91Ó°ÊÓ

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

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