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college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.61
Simplify: $-10-4(n-5)$
$10-4 n$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.9.7
Solve the following systems of equation: $x y=90$ $(x-5)(y+1)=120$
$(45,2),(-10,-9)$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.8.42
Evaluate the expression: $\frac{8 i}{6-7 i}$
$\frac{48 i-56}{85}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.8.9
Find three consecutive integers such that their sum is 108.
$35,36,37$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.5.31
Find a quadratic equation with the solutions $2 \pm \sqrt{6}$.
$x^{2}-4 x-2=0$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.1.5
Specify the domain of the function: $f(x)=x^{2}-3 x-4$
all real numbers
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.6.21
Find the square: $(p+7)^{2}$
$p^{2}+14 p+49$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.1.36
Simplify: $\frac{k^{2}-12 k+32}{k^{2}-64}$
$\frac{k-8}{k+4}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.47
Distribute: $-9 x(4-x)$
$-36 x+9 x^{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.3.4
Write the number in scientific notation: 1.09
$1.09 \times 10^{0}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.6.15
Solve the proportion: $\frac{3}{10}=\frac{a}{a+2}$
$a=\frac{6}{7}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.3.2.31
Solve the compound inequality and give interval notation: $2 x+9 \geqslant 10 x+1$ and $3 x-2<7 x+2$
$-1<x \leqslant 1:(-1,1]$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.4.31
Simplify: $\frac{\sqrt{2 p^{2}}}{\sqrt{3 p}}$
$\frac{\sqrt{6 p}}{3}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.4.28
Evaluate $\left(7+4 m+8 m^{4}\right)-\left(5 m^{4}+1+6 m\right)$.
$3 m^{4}-2 m+6$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.10.1
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.
12
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.4.19
Solve the equation: $9^{2 n+3}=243$
$-\frac{1}{4}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.2.5.11
Find the slope of a line perpendicular to the given line: $y=-\frac{1}{3} x$
3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.1.19
Evaluate the expression: $(-8)-(-5)$
-3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.4.11
Solve the equation: $\frac{3}{2}\left(\frac{7}{3} n+1\right)=\frac{3}{2}$
0
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.1.28
Evaluate the expression: $7-3$
4
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.2.4
Solve: $4 x^{3}-2=106$
3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.1.35
Solve the equation: $13 a=-143$
-11
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.2.77
Evaluate the expression: $\left(-\frac{15}{8}\right)+\frac{5}{3}$
$-\frac{5}{24}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.2.34
Simplify the expression: $\frac{n-7}{n^{2}-2 n-35} \div \frac{9 n+54}{10 n+50}$
$\frac{10}{9(n+6)}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.8.43
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.
14,16
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.3.29
Build up each fraction by finding the Least Common Denominator: $\frac{4 x}{x^{2}-x-6}, \frac{x+2}{x-3}$
$\frac{4 x}{(x-3)(x+2)}, \frac{x^{2}+4 x+4}{(x-3)(x+2)}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.17
Evaluate using the given values: $k \times 3^{2}-(j+k)-5$; $j=4, k=5$
36
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.1.37
Simplify: $-8 \sqrt{180 x^{4} y^{2} z^{4}}$
$-48 x^{2} z^{2} y \sqrt{5}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.4.4.18
Solve the following systems of equation: $x+2 y-3 z=9$ $2 x-y+2 z=-8$ $3 x-y-4 z=3$
$(-1,2,-2)$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.6.3
Find the product: $(1+3 p)(1-3 p)$
$1-9 p^{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.4.13
Multiply and simplify: $(2+2 \sqrt{2})(-3+\sqrt{2})$
$-2-4 \sqrt{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.5.3
Solve the equation $\frac{f}{g} x=b$ for $\mathrm{x}$.
$x=\frac{\mathrm{gb}}{f}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.3.20
Simplify and write the answer in scientific notation: $\frac{7.2 \times 10^{-1}}{7.32 \times 10^{-1}}$
$9.836 \times 10^{-1}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.7.19
Divide: $\frac{10 x^{2}-32 x+9}{10 x-2}$
$x-3+\frac{3}{10 x-2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.6.12
Solve the absolute value equation: $|9 p+6|=3$
$-\frac{1}{3},-1$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.4.32
Add or subtract the rational expressions and simplify: $\frac{4 x}{x^{2}-2 x-3}-\frac{3}{x^{2}-5 x+6}$
$\frac{4 x+1}{(x+1)(x-2)}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.6.5
Find the principal that will amount to $\$ 2500$ if invested at $5 \%$ interest compounded semiannually for 7.5 years.
1726.16
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.3.2.18
Solve the compound inequality and give interval notation: $1 \leqslant \frac{p}{8} \leqslant 0$
No solution : $\oslash$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.6.25
Simplify and express with positive exponents: $\frac{3 y^{-\frac{5}{4}}}{y^{-1} \cdot 2 y^{-\frac{1}{3}}}$
$\frac{3 y^{\frac{1}{12}}}{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.6.25
Solve the proportion: $\frac{2}{p+4}=\frac{p+5}{3}$
$p=-7,-2$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.7.23
Solve the equation for $x$: $\frac{3}{x+2}+\frac{x-1}{x+5}=\frac{5 x+20}{6 x+24}$
4,7
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.27
Combine Like Terms: $-7 x-2 x$
$-9 x$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.3.6
State if the given functions are inverses: $f(x)=\frac{x-5}{10}$ $h(x)=10 x+5$
Yes
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.5.24
Solve the equation $\mathrm{q}=6(L-p)$ for $\mathrm{L}$.
$L=\frac{q+6 p}{6}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.7.6
Divide: $\frac{5 p^{4}+16 p^{3}+16 p^{2}}{4 p}$
$\frac{5 p^{3}}{4}+4 p^{2}+4 p$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.5.9
Find the product: $(8 b+3)(7 b-5)$
$56 b^{2}-19 b-15$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.4.4.26
Solve the following systems of equation: $2 x+y=z$ $4 x+z=4 y$ $y=x+1$
$(1,2,4)$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.2.40
Solve the equation: $4+\frac{a}{3}=1$
-9
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.3.27
Solve: $n^{2}=-21+10 n$
7,3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.5.34
Solve the equation: $\log _{7}-3 n=4$
$-\frac{2401}{3}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.6.27
Solve the following equation: $x^{8}-17 x^{4}+16=0$
$\pm 1, \pm i, \pm 2, \pm 2 i$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.10.17
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?
$\mathrm{r}=5$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.2.15
Simplify. Your answer should contain only positive expontents: $\frac{u^{2}}{4 u^{0} v^{3} \cdot 3 v^{2}}$
$\frac{u^{2}}{12 v^{5}}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.1.40
Simplify: $\frac{2 x^{4} y^{5} \cdot 2 z^{10} x^{2} y^{7}}{\left(x y^{2} z^{2}\right)^{4}}$
$4 x^{2} y^{4} z^{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.4.26
Solve the equation: $625^{2 x}=25$
$\frac{1}{4}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.2.22
Simplify the expression: $\frac{2 r}{r+6} \div \frac{2 r}{7 r+42}$
7
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.3.3
State if the given functions are inverses: $f(x)=\frac{-x-1}{x-2}$ $g(x)=\frac{-2 x+1}{-x-1}$
Yes
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.6.26
Solve the proportion: $\frac{5}{n+1}=\frac{n-4}{10}$
$n=-6,9$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.6.22
Solve the absolute value equation: $3-|6 n+7|=-40$
$6,-\frac{25}{3}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.4.12
Add or subtract the rational expressions and simplify: $\frac{2 a-1}{3 a^{2}}+\frac{5 a+1}{9 a}$
$\frac{5 a^{2}+7 a-3}{9 a^{2}}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.9.11
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.
10,6
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.2.2.14
Find the slope of the line through the points $(13,-2)$ and $(7,7)$.
$-\frac{3}{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.7.11
Solve the equation for $x$: $\frac{4-x}{1-x}=\frac{12}{3-x}$
$-5,0$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.71
Simplify: $5(1-6 k)+10(k-8)$
$-75-20 k$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.1.12
Simplify: $\left(3^{2}\right)^{3}$
$3^{6}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.8.46
Evaluate the expression: $\sqrt{-12} \sqrt{-2}$
$-2 \sqrt{6}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.4.24
Solve the equation: $-\frac{149}{16}-\frac{11}{3} r=-\frac{7}{4} r-\frac{5}{4}\left(-\frac{4}{3} r+1\right)$
$-\frac{9}{4}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.7.1
Reduce the following radical: $\sqrt[8]{16 x^{4} y^{6}}$
$\sqrt[4]{4 x^{2} y^{3}}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.7.3
Solve the equation for $x$: $x+\frac{20}{x-4}=\frac{5 x}{x-4}-2$
3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.7.15
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?
$7 \times 9$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.4.39
Solve the equation: $5^{-3 n-3} \cdot 5^{2 n}=1$
-3
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.5.33
Find a quadratic equation with the solutions $1 \pm 3 i$.
$x^{2}-2 x+10=0$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.1.11
State the excluded values for $\frac{10 m^{2}+8 m}{10 m}$
0
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.31
Combine Like Terms: $x-10-6 x+1$
$-5 x-9$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.1.14
Solve the equation: $\frac{5}{9}=\frac{b}{9}$
5
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.4.7
Evaluate using the given values: $5 j+\frac{k h}{2}$; $h=5, j=4, k=2$
25
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.5.12
Simplify: $\frac{5}{2 \sqrt{3}-\sqrt{2}}$
$\frac{2 \sqrt{3}+\sqrt{2}}{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.3.12
Find the Least Common Denominator: $5 x^{2} y, 25 x^{3} y^{5} z$
$25 x^{3} y^{5} z$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.3.7
Solve: $0=-8(p-5)$
5
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.6.29
Solve the absolute value equation: $-7+8|-7 x-3|=73$
$-\frac{13}{7}, 1$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.10.3.30
Find the inverse of the function: $f(x)=\frac{5 x-5}{4}$
$f^{-1}(x)=\frac{5+4 x}{5}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.7.33
Divide: $\frac{3 n^{3}+9 n^{2}-64 n-68}{n+6}$
$3 n^{2}-9 n-10-\frac{8}{n+6}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.4.43
Add or subtract the rational expressions and simplify: $\frac{2 x+7}{x^{2}-2 x-3}-\frac{3 x-2}{x^{2}+6 x+5}$
$\frac{-(x-29)}{(x-3)(x+5)}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.6.26
Solve the following equation: $8 x^{6}+7 x^{3}-1=0$
$\frac{1}{2},-1, \frac{-1 \pm i \sqrt{3}}{4}, \frac{1 \pm i \sqrt{3}}{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.3.9
Simplify: $2 \sqrt{2}-3 \sqrt{18}-\sqrt{2}$
$-8 \sqrt{2}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.5.40
Find the product: $3(2 x+3)(6 x+9)$
$36 x^{2}+108 x+81$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.1.26
Solve the equation: $3 n=24$
8
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.8.12
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?
$4 \frac{4}{9}$ days
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.5.25
Simplify: $\frac{a+\sqrt{\mathrm{ab}}}{\sqrt{a}+\sqrt{b}}$
$\sqrt{a}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.4.5.15
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.
$13 \mathrm{n}, 5 \mathrm{~d}$
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college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.7.5.36
Simplify: $\frac{x^{-3}+y^{-3}}{x^{-2}-x^{-1} y^{-1}+y^{-2}}$
$\frac{x+y}{x y}$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.0.3.22
Solve: $\frac{-9 \cdot 2-(3-6)}{1-(-2+1)-(-3)}$
-3
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.1.3
Solve: $\sqrt{6 x-5}-x=0$
1,5
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.4.10
Multiply and simplify: $5 \sqrt{15}(3 \sqrt{3}+2)$
$45 \sqrt{5}+10 \sqrt{15}$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.5.9
Find a quadratic equation with the solutions $-4$ and 11.
$x^{2}-7 x-44=0$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.1.16
Simplify: $\sqrt{100 n^{3}}$
$10 n \sqrt{n}$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.8.6.23
Simplify and express with positive exponents: $\frac{a^{\frac{3}{4}} b^{-1} \cdot b^{\frac{7}{4}}}{3 b^{-1}}$
$\frac{b^{\frac{7}{4}} a^{\frac{3}{4}}}{3}$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.9.5.8
Find a quadratic equation with the solutions $-2$ and $-5$.
$x^{2}+7 x+10=0$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.5.5.1
Find the product: $6(p-7)$
$6 p-42$
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra
college_math.Beginning_and_Intermediate_Algebra
exercise.1.2.6
Solve the equation: $-4-b=8$
-12
Creative Commons Attribution 3.0 Unported License (CC BY 3.0)
college_math.algebra