One positive number is 8 more than another. the sum of their squares is 130. find both numbers

first number: x

second number: x + 8

(x)² + (x + 8)² = 130

x²  + x² + 16x + 64  = 130

    2x² + 16x  + 64 = 130      

       x² + 8x + 32 = 65       divided both sides by 2

         x² + 8x - 33 = 0       subtracted 65 from both sides

        (x + 11)(x - 3) = 0

x + 11 = 0     x - 3 = 0

 x = -11          x = 3              disregard -11 because it's not a positive number

second number: x + 8   = (3) + 8   = 11

3 and 11

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: