Exam 11: P Prerequisites

Solve the equation $x^{2}+5=8 x$ by completing the square. Show all steps.

Find the equation of the line that passes through the point (10, -3) and whose graph is perpendicular to the graph of y=5x-2.

A projectile is launched straight up from the ground with an initial velocity of $320 \frac{\mathrm{ft}}{\mathrm{sec}}$ . At what time(s) will the projectile be at least 1,584 feet above the ground? Directions: Show all work where appropriate. A graphing calculator may be necessary to answer some questions.

Solve graphically: $|6-4 x|=5$

Complete the table of solutions for the equation y=-3 x+2 x y -2 3 -4 5

Name the algebraic property or properties illustrated by the equation. 3(x+y)=3 x+3 y

Find the equation of a line that has x-intercept 2 and y-intercept -7. Write the equation in slope-intercept form.

Last week a theater purchased an air conditioner for $\$ 24,000$ . The air conditioner's value will depreciate $\$ 4,000$ a year for each of the next 6 years. The equation $y=24,000-4,000 x, 0 \leq x \leq 6$ models the air conditioner's value, where $y$ is the value of the air conditioner and $x$ is the number of years after purchase. In how many years will the value of the air conditioner be $\$ 8,000$ ?

Solve the inequality $|3 x-4| \geq 2$ algebraically. Write the solution in interval notation and draw its number line graph.

$\text { Solve the equation } x^{2}+14 x=-9 \text { by completing the }$ square.

Use the quadratic formula to solve $6 x^{2}-4 x+5=0$

Solve the inequality |2x+1|<5 algebraically.