Exam 1: Equations, Inequalities, and Applications

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }$

Solve the problem. -The product of 6 and the square of a number is 24. Find the number(s).

Find the real solutions, if any, of the equation. Use the quadratic formula. -3x² + 12x + 1 = 0

Determine whether the equation is linear or nonlinear. - $\frac { 9 } { x } + 1 = 7$

Solve the problem. -A ball is thrown vertically upward from the top of a building 144 feet tall with an initial velocity of 128 feet per second. The distance s (in feet)of the ball from the ground after t seconds is s = 144 + 128t - 16t2. After how many seconds will the ball pass the top of the building on its way down?

Solve the equation. - $x \left( x ^ { 2 } + 8 \right) = 3 + x ^ { 3 }$

Perform the desired operation. Write the answer in the form a + bi. - $( - 2 + i ) ( - 2 - i )$

Solve the problem. -A chemist needs 190 milliliters of a 66% solution but has only 42% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Solve the equation after making an appropriate substitution. - $x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0$

Solve the linear inequality. Express the solution in set-builder notation. - $2 x + 6 < 14$

Solve the problem. -The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is 54 square feet, find its dimensions.

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - $0 \leq \frac { 3 x + 4 } { 3 } < 4$

Solve the polynomial inequality. Express the solution in interval notation. - $( x + 4 ) ( x - 4 ) ( x - 5 ) > 0$

Solve the equation by completing the square. - $9 x ^ { 2 } + 36 x + 20 = 0$

Solve the equation after making an appropriate substitution. - $3 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 0$

Solve the equation. -9x - (3x - 1)= 2

Perform the indicated operations and write the result in standard form. - $\frac { - 6 - \sqrt { - 180 } } { 6 }$

Solve the problem. -Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 126 miles in the same time that Carl travels 120 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed?

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } ^ { 18 }$

Solve the problem. -George and Matt have a painting business. George has less experience and it takes him 3 hours more to paint a medium sized room than it takes Matt. Working together they can paint a medium sized room in 6 hours. How long does it take each of them working individually? Round to the nearest tenth of an hour.