benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / The figure below represents a figure with a total of 120 triangles and n points labeled as vertices on the horizontal base. What is the value of n? [asy]size(250,400); pair P = (3,…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The figure below represents a figure with a total of 120 triangles and nn points labeled as vertices on the horizontal base. What is the value of nn? [asy]size(250,400); pair P = (3,4); real r = .05; draw((0,0)--P); draw((1,0)--P); draw((3,0)--P); draw((4.5,0)--P); draw((7,0)--P); draw((7,0)--(8,0)); fill(circle((8+3r,0),r)); fill(circle((8+7r,0),r)); draw((8+15r,0)--(9+15r,0)); draw((9+15r,0)--P); draw((11+15r,0)--P); fill(circle((8+11r,0),r)); draw((0,0)--(7,0)); draw((9+15r,0)--(11+15r,0)); label("PP",P,N); label("A1A_1",(0,0),S); label("A2A_2",(1,0),S); label("A3A_3",(3,0),S); label("A4A_4",(4.5,0),S); label("A5A_5",(7,0),S); label("An−1A_{n-1}",(9+15r,0),S); label("AnA_n",(11+15r,0),S);[/asy]
Plain-text mathematical notation (without MathML)
The figure below represents a figure with a total of 120 triangles and n points labeled as vertices on the horizontal base. What is the value of n?

[asy]size(250,400);
pair P = (3,4);
real r = .05;
draw((0,0)--P); draw((1,0)--P); draw((3,0)--P); draw((4.5,0)--P); draw((7,0)--P); draw((7,0)--(8,0)); fill(circle((8+3r,0),r)); fill(circle((8+7r,0),r)); draw((8+15r,0)--(9+15r,0)); draw((9+15r,0)--P); draw((11+15r,0)--P); fill(circle((8+11r,0),r)); draw((0,0)--(7,0)); draw((9+15r,0)--(11+15r,0));
label("P",P,N); label("A₁",(0,0),S); label("A₂",(1,0),S); label("A₃",(3,0),S); label("A₄",(4.5,0),S); label("A₅",(7,0),S); label("A_(n−1)",(9+15r,0),S); label("A_(n)",(11+15r,0),S);[/asy]
Original LaTeX notation
The figure below represents a figure with a total of 120 triangles and $n$ points labeled as vertices on the horizontal base. What is the value of $n$?

[asy]size(250,400);
pair P = (3,4);
real r = .05;
draw((0,0)--P); draw((1,0)--P); draw((3,0)--P); draw((4.5,0)--P); draw((7,0)--P); draw((7,0)--(8,0)); fill(circle((8+3r,0),r)); fill(circle((8+7r,0),r)); draw((8+15r,0)--(9+15r,0)); draw((9+15r,0)--P); draw((11+15r,0)--P); fill(circle((8+11r,0),r)); draw((0,0)--(7,0)); draw((9+15r,0)--(11+15r,0));
label("$P$",P,N); label("$A_1$",(0,0),S); label("$A_2$",(1,0),S); label("$A_3$",(3,0),S); label("$A_4$",(4.5,0),S); label("$A_5$",(7,0),S); label("$A_{n-1}$",(9+15r,0),S); label("$A_n$",(11+15r,0),S);[/asy]

level

Level 4

type

Counting & Probability

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
b0025c24-0d9b-5cc5-b5ac-46c4a8f70357
task_key
counting~5fand~5fprobability--test--b0025c24-0d9b-5cc5-b5ac-46c4a8f70357
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import