6) which number is an irrational number? a) 3.5 b) 36 c) 48 d) 37 100

3.5, 36, 48, and 37,100 are all rational numbers. If you meant to say "37.100", then that would be irrational. However, I think you made a mistake because we don't know what's supposed to be between 37 and 100.

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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.

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