A gardener is planting two types of trees:

Type A is 3 feet tall and grows at a rate of 15 inches per year.

Type B is 6 feet tall and grows at a rate of 11 inches per year.

Algebraically determine exactly how many years it will take for these trees to be the same height.
i dont get it ive tried everything that i know and still got stuck

Solution:

Let "x" be the number of years

Type A is 3 feet tall and grows at a rate of 15 inches per year

1 feet = 12 inches

3 feet = 12 x 3 = 36 inches

Equation: 36 + 15x eqn 1

Type B is 6 feet tall and grows at a rate of 11 inches per year

6 feet = 6 x 12 = 72 inches

Equation: 72 + 11x eqn 2

For both trees to be of same height, eqn 1 must be equal to eqn 2

36 + 15x = 72 + 11x

15x - 11x = 72 - 36

4x = 36

Thus it takes 9 years for both trees to be of same height

$32,660

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