Describe the transformation that takes f(x) =|x| to g(x)= -|x+4| -1

Translation 4 units to left, reflection about x-axis and then translation 1 unit up.

Step-by-step explanation:

We are given the applying some transformations to f(x) = |x| gives g(x) = -|x+4|+1.

Now, at the start f(x) is translated 4 units to the left i.e. f(x) is shifted 4 units to the left.

This gives us the new function as |x+4|.

Now, this new function is reflected about x-axis i.e. it is flipped across x-axis.

So, we get the new function - |x+4|.

Finally, we can see that - |x+4| is translated 1 units upwards i.e. it is shifted 1 unit up.

This gives us the required function g(x) = - |x+4| + 1 as shown below.

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

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)