Ross is analyzing a circle , y^2+x^2=64 and a linear function g(x), will they intersect ?

x. g(x)
-1. -4.5
0. -4
1. -3.5

yes at positive x coordinates
yes at negative x coordinates
yes at positive and negative x coordinates
no, they will not intersect

so the answer is no they will not intersect

Step-by-step explanation:

find what g(x) is

y intercept is -4

slope is 1/2

so

y=1/2x-4

so sub that for y in other equation

(1/2x-4)^2+x^2=64

1/4x^2-4x+16+x^2=64

times 4 bot sides

x^2-16x+64+4x^2=256

minus 256 both sides

x^2-16x+4x^2-192=0

5x^2-16x-192=0

factor

(x-8)(5x+24)=0

set to zero

x-8=0

x=8

5x+24=0

5x=-24

x=-24/5

at x=-24/5 and 8

so at positive and negative coordinates

y + 11 = (1/4)(x + 16)

step-by-step explanation:

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6