Exam 2: Equations and Inequalities

Solve the rational inequality. Write the solution set in interval notation. -A coin is tossed upward from a balcony $320 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$ . During what interval of time will the coin be at a height of at least $80 \mathrm { ft }$ ? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right.$ . $)$

Solve the equation. - $\frac { 7 x } { 9 } - 8 = x$

Solve the problem. -A ball is thrown downward from a window in a tall building. Its position at time t in seconds is $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$ where s is in feet. How long (to the nearest tenth) will it take the ball to fall 140 feet?

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 49 ) ^ { 2 } < 0$

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 252 miles in the same time that Dana travels 236 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they Travel the same length of time, at what speed does Chuck travel?

Indicate whether the statement is true always, sometimes, or never. -The sum of two imaginary numbers is an imaginary number.

Graph the solution set. - $| x | < 9$

Solve the problem. -In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 2 }$ hour longer. How far did she travel to the Appointment?

Write the statement as an absolute value inequality. -The average annual growth rate of Palmetto palms in inches satisfies the inequality $| \mathrm { x } - 4.72 | \leq 3.59$ . What range of growth corresponds to this inequality?

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 8 } - \frac { 8 } { x + 8 } = \frac { 128 } { x ^ { 2 } - 64 }$

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. - $t ^ { 2 } + 12 t + 36 = 0$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { rm } = \mathrm { t } ^ { 2 } - \mathrm { mt }$ , for $\mathrm { t }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { x + 3 } = x - 3$

Solve the problem. -Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are $\frac { 1 } { 3 }$ mile apart?

Solve the problem. -Your company uses the quadratic model y $y = - 11 x ^ { 2 } + 350 x$ 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 6?

Solve the equation. - $2 x + 1 - 5 ( x + 1 ) = - 7 x - 1$

Solve the problem. -An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 70 mph. On the return trip, the plane must fly against this wind, which decreases its normal speed By the same amount. The flight from Metro City takes 2.70 hours and the return trip takes 4)35 hours. How far is it from Metro City to Gotham?

Write the inequality in interval notation. - $x \geq - 6$

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

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 7 x } { x - 7 } - \frac { 4 } { x } = \frac { 28 } { x ^ { 2 } - 7 x }$