Which phrase best describes a theorem in an axiomatic system? a.) the accepted meaning of a term b.) an assumption made with little supporting evidence c.) an accepted fact that cannot be proven d.) a statement proven to be true using logic e.) a list of geometric facts

D

Step-by-step explanation:

In Maths, axioms are basically set of propositions from which we can derive true statements from logic. Then these statements are known as theorems.

Hence, defining theorem in an axiomatic way means that a statements that we derive from axioms (propositions) using logic and that is proven to be true.

From the answer choices, we see D goes with this, hence D is the correct answer.

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: