What is the constant of variation for the quadratic variation?

Hello mate!

A simple quadratic equation has the form y = kx^2, where k is the constant of variation.

Our equation is 6y = 4x^2

The first thing we should do is isolate y on one side of the equation, dividing by 6 on both sides:

y = (4/6)x^2 = (2/3)x^2

then in our equation, y = (2/3)x^2, the constant of variation is 2/3.

Then the right answer is the second option.

(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