The first bricklayer can build a wall in 15 days, the second bricklayer can build the same wall in 20 days. How long will it take them to build the wall together?

It takes 8  4/7 days for both bricklayers to build the wall together.

Step-by-step explanation:  

The first bricklayer takes 15 days to build the wall, which means it builds 1/15 of the wall per day.

The second bricklayer takes 20 days to build the wall, which means it builds 1/20 of the wall per day.

So if they build the wall together, the expression below will tell how much of the wall they build per day together.

1/15 + 1/20

To add the fractions, we must find a common denominator, which is 60.  

4/60 + 3/60, which equals 7/60.

So, they can build 7/60 of the wall per day together.  How many days will it take them?  We must find how many times 7 fits into 60, which can be done by solving 60/7, which is 8 4/7.  

So, it takes 8 4/7 days for both bricklayers to build the wall together.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this

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)