According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4? Plus-or-minus one-ninth, Plus-or-minus two-ninths, Plus-or-minus one-third, Plus-or-minus four-ninths, Plus-or-minus two-thirds, Plus-or-minus1, Plus-or-minus four-thirds, Plus-or-minus2, Plus-or-minus4 Plus-or-minus one-fourth, Plus-or-minus one-half, Plus-or-minus three-fourths, Plus-or-minus1, Plus-or-minus three-halves, Plus-or-minus nine-fourths, Plus-or-minus3, Plus-or-minus nine-halves, Plus-or-minus9 One-ninth, Two-ninths, One-third, Four-ninths, Two-thirds, 1, Four-thirds, 2, 4 One-fourth, One-half, Three-fourths, 1, Three-halves, Nine-fourths, 3, Nine-halves, 9

A, b, c, and d have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. which sentence about the points is true? a. a, b, c, and d lie on the same line. b. and are perpendicular lines. c. and are parallel lines. d. and are intersecting lines but are not perpendicular. e. and are parallel lines.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

The length of the line segment ac is 8x-9 what is the value of x