Express the given quantity in terms of the indicated variable. The area (in ft) of a rectangle that is eight times as long as it is wide;
w = width of the rectangle (in ft)
ft2
X
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Step-by-step explanation:

Area of a rectangle is expressed as Length * Width

X = L*W where X is the area of the rectangle in fe²

If the triangle is eight times as long as it is wide, then L = 8W

Substitute L = 8W into the formula for calculating the area of a triangle, we will have;

X = L*W

X = (8W)*W

X = 8W²

The expression X in terms of W is therefore X = 8W²

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

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