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• 2016 AMC 10A Problems/Problem 7
  ...200, 90</math> are all equal to <math>x</math>. What is the value of <math>x</math>? Since <math>x</math> is the mean,
  2 KB (268 words) - 17:19, 27 September 2023
• 2016 AMC 10A Problems/Problem 11
  ...8}{2} = \frac{(5+8)(1)}{2} = \boxed{\textbf{(D)}\ 6\frac{1}{2}}</math>. ~[[User:emerald_block|emerald_block]] <math>\\ y_1 = -\frac{3}{8}x + b</math>
  8 KB (1,016 words) - 23:17, 30 December 2023
• Cauchy-Schwarz Inequality
  ...h>k</math> is a positive integer. Show that <math>f(x)\le k^2+1</math>. ([[User:Temperal/The_Problem_Solver's Resource Competition|Source]])
  13 KB (2,048 words) - 14:28, 22 February 2024
• 1984 AIME Problems/Problem 6
  Consider the region of the plane between <math>x=16</math> and <math>x=17</math>. The parts of the circles centered at <math>(14,92)</math> and <m Solution by [[User:a1b2|a1b2]]
  6 KB (1,022 words) - 18:29, 22 January 2024
• 1984 AIME Problems/Problem 12
  ...ber of roots <math>f(x)=0</math> must have in the interval <math>-1000\leq x \leq 1000</math>?<!-- don't remove the following tag, for PoTW on the Wiki If <math>f(2+x)=f(2-x)</math>, then substituting <math>t=2+x</math> gives <math>f(t)=f(4-t)</math>. Similarly, <math>f(t)=f(14-t)</math>
  3 KB (588 words) - 13:37, 22 July 2020
• 1985 AIME Problems/Problem 10
  where <math>x</math> is a [[real number]], and <math>\lfloor z \rfloor</math> denotes the ...t all of the numbers are even, we can reduce this to any real number <math>x</math> between <math>0</math> to <math>\frac 12</math>, as this will be equ
  12 KB (1,859 words) - 17:16, 28 March 2022
• 1988 AIME Problems/Problem 13
  ...h> if <math>a</math> and <math>b</math> are integers such that <math>x^2 - x - 1</math> is a factor of <math>ax^{17} + bx^{16} + 1</math>. x^2 - x - 1 = 0&\Longrightarrow x^n = F_n(x), \ n\in N \\
  10 KB (1,595 words) - 15:30, 24 August 2024
• 1989 AIME Problems/Problem 10
  ...t <math>h</math> meet <math>c</math> at <math>P</math>, and let <math>AP = x, BP = y</math>. label("$x$", (A+P)/2, S);
  8 KB (1,401 words) - 20:41, 20 January 2024
• 1993 AIME Problems/Problem 15
  pair [] x=intersectionpoints(C--H,circle((2,1),1)); dot(x[0]); label("$S$",x[0],SW);
  3 KB (449 words) - 20:39, 21 September 2023
• 1993 AIME Problems/Problem 13
  ...tute <cmath>y= \frac{xt}{100}</cmath> into <math>(2)</math> and get <cmath>x=\frac{5000}{\sqrt{100^2+t^2}}.</cmath> Now substitute this and <cmath>y=\fr ...r Jenny. Let <math>O</math> be the center of the building. Also, let <math>X</math> be the intersection of <math>AC</math> and <math>BD</math>. Finaly,
  8 KB (1,388 words) - 03:38, 27 August 2024
• 2000 AMC 12 Problems/Problem 8
  -[[User:Integralarefun|Integralarefun]] ([[User talk:Integralarefun|talk]]) 18:21, 29 July 2023 (EDT) <math>1+x(x-2+x)</math>
  8 KB (1,226 words) - 22:15, 25 July 2024
• Pick's Theorem
  Solution by [[User:a1b2|a1b2]] ...ides are parallel to the axes. Suppose that the side parallel to the <math>x</math>-axis has length <math>a</math>, and the side parallel to the <math>y
  7 KB (1,253 words) - 15:11, 14 September 2024
• 1987 IMO Problems/Problem 4
  ...ath>, so that <math>f(x) = f(y) \;{\rm mod }\; 1987</math> whenever <math>x = y \;{\rm mod }\; 1987</math>, and hence <math>g</math> is well defined. ...<math>g</math> satisfies the identity <math>g(g(x)) = x</math>, for <math>x \in Z_{1987}</math>. Thus, <math>g</math> is an invertible function on a
  5 KB (923 words) - 18:51, 21 January 2024
• LaTeX:Math
  The solution to $\sqrt{x}=5$ is $x=25$. The solution to \[\sqrt{x} = 5\] is \[x=25.\]
  8 KB (1,319 words) - 08:03, 5 August 2024
• LaTeX:Layout
  ...rg/tex-archive/macros/latex/contrib/geometry/geometry.pdf geometry package user manual] for more detailed possibilities. As another example, if you want a $x + y$
  29 KB (4,929 words) - 12:26, 12 September 2024
• 2007 AMC 12A Problems/Problem 5
  ...{10500}{0.28}\ = 37500 \mathrm{(D)}</math>. [[User:Ankitamc|Ankitamc]] ([[User talk:Ankitamc|talk]]) 13:32, 17 January 2021 (EST)AnkitAmc.
  2 KB (235 words) - 11:27, 3 June 2021
• 2007 AMC 12A Problems/Problem 25
  ...1 + 12 + 45 + 56 + 15 = \boxed{\mathrm{(E)}\ 129}</math> spacy subsets. ~[[User:emerald_block|emerald_block]] \end{bmatrix}</math>, where <math>f(x)</math> is <math>x\times\begin{bmatrix}
  9 KB (1,461 words) - 22:07, 27 January 2024
• 2005 AMC 12A Problems/Problem 15
  pair D=dir(aCos(C.x)), E=(-D.x,-D.y); pair D=dir(aCos(C.x)), e=(-D.x,-D.y);
  14 KB (1,970 words) - 16:02, 18 August 2023
• 1999 PMWC Problems
  ...Asymptote conversion, documentation at artofproblemsolving.com/Wiki, go to User:Azjps/geogebra */ ...Asymptote conversion, documentation at artofproblemsolving.com/Wiki, go to User:Azjps/geogebra */
  6 KB (703 words) - 20:21, 21 April 2014
• Factor Theorem
  ...ath> is a [[polynomial]], then <math>x-a</math> is a [[factor]] of <math>P(x)</math> if and only if <math>P(a)=0</math>. ...h>, where <math>Q(x)</math> is a polynomial with <math>\deg(Q(x)) = \deg(P(x)) - 1</math>. Then <math>P(a) = (a - a)Q(a) = 0</math>.
  3 KB (510 words) - 17:04, 28 September 2024

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