Exam 2: Equations and Inequalities

Solve the problem. -The outside of a picture frame has a length which is 3 cm more than width. The area enclosed by the outside of the picture frame is 130 square cm. Find the width of the outside of the picture frame.

Solve the problem. -How much pure acid should be mixed with 8 gallons of a 50% acid solution in order to get an 80% acid solution?

Solve the problem. -If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given By the formula $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { 2 }$ . If a principal amount of $5000 grows to $6050.00 in two years, what is The interest rate?

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 3 ) ^ { 2 / 3 } - 2 ( x + 3 ) ^ { 1 / 3 } - 3 = 0$

Simplify the power of i. - $\mathrm { i } ^ { - 47 }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } - 8 x ^ { 2 } > 0$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x - 18 \leq 0$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 1 = 0$

Solve the problem. -Tom Quig traveled 240 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 7 Hours, how many miles did he drive at the reduced speed?

Solve the problem. -A cylindrical container has a volume of $1088 \pi \mathrm { m } ^ { 3 }$ and a radius of 8 m. Find the height of the container.

Write the inequality in interval notation. - $- 8 \leq x$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 7 + 3 x ) ^ { 2 } \leq - 25$

Solve the equation. - $| 7 x + 4 | = | 1 - 4 x |$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 16 } { x + 2 } = 1 + \frac { 2 } { x - 4 }$

Decide whether or not the equations are equivalent. - x=-8 =64

Solve the rational inequality. Write the solution set in interval notation. - $\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $3 - 9 \mathrm { i }$

Graph the solution set. - $| x | \neq 5$

Write the statement as an absolute value inequality. - $p$ is 2 units from 6

Solve the equation. - $\left| x ^ { 2 } + 9 \right| = | 6 x |$