trapezoid definition

trapezoid definition: The trapezoid is a blocked flat stature surrounded by four line segments with two elevations is parallel and two faces are nonparallel. The analogous surfaces are named as base and nonparallel sides are named as legs but the isosceles trapezoid having equivalent length. The word trapezoid is cam from trapezium.

The line segments are made trapezoid. The parallel bases and equivalent to semi sum of their lengths. The elevation of a trapezoid is vertical distance among the bases. The region of a trapezoid is equivalent to partly the product of the altitude and the addition of the base surfaces

The formula for area of trapezoid = 1/2*(a+b)*h.

Description:

A indicates the base value.

B indicates another base value.

H indicates the height of trapezoid

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inverse of matrix

Let us learn about inverse of matrix

A matrix can be defined as the table of values arranged in row and column form which represent one or more linear algebraic equations.

There are many different ways to solve a matrix based on the given linear equations.

The operations performed over the matrix are multiplication, division, addition, subtraction and even inverse.

Solving matrices may be difficult at first, but with hard-working, studying and practice you can be able to work through any matrix problem.

• Let us consider the given problem(s) and form the matrix from the given linear equations. You are supposed to solving two or more problems given in algebraic or linear form.

• Rewrite these equations into matrix form, by start writing the numbers left of the equal symbol in equation 1 over the numbers left of the equal symbol in equation 2. This matrix can be named as "A."

• Now replace the letter x over letter y. this matrix can be named as "X."

• At last, write the number right of the equal symbol in equation 1 over the number right of the equal symbol in equation 2.

• This is referred as matrix "B."

Inverse of a Matrix:

To determine the inverse of the given matrix A. The inverse of a function can be obtained by dividing the function by 1, the inverse of A matrix can be obtained by placing a 1 on the cross-multiplied value of the matrix A.

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factors of 63

The factors of 63 are 1, 3, 7, 9, 21, and 63.

A factor tree is the diagram which is used to split a number by dividing it commonly and shows the different parts of the number. The way we split the number into factors will be like a tree. The numbers left in the edge will be a prime number. So that it cannot be simplified further. Now we are going to create a Prime factor tree for 63.

Prime Factor Tree for 63:

63

/ \

/ \

/ \

21 3

/ \

/ \

7 3

63 = 7 x 3 x 3.

How to Make a Prime Factor Tree for 63:

We need to make the factor tree of 63. we can split 63 by multiplying 21 and 3. So 21 x 3 = 63. And when we further simplify we will get 7and 3 as the factors of 21. Here 3 is a prime number, so we can simplify 21and the factors of 21 is 7 and 3. 7 is a prime number and 3 is a prime number. So we cannot simplify it further. So we can stop with this. so the factors of 63 is 7, 3, 3

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stratified sample

Stratified sample statistics is one of the method in probability sampling in statistics. The stratified sample statistics having another name which is called proportional or quota sample statistics. In this we are dividing our population into homogeneous subgroups and we are taking a sample random sample from each sample groups. This is called simple sample statistics. It is one of the important approach which gives the more precise estimates but not in all times.

Strategies of Stratified Sample Statistics:

Sampling fraction of each of the strata used by the proportional allocation which is proportional to the total population. Let us consider an example

If the total population consists of 40% of mens and 60% women then the relative size of the above population is 2 women and 3 mens. It will reflect the proportion.

2. If the stratum is proportionate to the standard deviation of the each variable mean then it is called optimum allocation. In this we will take the large samples into the strata with the highest variability to generate least possible variance.

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exponential growth formula

Let us learn about exponential growth formula

Exponential growth (including exponential decay) occurs when the growth rate of a mathematical function is proportional to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression).

A function is said to be Exponential growth that including exponential decay when the growth rate of that mathematical function is proportional to the function's current value. In a discrete domain of definition with equal intervals of the function is called as geometric growth or geometric decay. The exponential growth model is also called as the Malthusian growth model.

Exponential Growth Formula:

Exponential formula defines the X as exponentially on time t.

X(t) = a . b^(t/r)

"a" denotes the initial value

a = x,

X(0) = a,

b= a

It denotes the positive growth of the factor, t = time required

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factors of 25

Let us learn about "factors of 25"

A factor of a number is an exact divisor of that number. In other words, a factor of a number is that number which completely divides the number without leaving a remainder. Each of the numbers 1, 2, 3, 4, 6 and 12 is a factor of 12. However, none of the numbers 5, 7, 8, 9,10 and 11 is a factor of 12.

A natural number is called a prime or a prime number if it has exactly two distinct natural number divisors. Natural numbers greater than 1 that are not prime are called composite. Therefore, 1 is not prime, since it has only one divisor, namely 1. However, 2 and 3 are prime, since they have exactly two divisors.In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. Numbers that are not prime is called composite. 20 is a composite number. Examples of prime numbers are 2, 3, 5, 7, 11 and 13.

Prime Factors of 25

The Factors are numbers you multiply to get other number. For instance, the factors of 30 are 6 and 5, because 6×5 = 30. Some numbers are more than one factor (more than one way of being factorization). For instance, 15 can be factored as the 1×15, 3×5, or 5×3.

The number that can only be factor as 1 times itself is called prime. The few prime’s numbers are 2, 3, 5, 7, 11, and 13. The number 1 is not regard as to a prime, and is usually not included in factorizations.

Prime factors of 25 – Example problems:

Problem 1:

Find the prime factors of 25

Solution:

Prime factors of 25

25 = 5 * 5

= 5² = Prime factors of 25 = 5²

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Triangle rectangle

Let us learn about "triangle rectangle"

As per the basic geometry, the area of a triangle is defined as half the product of its base and height. Similarly the formula for the area of a rectangle is the product of its base (length) and height (width).

This gives an indication that a relation is possible between the area of any triangle inscribed in a rectangle. After a closer study it has been established that the area of a triangle as half a rectangle. The triangle may be the any triangle inscribed inside the rectangle

A rectangle is placed inside an isoceles right triangle in such a way that the two vertices of the rectangle lie on the hypotenuse, and the other two vertices lie on the legs.

The area of the triangle is 2 square units, and the area of the rectangle is one quarter of that.

The rectangle, like the square, is one of the most commonly known quadrilaterals. It is defined as having all four interior angles 90° (right angles).

Properties of a rectangle

• Opposite sides are parallel and congruent Adjust the rectangle above and satisfy yourself that this is so.
• The diagonals bisect each other
• The diagonals are congruent

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