At practice, Carlos eats half as many apples as Alex, and also eats 2 tangerines. He eats 4 pieces of fruit in total. The equation 0.5x + 2 = 4 describes this situation. What does the variable represent?

Step-by-step explanation:

In this scenario, the variable x represents the total number of apples that Alex has eaten. Since Carlos has eaten half as many apples as Alex this would be represented as 0.5 and is why it is being multiplied by the variable x. The 2 in this scenario represents the tangerines that Carlos has also eaten, while the 4 represents the total number of fruits that Carlos has eaten.

360 different combinations

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: