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1990 AJHSME Problems/Problem 8
<math>\text{(A)}\ \text{45 dollars} \qquad \text{(B)}\ \text{52 dollars} \qquad \text{(C)}\ \text{54 d {{AJHSME box|year=1990|num-b=7|num-a=9}}

748 bytes (107 words) - 00:05, 5 July 2013
2009 IMO Problems/Problem 4
...e the incentre of triangle <math>ADC</math>. Suppose that <math>\angle BEK=45^\circ</math>. Find all possible values of <math>\angle CAB</math>. {{IMO box|year=2009|num-b=3|num-a=5}}

584 bytes (94 words) - 01:17, 19 November 2023
2009 IMO Problems
...1,\ldots,k-1</math>. Prove that <math>n</math> doesn't divide <math>a_k(a_1-1)</math>. ...e the incentre of triangle <math>ADC</math>. Suppose that <math>\angle BEK=45^\circ</math>. Find all possible values of <math>\angle CAB</math>.

3 KB (509 words) - 09:23, 10 September 2020
1991 AJHSME Problems/Problem 19
...umbers, we let them be <math>1,2,3,4,5,6,7,8,9</math>. Their sum is <math>45</math>. ...he sum of all ten is <math>100</math> so the last number must be <math>100-45=55\rightarrow \boxed{\text{C}}</math>.

895 bytes (135 words) - 12:16, 8 October 2015
1992 AJHSME Problems
<math>\dfrac{10-9+8-7+6-5+4-3+2-1}{1-2+3-4+5-6+7-8+9}=</math> label("$c$",(2-sqrt(3)/10,0.1),WNW);

17 KB (2,346 words) - 13:36, 19 February 2020
1993 AJHSME Problems
label("$45$",(4,-.25),S); ...y of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has only twenty-two 2's. How far can he number the pages of his scrapbook with these digits

14 KB (1,797 words) - 11:13, 28 December 2022
2005 AMC 10A Problems/Problem 19
...ed with their bases on a line. The center square is lifted out and rotated 45 degrees, as shown. Then it is centered and lowered into its original locati ...>DE</math> is 1 inch. Then, because <math>DEC</math> is a <math>45^{\circ}-45^{\circ}-90^{\circ}</math> triangle, <math>EC=\frac{\sqrt{2}}{2}</math>, and

3 KB (315 words) - 12:46, 14 December 2021
2010 AMC 12A Problems
What is <math>\left(20-\left(2010-201\right)\right)+\left(2010-\left(201-20\right)\right)</math>? Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullsey

12 KB (1,817 words) - 15:00, 12 August 2020
2010 AMC 12A Problems/Problem 19
<math>\textbf{(A)}\ 45 \qquad \textbf{(B)}\ 63 \qquad \textbf{(C)}\ 64 \qquad \textbf{(D)}\ 201 \q ...math> marbles, we must draw a white marble from boxes <math>1, 2, \ldots, n-1,</math> and draw a red marble from box <math>n.</math> Thus, <cmath>P(n) =

2 KB (379 words) - 18:30, 10 July 2022
2010 AMC 12A Problems/Problem 25
...ormed, so the total number of quadrilaterals for this case is <math>3\cdot{45} = 135</math>. ...th> square case, and <math>7</math> rectangle cases, there are <math>2255-1-2\cdot7=2240</math> quadrilaterals counted 4 times. Thus there are <math>1+7

8 KB (1,315 words) - 03:33, 23 January 2021
2010 AMC 10A Problems
.... The numbers <math>x</math> and <math>x+32</math> are three-digit and four-digit palindromes, respectively. What is the sum of the digits of <math>x</m ...3,4,5,6,7,8\}</math> and also arranges them in descending order to form a 3-digit number. What is the probability that Bernardo's number is larger than

13 KB (1,902 words) - 11:20, 5 March 2023
2010 AMC 10B Problems
What is <math>100(100-3)-(100\cdot100-3)</math>? ...ings during her <math>9</math>-hour work day. The first meeting took <math>45</math> minutes and the second meeting took twice as long. What percent of h

12 KB (1,817 words) - 22:44, 22 December 2020
2010 AMC 12B Problems
...ings during her <math>9</math>-hour work day. The first meeting took <math>45</math> minutes and the second meeting took twice as long. What percent of h In <math>\triangle ABC</math>, <math>\cos(2A-B)+\sin(A+B)=2</math> and <math>AB=4</math>. What is <math>BC</math>?

12 KB (1,845 words) - 13:00, 19 February 2020
Mock AIME 1 2010 Problems
Find the last three digits of the number of 7-tuples of positive integers <math>(a_1, a_2, a_3, a_4, a_5, a_6, a_7)</math> ...be the set of all points <math>P</math> such that <math>m \angle APB \geq 45^{\circ}</math>. Find the last three digits of the largest integer less than

7 KB (1,297 words) - 01:29, 25 November 2016
Proofs without words
http://mathoverflow.net/questions/8846/proofs-without-words http://gurmeet.net/computer-science/mathematical-recreations-proofs-without-words/

55 KB (7,986 words) - 17:04, 20 December 2018
2010 AIME I Problems/Problem 9
...c {15}{7}</math> and so the sum is <math>28 - \frac {45}{7} = \frac {196 - 45}{7}</math> giving <math>151 + 7 = \fbox{158}</math>. .... Move 28 over, divide both sides by 3, then cube to get <math>k^3-6k^2+12k-8 = k^3+22k^2+18k</math>. The <math>k^3</math> terms cancel out, so solve th

3 KB (483 words) - 07:35, 4 November 2022
2010 AIME I Problems/Problem 15
...p(ABM)}{p(CBM)} = \frac {12 + d + x}{28 + d - x}</math>. Equating and cross-multiplying yields <math>25x + 2dx = 15d + 180</math> or <math>d = \frac {25 ...the polynomial by <math>2</math>. The only such <math>x</math> in the above-stated range is <math>\frac {22}3</math>.''

14 KB (2,210 words) - 13:14, 11 January 2024
2010 AIME II Problems
Let <math>K</math> be the product of all factors <math>(b-a)</math> (not necessarily distinct) where <math>a</math> and <math>b</math> ...of <math>P(z)</math> are <math>w+3i</math>, <math>w+9i</math>, and <math>2w-4</math>, where <math>i^2=-1</math>. Find <math>|a+b+c|</math>.

8 KB (1,246 words) - 21:58, 10 August 2020
2010 AIME II Problems/Problem 14
...math>ABC</math> with [[right angle]] at <math>C</math>, <math>\angle BAC < 45^\circ</math> and <math>AB = 4</math>. Point <math>P</math> on <math>\overli ...inewidth(0.7)+fontsize(10)); size(250); real lsf = 0.5; /* changes label-to-point distance */

10 KB (1,507 words) - 00:31, 19 November 2023
1994 AJHSME Problems
...day Maria must work <math>8</math> hours. This does not include the <math>45</math> minutes she takes for lunch. If she begins working at <math>\text{7 draw(circle((45.5,-1.5),1));

16 KB (2,292 words) - 13:36, 19 February 2020

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