Exam 1: Equations, Inequalities, and Modeling

Solve the problem. -The temperature of water in a certain lake on a day in October can be determined by using the model y = 15.2 - 0.537x where x is the number of feet down from the surface of the lake and y is the Celsius Temperature of the water at that depth. Based on this model, how deep in the lake is the water 8 degrees? (Round to the nearest foot.)

Write an absolute value inequality that has the given solution set. -

State the value of the discriminant and the number of real solutions. -3 + 12x + 1 = 0

Write the standard equation for the circle. -

Write the expression in the form a + bi, where a and b are real numbers. -

Solve the problem. -The cost, c, in dollars of car rental is , where m is the number of miles driven. Estimate the cost of car rental if the number of miles driven is 32.

Solve the problem. -Jim had grades of 67 and 88 on two chemistry tests. What is the lowest score he can get on the third test to maintain an average of 75?

Write the quotient in the form a + bi. -

Solve the problem. -A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 18 inches across and requires 2.2 bags of concrete in order to fill it to ground level. What is the depth of the hole? Round Your answer to the nearest inch. (One bag of concrete, when mixed with the appropriate amount of water, Makes of material.)

Decide whether the given number is a solution to the equation preceding it. -

Solve the absolute value inequality. Write the solution set using interval notation. -

Find the real or imaginary solutions by using the quadratic formula. -x2 + 3x - 54 = 0

Use the method of your choice to find all real solutions of the equation. - = 14

Find the x- and y-intercepts for the equation. Then graph the equation. -6x - 24y = 24

Find the x- and y-intercepts for the equation. Then graph the equation. --6x - 36y = 36

Solve the problem. -At $10 per ticket, the Casper Coyotes will fill all 7000 seats in the assembly hall. The manager knows that for every $1 increase in the price, 100 tickets will go unsold. Write the number of tickets sold, n, as a function of the Ticket price, p. How much money will be taken in if the tickets are $15 each? Hint: Find the equation of the line Through (10, 7000), (11, 6900), (12, 6800), etc.

Solve the problem. -One maid can clean the house in 3 hours. Another maid can do the job in 5 hours. How long will it take them to do the job working together?

Find the real solutions for the given quadratic equation. Round results to two decimal places. - + 2.3x + 8.2 = 0

Solve the problem. -Martha can rake the leaves in her yard in 5 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. -