Alady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 20 in. piece of cardboard as shown in the diagram. she figures that for versatility the area of the bottom must be 80 in. squared. what size of square should she cut from each corner?

Lets say she cuts squares of x by x in length.

Area of bottom will be (20 - 2x)(11 - 2x) = 80 inches squared

220 - 40x - 22x + 4x^2 = 80

4x^2 - 62x + 140 = 0

x^2 - 15.5x + 35 = 0

Using quadratic equation;

you get x = 2.743753901 0r 12.7562461 inches

The length of the square cannot be more than 11 inches

So the only squares you can cut are:

2.743753901 inches by 2.743753901 inches squares.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)