Exam 1: Equations and Inequalities

Solve the problem. -A contractor builds a swimming pool with cross section in the shape of a trapezoid. The deep end is 9 ft deep and the shallow end is 3 ft deep. The length of the pool is 60 ft and the width is 25 ft. AsThe pool is being filled, find the volume of water when the depth is 4 ft.

Choose the one alternative that best completes the statement or answers the question. -It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of A minute.

Choose the one alternative that best completes the statement or answers the question. Solve the inequality. Write the solution set in interval notation. - $9 ( x - 3 ) - 8 x \geq - 3$

Choose the one alternative that best completes the statement or answers the question. Simplify the expression in terms of i: - $\sqrt { - 18 }$

Find the values of x for which the expression equals zero. - $\sqrt { 4 - x ^ { 2 } } - x \left( \frac { 1 } { 2 } \right) \frac { 1 } { \sqrt { 4 - x ^ { 2 } } } ( 2 x )$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A train ride is $\$ 3.40$ per ride. Write a model for the cost $C$ (in $\$$ ) for $x$ rides on the train.

Solve the equation. - $4 d ^ { 2 / 3 } - 9 d ^ { 1 / 3 } - 9 = 0$

Simplify and write the result in standard form, a + bi. - $\frac { - 8 - 10 i } { - 2 }$

In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y'. - $- 5 ( x + y ) ^ { 2 } - 5 ( x + y ) ^ { 2 } y ^ { \prime } + 5 y ^ { 2 } y ^ { \prime } = - 5 x ^ { 2 }$

Solve the problem. -The yearly depreciation rate for a certain vehicle is modeled by $r = 1 - \left( \frac { V } { C } \right) ^ { 1 / n }$ , where V is the value of the car after n years, and C is the original cost. a. Determine the depreciation rate for a car that originally cost $18,000 and is worth $11,000 after 3 yr. Round to the nearest tenth of a percent. b. Determine the original cost of a truck that has a yearly depreciation rate of 14% and is worth $12,000 after 5 yr. Round to the nearest $100.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The zero product property indicates that if ( $( 5 x + 1 ) ( x - 4 ) = 0$ , then = 0 or = 0.

Solve the inequality. Write the solution set in interval notation. - $\frac { 9 } { 8 } - 5 y < \frac { 5 } { 4 } \quad \text { and } \frac { 4 } { 7 } y + 1 < \frac { 9 } { 14 }$

Solve the absolute value inequality. Write the solution in interval notation. - $\left| \frac { m - 12 } { 4 } \right| < 19$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 3 } { x } + \frac { 3 } { x - 4 } = \frac { 3 x - 9 } { x - 4 }$

Solve the absolute value equation. - $| 2 r + 3 | = | 5 r - 17 |$

Solve the equation by using substitution. - $z ^ { 2 / 3 } + 2 z ^ { 1 / 3 } - 15 = 0$

Perform the indicated operation. Write the answer in the form a + bi. - $\frac { - 8 + 3 i } { 5 + 7 i }$

Simplify the expression. - $\sqrt { - 81 } \cdot \sqrt { - 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If $6000 is borrowed at 7.5% simple interest for 2 yr, then the amount of interest is .

Solve the equation by using the quadratic formula. - $( 3 w - 2 ) ( w - 1 ) = - 3$