Exam 1: Equations and Inequalities

Solve the problem. -A rock falls from a tower that is 176 feet high. As it is falling, its height is given by the formula $h = 176 - 16 t ^ { 2 }$ . How many seconds (in tenths) will it take for the rock to hit the ground $( h = 0 )$ ?

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $8 + 3 z ^ { 2 } = 3 z$

Solve the problem. -Walt made an extra $8000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $247.50 in interest. How much was invested at 3.25%?

Solve the inequality. Write the solution set in interval notation. - $| x - 5 | \geq 0$

Graph the solution set. - $| x | > - 1$

Decide whether or not the equations are equivalent. - x=-3 =9

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $t ^ { 2 } + 6 t + 9 = 0$

Solve the equation. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

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

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 1.25% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $825. Find the amount Invested at 1.25%.

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

Solve the equation. - $x ^ { 2 } - 13 = 0$

Solve the equation. - $\frac { 10 } { x - 2 } = 1 + \frac { 12 } { x + 2 }$

Solve the equation by completing the square. - $4 x ^ { 2 } - 2 x - 6 = 0$

Solve the equation. - $\left| \frac { 2 } { x + 2 } \right| = 5$

Solve the equation by the square root property. - $x ^ { 2 } = 49$

Solve the equation. - $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

Indicate whether the statement is true always, sometimes, or never. -When i is raised to an even power, the result is -1.

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. - $2 i , - 2 i$

Solve the problem. -The length of a rectangle is 10 inches more than its width. If 5 inches are taken from the length and added to the width, the figure becomes a square with an area of 121 square inches. What are the Dimensions of the original figure?