Which expression represents the difference quotient of the function f (x) = negative StartRoot 2 x EndRoot?

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.

Benjamin is making bow ties. how many 1/2yards lomg bow ties can he make if he has 18 feet of fabric?

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.)