The length of a rectangular dining hall is 8 feet less than twice it’s width. the perimeter of the room will be 134 feet. what are the dimensions of the dining hall? explain.

Length = 42, Width = 25

Step-by-step explanation:

You write out the equation for the length, which is L=2w-8 (Length is L and width is W) You substitute in the length in the original equation, 2L + 2W = 134 ( I got this equation from knowing that 2 lengths plus 2 widths equals the perimeter, 134.) Substitute 2w-8 for L, you're left with 2(2w-8) + 2w = 134. Simplify further, you have 4w-16+2w=134. Once you're done, you have W=25. Plug that back into the original equation, then solve. L = 2(25)-8, L=42.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

2

step-by-step explanation: