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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: $(5 p-6)+(1-p)$
$\boxed{4 p-5}$