The sum of two numbers is 116 and their difference is 18. Find the larger number.

67

Step-by-step explanation:

let larger number be x and the other be y.

x - y = 18

x = 18+y

now, x + y = 116

therefore, 18+y+y= 116

18 + 2y =116

2y = 116-18

2y = 98

y = 98/2 = 49

larger number = 49 + 18 = 67

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: