WILL GIVE THANKS, BRAINIEST, AND 5 STARS! PLEASE HELP!

24

Step-by-step explanation:

h(x) = x - 5, x < 0   This formula would be used for h(-30). Since -30 is less than 0.

h(x) = x - 5, x < 0 ← You can now ignore the x<0.

h(-30) = (-30) - 5      Input the -30 as x.

h(-30) = - 5         Simplify

h(-30) = -15 - 5          Simplify further

h(-30) = -20

Next

h(x) = x - 2, x < 0   This formula would be used for h(30). Since 30 is greater than 0.

h(x) = x - 2, x ≥ 0  ← You can ignore the x≥0.

h(30) = (30) - 2         Input the 30 as x.

h(30) = - 2              Simplify

h(30) = 6 - 2               Simplify further

h(30) = 4

Finally the problem is asking for h(30) - h(-30) = ?

h(30) - h(-30)    

(4) - (-20)   Substitute the value of h(30) and the value of h(-30).

4 + 20       You distribute the - sign into the parentheses. A negative times a

24             negative is a positive. That is how the equation had become 4 + 20 towards the end. Which is equal to 24.

So the answer is 24.

do your own work and don"t cheat.

step-by-step explanation:

(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