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A man has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, find the dimensions of his garden.
A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.
84 mi
For the following exercises, use the quadratic equation to solve.
${x}^{2}-5x+9=0$
For the following exercises, name the horizontal component and the vertical component.
$\mathrm{-2}-i$
horizontal component $\text{\hspace{0.17em}}\mathrm{-2};$ vertical component $\text{\hspace{0.17em}}\mathrm{-1}$
For the following exercises, perform the operations indicated.
$\left(9-i\right)-\left(4-7i\right)$
$2\sqrt{-75}+3\sqrt{25}$
$-6i(i-5)$
$\sqrt{-4}\xb7\sqrt{-12}$
$\sqrt{-2}\left(\sqrt{-8}-\sqrt{5}\right)$
$\mathrm{-4}-i\sqrt{10}$
$\frac{2}{5-3i}$
For the following exercises, solve the quadratic equation by factoring.
$2{x}^{2}-7x-4=0$
$25{x}^{2}-9=0$
For the following exercises, solve the quadratic equation by using the square-root property.
${x}^{2}=49$
For the following exercises, solve the quadratic equation by completing the square.
${x}^{2}+8x-5=0$
For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution .
$2{x}^{2}-5x+1=0$
For the following exercises, solve the quadratic equation by the method of your choice.
${(x-2)}^{2}=16$
For the following exercises, solve the equations.
${x}^{\frac{3}{2}}=27$
$4{x}^{3}+8{x}^{2}-9x-18=0$
$\sqrt{x+9}=x-3$
$\left|3x-7\right|=5$
$\left|2x+3\right|-5=9$
$x=\frac{11}{2},\frac{\mathrm{-17}}{2}$
For the following exercises, solve the inequality. Write your final answer in interval notation.
$5x-8\le 12$
$\frac{x-1}{3}+\frac{x+2}{5}\le \frac{3}{5}$
$\left|5x-1\right|>14$
For the following exercises, solve the compound inequality. Write your answer in interval notation.
$\mathrm{-4}<3x+2\le 18$
For the following exercises, graph as described.
Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.
$\left|x+3\right|\ge 5$
Graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true.
$x+3<3x-4$
Where the blue is below the orange line; point of intersection is $\text{\hspace{0.17em}}x=\mathrm{3.5.}$
$\left(3.5,\infty \right)$
Graph the following: $\text{\hspace{0.17em}}2y=3x+4.$
$y=\frac{3}{2}x+2$
x | y |
---|---|
0 | 2 |
2 | 5 |
4 | 8 |
Find the x- and y -intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.
$3x-4y=12$
$\left(0,\mathrm{-3}\right)$ $\left(4,0\right)$
Find the exact distance between $\text{\hspace{0.17em}}\left(5,\mathrm{-3}\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(-2,8\right).\text{\hspace{0.17em}}$ Find the coordinates of the midpoint of the line segment joining the two points.
Write the interval notation for the set of numbers represented by $\text{\hspace{0.17em}}\left\{x|x\le 9\right\}.$
$\left(-\infty ,9\right]$
Solve for x : $\text{\hspace{0.17em}}5x+8=3x-10.$
Solve for x : $\text{\hspace{0.17em}}3\left(2x-5\right)-3\left(x-7\right)=2x-9.$
$x=\mathrm{-15}$
Solve for x : $\text{\hspace{0.17em}}\frac{x}{2}+1=\frac{4}{x}$
Solve for x : $\text{\hspace{0.17em}}\frac{5}{x+4}=4+\frac{3}{x-2}.$
$x\ne \mathrm{-4},2;$ $x=\frac{-5}{2},1$
The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.
Solve for x . Write the answer in simplest radical form.
$\frac{{x}^{2}}{3}-x=\frac{\mathrm{-1}}{2}$
$x=\frac{3\pm \sqrt{3}}{2}$
Solve: $\text{\hspace{0.17em}}3x-8\le 4.$
Solve: $\text{\hspace{0.17em}}\left|2x+3\right|<5.$
$\left(\mathrm{-4},1\right)$
Solve: $\text{\hspace{0.17em}}\left|3x-2\right|\ge 4.$
For the following exercises, find the equation of the line with the given information.
Passes through the points $\text{\hspace{0.17em}}\left(-4,2\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(5,\mathrm{-3}\right).$
$y=\frac{\mathrm{-5}}{9}x-\frac{2}{9}$
Has an undefined slope and passes through the point $\text{\hspace{0.17em}}\left(4,3\right).$
Passes through the point $\text{\hspace{0.17em}}\left(2,1\right)\text{\hspace{0.17em}}$ and is perpendicular to $\text{\hspace{0.17em}}y=\frac{-2}{5}x+3.$
$y=\frac{5}{2}x-4$
Add these complex numbers: $\text{\hspace{0.17em}}(3-2i)+(4-i).$
Simplify: $\text{\hspace{0.17em}}\sqrt{\mathrm{-4}}+3\sqrt{\mathrm{-16}}.$
$14i$
Multiply: $\text{\hspace{0.17em}}5i\left(5-3i\right).$
Divide: $\text{\hspace{0.17em}}\frac{4-i}{2+3i}.$
$\frac{5}{13}-\frac{14}{13}i$
Solve this quadratic equation and write the two complex roots in $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ form: $\text{\hspace{0.17em}}{x}^{2}-4x+7=0.$
Solve: $\text{\hspace{0.17em}}{\left(3x-1\right)}^{2}-1=24.$
$x=2,\frac{-4}{3}$
Solve: $\text{\hspace{0.17em}}{x}^{2}-6x=13.$
Solve: $\text{\hspace{0.17em}}4{x}^{2}-4x-1=0$
$x=\frac{1}{2}\pm \frac{\sqrt{2}}{2}$
Solve:
$\sqrt{x-7}=x-7$
Solve: $\text{\hspace{0.17em}}{\left(x-1\right)}^{\frac{2}{3}}=9$
For the following exercises, find the real solutions of each equation by factoring.
${\left(x+5\right)}^{2}-3\left(x+5\right)-4=0$
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