Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ? triangles WXZ and XYZ that share side XZ with right angle XZW, WZ equals 16, XZ equals 12, and YZ equals 9

Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate.

16 over 12 equals 9 over 12
16 over 12 equals 12 over 9
12 over 12 equals 16 over 9
12 over 16 equals 16 over 9

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.)