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.

5

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3