Proofs

7 Marsi

Festën e mësuesit

Ne do ta festojmë

Lulet më të bukura

Ne do ti dhurojmë.

Vijmë tek ti mësues

Buzëqeshjen ta dhurojmë

Kënga krahët reh si flutur

Midis jush jam e lumtur.

An estimated value is an approximate value that is calculated based on available information, assumptions, or simplifications. It is used when the exact value is not known or is difficult to determine. An actual value, on the other hand, is the precise and accurate value of a quantity obtained through direct measurement or observation. It represents the true value of the quantity being measured.

Oh, dude, let me break it down for you. So, equal angles have the same measure, like they're twins or something, while congruent angles are basically the same angle just chilling in different places. It's like saying two people are equally tall versus being the exact same person in two different places. Cool, right?

Oh, dude, the classic 555 number! Yeah, that number is often used in movies and TV shows because it's not a real working number. So, if you see a character dialing 555 on screen, it's just a fake number to protect people's privacy. Like, imagine if every time someone in a movie gave out their number, they started getting calls from random fans or telemarketers. That would be a nightmare, right? So, 555 it is!

You can use a variety of postulates or theorems, among others:

SSS (Side-Side-Side)

ASA (Angle-Side-Angle - any two corresponding sides* and a corresponding angle)

SAS (Side-Angle-Side - the angle MUST be between the two sides, except:)

RHS (Right angle-Hypotenuse-Side - this is only ASS which works)

* if two corresponding angles are the same, then the third corresponding angle must also be the same (as the angles of a triangle always sum to 180°), and that can be substituted for one angle of ASA to get AAS or SAA.

Well, honey, the answer to "3 plus 2a equals" is simply "3 + 2a." I mean, come on now, it's right there in the question! Just leave it as is unless you want to simplify it further, but that's as far as I'm willing to go with math today, darling.

Circles and triangles are geometric shapes with distinct properties, but they can be related through various geometric principles. For example, a circle can be inscribed in a triangle or a triangle can be inscribed in a circle. Additionally, the circumcircle of a triangle is a circle that passes through all three vertices of the triangle. These relationships demonstrate the interconnected nature of geometric shapes and the principles that govern their properties.

To show that ( A \oplus B = (A \cup B) - (A \cap B) ), we need to prove two inclusions.

For the first inclusion, let ( x \in A \oplus B ). This means that ( x ) is in exactly one of ( A ) or ( B ), but not both. Therefore, ( x ) is in ( A ) or ( B ), but not in their intersection. Hence, ( x \in (A \cup B) - (A \cap B) ).

For the second inclusion, let ( x \in (A \cup B) - (A \cap B) ). This means that ( x ) is in either ( A ) or ( B ), but not in their intersection. Thus, ( x ) is in exactly one of ( A ) or ( B ), leading to ( x \in A \oplus B ).

Therefore, we have shown that ( A \oplus B = (A \cup B) - (A \cap B) ).

Yes, if x is an integer divisible by 3, then x^2 is also divisible by 3. This is because for any integer x, x^2 will also be divisible by 3 if x is divisible by 3. This can be proven using the property that the square of any integer divisible by 3 will also be divisible by 3.

It is irrational.

The proof depends on the proof that sqrt(5) is irrational. However, judging by this question, I suggest that you are not yet ready for that proof.

So, assume that sqrt(5) is irrational. Any multiple of an irrrational number by a non-zero rational isirrational.

For suppose 2*sqrt(5) were rational

that is 2*sqrt(5) = p/q for some integers p and q, where q is nonzero.

then dividing both isdes by 2 gives sqrt(5) = p/(2q) where p and 2q are both integers and 2q in non-zero.

But that implies that sqrt(5) is rational!

That is a contradiction so 2*sqrt(5) cannot be rational.

The number of columns in the first matrix must equal the number of rows in the second.

No, because trigonometry is a big subject: there are many formulae.

This usually means the upcoming lemma is an adaption of a previous lemma to a mathematical object related to the one in the first lemma.

If

Factors of 15 are 1, 3, 5 and 15.

Starting with the greatest number, 15 is not divisible by 130.

Then, 5 is both divisible by 130 and 10000.

So the answer is 5.

draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.

2234.

U don't, because it isn't true. Draw a trapezoid. Now lengthen the base and the other parallel edge by any amount u want (the same amount, of course). U now still have a trapezoid, but the base is longer and the sides are the same as they were before.

There are more than two but the two most common ones are plane trig and spherical trig.

Let p be even and q be odd. Since p is even, p = 2n for some natural number n. Then the product pq = 2nq, an even number.

Use a direct proof;

Suppose Tom minimises the largest difference between two numbers. For this to be true, Tom must pick consecutive numbers. If Tom picks 10 consecutive numbers the maximum difference must be 9. Given that tom picks one more number, there must be two numbers who differ by 10 for all selections.

Nonagon

There are three pairs of equal sides.

square no. Means reapeating the particular no. Twice. For ex. 1* 1equal 1, 4 * 4 equal 16, 7 * 7 equal 49. The no.s 1, 4, 49 are sq. Nos . 2 * 3 equals 6 and 5 * 2 equalls 10 are not a square no. Two identical no are multiplied and tie resultent is called a square no. Any two identical nos are multiplied does not give 14. So...

3*3 = 9 and 4*4=16. There are no integers between 3 and 4 so there are no square numbers between 9 and 16.