data_source
stringclasses 9
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stringlengths 14
17
| problem
stringlengths 14
1.32k
| answer
stringlengths 1
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stringclasses 8
values | data_topic
stringclasses 7
values | solution
stringlengths 1
991
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|---|---|---|---|---|---|---|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.2.12
|
Solve the equation: $-6=15+3 p$
|
-7
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-7
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.5
|
Evaluate $\frac{b+2}{b^{2}+4 b+4}$ when $b=0$
|
$\frac{1}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.1.4
|
Solve the equation: $-14=x-18$
|
4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.3.21
|
Solve: $-2-5(2-4 m)=33+5 m$
|
3
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
3
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.16
|
Evaluate the expression: $(-1)-8$
|
-9
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-9
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.15
|
Find the square of $-7 i$
|
-49
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-49
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.8.19
|
A sink has two faucets, one for hot water and one for cold water. The sink can be filled by a cold-water faucet in 3.5 minutes. If both faucets are open, the sink is filled in 2.1 minutes. How long does it take to fill the sink with just the hot-water faucet open?
|
$5 \frac{1}{4} \mathrm{~min}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5 \frac{1}{4} \mathrm{~min}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.24
|
Simplify: $8 \sqrt{112 p^{2}}$
|
$32 p \sqrt{7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
32 p \sqrt{7}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.53
|
Evaluate the expression: $\frac{1}{3}+\left(-\frac{4}{3}\right)$
|
-1
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.21
|
Combine Like Terms: $r-9+10$
|
$r+1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
r+1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.26
|
Simplify: $\sqrt[3]{64 u^{5} v^{3}}$
|
$4 u v \sqrt[3]{u^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 u v \sqrt[3]{u^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.15
|
You lend $\$ 100$ at $10 \%$ continuous interest. If you are repaid 2 months later, what is owed?
|
101.68
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
101.68
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.8
|
Find the product: $(2 r+3)(2 r-3)$
|
$4 r^{2}-9$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 r^{2}-9
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.6.29
|
Simplify and express with positive exponents: $\frac{\left(m^{2} n^{\frac{1}{2}}\right)^{0}}{n^{\frac{3}{4}}}$
|
$\frac{1}{n^{\frac{3}{4}}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{n^{\frac{3}{4}}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.5.30
|
Solve: $\frac{\frac{x+1}{x-1}-\frac{1-x}{1+x}}{\frac{1}{(x+1)^{2}}+\frac{1}{(x-1)^{2}}}$
|
$x^{2}-1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x^{2}-1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.3
|
Simplify: $(7 i)-(3-2 i)$
|
$-3+9 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-3+9 i
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.36
|
Carolyn's age is triple her daughter's age. In eight years the sum of their ages will be 72 . How old are they now?
|
14,42
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
14,42
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.4.29
|
Simplify: $\frac{5 x^{2}}{4 \sqrt{3 x^{3} y^{3}}}$
|
$\frac{5 \sqrt{3 x y}}{12 y^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5 \sqrt{3 x y}}{12 y^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.23
|
Simplify: $\frac{4 x^{3} y^{4}}{3 x y^{3}}$
|
$\frac{4 x^{2} y}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{4 x^{2} y}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.80
|
Simplify: $\left(7 a^{2}+7 a\right)-\left(6 a^{2}+4 a\right)$
|
$a^{2}+3 a$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
a^{2}+3 a
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.40
|
Simplify the expression: $\frac{12 x+24}{10 x^{2}+34 x+28} \cdot \frac{15 x+21}{5}$
|
$\frac{18}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{18}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.26
|
A kerosene lamp is 95 years old, and an electric lamp is 55 years old. How many years ago was the kerosene lamp twice the age of the electric lamp?
|
15
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
15
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.5.14
|
Simplify: $\frac{4}{\sqrt{2}-2}$
|
$-2 \sqrt{2}-4$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-2 \sqrt{2}-4
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.6.10
|
Solve the proportion: $\frac{9}{n+2}=\frac{3}{9}$
|
$n=25$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
n=25
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.1.28
|
Simplify: $\frac{28 m+12}{36}$
|
$\frac{7 m+3}{9}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{7 m+3}{9}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.34
|
Find the product: $(8 n+7)(8 n-7)$
|
$64 n^{2}-49$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
64 n^{2}-49
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.9.3
|
Pat is 20 years older than his son James. In two years Pat will be twice as old as James. How old are they now?
|
18,38
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
18,38
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.69
|
Evaluate the expression: $\frac{1}{5}+\frac{3}{4}$
|
$\frac{19}{20}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{19}{20}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.1.10
|
Solve the equation: $22=16+m$
|
6
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.2.32
|
Solve the equation: $\frac{m}{4}-1=-2$
|
-4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-4
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.52
|
Find quotient: $\frac{27}{3}$
|
9
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
9
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.22
|
Evaluate the expression: $1+(-1)$
|
0
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.16
|
Solve each equation by completing the square: $8 a^{2}+16 a-1=0$
|
$\frac{-4+3 \sqrt{2}}{4}, \frac{-4-3 \sqrt{2}}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{-4+3 \sqrt{2}}{4}, \frac{-4-3 \sqrt{2}}{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.5.4
|
A purse contains $\$ 3.90$ made up of dimes and quarters. If there are 21 coins in all, how many dimes and how many quarters were there?
|
$9 \mathrm{~d}, 12 \mathrm{q}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
9 \mathrm{~d}, 12 \mathrm{q}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.7.28
|
Divide: $\frac{4 n^{2}-23 n-38}{4 n+5}$
|
$n-7-\frac{3}{4 n+5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
n-7-\frac{3}{4 n+5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.38
|
Distribute: $3(8 v+9)$
|
$24 v+27$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
24 v+27
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.2.21
|
Simplify: $-2 \sqrt[3]{-48 v^{7}}$
|
$4 v^{2} \sqrt[3]{6 v}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 v^{2} \sqrt[3]{6 v}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.40
|
Find a quadratic equation with the solutions $\frac{-2 \pm i \sqrt{15}}{2}$.
|
$4 x^{2}+8 x+19=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 x^{2}+8 x+19=0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.6.22
|
A candy mix sells for $\$ 2.20$ per kilogram. It contains chocolates worth $\$ 1.80$ per kilogram and other candy worth $\$ 3.00$ per kilogram. How much of each are in 15 kilograms of the mixture?
|
10,5
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
10,5
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.66
|
Evaluate the expression: $\frac{1}{2}-\frac{11}{6}$
|
$-\frac{4}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{4}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.8.13
|
Two people working together can complete a job in 6 hours. If one of them works twice as fast as the other, how long would it take the faster person, working alone, to do the job?
|
9 hours
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
9 hours
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.10.8
|
A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?
|
10
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
10
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.27
|
Simplify: $2 x\left(x^{4} y^{4}\right)^{4}$
|
$2 x^{17} y^{16}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2 x^{17} y^{16}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.3
|
Simplify and leave your answer as an improper fraction: $\frac{35}{25}$
|
$\frac{7}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{7}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.4.20
|
Solve the following systems of equation:
$4 x-7 y+3 z=1$
$3 x+y-2 z=4$
$4 x-7 y+3 z=6$
|
no solution
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
no solution
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.8.17
|
It takes 10 hours to fill a pool with the inlet pipe. It can be emptied in $15 \mathrm{hrs}$ with the outlet pipe. If the pool is half full to begin with, how long will it take to fill it from there if both pipes are open?
|
15 hours
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
15 hours
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.4.39
|
Evaluate $\left(8-b+7 b^{3}\right)-\left(3 b^{4}+7 b-8+7 b^{2}\right)+\left(3-3 b+6 b^{3}\right)$.
|
$-3 b^{4}+13 b^{3}-7 b^{2}-$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-3 b^{4}+13 b^{3}-7 b^{2}-
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.3.31
|
Solve: $-57=-(-p+1)+2(6+8 p)$
|
-4
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-4
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.19
|
Solve the following equation: $x^{4}-2 x^{2}-3=0$
|
$\pm i, \pm \sqrt{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\pm i, \pm \sqrt{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.6.31
|
Find the square: $(5+2 r)^{2}$
|
$25+20 r+4 r^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
25+20 r+4 r^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.9
|
Simplify: $6 \sqrt{128}$
|
$48 \sqrt{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
48 \sqrt{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.1.2
|
Solve the equation: $14=b+3$
|
11
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
11
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.5.22
|
Simplify: $\frac{2+\sqrt{10}}{\sqrt{2}+\sqrt{5}}$
|
$\sqrt{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.6.30
|
How many ounces of water evaporated from 50 oz of a $12 \%$ salt solution to produce a $15 \%$ salt solution?
|
10
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
10
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.3.29
|
Simplify: $3 \sqrt[4]{2}-2 \sqrt[4]{2}-\sqrt[4]{243}$
|
$\sqrt[4]{2}-3 \sqrt[4]{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[4]{2}-3 \sqrt[4]{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.7.4
|
Find the value: $\sin 50^{\circ}$
|
0.7660
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
0.7660
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.15
|
Solve each equation by completing the square: $5 k^{2}-10 k+48=0$
|
$\frac{5+i \sqrt{215}}{5}, \frac{5-i \sqrt{215}}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5+i \sqrt{215}}{5}, \frac{5-i \sqrt{215}}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.34
|
Find product: $(-7)(-2)$
|
14
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
14
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.10.13
|
A, who travels 4 miles an hour starts from a certain place 2 hours in advance of B, who travels 5 miles an hour in the same direction. How many hours must B travel to overtake A?
|
8
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
8
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.4.14
|
Solve the equation: $\frac{1}{3}\left(-\frac{7}{4} k+1\right)-\frac{10}{3} k=-\frac{13}{8}$
|
$\frac{1}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.17
|
Given $f(t)=3^{t}-2$, find $f(-2)$
|
$-\frac{17}{9}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{17}{9}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.3.48
|
Solve: $2 p^{2}-p+56=-8$
|
$\frac{1+i \sqrt{511}}{4}, \frac{1-i \sqrt{511}}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1+i \sqrt{511}}{4}, \frac{1-i \sqrt{511}}{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.2.42
|
Find quotient: $\frac{5}{3} \div \frac{7}{5}$
|
$\frac{25}{21}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{25}{21}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.15
|
Add or subtract the rational expressions and simplify: $\frac{5 x+3 y}{2 x^{2} y}-\frac{3 x+4 y}{x y^{2}}$
|
$\frac{3 y^{2}-3 x y-6 x^{2}}{2 x^{2} y^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{3 y^{2}-3 x y-6 x^{2}}{2 x^{2} y^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.4.28
|
Solve the equation: $-\frac{8}{3}-\frac{1}{2} x=-\frac{4}{3} x-\frac{2}{3}\left(-\frac{13}{4} x+1\right)$
|
$-\frac{3}{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{3}{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.6.3
|
Solve the proportion: $\frac{7}{6}=\frac{2}{k}$
|
$k=\frac{12}{7}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
k=\frac{12}{7}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.5.27
|
Solve the equation: $\log _{11} k=2$
|
121
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
121
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.8.26
|
A cargo container is $50 \mathrm{ft}$ long, $10 \mathrm{ft}$ wide, and $8 \mathrm{ft}$ tall. Find its volume in cubic yards and cubic meters.
|
$148.15 \mathrm{yd}^{3} ; 113 \mathrm{~m}^{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
148.15 \mathrm{yd}^{3} ; 113 \mathrm{~m}^{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.5.6
|
$\$ 3.75$ is made up of quarters and half dollars. If the number of quarters exceeds the number of half dollars by 3, how many coins of each denomination are there?
|
$7 \mathrm{q}, 4 \mathrm{~h}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
7 \mathrm{q}, 4 \mathrm{~h}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.5.7
|
Solve the equation $\mathrm{E}=\mathrm{mc}^{2}$ for $\mathrm{m}$.
|
$m=\frac{E}{c^{2}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
m=\frac{E}{c^{2}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.1
|
Simplify the expression: $\frac{8 x^{2}}{9} \cdot \frac{9}{2}$
|
$4 x^{2}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 x^{2}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.4.24
|
Solve the equation: $4^{2 n}=4^{2-3 n}$
|
$\frac{2}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{2}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.6.4
|
Find the principal that will amount to $\$ 3000$ if invested at $3 \%$ interest compounded semiannually for 10 years.
|
2227.41
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
2227.41
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.6.15
|
Solve the following equation: $x^{\frac{2}{3}}-35=2 x^{\frac{1}{3}}$
|
$-125,343$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-125,343
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.7.23
|
Divide: $\frac{n^{2}-4}{n-2}$
|
$n+2$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
n+2
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.5.30
|
Solve the equation $\mathrm{L}=\pi\left(r_{1}+r_{2}\right)+2 d$ for $r_{1}$.
|
$r_{1}=\frac{L-2 d-\pi r^{2}}{\pi}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
r_{1}=\frac{L-2 d-\pi r^{2}}{\pi}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.5.36
|
Simplify: $\frac{-1+\sqrt{5}}{2 \sqrt{5}+5 \sqrt{2}}$
|
$\frac{2 \sqrt{5}-5 \sqrt{2}-10+5 \sqrt{10}}{30}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{2 \sqrt{5}-5 \sqrt{2}-10+5 \sqrt{10}}{30}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.2.21
|
Solve: $(3 x-2)^{\frac{4}{5}}=16$
|
$-\frac{34}{3},-10$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-\frac{34}{3},-10
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.8.20
|
Let the first angle of a triangle be $x$ degrees. Find the measures of the second and third angles.
|
$30,90,60$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
30,90,60
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.1.5
|
Simplify: $3 m \cdot 4 m n$
|
$12 m^{2} n$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
12 m^{2} n
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.3.25
|
Solve the following system of equations by elimination:
$9 x+6 y=-21$
$-10 x-9 y=28$
|
$(-1,-2)$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
(-1,-2)
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.3
|
Find a quadratic equation with the solutions 20 and 2.
|
$x^{2}-22 x+40=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
x^{2}-22 x+40=0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.22
|
Combine the following radicals: $\sqrt[5]{a^{2} b^{3}} \sqrt[4]{a^{2} b}$
|
$\sqrt[20]{a^{18} b^{17}}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[20]{a^{18} b^{17}}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.5.2.28
|
Simplify. Your answer should contain only positive expontents: $\frac{2 y x^{2} \cdot x^{-2}}{\left(2 x^{0} y^{4}\right)^{-1}}$
|
$4 y^{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
4 y^{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.39
|
Find product: $(9)(-4)$
|
-36
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-36
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.1.47
|
Find quotient: $\frac{-49}{-7}$
|
7
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
7
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.1.26
|
Simplify: $\sqrt{72 a^{3} b^{4}}$
|
$6 b^{2} a \sqrt{2 a}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
6 b^{2} a \sqrt{2 a}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.8.6
|
Simplify: $(-8 i)-(7 i)-(5-3 i)$
|
$5-12 i$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5-12 i
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.8.7.9
|
Reduce the following radical: $\sqrt[8]{x^{6} y^{4} z^{2}}$
|
$\sqrt[4]{x^{3} y^{2} z}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\sqrt[4]{x^{3} y^{2} z}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.3.27
|
Find the inverse of the function: $g(x)=\frac{8-5 x}{4}$
|
$g^{-1}(x)=\frac{-4 x+8}{5}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
g^{-1}(x)=\frac{-4 x+8}{5}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.4.5.17
|
A postal clerk sold some $15 \mathbb{C}$ stamps and some $25 \mathbb{C}$ stamps. Altogether, 15 stamps were sold for a total cost of $\$ 3.15$. How many of each type of stamps were sold?
|
$615 \mathbb{C}, 925 \mathbb{C}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
615 \mathbb{C}, 925 \mathbb{C}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.4.28
|
Solve the equation: $216^{2 n}=36$
|
$\frac{1}{3}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{3}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.6.1
|
Solve the absolute value equation: $|x|=8$
|
$8,-8$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
8,-8
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.10.1.40
|
Given $h(n)=5^{n-1}+1$, find $h\left(\frac{n}{2}\right)$
|
$5^{\frac{-2+n}{2}}+1$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
5^{\frac{-2+n}{2}}+1
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.2.19
|
Solve: $(x-1)^{-\frac{5}{2}}=32$
|
$\frac{5}{4}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5}{4}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.9.5.15
|
Find a quadratic equation with the solutions $\frac{3}{7}$ and 4.
|
$7 x^{2}-31 x+12=0$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
7 x^{2}-31 x+12=0
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.0.4.56
|
Simplify: $-8 x+9(-9 x+9)$
|
$-89 x+81$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
-89 x+81
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.4.10
|
Add or subtract the rational expressions and simplify: $\frac{x+5}{8}+\frac{x-3}{12}$
|
$\frac{5 x+9}{24}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{5 x+9}{24}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.7.2.42
|
Simplify the expression: $\frac{a^{3}+b^{3}}{a^{2}+3 \mathrm{ab}+2 b^{2}} \cdot \frac{3 a-6 b}{3 a^{2}-3 \mathrm{ab}+3 b^{2}} \div \frac{a^{2}-4 b^{2}}{a+2 b}$
|
$\frac{1}{a+2 b}$
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
\frac{1}{a+2 b}
|
college_math.Beginning_and_Intermediate_Algebra
|
exercise.1.8.44
|
The total cost for tuition plus room and board at State University is $\$2,584$. Tuition costs $\$704$ more than room and board. What is the tuition fee?
|
1644
|
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
|
college_math.algebra
|
1644
|
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