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2. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   The solution set for the equations x − y = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

3. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

   en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

   The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...

4. Quintic function - Wikipedia

   en.wikipedia.org/wiki/Quintic_function

   An example of a more complicated (although small enough to be written here) solution is the unique real root of x 5 − 5x + 12 = 0. Let a = √ 2φ −1, b = √ 2φ, and c = 4 √ 5, where φ = ⁠ 1+ √ 5 / 2 ⁠ is the golden ratio. Then the only real solution x = −1.84208... is given by

5. Banach–Tarski paradox - Wikipedia

   en.wikipedia.org/wiki/Banach–Tarski_paradox

   The proof sketched above requires 2 × 4 × 2 + 8 = 24 pieces - a factor of 2 to remove fixed points, a factor 4 from step 1, a factor 2 to recreate fixed points, and 8 for the center point of the second ball. But in step 1 when moving {e} and all strings of the form a n into S(a −1), do this to all orbits except one. Move {e} of this last ...

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   Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.

7. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

   en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

   In mathematics, the infinite series ⁠ 1 / 2 ⁠ + ⁠ 1 / 4 ⁠ + ⁠ 1 / 8 ⁠ + ⁠ 1 / 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.

8. USWNT beats Netherlands 2-1 in goalkeeper Alyssa Naeher's ...

   www.aol.com/uswnt-beats-netherlands-2-1...

   Alyssa Naeher ended her national team career with one last win. The stalwart goalkeeper made two critical saves in her final match for the United States, and the Americans beat the Netherlands 2-1 ...

9. Stoinis completes Australia clean sweep of Pakistan in T20 series

   www.aol.com/pakistan-wins-toss-bats-final...

   Marcus Stoinis bludgeoned 61 not out off 27 balls and Australia swept Pakistan 3-0 in the Twenty20 series with a seven-wicket victory on Monday. Stoinis smacked five sixes – three in one over ...