1957 AMC 12 Problem 23

Attempt Problem 23 of the 1957 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1957 AMC 12 solutions, or check the answer key.

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23.

The graph of

x^2+y=10

and the graph of

x+y=10

meet in two points. The distance between these two points is:

less than

1

1

\sqrt2

2

more than

2

Set the two expressions for

y

equal

The resulting equation is

x^2=x

At an intersection,

10-x^2=10-x,

x=0

x=1.

The points are

(0,10)

and

(1,9).

Their distance is

\sqrt{(1-0)^2+(9-10)^2}=\sqrt2.

Therefore, the correct answer is C.

Problem 23 in other years