Iwill gives one and one half dozen cookies take 2/3 of a cup of sugar. how much is needed to make 90 cookies?

3 1/3 cups

Step-by-step explanation:

one and one half dozen = 1.5 * 12 = 18 cookies

18 cookies    90 cookies

=

2/3 cup          x cups

using cross products

18 * x = 2/3 * 90

18 x = 60

divide each side by 18

x = 60/18    

divide top and bottom by 6

x = 10/3

change the improper fraction to a mixed number

3 goes into 10 3 times with 1 left over

x = 3 1/3 cups

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

a - base

b - exponent

so,