Exam 1: Equations, Inequalities, and Modeling

Use the appropriate formula to solve the problem. -The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 60 m. What are the length and width of the rectangle?

Use a calculator to help solve the equation. Round approximate answers to three places. --355.825x = -478.128

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

Solve the equation. -

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

Decide whether the given number is a solution to the equation preceding it. -9m + 8 = 46; 4

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. -(6 - 8i)(2 - 2i)

Find the equation of the line through the given pair of points in standard form using only integers. -(4, -2) and (-1, 1)

Use the appropriate formula to solve the problem. -The area of a trapezoid is 88 square feet. If the bases are 8 and 14 feet, find the height of the trapezoid.

Solve the problem. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). By using linear regression, the following function is obtained: y = 14.6 + 0.211x Where x is temperature and y is growth in millimeters. Use this function to predict the growth of a plant if the Temperature is 58.

The distance d from the point to the line Ax + By = C is given by the formula d Find the exact distance from the given point to the given line. -(-7, 3), 6x + 8y = 3

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 150 m. The hypotenuse is 50 m longer than the length of the longer leg. How long is the longer leg?

Find the center and radius of the circle. -

Find the center and radius of the circle. -

Find the product of the complex number and its conjugate. -4 - 6i

Solve for the indicated variable. -Solve for r.

Solve the absolute value equation. -

Decide whether the given number is a solution to the equation preceding it. -7p + 5p - 4 = 32; 3

Find the real or imaginary solutions by completing the square. - + 10z + 3 = 0

Solve the equation. -4(2z - 2) = 7(z + 4)