Which of the following expressions is equal to x^2+16? A. (x + 4i)(x-4i)
B. (x +4i)^2
C. (x-4i)^2
D. (x + 2i)(x - 8i)

A

Step-by-step explanation:

x² + 16 = 0

x² = - 16

x² = i² * 4²            {i²  = -1}

x² = (4i)²

x=√(4i)²

x=±4i

x² + 16 = (x + 4i)(x - 4i)

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: