Exam 1: Precalculus Diagnostic

Kyle went to the post office and spent $23.73 on 55 stamps. He bought 27¢ stamps for the postcards, 42¢ stamps for the letters addressed to friends in the U.S., and 94¢ stamps for each letter to England. Kyle bought 3 times as many postcard stamps as those for the letters to England. How many postcard stamps did Kyle buy? (Hint: use matrices.)

Solve for x . (Write your answer in interval notation.)

Given the following matrices, find AB, if possible.

Given . Evaluate

Solve for x. (If there is more than one solution, separate each solution for x with a comma.)

Solve for x . (Round your final answer to one decimal place, but do NOT round until the final step!)

List any vertical or horizontal asymptotes, if they exist, for the following function.

A straight line, l, passes through . For a point which lies on line l, as the value of x decreases by 2, what happens to the value of y?

Simplify:

Simplify completely:

The hypotenuse of a right triangle is 18 cm. more than one of the legs. If the other leg is 108 cm., how long is the hypotenuse (in cm.)?

Evaluate:

Find the vertex of the following fuction.

Solve for x

If g(t)=9 t² - t + 10 , find, expand, and simplify g(t - 5) .

Two ships leave port in different directions. The first ship leaves at 8 a.m. traveling due east at 32 knots. The second ship leaves three hours later traveling due north at 36 knots. How far apart are the two ships at 11 p.m.? (1 knot = 1 nautical mile per hour. Round your answer to two decimal places.)

Solve. (If your solution has more than one interval, list them in order from left ot right, separate by commas as necessary.)

Write the intersection or union of the following inequalities in interval notation:

Write the equation of a circle, in standard form, whose diameter is AB, where A = (-2, 11) and B = (6, 23).