If p is the smallest prime factor of 511, then a. 18 ≤ p ≤ 23
b. 10 ≤ p ≤ 17
c. 3 ≤ p ≤ 9
d. none of these

C.

Step-by-step explanation:

The prime factor decomposition of 511 is , where 7 is the smallest prime factor. Hence, the correct answer is C.

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:

true !

step-by-step explanation: