For a warm up, Samuel runs 200 yards less than half the maximum distance he can run. This is represented by the equation r=1/2x−200, where x represents the maximum distance he can run and r represents the distance run during his warm up. If Samuel ran 1,600 yards during his warm up, what is the maximum distance he can run? HURRY WILL GIVE BRAINLIEST 1

Solve 2 - 3 cos x = 5 + 3 cos x for 0° ≤ x ≤ 180° a. 150° b. 30° c. 60° d. 120°

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.)

Stefanie is painting her bedroom. she can paint 2 1/3 square feet in 4/5 of an hour. how many square feet can she paint in one hour?