A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building? This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

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C is the midpoint of BD then BC congruent CD [URL='https://www.mathcelebrity.com/proofs.php?num=cisthemidpointofbd&pl=Prove']True using this proof[/URL]

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Let n be an integer. If n^2 is odd, then n is odd Proof by contraposition: Suppose that n is even. Then we can write n = 2k n^2 = (2k)^2 = 4k^2 = 2(2k) so it is even [I]So an odd number can't be the square of an even number. So if an odd number is a square it must be the square of an odd number.[/I]

Let x be an integer. If x is odd, then x^2 is odd Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer. [U]Squaring x, we get:[/U] x^2 = (2n + 1)^2 = (2n + 1)(2n + 1) x^2 = 4n^2 + 4n + 1 x^2 = 2(2n^2 + 2n) + 1 2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even So adding 1 is an odd number [MEDIA=youtube]GlzV80M33x0[/MEDIA]

Free Proofs Calculator - Various Proofs in Algebra

[URL='https://www.mathcelebrity.com/proofs.php?num=prove0%21%3D1&pl=Prove']Prove 0! = 1[/URL] Let n be a whole number, where n! represents: The product of n and all integers below it through 1. The factorial formula for n is n! = n · (n - 1) · (n - 2) · ... · 3 · 2 · 1 Written in partially expanded form, n! is: n! = n · (n - 1)! [SIZE=5][B]Substitute n = 1 into this expression:[/B][/SIZE] n! = n · (n - 1)! 1! = 1 · (1 - 1)! 1! = 1 · (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! ? 1 which contradicts the equation above [MEDIA=youtube]wDgRgfj1cIs[/MEDIA]

Use proof by contradiction. Assume sqrt(2) is rational. This means that sqrt(2) = p/q for some integers p and q, with q <>0. We assume p and q are in lowest terms. Square both side and we get: 2 = p^2/q^2 p^2 = 2q^2 This means p^2 must be an even number which means p is also even since the square of an odd number is odd. So we have p = 2k for some integer k. From this, it follows that: 2q^2 = p^2 = (2k)^2 = 4k^2 2q^2 = 4k^2 q^2 = 2k^2 q^2 is also even, therefore q must be even. So both p and q are even. This contradicts are assumption that p and q were in lowest terms. So sqrt(2) [B]cannot be rational. [MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Free Pythagorean Theorem Calculator - Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

Free Pythagorean Theorem Trig Proofs Calculator - Shows the proof of 3 pythagorean theorem related identities using the angle θ:
Sin²(θ) + Cos²(θ) = 1
Tan²(θ) + 1 = Sec²(θ)
Sin(θ)/Cos(θ) = Tan(θ)

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Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages Set up a proportion of pages to minutes: 16 pages/8 minutes = 108 pages / p minutes We want to solve for p. Type [I][URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=108&den1=8&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']16/8 = 108/p[/URL][/I] into the search engine. We get p = [B]54 minutes[/B]

The difference between the squares of two consecutive numbers is 141. Find the numbers Take two consecutive numbers: n- 1 and n Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is: 2n - 1 = d Proof of this: n^2- (n - 1)^2 = d n^2 - (n^2 - 2n + 1) = d n^2 - n^2 + 2n - 1 = d 2n - 1 = d Given d = 141, we have 2n - 1 = 141 Add 1 to each side: 2n = 142 Divide each side by 2: 2n/2 = 142/2 n = [B]71[/B] Therefore, n - 1 = [B]70 Our two consecutive numbers are (70, 71)[/B] Check your work 70^2 = 4900 71^2 = 5041 Difference = 5041 - 4900 Difference = 141 [MEDIA=youtube]vZJtZyYWIFQ[/MEDIA]

Free Two Column Proof Calculator - Shows you the details behind a two column proof including the five parts and examples