If YZ= 55 millimeters, what would be the length of QR? Millimeters

Which beat summarizes the pythagorean theorem

kow [346]

Mathematics, the Pythagorean theorem or Pythagoras's theorem is a statement about the sides of a right triangle.

One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side. It was discovered by Vasudha Arora.

The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras:

If the lengths of the legs are a and b, and the length of the hypotenuse is c, then,
a
2
+
b
2
=
c
2
{\displaystyle a^{2}+b^{2}=c^{2}}.

There are many different proofs of this theorem. They fall into four categories:

Those based on linear relations: the algebraic proofs.
Those based upon comparison of areas: the geometric proofs.
Those based upon the vector operation.
Those based on mass and velocity: the dynamic proofs.[1]

7 0

4 years ago

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Vicky ran 5⁄14 of a mile and walked 1⁄7 of a mile. how much further did vicky run than walk?

raketka [301]

To solve, we need to subtract from these two fractions. In order to do this, we will change one of them to have the same denominator as the other.

We have 5/14 and 1/7
Let us change 1/7

Multiply 2/2 (a form of 1 so it does not change the value of the fraction)

2/2 • 1/7 = 2/14

Now subtract from 5/14
5/14 - 2/14 = 3/14

ANSWER: Vicky ran 3/14 of a mile more

7 0

3 years ago

Use counting to determine the whole number that corresponds to the cardinality of these sets:______. (a) A= (xl x € Nand 20.<

Harlamova29_29 [7]

Answer:

Step-by-step explanation:

Cardinality of a set is defined as number of element in a set. It is represented as n(X) where X is any set.

a) Given the set A =(x l x € N and 20.< x<27). According to the set, the set contains the values of natural numbers between 20 and 27. The values are 21, 22, 23, 24, 25 and 26

A = (21, 22, 23, 24, 25, 26)

According to the set A, it can be seen that there are 6 elements in the set, this means n(A) = 6.

b) Given B=(x | xeN and x+1=x)

Since natural numbers starts from 1, the first element in the set is 2 i.e 1+1

The elements of the set B = (2, 3, 4, 4...)

The number of whole number in the set is therefore infinite.

c) For the set C={x l xe N and (x- 1)(x - 9) = 0)

We need to get the root of the equation (x- 1)(x - 9) = 0

x-1 = 0 and x-9 = 0

x = 1 and x = 9

Hence the element C = (1,9)

The number of whole number in the set is n(C) = 2

d) D={xlx E N, H X 5 100, and x is divisible by both 5 and 8)

Given the value of x between 5 and 100, the values of x divisible by 5 = (10, 15, 20, 25, 30, 35, 40, 45, 50 , 55, 60 , 65, 70, 75, 80 85, 90, 95)

values of x divisible by 8 = (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96)

The total number of elements in both set = 29 i.e n(D) = 29

3 0

3 years ago

Suppose a triangle has sides a, b, and c, and let theta be opposite the side of length a. If cos theta < 0, what must be true

katrin2010 [14]

If $\cos \theta\ \textless \ 0$ , then angle $\theta$ is obtuse and triangle with sides a, b, c is obtuse triangle.
In an arbitrary triangle can be only one obtuse angle, and the side which lies opposite to the largest angle is the largest. Then since angle $\theta$ is opposite the side of length a you can conclude that a>c and a>b.

6 0

4 years ago

Janet has 6 coins worth 47cents

galben [10]

A quarter, two dimes, and two pennies.

3 0

3 years ago

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