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. - $5 + 4 \sqrt { 2 } , 5 - 4 \sqrt { 2 }$

Solve the inequality. Write the solution set in interval notation. - $| 9 - x | \leq 4$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 4 x + 5 } { x - 2 } \leq 0$

Solve the equation. - $( - 2 + 4 x ) ^ { 1 / 3 } + ( - 3 + 6 x ) ^ { 1 / 3 } = 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $5 ( 2 x - 31 ) = 10 x - 155$

Solve for the indicated variable. - $V = \frac { 1 } { m } \sqrt { 2 V e m }$ , for $m$

Solve the problem. -Your company uses the quadratic model y = -11x2 + 350x to represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in Week 20?

Solve and graph the inequality. Give answer in interval notation. - $- 10 x - 12 \leq - 11 x - 17$

Solve the problem. -Your home state uses a linear model y= 48(x - 70) + 5750 to predict the number of vacationers (y) as compared to the average temperature for that week (x). Find the number of vacationers Predicted for a week with an average temperature of 79 degrees.

Solve the problem. -A coin is tossed upward from a balcony $176 \mathrm { ft }$ high with an initial velocity of $16 \mathrm { ft } / \mathrm { sec }$ . During what interval of time will the coin be at a height of at least $80 \mathrm { ft }$ ? $\left( \mathrm { h } = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { 0 } \mathrm { t } + \mathrm { h } _ { 0 } \right.$ .)

Solve the formula for the indicated variable. - $A = b h$ , for $b$

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. -4,2

Solve the problem. -If an amount of money, called the principal, $\mathrm { P }$ , 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 $A = P ( 1 + r ) ^ { 2 }$ . If a principal amount of $\$ 5500$ grows to $\$ 7147.80$ in two years, what is the interest rate?

Solve the equation using the quadratic formula. - $5 x ^ { 2 } = - 12 x - 1$

Solve the inequality. Write the solution set in interval notation. - $| x + 5 | - 2 > 12$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 x } { - 5 x + 9 } \geq 13$

Solve the equation. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

Solve the inequality. Write the solution set in interval notation. - $| 7 x + 1 | > - 8$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 20 } \cdot \sqrt { - 5 } } { \sqrt { 4 } }$

Solve the inequality. Write the solution set in interval notation. - $| x + 3 | < 2$