Simplify 12e^5 divided 3e^3

4

Step-by-step explanation:

12e⁵÷3e⁵=    4e⁰= 4( a number or letter or anything raised to 0 gives 1, since e was raised to 0, the answer is 4)

when 12e⁵ is divided by 3e⁵, 12 is divided by 3 and according to the laws of exponents, when a⁵ is divided by a³, the answer is a⁵⁻³= a²

another law states that, a⁰= 1

so, 12e⁵÷3e⁵= 4e⁵⁻⁵=4e⁰= 4×1=4

when a⁵ is multiplied by a⁴ or ⁵, the answer will be the sum of the powers, if it is divided, the answer is the difference between the powers

(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