Exam 1: Equations and Inequalities

Solve a Quadratic Equation by Completing the Square Write the word or phrase that best completes each statement or answers the question. Solve the equation by completing the square. -

Solve the problem. -The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, whichusually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 perpound. They have a 70-pound barrel of the raisins. How many pounds of the nuts should they mix withthe barrel of raisins so that they hit their target value of $6 per pound for the mixture?

Solve the equation by the Square Root Method. -

Write the expression in the standard form a + bi. -If z = 4 - 2i, evaluate z +

Solve the inequality. Express your answer using interval notation. -

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The profit derived from the sale of x video cameras is $330 per unit less the sum of $2,100 costs plus $120per unit.

Find the real solutions, if any, of the equation. Use the quadratic formula and a calculator. Express any solutions rounded to two decimal places. Use 3.14 to approximate -

Find the real solutions of the equation by factoring. -

Express the graph shown using interval notation. Also express it as an inequality involving x. -

Solve the problem. -Two friends decide to meet in Chicago to attend a Cubʹs baseball game. Rob travels 78 miles in the sametime that Carl travels 64 miles. Robʹs trip uses more interstate highways and he can average 7 mph morethan Carl. What is Robʹs average speed?

Find the real solutions of the equation. -(

Write the expression in the standard form a + bi. -

Solve the equation. -

Solve the inequality. Express your answer using interval notation. -

Find the real solutions of the equation. -

Solve the equation. -11x = -10 +

Write the interval as an inequality involving x, and illustrate the inequality using the real number line. -

Solve the problem. -A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 51 inches more than thewidth. What are the dimensions of the carpet?

Solve the equation. -

Write the word or phrase that best completes each statement or answers the question. -An open box is to be constructed from a square sheet of plastic by removing a square of side 2 inches fromeach corner, and then turning up the sides. If the box must have a volume of 242 cubic inches, find thelength of one side of the open box.