F ( n ) = 45 ⋅ ( 4 5 ) n − 1 f(n)=45⋅(54)n−1f, left parenthesis, n, right parenthesis, equals, 45, dot, left parenthesis, start fraction, 4, divided by, 5, end fraction, right parenthesis, start superscript, n, minus, 1, end superscript Complete the recursive formula of f ( n ) f(n)f, left parenthesis, n, right parenthesis. f ( 1 ) = f(1)=f, left parenthesis, 1, right parenthesis, equals f ( n ) = f ( n − 1 ) ⋅ f(n)=f(n−1)⋅f, left parenthesis, n, right parenthesis, equals, f, left parenthesis, n, minus, 1, right parenthesis, dot

(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

i don't see any steps below, sweetheart