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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_14 / The graph of y=x²+2x−15 intersects the x-axis at points A and C and the y-axis at point B. What is the numerator of the simplest fraction that represents tan(∠ABC)?

Problem

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problem

The graph of

y=x^2+2x-15

intersects the

x

-axis at points

A

and

C

and the

y

-axis at point

B

. What is the numerator of the simplest fraction that represents

\tan(\angle ABC)

Plain-text mathematical notation (without MathML)

The graph of y=x²+2x−15 intersects the x-axis at points A and C and the y-axis at point B. What is the numerator of the simplest fraction that represents tan(∠ABC)?

Original LaTeX notation

The graph of $y=x^2+2x-15$ intersects the $x$-axis at points $A$ and $C$ and the $y$-axis at point $B$. What is the numerator of the simplest fraction that represents $\tan(\angle ABC)$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_14
task_id: 80a39553-9363-5723-9f08-cc3feed79c9f
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f14
task_revision_id: 2
config / split: default / train

Official source

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