1. In the Opener, you may have noticed some unit rates. For example, you saw the rate of 2 bananas/1 orange and the rate of 2 apples/1 bunch of grapes. A unit rate is a comparison of two measurements in which one of the terms has a
value of 1.

Consider the relationship represented on each scale. Describe each relationship as a rate, using the names of the fruits as the units.

a. The scale indicates that strawberries balance apple(s). Write this as a unit rate.

Unit rate:

b. The scale indicates that limes balance apple(s). Write this as a unit rate.

Unit rate:

2. Using the information from the two balances pictured in problem 1, write another rate. Sketch a new balance scale that represents this rate.

Unit rate:

(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

answer:

at time x=0 we have 1000, at time x=1 we have 2000, at time x=2 we have 4000.  

so that's an initial value of 1000 and a ratio of 2,

y = 1000 (2^x)

hope this !