Michael has $15 and wants to buy a mixture of school lunches to feed at least three classmates. a sandwich costs $2, and hot lunch costs $3.
this system of inequalities models the scenario:
2x + 3y ≤ 15
x + y ≥ 3
part a: describe the graph of the system of inequalities, including shading and the types of lines graphed. provide a description of the solution set. (4 points)
part b: is the point (5, 1) included in the solution area for the system? justify your answer mathematically. (3 points)
part c: choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Which of these tables represents a non-linear function?

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. which set of triangles shows the similar triangles created by the altitude in the diagram?

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.)