Chapter 2

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). $$ (4,1)(-2,-3)(5,0) $$

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. $$ |3 x-4|=8 $$

For the following exercises, solve the quadratic equation by completing the square. Show each step. $$ 2 x^{2}-3 x-1=0 $$

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

For the following exercises, use the formula given to solve for the required value. \(S u m=\frac{1}{1-r}\) is the formula for an infinite series sum. If the sum is \(5,\) find \(r\).

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

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. $$ |4 x+1|-3=6 $$

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

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

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. $$ |2 x-1|-7=-2 $$

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

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, 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. $$ |2 x+1|-2=-3 $$

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

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

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

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

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

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

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

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. $$ -|2 x+1|=-3 $$

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

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 slopeintercept formula: \(y=m x+b\)

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

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

For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. $$ 6 x^{2}-x-2=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{2+\sqrt{-12}}{2} $$

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. $$ \begin{array}{l} 3 x-2 y=5 \\ 6 y-9 x=6 \end{array} $$

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

For the following exercises, graph both straight lines (left-hand side being y1 and right-hand side being \(y 2\) ) 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. $$ x+3<3 x-4 $$

For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. $$ 4(t-1)^{2}-9(t-1)=-2 $$

For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. $$ 2 x^{2}+5 x+3=0 $$

For the following exercises, perform the indicated operation and express the result as a simplified complex number. $$ \frac{4+\sqrt{-20}}{2} $$

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. The area of a trapezoid is given by \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right) .\) Use the formula to find the area of a trapezoid with \(h=6, \quad b_{1}=14, \quad\) and \(b_{2}=8\)

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. $$ \begin{array}{l} y=\frac{3 x+1}{4} \\ y=3 x+2 \end{array} $$

For each of the following exercises, find and plot the \(x\) - and \(y\) -intercepts, and graph the straight line based on those two points. $$ 4 x-3 y=12 $$