sydneyanderson4
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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

Respuesta :

apologiabiology
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

Answer: 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

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