Exam 1: Equations and Inequalities

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 8 + \sqrt { 13 } , - 8 - \sqrt { 13 }$

Solve the equation. - $\sqrt { x + 3 } = x - 3$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 4 x + 1 } { x - 5 } \right| \geq 0$

Simplify the power of i. - $\frac { 1 } { i ^ { - 9 } }$

Solve the equation. - $\sqrt { x + 7 } + 5 = x$

Solve the equation. - $( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$

Solve the equation. - $| x + 2 | = 0$

Solve for y. - $7 x + 6 = 6 y - 3$

Solve the equation. - $( x - 2 ) ^ { 2 / 3 } - 9 ( x - 2 ) ^ { 1 / 3 } + 20 = 0$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { m } + \frac { 1 } { t }$ , for $t$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { - 2 } \leq 3$

Solve the problem. -Find two consecutive even integers whose product is 1088 .

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $\mathrm { C } = 12 ^ { \circ }$

Simplify the power of i. -¡53

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Solve the cubic equation using factoring and the quadratic formula. - $\mathrm { x } ^ { 3 } + 64 = 0$

Solve the equation. - $| 2 x + 8 | - 9 = - 5$

Solve the formula for the indicated variable. - $\mathrm { R } = \mathrm { nE } - \mathrm { nr }$ , for $\mathrm { n }$

Find the sum or difference. Write the answer in standard form. - $\mathrm { i } \sqrt { 5 } + 5 - ( 1 + 9 \mathrm { i } \sqrt { 5 } ) - ( 2 - \mathrm { i } \sqrt { 5 } )$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -0