Arectangular picture frame has outside dimensions of 8 inches wide and 10 inches tall. if the glass on the picture frame has an area of 48 square inches. how wide is the width of the picture frame if the frame is the same width all the way around the picture?

1 inch

Step-by-step explanation:

If we call the thickness of the frame x, then the dimensions of the glass are:

w = 8 − 2x

h = 10 − 2x

The area of the glass is width times height:

48 = (8 − 2x) (10 − 2x)

Distribute and simplify:

48 = 80 − 16x − 20x + 4x²

0 = 4x² − 36x + 32

0 = x² − 9x + 8

Factor and solve:

0 = (x − 1) (x − 8)

x = 1 or x = 8

x can't be more than 4 (half the width of the frame), so x = 1 inch.

number one is the correct answer

step-by-step explanation: dogs and cats are mentioned, no other animals

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3