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

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

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:

Sin^{2}(θ) + Cos^{2}(θ) = 1

Tan^{2}(θ) + 1 = Sec^{2}(θ)

Sin(θ)/Cos(θ) = Tan(θ)

Sin

Tan

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