Exam 1: Preliminaries

A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the following figure, find the total distance covered on the tour. __________

Ivan wishes to determine which antenna he should purchase for his home. The TV store has supplied him with the information: Ivan wishes to receive Channel 17 (VHF) that is located 22 mi east and 41 mi north of his home and Channel 38 (UHF) that is located 24 mi south and 44 mi west of his home. Which model will allow him to receive both channels at the least cost? (Assume that the terrain between Ivan's home and both broadcasting stations is flat.)

Using data compiled by the Admissions Office at Faber University, college admissions officers estimate that 55% of the students who are offered admission to the freshman class at the university will actually enroll. If the desired freshman class size for the upcoming academic year is 1,650 students, how many students should be admitted?

Find the distance between the points and .

Use the fact that to evaluate the expression without using a calculator.

Perform the indicated operations and simplify the expression.

A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of at least $14,000 on the commodity?

Find the real roots of the equation by factoring.

Rationalize the numerator of the expression.

Simplify the expression.

Metro Department Store's annual sales (in millions of dollars) during the past 5 yr were Derive an equation of the line L through the points corresponding to the first and fifth years.

Perform the indicated operations and simplify the expression.

Perform the indicated operations and simplify the expression.

Simplify the expression. (Assume that r, s, and t are positive.)

Find an equation of the circle with center at (-a, -a) and radius 6a.

Factor out the greatest common factor from the expression.

The diameter x (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality What is the smallest diameter a ball bearing in the batch can have?

Perform the indicated operations and simplify the expression.

Refer to the following figure. What are the coordinates of point B?

Find an equation of the line that passes through the point (- 6, 5) and is parallel to the line 2x - 3y - 4 = 0.