Write the equation in standard form for the circle that has a diameter with endpoints (-4,2) and (–4,–14).

(x + 4)² + (y + 6)² = 64

Step-by-step explanation:

The standard form of equation of a circle is given as;

(x - a)² + (y - b)² = r²

Where;

a and b are the centre coordinates and r is the radius.

First of all, let's Calculate the midpoint coordinates.

This gives;

((-4 + (-4))/2), (2 + (-14))/2)

This is now (-4, -6)

Distance of radius is;

r = √((-4 - (-4))² + (-6 - 2)²)

r = 8

Equation of circle is now;

(x - (-4))² + (y - (-6))² = 8²

This gives;

(x + 4)² + (y + 6)² = 64

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3