Aidan was frustrated that he needed to write so much when solving an equation. He decided to come up with a shortcut for recording his work to solve a new equation. As you look at Aidan's recording at right of how he solved 2x+4=-12 below, visualize an Equation Mat with algebra tiles. Then answer the questions for each step below. A. Check Aidan's solution in the original equation. Is his solution correct? 2x A 4 = -12 B. Plug x= -8 back into the original equation to check if it is true. -4 -4 2 -16 | 2 2. x = -8​

Triangle xyz has vertices x(1,3), y(0,0)

1. which of the following algebraic equations is equivalent to ? x^n = a a^n = x a^x = n x^a = n 2. 16^1/4= 1/2 2 4 3. (-36)^1/2= -6 1/6 no real number 4. 8^2/3= 4 8 16√2 )^5/2= 7,776 1/7,776 no real number 6. m ^ the square root of a^2m simplified is: 7. the square root of 3^3 times the square root of 2 simplified and in radical form is:

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.)