Identify the domain of the graphed function.

(-4,-2) U (-2,4]

Step-by-step explanation:

Domain is the set of x values for which the function is defined.

We look at the x  values on the graph

the graph starts at -4 and we have a hole at x=-4

For a hole we use parenthesis

Graph starts at -4  and ends at -2. Both -4  and -2  have hole, so we use parenthesis.

So interval is (-4,-2)

From -2  to  4 , there is no hole or break in between. the graph is continuous from -2  to 4

so interval is (-2, 4]

combine both intervals

(-4,-2) U (-2,4]

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240