A recipe requires ¼ cup of milk for each ⅙ cup of cheese. How many cups of cheese are needed for each cup of milk?

2/3 cups of cheese

Step-by-step explanation:

1/4 cup of milk = 1/6 cup of cheese

1 cup of milk = 1 cup of milk x 1/6 cup of cheese

                                     1/4 cup of milk

 = 1 / 1

    6    4

= 1 x 4

 6    1

= 4/6

= 2/3 cups of cheese

answer:   n ≤ -3 or n < -5

step-by-step explanation:

-5 + 2n ≥ -11

+5             +5

2n ≥ -6

2/2 ≤ -6/2

n ≤ -3

-6 - 10n > 44

+6           +6

-10n > 50

-10/-10 50/-10

n < -5

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: