Dina invests £450 in a savings account with annual compound interest. After five years, there is £534.46 in the account.

What interest rate has she been receiving?

3.3%

Step-by-step explanation:

compound interest: A = Pe^(rt)

A = 534.46

P = 450

t = 5

534.46/450 = e^(5r)

e^(5r) = 1.18

lne^(5r) = ln 1.18

(5r)lne = ln1.18

ln1.18 = 5r

5r = 0.165

r = 0.033

or 3.3%

4 + 5 7/9= 9 7/9

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