An office manager will spend a total of $37 comma 500 on computers at $1500 each and printers at $1200 each. Write the number of computers purchased as a function of the number of printers purchased. Find and interpret the slope.

the slope is -(4/5) for an increasing number of printers bought the number of the computers bought will decrease.

Step-by-step explanation:

firstly we are told that we must write the number of computers purchased as a function of the number of printers purchased therefore this tells us that we must let X be the number of printers and let Y be the number of Computers purchased.

on the statement we are told the costs per computer of $1500 and we are also told the cost per printer which is $1200 each then they further tell us that we have a total of $37500 to spend so if we put this in one equation it will be :

$1500Y + $1200X = $37500 because we let the number of each computers bought be Y and each of the number of printers bought be X.

now we will solve for to make Y the subject of the formula as we are told above that the number of computers(Y) purchased is a function of the number of printers(X) bought.

$1500Y = $37500 - $1200X    ,we transpose the dependent variable then we divide the whole equation by $1500 to make Y the subject of the formula.

Y= 25 - (4/5)X then we rearrange to the format Y= mX + c

Y= -(4/5)X +25

then we get a negative slope which tells us that for an increasing number of printers bought the number of the computers bought will decrease.

37500 = 1500 X + 1200 Y

Step-by-step explanation:

Total $37500 is spend on both computer and printers and 1500 at each computer and 1200 at each printer.

Where X=number of Computer and Y = number of printers so we have

equation  is equal to 37500 = 1500X + 1200Y

Function:     1500X = 1200 Y -  37500

                  X = 1200 Y     -   37500

                          1500            1500

                   X = 3/4 Y  -    25.

Slope (m)=?

   we have Y = mx +b

               by comparison with equation

             X = 3/4 y + (-b)

then m=3/4=.75

if each printer is purchased we predict that office manger cost 24.5 each increase in computer

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8