Decide whether or not each equation represents a proportional relationship. a. the remaining length (l) of 120-inch rope after x inches have been cut off: 120−x=l b. the total cost (t) after 8% sales tax is added to an item's price (p): 1.08p=t c. the number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x=m4 d. the volume (v) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: v=12s2 problem 3

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step-by-step explanation:

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step-by-step explanatio89

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)