The lengths of two sides of a triangle are shown. Side 1: 8x2 − 5x − 2

Side 2: 7x − x2 + 3

The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)

Part B: What is the length of the third side of the triangle? Show your work. (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Afactory adds 3 red drops and 2 blue drops of coloring to white paint to make each pint of purple paint. the factory will make 50 gallons of the purple paint.how many drops of red and blue coloring will the factory need in the 50 gallon batch of purple paint.

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.)

The ratio of the height of two similar cylinders is 4 to 3 what is the ratio of their volumes