Given the function f(x)= 2|x+6|-4, for what values of x is f(x)=6?

x = -1 or x = -11

Step-by-step explanation:

f(x)= 2|x+6|-4

2|x+6|-4 = 6

2|x+6| = 6+4

2|x+6|=10

|x+6| = 10/2

|x+6| = 5

x+6 = ±5

x = ±5 - 6

x = -1 or x = -11

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)