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proof - an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the
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]...

Additive Identity Property
Free Additive Identity Property Calculator - Displays the line by line proof for the additive identity property Numerical Properties

C is the midpoint of BD then BC congruent CD
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]

Consecutive Interior Angles
Free Consecutive Interior Angles Calculator - Shows you a proof of consecutive interior angles using parallel lines and a transversal

DeMorgans Laws
Free DeMorgans Laws Calculator - Demonstrates DeMorgans Laws including the proof

Let n be an integer. If n^2 is odd, then n is odd
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
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]

Proofs
Free Proofs Calculator - Various Proofs in Algebra

Prove 0! = 1
[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]

Prove sqrt(2) is irrational
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]

Pythagorean Theorem
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

Pythagorean Theorem Trig Proofs
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)

Rule of 72
Free Rule of 72 Calculator - Calculates how long it would take money to double (doubling time) using the rule of 72 interest approximation as well as showing the mathematical proof of the Rule of 72.

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages
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
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]

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