Exam 17: Algebra and Math Problems

Justin is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 5% sales tax plus a state-mandated $36 fee for disposing of his old tires. If Justin has determined that he will spend less than $502.20 total, then what is the price range he can spend on the tire set?

The formulas b = 0.03t + 2.13 and m = 0.22t + 1.12 give an approximate model for the yearly average price b of a bushel of barley and m of a bushel of millet over the past five years, where t is the number of years since 1994. What is the first year in which the price of barley exceeded $2.19/bu and the price of millet exceeded $2.00/bu? Show your work.

Solve 3^{10x - 8} = 9^{4x - 1}.

Complete the rewriting of the given series using the new index as indicated. (4i + 4) =

Find four consecutive integers whose sum is 138.

The owner of a hobby store bought a case of 9-volt batteries for $70.00. He marked the price up such that his profit was $2.80 per battery. After selling 20 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

Solve the equation. Watch for extraneous solutions.

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = - x² 2x² - y² = 1

Find the product. (3a + 4)(2a + 1)

Find the sum of the given infinite geometric series. 36 + 30 + 25 + ...

Determine all asymptotes for the graph of the given function. Show your work.

Find the inverse of the given function and include any domain restrictions. f (x) = (x - 4)²

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. Show your work. y = 2x² - 5x + 2

Write the expression without negative exponents.

Find the complex solutions.

Simplify.

Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 24's and nine 16's. A swing uses three 24's and six 16's. Conrad currently has 120 24's and 198 16's in his inventory. If tables sell for $60 and swings sell for $25, how many of each items should Conrad make in order to maximize his revenue?

Which, if any, of the ordered pairs (1, 2), (-1, 4), (-1, -1), and (5, -3) satisfy the system of inequalities? x - y > 0 4x² + y² ≥ 4

Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?

Use the binomial theorem to expand the given binomial. (m + 1)³