Exam 1: Equations, Inequalities, and Modeling

Solve the problem. -A car rental company has two rental rates. Rate 1 is $81 per day plus $.18 per mile. Rate 2 is $162 per day plus $.09 per mile. If you plan to rent for one day, how many miles would you need to drive to pay less by taking Rate 2?

Solve the problem. -The cost, T, in hundreds of dollars, of tuition at one community college is given by where c is the number of credits for which a student registers. Estimate the cost of tuition if a student registers for 13 credits.

Solve the problem. -The temperature, t, in degrees Fahrenheit, of water being heated is where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation. -20k + 71 = 4(5k + 17)

Solve the problem. -The population p, in thousands, of one town can be approximated by where d is the number of years since 1985. Estimate the population of the town in the year 1994.

Find the real or imaginary solutions by using the quadratic formula. - + 8m + 2 = 0

For the equation in the form + bx + c = 0, determine the number of real solutions by examining the graph of y = + bx + c. - + 3x - 33 = 0

Use the square root property to find all real or imaginary solutions to the equation. - = 36

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

Find the real or imaginary solutions by completing the square. - + 12a + 11 = 0

Find the x- and y-intercepts for the equation. Then graph the equation. -6x - 3y = 1.8

Write an inequality of the form k or of the form k so that the inequality has the given solution set. -

Solve for the indicated variable. -Solve for v.

Solve the equation by factoring. -21 - + 4x = 0

Solve the problem. -The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). By using linear regression, the following function is obtained: y = 55.8 + 2.79x where x is the Cost of advertising (in thousands of dollars) and y is number of products sold (in thousands). Use this function To predict the number of products sold (in thousands of dollars) if the cost of advertising is $11,000.

Solve the compound inequality. Write the solution set using interval notation and graph it. -

Solve the problem. -Find the value of k so that the graph of 13y + kx = 4 and the line containing the points (5, -8) and (2, 4) are perpendicular.

Graph the equation in the rectangular coordinate system. -y + 2 = 0

Evaluate the indicated power of i. -

Solve the compound inequality. Write the solution set using interval notation and graph it. -