Aubree just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 15 inches and after burning for 8 hours, the candle's height was down to 5 inches. Write an equation for L, L, in terms of t, t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.

L=15-8t

Step-by-step explanation:

Given data

initial length= 15in

time of burning = 8 hours

final length = 5in

let the length of the candle be L

and the number of hours burnt be t

given that the initial length was 15in

the expression to represent the L in  terms of t is given as

L=15-8t

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

(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