The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. the area of the resulting rectangle is 90ft squared. find the original area of the square.

the original area is 64ft squared or 169ft squared more perdurable 64  

Step-by-step explanation:

(x-2)(x+7)=90

x^2 +5x -14=90

x^2 +5x -14 -90=90-90

x^2 +5x -104=0

factor it out

(x−8)(x+13)=0

so 8 or -13

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)

answer: correct

step-by-step explanation: