91Ó°ÊÓ

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$ 9 x^{2}-k x+4=0 $$

Write the augmented matrix for each system. Then solve the system. $$ \left\\{\begin{aligned} 3 x+y-2 z &=-3 \\ x-3 y-z &=-2 \\ 2 x+2 y+3 z &=11 \end{aligned}\right. $$

Solve each equation. $$ x^{2}-30=-79 $$

a. The area of a rectangle is 36 \(\mathrm{in.}^{2} .\) The perimeter of the rectangle is 36 \(\mathrm{in.}\) Write an equation using one variable to find the dimensions of the rectangle. b. Find the dimensions of the rectangle to the nearest hundredth of an inch.

Multiple Choice In a complex number plane, what geometric figure describes the complex numbers with absolute value 10\(?\) $$ \begin{array}{ll}{\text { A square }} & {\text { B circle }} \\ {\text { C line }} & {\text { D two points }}\end{array} $$

Critical Thinking The graphs of each pair of functions intersect. Find their points of intersection without using a calculator. Hint: Solve as a system using substitution. $$ \begin{array}{l}{y=x^{2}-2} \\ {y=3 x^{2}-4 x-2}\end{array} $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=-2 x^{2}+3 x-1 $$

Without graphing, tell how many \(x\) -intercepts each function has. $$ y=0.25 x^{2}+2 x+4 $$

Factor each expression completely. $$ 3 x^{2}-24 x-27 $$

Writing Describe the family of quadratic functions whose members each have \((3,4)\) as its vertex.