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  • If you didn't understand the third case / summation, all they did was subtract the summat {{ARML box|year=2005|state=Alabama|num-b=6|num-a=8}}
    1 KB (193 words) - 21:13, 18 May 2021
  • For two [[number]]s <math>a</math> and <math>b</math>: ...</math> if <math>a</math> is greater than <math>b</math>, that is, <math>a-b</math> is positive.
    12 KB (1,798 words) - 16:20, 14 March 2023
  • <math>\textbf{(A)}\ 19 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 29 \qquad \textbf{(E)}\ ...lowing conditions, the system of equation should be constructed. (It doesn't matter which variable is which.)
    1 KB (200 words) - 23:35, 28 August 2020
  • ...ent colors (one red, one blue, one yellow, and one black), the Martian can't select a fifth sock without creating a pair. We may use this to prove the p ...Pigeonhole Principle guarantees that two numbers will share the same <math>b</math> value. These numbers are multiples—if we define the two numbers <m
    11 KB (1,985 words) - 21:03, 5 August 2023
  • ...h>3!</math> different [[permutations]] of those letters. Since order doesn't matter with combinations, there is only one combination of those three.(<ma ...cause the combinations are the coefficients of <math>2^n</math>, and a and b disappear because they are 1, the sum is <math>2^n</math>.
    4 KB (615 words) - 11:43, 21 May 2021
  • ...f and only if there exists a constant <math>t</math> such that <math>a_i = t b_i</math> for all <math>1 \leq i \leq n</math>, or if one list consists of ...there exists a scalar <math>t</math> such that <math>\overrightarrow{v} = t \overrightarrow{w}</math>, or if one of the vectors is zero. This formulati
    13 KB (2,048 words) - 15:28, 22 February 2024
  • ...a [[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>: ...y holding when <math>A^*, B^*, C^*</math> are collinear, i.e. when <math>A,B,C</math> lie on a circle containing <math>D.</math> Additionally, by the In
    7 KB (1,198 words) - 20:39, 9 March 2024
  • <cmath>z'=\frac{az+b}{cz+d},\quad a,b,c,d\in\mathbb{Z}, ad-bc=1.</cmath> <cmath>\left(\begin{array}{cc}a&b\\c&d\end{array}\right)z=\frac{az+b}{cz+d}.</cmath>
    5 KB (849 words) - 16:14, 18 May 2021
  • These two examples use options specifically based on digits, but this isn't the entire picture of constructive counting. The following example uses con ...e to populate with <math>4</math> <math>A</math>s and <math>3</math> <math>B</math>s. Using constructive counting is an idea, but there are multiple way
    12 KB (1,896 words) - 23:55, 27 December 2023
  • <cmath>\int_{x_i}^{\bar{x}} F'(t) \, dt \ge \int_{x_i}^{\bar{x}} F'(\bar{x}) \, dt .</cmath> <cmath>\int_{\bar{x}}^{x_i} F'(t) \, dt \le \int_{\bar{x}}^{x_i} F'(\bar{x}) \, dt .</cmath>
    3 KB (623 words) - 13:10, 20 February 2024
  • ...''function from <math>A</math> to <math>B</math>'' (written <math>f: A \to B</math>) if and only if ...math>a \in A</math> there is some <math>b \in B</math> such that <math>(a, b) \in f</math>, and
    10 KB (1,761 words) - 03:16, 12 May 2023
  • ...entary counting''' is a [[counting]] method where one counts what they don't want, then subtracts that from the total number of possibilities. In proble ...|A| - |B^c|</math>, where <math>B^c</math> is the [[complement]] of <math>B</math>. In most instances, though, <math>A</math> is obvious from context a
    8 KB (1,192 words) - 17:20, 16 June 2023
  • ...a of the circle be <math> A </math> and the area of the triangle be <math> T </math>. We have three cases then. ...r it cannot be both <math>P>T</math> and <math>P<T</math>. So <math>A\not >T</math>.
    9 KB (1,555 words) - 20:05, 2 November 2023
  • '''Common number bases''' are 2, 8, 10 and 16. The base doesn't necessarily have to be an [[integer]]. There are [[complex base | complex]] ...s base 16. The digits in hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. One of its common uses is for color charts. Hexadecimal n
    2 KB (351 words) - 10:39, 1 October 2015
  • <math>\textbf{(A)}\,\textdollar 28000 \qquad \textbf{(B)}\,\textdollar 32000 \qquad \textbf{(C)}\,\textdollar 35000 \qquad \textbf{ Let <math>A</math>, <math>T</math> be Kristin's annual income and the income tax total, respectively. N
    1 KB (203 words) - 01:25, 1 March 2024
  • The inequality states that in for four points <math>A, B, C, D </math> in the plane, ...ateral with diagonals <math>AC </math> and <math>BD </math> OR if <math>A, B, C, D</math> are collinear.
    3 KB (602 words) - 09:01, 7 June 2023
  • This section is for people who know what [[integral]]s are but don't know the Fundamental Theorem of Calculus yet, and would like to try to figu ...distance that the object travels between times <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.
    11 KB (2,082 words) - 15:23, 2 January 2022
  • ...ath>, <math>\vec{y}</math>, <math>\vec{z}</math>, and real numbers <math>a,b</math>, #<math>(ab)\vec{x}=a(b\vec{x})</math> ([[Associative]] in scalar)
    7 KB (1,265 words) - 13:22, 14 July 2021
  • Therefore by: <cmath>(a^b)^c=a^{bc}</cmath> and identities 1 and 2 above (2 being used twice), we get ...t value <math>c</math> such that <math>a^c=mx+b</math> for given <math>a,m,b</math> being integers (as well as <math>c,x</math> the unknowns being integ
    4 KB (680 words) - 12:54, 16 October 2023
  • ...cate that the following proof emphasizes on a particular case, but doesn’t affect the validity of the proof in general. ...ay "WLOG, let <math>a > b > c</math>." if <math>a</math> could equal <math>b</math> or <math>c</math>.
    2 KB (280 words) - 15:30, 22 February 2024

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