When a certain ball is dropped, the function f(x) = 9(0.2)x models the ball's height in feet after each bounce, where x is the bounce number. To the nearest hundredth foot, what is the height after the third bounce?

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.

the diagram shows you   triangle def with de=4, df=9 and de≠df≠ef.

the sum of the lengths of two triangles' sides are always greater than the length of the third side:

substitute sides lengths:

then 5< ef< 13 (option 3 is true).

def is a scalene triangle with all sides of different lengths (option 5 is true, option 2 is false).

answer: correct choices are 1, 3 and 5

approximately 5 hours 32 minutes

let x be the amount of it takes both pumps to fill and 1 pump to empty

so the pumps fill/empty at the rate of per hour

first pump fills at a rate of per hour

second pump fills at a rate of per hour

third pump empties at a rate of per hour

together the reservoir fills at a rate of

+ - =

multiply each term by 720x

120x + 90x - 80x = 720

130x = 720 ( divide both sides by 130 )

x = = 5. hours

(0. × 60 ≈ 32 minutes )

time taken to fill reservoir is 5 hours 32 minutes