Find an equation for the sphere with the given center and radius. 7) 7) center (0, - 8 , - 1 ), radius = 10

The general equation  of a sphere with center at (a, b, c) and radius r is

(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2.

Here, the equation is

x^2 + (y+8)^2 + (z+1)^2 = 10^2.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)