Michael went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 40 grams of sugar and each bottle of juice has 20 grams of

sugar. Michael purchased a total of 11 bottles of juice and soda which collectively

contain 300 grams of sugar. Write a system of equations that could be used to

determine the number of bottles of soda purchased and the number of bottles of juice

purchased. Define the variables that you use to write the system.

y

=

System of Equations:

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Look at triangle wxy what is the length (in centimeters) of the side wy of the triangle?

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.)