Determine which of (a)-(d) form a solution to the given system for any choice of the free parameter. (HINT: All parameters of a solution must cancel completely when substituted into each equation.) 3x1 + 8x2 − 14x3 = 9 x1 + 3x2 − 4x3 = 1

Each equation given below describes a parabola. which statement best compares their graphs? x = 2y^2 x = 8y^2

Find the value of x. round the length to the nearest tenth

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.)