Chapter 2

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{-5+3 i}{2 i} $$

Solve the quadratic equation by completing the square. Show each step. $$ 6 p^{2}+7 p-20=0 $$

For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). $$(4,1)(-2,-3)(5,0)$$

\(F=m a\) indicates that force \((F)\) equals mass \((m)\) times acceleration \((a)\). Find the acceleration of a mass of \(50 \mathrm{~kg}\) if a force of \(12 \mathrm{~N}\) is exerted on it.

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ 2 x-5<-11 \text { or } 5 x+1 \geq 6 $$

For the following exercises, solve the equation involving absolute value. $$ |1-4 x|-1=5 $$

Solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ 2 x-5<-11 \text { or } 5 x+1 \geq 6 $$

For the following exercises, find the equation of the line using the given information. \((1,7)\) and \((3,7)\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{6+4 i}{i} $$

Solve the quadratic equation by completing the square. Show each step. $$ 2 x^{2}-3 x-1=0 $$

For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). $$ (-1,2)(0,4)(2,1) $$

For the following exercises, solve the equation involving absolute value. $$ |4 x+1|-3=6 $$

Solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. $$ x+7

For the following exercises, find the equation of the line using the given information. The slope is undefined and it passes through the point \((2,3) .\)

For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. Solve for \(W : P=2 L+2 W\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{2-3 i}{4+3 i} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 2 x^{2}-6 x+7=0 $$

For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line). $$(-3,0)(-3,4)(-3,-3)$$

For the following exercises, graph the 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. $$ |x-1|>2 $$

For the following exercises, solve the equation involving absolute value. $$ |2 x-1|-7=-2 $$

Graph the 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. $$ |x-1|>2 $$

For the following exercises, find the equation of the line using the given information. The slope equals zero and it passes through the point \((1,-4) .\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{3+4 i}{2-i} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ x^{2}+4 x+7=0 $$

For the following exercises, graph the 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. $$ |x+3| \geq 5 $$

For the following exercises, solve the equation involving absolute value. $$ |2 x+1|-2=-3 $$

Graph the 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. $$ |x+3| \geq 5 $$

For the following exercises, find the equation of the line using the given information. The slope is \(\frac{3}{4}\) and it passes through the point \((1,4)\)

For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. Solve for \(f : \frac{1}{p}+\frac{1}{q}=\frac{1}{f}\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{2+3 i}{2-3 i} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 3 x^{2}+5 x-8=0 $$

Name the quadrant in which the following points would be located. If the point is on an axis, name the axis. a. \((-3,-4) \quad\) b. \((-5,0) \quad\) c. \((1,-4) \quad\) d. \((-2,7) \quad\) e. \((0,-3)\)

Solve for \(f: \frac{1}{p}+\frac{1}{q}=\frac{1}{f}\)

For the following exercises, graph the 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. $$ |x+7| \leq 4 $$

For the following exercises, solve the equation involving absolute value. $$ |x+5|=0 $$

For the following exercises, find the equation of the line using the given information. \((-1,3)\) and \((4,-5)\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \sqrt{-9}+3 \sqrt{-16} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 9 x^{2}-30 x+25=0 $$

For each of the following exercises, construct a table and graph the equation by plotting at least three points. $$y=\frac{1}{3} x+2$$

For the following exercises, graph the 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. $$ |x-2|<7 $$

For the following exercises, solve the equation involving absolute value. $$ -|2 x+1|=-3 $$

Graph the 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. $$ |x-2|<7 $$

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. \(y=2 x+7\) \(y=-\frac{1}{2} x-4\)

For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. Solve for \(m\) in the slope-intercept formula: \(y=m x+b\)

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ -\sqrt{-4}-4 \sqrt{-25} $$

Determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$2 x^{2}-3 x-7=0$$

For each of the following exercises, construct a table and graph the equation by plotting at least three points. $$y=-3 x+1$$

For the following exercises, graph the 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. $$ |x-2|<0 $$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ x^{4}-10 x^{2}+9=0 $$

Graph the 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. $$ |x-2|<0 $$