Thomas wants to make a box with no lid out of cardboard sheet to use as a food dish for his dog. he plans to make the box shape by cutting four congruent squares from all corners of the sheet.
1.) thomas buys a cardboard sheet that is 12 by 8 inches. create an equation for this situation, find the zeros, and sketch the function.
2.) what is the size of the cutout he needs to make so that he can fit the maximum amount of food in the box?
3.) if thomas wants a volume of 12 cubic inches, what size does the cutout need to be? what would be the dimensions of this box?
4.) using complete sentences, explain the connection between the cutout and the volume of the box.
5.) design an equation that would work for any cardboard sheet length, q, and width, p.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,