Patrick and brooklyn are making decisions about their bank accounts. patrick wants to deposit $300 as a principle amount, with an interest of 3% compounded quarterly. brooklyn wants to deposit $300 as the principle amount, with an interest of 5% compounded monthly. explain which method results in more money after 2 years. show all work.

The correct answer is:

Brookyln's method results in more money after 2 years.

Explanation:

The formula for compound interest is:

,

where A is the total amount, p is the principal invested, r is the interest rate as a decimal number, n is the number of times the interest is compounded per year, and t is the number of years.

For Patrick's method, p = $300; r = 3% = 3/100 = 0.03; n = 4; and t = 2:

For Brooklyn's method, p = $300; r = 5% = 5/100 = 0.05; n = 12; and t = 2:

Brooklyn's method makes more money in 2 years.

(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