Proofs

It might not seem like math is useful at all, but it really is! For example, one major application of geometry would be working with areas and volumes. We encounter volumes every day; recipes, food labels, etc. Additionally, areas are quite useful; flooring is sold by the square foot, for example.

A good source of "real world" applications of mathematics can be found in word problems in many textbooks.

A bathtub. It will hold at least 1 litre of water.

The major mistake most homeowners make when putting their property up for sale is not choosing the correct price to list at. This is a mistake that can set you off down the wrong path with your home, causing you to lose both time and money.

A home that is listed too high is likely to push potential buyers away, especially if there are much better deals around for similar homes. Putting your home up for too low though might provoke skepticism as well, which won’t help get the property off your hands either.

Even if you do make a sale off the total, you might be leaving money on the table.

It’s important to do a lot of research before deciding on what price to list your home. Look at other similar homes in your neighborhood. Try to keep your intended price at or around these prices.

This will ensure a smoother, quicker sales process once your home is available for purchase to the public. You might need to rely on help from a local expert to land on the proper sales price for your home.

It can help to work with someone that has no bias or emotional attachment to the property. You’re more likely to land on a price that you can all be happy with.

One, unless you suppose they're descending through planes, then infinite. But one that they both occupy.

It is 60

55% 20%

Let's start out with the basic inequality 1 < 2 < 4.

Now, we'll take the square root of this inequality:

1 < √2 < 2.

If you subtract all numbers by 1, you get:

0 < √2 - 1 < 1.

If √2 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √2. Therefore, √2n must be an integer, and n must be the smallest multiple of √2 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.

Now, we're going to multiply √2n by (√2 - 1). This gives 2n - √2n. Well, 2n is an integer, and, as we explained above, √2n is also an integer; therefore, 2n - √2n is an integer as well. We're going to rearrange this expression to (√2n - n)√2 and then set the term (√2n - n) equal to p, for simplicity. This gives us the expression √2p, which is equal to 2n - √2n, and is an integer.

Remember, from above, that 0 < √2 - 1 < 1.

If we multiply this inequality by n, we get 0 < √2n - n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √2p < √2n. We've already determined that both √2p and √2n are integers, but recall that we said n was the smallest multiple of √2 to yield an integer value. Thus, √2p < √2n is a contradiction; therefore √2 can't be rational and so must be irrational.

Q.E.D.

The GCF is 12.

Nine.

A data set.

Yes. For example, 3, 5, 7. In fact, there are infinitely many prime numbers. For a proof, see this link:

http://primes.utm.edu/notes/proofs/infinite/euclids.html

3

Sorry, I cannot.

The well-written proof can be found in the Wikipedia article, which can be located in a link below.

The gcd is 3.

It has been recently discovered (Aug 2017), by researchers at the University of New South Wales, that a 3,700 year old Babylonian tablet, known as Plimpton 332, contained tables of trigonometric ratios. The tablet is approx 1500 years older than the Greek astronomer Hipparchus who has long been regarded as the father of trigonometry. So, with that one discovery, the history of trigonometry has become less brief and its origins have been shifted from Europe to the Middle East. It is not yet clear what else the Babylonians achieved in the intervening 1500 years.

because they just are

The browser which is used for submitting questions is crap (to be polite)! It is therefore likely that I cannot see the question as you would have wished. But, as far as I can make out, the answer is probably not.

Algebra 1 is called 'AB' because it covers the first two parts of algebra, whereas algebra 2 is called 'BC' because it covers the second two parts.

It's 3

60 to 1

AFTER whoever wrote this question takes a course to improve their ENGLISH...

Check out these articles for a simple free tool and tutorial that will make trig simple enough for ANYBODY to understand!

http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html

http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html

http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html

Euclid was a Greek Mathematician from Alexandria (Egypt) and his book, the Elements, was the first systematic exposition of the subject. So the answer to the queston is "No".