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Proofs

Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.

1,294 Questions

How do you prove that sum of the two exterior angles of a quadrilateral is equal to the sum of the interior angles at the other two vertexes?

Let there be a line A-----------B. From A draw a line D upwards. From B draw a line C upwards.

D C

Z

A B P

Draw an arbitrary point Z and connect it with zdc and zab. Let interior angles ADC= 1 and BCD=2. Exterior angles ZAD=x and CBP(another arbitrary poion)=y. Let a and b be other two interior angles with point A and B.

Now in triangle ZBC

angle Z+b+2=180. Also b+y=180

y=Z+2--------(L)

In triangle ZAD, Z+x+180-1=180; Z+x=1 or x=1-z--------(M)

Adding L and M x+y=1+2

What has a measure more than 180 but less than 360?

A Reflex Angle is one which is more than 180° but less than 360°

If the occurrence of B makes A more likely does the occurrence of A make B more likely?

This is a tricky question, but if you study probability, re-writing it in mathematical notations and using simple definitions and algebra would show you that the answer is yes.

We could rewrite the question as:

if B occur, A is more likely to occur,

Probability of A happening given B happened > probability of A happening

P( A given B) > P(A)

Is it true that in this case, P(B given A) > P(B)?

by definition,

P( B given A) = P(A and B) / P( A) = P( A given B) * P(B) / P(A)

Since P( A given B) > P(A),

then P( A given B)/ P(A) > 1

thus

P( B given A) > P(B)

and the answer is true, occurence of A makes B more likely.

Say A = lung cancer, B = smoking. If someone is smoking, they are more likely to have lung cancer. If someone has lung cancer, they are more likely to be a smoker or have smoked (compared to being a non-smoker).

What is BPT system?

This abbreviation is not commonly used in Algebra or Geometry.

Beer Pong Tournament?

What is a reason a customer might choose 1 gas station over another?

If u are paying family feud the answers are:

prices

service

convenient

location

better gas

What is Euclid's division lemma?

Given Positive Integers a and b there exists unique integers q and r satisfying a=bq+r; 0 lesser than or equal to r<b

Does the focal length of mirror changes if it is immersed in liquid?

No. Light behaves the same way in the liquid as it would in the air (as far as reflection is concerned, so the focal length of a mirror would not change if it were immersed in liquid.

A sample natural gas contains 8.24 moles of methane 0.421 moles of Ethelin 0.116moles of propane if the total pressure of the gases is 1.77atm what are the partial pressures of the gases?

First you need to find the mole ratio of the gases. So take the moles of the gas and divide it by the total moles. After you've done that, you can set that equal to the partial pressure equation, P1 divided by Ptotal. Multiple Ptotal to both sides and you will get the answer

Prove that every a cyclic group is an abelia?

Let G be the cyclic group generated by x, say. Ten every elt of G is of the form x^a, for some a

Is 2-SAT problem is p-complete and how?

an equation that can be written in the form ax= b where a and b are constants and a is not equal to 0

What can be concluded about two angles that each form a linear angle with angle 4?

Let's call the two angles angle 1 and angle 2. We are given that angle 1 and angle 4 form a linear angle and that angle 2 and angle 4 form a linear angle.

Because linear angles measure 180 degrees, we arrive at:

m<1 + m<4 = 180

m<2 + m<4 = 180.

By subtracting the second equation from the first, we get:

m<1 - m<2 = 0.

And finally:

m<1 = m<2.

Thus, angle 1 is congruent to angle 2.

Does combustion occur at the inner cone or the outer cone?

Of a Bunsen Burner flame? Combustion takes place in all parts of the flame.

Is the function n divided by 3 one to one and onto?

This depends on how you define your domain and codomain. f(n)=n/3 is one to one and onto when f is from R to R, but if we define f: X --> Y, where X = [0,3] and Y = [0,3], then f maps [0,3] to [0,1], so f is not onto in this case.

What does math have to do with prosthetic legs?

Math has been used to calculate the stresses in the prosthetic and to dimension the construction.

If you get fouled at the three point line what happens?

If your shooting, you get 3 free throws, if not, it's just a regular foul and you just throw the ball in.