12}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.25
|
Simplify: $\frac{20}{4 p+2}$
|
$\frac{10}{2 p+1}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.5.25
|
Solve the equation: $\log _{2} x=-2$
|
$\frac{1}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.32
|
Simplify the expression: $\frac{9 x^{3}+54 x^{2}}{x^{2}+5 x-14} \cdot \frac{x^{2}+5 x-14}{10 x^{2}}$
|
$\frac{9(x+6)}{10}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.6.12
|
Evaluate: $100^{-\frac{3}{2}}$
|
$\frac{1}{1000}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.5.32
|
Simplify: $\frac{a b}{a \sqrt{b}-b \sqrt{a}}$
|
$\frac{a \sqrt{b}+b \sqrt{a}}{a-b}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.13
|
Find the product: $(4 m-8 n)(4 m+8 n)$
|
$16 m^{2}-64 n^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.3.11
|
Solve the following system of equations by elimination:
$2 x-y=5$
$5 x+2 y=-28$
|
$(-2,-9)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.38
|
Evaluate the expression: $\frac{4}{4+6 i}$
|
$\frac{4-6 i}{13}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.10.19
|
By going 15 miles per hour faster, a train would have required 1 hour less to travel 180 miles. How fast did it travel?
|
$45 \mathrm{mph}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.35
|
Simplify: $\frac{x^{-2}-6 x^{-1}+9}{x^{2}-9}$
|
$\frac{(1-3 x)^{2}}{x^{2}(x+3)(x-3)}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.23
|
Find a quadratic equation with the solutions $\pm \frac{1}{5}$.
|
$25 x^{2}-1=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.31
|
Simplify: $\frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}$
|
$\frac{y-x}{x y}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.5
|
Solve the following equation: $a^{4}-50 a^{2}+49=0$
|
$\pm 1, \pm 7$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.6.16
|
Solve the proportion: $\frac{x+1}{9}=\frac{x+2}{2}$
|
$v=-\frac{16}{7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.21
|
Find the slope of the line through the points $(12,-19)$ and $(6,14)$.
|
$-\frac{11}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.10.16
|
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?
|
3
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.3.3
|
Solve: $-5(-4+2 v)=-50$
|
7
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.5.32
|
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.
|
$\$ 3000 @ 4.6 \%$ $\$ 4500$ @ 6.6\%
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.7.35
|
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 $40 \mathrm{~W} / \mathrm{m}^{2}$ ?
|
$2.5 \mathrm{~m}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.13
|
Solve each equation by completing the square: $6 x^{2}+12 x+63=0$
|
$\frac{-2+i \sqrt{38}}{2}, \frac{-2-i \sqrt{38}}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.10.15
|
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?
|
2
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.2.14
|
Simplify. Your answer should contain only positive expontents: $\frac{2 x y^{2} \cdot 4 x^{3} y^{-4}}{4 x^{-4} y^{-4} \cdot 4 x}$
|
$\frac{x^{7} y^{2}}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.57
|
Evaluate the expression: $i^{154}$
|
-1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.1.13
|
Solve the equation: $-9=\frac{n}{12}$
|
-108
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.5.34
|
Find the product: $5(x-4)(2 x-3)$
|
$10 x^{2}-55 x+60$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.34
|
Simplify: $8 \sqrt[3]{-750 x y}$
|
$-40 \sqrt[3]{6 x y}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.40
|
Simplify: $-\sqrt{32 x y^{2} z^{3}}$
|
$-4 y z \sqrt{2 x z}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.4
|
Simplify: $\sqrt[3]{250}$
|
$5 \sqrt[3]{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.7.34
|
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 $94 \mathrm{~N} ?$
|
$8.2 \mathrm{mph}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.9
|
Simplify: $(i)-(2+3 i)-6$
|
$-8-2 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.6.28
|
Solve the proportion: $\frac{1}{n+3}=\frac{n+2}{2}$
|
$n=-4,-1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.8
|
Solve the following equation: $y^{4}-40 y^{2}+144=0$
|
$\pm 6, \pm 2$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.8.1
|
Solve the equation: $x + 3 = 19$
|
11
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.29
|
Find product: $(8)\left(\frac{1}{2}\right)$
|
4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.35
|
Given $h(t)=2|-3 t-1|+2$, find $h\left(n^{2}\right)$
|
$2\left|-3 n^{2}-1\right|+2$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.7.13
|
Solve the equation for $y$: $\frac{7}{y-3}-\frac{1}{2}=\frac{y-2}{y-4}$
|
$\frac{16}{3}, 5$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.15
|
Simplify and leave your answer as an improper fraction: $\frac{80}{60}$
|
$\frac{4}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.20
|
Simplify the expression: $\frac{x^{2}-7 x+10}{x-2} \cdot \frac{x+10}{x^{2}-x-20}$
|
$\frac{x+10}{x+4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.28
|
Evaluate the expression: $\frac{-3+2 i}{-3 i}$
|
$\frac{-3 i-2}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.44
|
Solve the following equation: $\left(2 x^{2}+3 x\right)^{2}=8\left(2 x^{2}+3 x\right)+9$
|
$-3,-1, \frac{3}{2},-\frac{1}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.3
|
Find the principal that will amount to $\$ 3500$ if invested at $4 \%$ interest compounded quarterly for 5 years.
|
2868.41
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.4.27
|
Simplify: $\frac{2 \sqrt{4}}{3 \sqrt{3}}$
|
$\frac{4 \sqrt{3}}{9}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.9.11
|
Solve the following systems of equation:
$x y=45$
$(x-5)(y+3)=160$
|
$(45,1),\left(-\frac{5}{3},-27\right)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.29
|
Simplify: $\frac{32 x^{2}}{28 x^{2}+28 x}$
|
$\frac{8 x}{7(x+1)}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.39
|
Simplify: $6 \sqrt[4]{648 x^{5} y^{7} z^{2}}$
|
$18 x y \sqrt[4]{8 x y^{3} z^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.8.20
|
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?
|
3.6 hours
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.31
|
Add or subtract the rational expressions and simplify: $\frac{5 x}{x^{2}-x-6}-\frac{18}{x^{2}-9}$
|
$\frac{5 x+12}{x^{2}+5 x+6}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.2.6
|
Simplify. Your answer should contain only positive expontents: $\left(m^{0} n^{3} \cdot 2 m^{-3} n^{-3}\right)^{0}$
|
1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.5.28
|
Solve the equation $S=\pi \mathrm{rh}+\pi r^{2}$ for $\mathrm{h}$.
|
$h=\frac{s-\pi r^{2}}{\pi r}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.8
|
State the excluded values for $\frac{27 p}{18 p^{2}-36 p}$
|
0,2
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.6.37
|
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?
|
1.2
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.16
|
Simplify: $(2 x y)^{4}$
|
$16 x^{4} y^{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.7.36
|
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?
|
$\mathrm{V}=100.5 \mathrm{~cm}^{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.7
|
Find the value that completes the square and then rewrite as a perfect square: $y^{2}-y+$
|
$\frac{1}{4} ;\left(y-\frac{1}{2}\right)^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.7.9
|
The area of a rectangle is $48 \mathrm{ft}^{2}$ and its perimeter is $32 \mathrm{ft}$. Find its length and width.
|
$4 \mathrm{ft} \times 12 \mathrm{ft}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.7.31
|
Solve the equation for $x$: $\frac{x-3}{x-6}+\frac{x+5}{x+3}=\frac{-2 x^{2}}{x^{2}-3 x-18}$
|
$\frac{13}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.6.29
|
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?
|
30
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.30
|
Find the square: $(8 x+5 y)^{2}$
|
$64 x^{2}+80 x y+25 y^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.8.26
|
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?
|
15 and $22.5 \mathrm{~min}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.6.31
|
Simplify and express with positive exponents: $\frac{\left(x^{-\frac{4}{3}} y^{-\frac{1}{3}} \cdot y\right)^{-1}}{x^{\frac{1}{3}} y^{-2}}$
|
$x y^{\frac{4}{3}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.3.11
|
Find the inverse of the function: $f(x)=(x-2)^{5}+3$
|
$f^{-1}(x)=\sqrt[5]{x-3}+2$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.7
|
Simplify: $(3-3 i)+(-7-8 i)$
|
$-4-11 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.53
|
Simplify: $9(b+10)+5 b$
|
$14 b+90$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.18
|
Find product: $(8 i)(-2 i)(-2-8 i)$
|
$-32-128 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.3
|
Reduce the following radical: $\sqrt[12]{64 x^{4} y^{6} z^{8}}$
|
$\sqrt[6]{8 x^{2} y^{3} z^{4}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.16
|
Solve: $\frac{1-\frac{1}{x}-\frac{6}{x^{2}}}{1-\frac{4}{x}+\frac{3}{x^{2}}}$
|
$\frac{x+2}{x-1}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.25
|
Find the slope of the line through the points $(-17,19)$ and $(10,-7)$.
|
$-\frac{26}{27}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.37
|
Given the points $(x,-7)$ and $(-9,-9)$ and a slope of $\frac{2}{5}$, find the value of $x$.
|
-4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.2
|
Simplify: $(3 i)-(7 i)$
|
$-4 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.55
|
Find quotient: $\frac{-8}{-2}$
|
4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.24
|
Solve each equation by completing the square: $6 n^{2}-12 n-14=4$
|
$3,-1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.1.9
|
Solve: $\sqrt{4 x+5}-\sqrt{x+4}=2$
|
5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.46
|
Find quotient: $\frac{30}{-10}$
|
-3
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.1
|
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.
|
6,16
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.28
|
Add or subtract the rational expressions and simplify: $\frac{2 x}{x^{2}-1}-\frac{3}{x^{2}+5 x+4}$
|
$\frac{2 x+3}{(x-1)(x+4)}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.19
|
Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now?
|
9,18
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.2.2.33
|
Given the points $(-3,-2)$ and $(x, 6)$ and a slope of $-\frac{8}{5}$, find the value of $x$.
|
-8
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.4.26
|
Simplify: $\frac{\sqrt{2}}{3 \sqrt{5}}$
|
$\frac{\sqrt{10}}{15}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.5
|
Fred is 4 years older than Barney. Five years ago the sum of their ages was 48 . How old are they now?
|
27,31
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.25
|
Find a quadratic equation with the solutions $\pm \sqrt{11}$.
|
$x^{2}-11=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.4.4
|
Simplify the expression $n^{3}-9 n^{2}+23 n-21$ when $n=5$.
|
-6
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.10
|
Specify the domain of the function: $y(x)=\frac{x}{x^{2}-25}$
|
$x \neq \pm 5$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.5.35
|
Find the product: $3(2 x+1)(4 x-5)$
|
$24 x^{2}-18 x-15$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.4.29
|
Solve the following systems of equation:
$-2 w+2 x+2 y-2 z=-10$
$w+x+y+z=-5$
$3 w+2 x+2 y+4 z=-11$
$w+3 x-2 y+2 z=-6$
|
$(1,-3,-2,-1)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.11
|
Evaluate the expression: $3-(-1)$
|
4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.13
|
Simplify: $\sqrt{192 n}$
|
$8 \sqrt{3 n}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.32
|
Simplify: $\frac{b^{2}+14 b+48}{b^{2}+15 b+56}$
|
$\frac{b+6}{b+7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.7.1
|
Find the value: $\cos 71^{\circ}$
|
0.3256
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.75
|
Simplify: $(5 p-6)+(1-p)$
|
$4 p-5$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
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