Vertex of a Triangle

Let us study Vertex formula of a Triangle,
Area of equilateral triangle (A) = a² x square units

a – side length

Perimeter of equilateral triangle (P) = a + a + a units

= 3 a units

Sides of equilateral triangles are equal in length. By using the distance formula we can find the distance between two vertex points of the equilateral triangle. The distance is the side length of equilateral triangle.

Distance between two vertices (a) =

I hope the above explanation was useful.

Find percentage

Find percentage:Percentages are numerators of fractions with denominator 100 and have been used in comparing results. Per cent is derived from Latin word ‘per centum’ meaning ‘per hundred’. Per cent is represented by the symbol % and means hundredths too.Finding percentages is one key topic in mathematics.Let us find percentage for the given problems.We can learn how to do percentages with the help of exaples.For ex:

Percentage means multiply by 100

Convert 0.47 to percentage

0.47 multiply by 100

=0.47 *100

= 47 %

Calculate the following 300 % of 30

Sol:

300 % means (300/100) = 3

Then multiply to the another number

= 3 *30

=90

The answer is 90.Hope you like the above example of Finding percentages.Please leave your comments, if you have any doubts.

How to divide

How to divide:Let us learn how to divide.Division means divide the groups into the equal parts. Division is similar to subtraction and opposite to multiplication. For example Ravi has 12 chocolates in hand. Ravi has two brothers and one sister. How to divide the chocolates are equal to each other. Each person gets 3 (12 /4) chocolates to each other. Here we do divide the groups (12) into equal (3) parts.Let us learn how to divide Decimals.Decimal number is a number. It must divided in to two parts. It’s known as whole number part and a fractional part. The dot (.) is calling the decimal point. Here we are going to learn about “how do divide decimals works”

Example: 841.125.

* Here the 8 represent 800.
* 4 represent 40.
* 1 represents 1 unit.
* 1 represent tenth place.
* 2 represent hundredths Place.
* Second 5 represent thousandths place.In the next Blog we will learn about How to divide fractions.Hope you like the above example of How to divide.Please leave your comments, if you have any doubts.

Geometry Constructions

Geometry Constructions:Let us now learn about Geometry Constructions,ancient scientists paid special attention to constructing geometric objects that had been described in some other way.Classical instruments allowed in geometric constructions are those with compass and straightedge.Compass constructions are very familiar.However, some problems turned out to be difficult or impossible to solve by these means alone,and ingenious constructions using parabolas and other curves, as well as mechanical devices, were found.Math constructions are different from geometric constructions.Hope you like the above example of Geometry Constructions.Please leave your comments, if you have any doubts.

Factoring of polynomials

Factoring of polynomials:Factoring of polynomials is the reverse process of multiplying polynomials.When we factor a real number, First we are getting for prime factors for real number that multiply together to give the same real number.For example, 32 = 4 x 4 x 2.When we are going to factor a polynomial, First we need to look for simpler polynomial expressions which are multiplied each other and give the same polynomial expression what we started with.For example, 3x2 + 9x = 3x(x + 3).Let us learn Examples on factoring polynomials.Problem 1:Factor the polynomial expression: x2 – 25.Solution:The given polynomial expression is x2 – 25.

Factoring it,

x2 – 25

= x2 – 52

This is in the form of a2 – b2 = (a + b) (a – b)

So,

= (x + 5)(x – 5)

Therefore, the factors are (x + 5)(x – 5).

Solving it,

x + 5 = 0

x = - 5

x - 5 = 0

x = 5

Therefore, Solutions are x = 5 , - 5.Let us learn in brief about Factoring Polynomials by Grouping.Factoring polynomials by grouping method is used for the expressions containing more than three terms.Hope you like the above example of Factoring of Polynomials.Please leave your comments, if you have any doubts.

Equation of a Line

Let us learn about Equation of a Line.An equation that defines a straight line is referred as the equation of the line.To Find equation of a line is very simple. We can find the equation of a line for the following conditions,if the slope and y intercept is given,if the slope and a point is given,if two points on the line are given.We can also learn how to write equation of a line,once we learn what equations mean.Hope you like the above example of Equation of a Line.Please leave your comments, if you have any doubts.

Introduction of Algebraic fractions

Are you having a tough time with Algebra ? Let me explain Algebraic Fractions,

Introduction to Algebra fraction solve: Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Here we are going to study about How to solve algebra fraction and its example problems.
Algebra fraction: In algebra fraction is a simple fraction it contains algebraic expression in either numerator or denominator.

Ex: = 3

I hope the above explanation was useful, now let me explain about fraction converter.

Fractional Decimal Notation

Introduction to fraction decimal notation:

Let us discuss the fraction decimal notation. The fraction notation is defined the part of whole number. The fraction is generally specifying two parts. The first part is numerator and second part is denominator. The numerator part is top part and denominator is bottom part. The decimal notation is same as the fraction notation. Decimal notation has decimal point. The example is 3.16.
Fraction Decimal Notation:

The fraction notation is numerator / denominator. Example is 4 / 6. The top number is known as the numerator and bottom number is known as the denominator.

* The 4 is called numerator.
* The 6 is called the denominator part.

The example of the fraction number is 9 / 7, 5/ 6 and etc.

The decimal point is very important part of the decimal notation. The example of the decimal notation is 63.147.

* The 63 is called the whole number.
* The dot (.) is called the decimal point.
* The 1 is called the tenth place of the number. The meaning is 1/10.
* The 4 is called the hundredth place of the number. The meaning is 4/100.
* The 7 is called the thousandth place of the number. The meaning is 7/1000.

The fraction notation is written the decimal notation. The example is 5/7 is fraction notation. The decimal notation of 5/7 is 0.71.

I hope the above explanation was useful, now let me explain about whole number definition.

What is linear equations in two variables

Let us study linear equations in two variables An excellent characteristic of equations in two variables is their adaptability to graphical analysis. The rectangular coordinate system is used in analyzing equations graphically. This system of horizontal and vertical lines, meeting each other at right angles and thus forming a rectangular grid, is often called the Cartesian coordinate system. It is named after the mathematician and French philosopher, Rene Descartes, who invented it.

A Linear equation is a first level algebraic expression with one, two or more variables equated to a constant. Graphically a linear equation with three variables represents a plane whereas. One or two variables is a straight line A simple linear equation is an equality between two algebraic expressions involving an unknown value called the variable. In a linear equation the exponent of the variable is always equal to 1.

The two sides of an equation are called Right Hand Side (RHS) and Left-Hand Side (LHS). They are written on either side of equal sign.

I hope the above explanation was useful.

Find percentage

Let us study how to find percentage,

You have 120 cows and 90% of them are female. How many female cows do you have?

In order to find the answers to questions like the one above, you need to know how to do this kind of calculation:

90% of 120

You also need to understand that when you find a percent of something, the answer has the same units as the number you are finding the percent of. For example:
50% of 200 carrots is 100 carrots 10% of $300 is $30 25% of 80 units is 20 units

Now let's look at the methods for finding a percent of a number:

Method 1 involves using the fraction instead of the percent. For example, if you were asked:

"What is 50% of 36?"

you would instead ask yourself:

"What is half of 36?"

This makes it easy to get the answer 18.

I hope the above explanation was useful, now let me explain about Fractions.

Basics of Circles

Let us study the basics of circles,
A circle is a plane figure bounded by one curved line where all of its point is at a constant distance from a fixed point in the plane, which is termed as the center of the circle. The constant distance of every point on the circle from its centre is called the radius of the circle. As we move ahead, it’s important for the learners to get acquainted with the basic terms related to a circle.

Circle: A circle is a set of those points in a plane, which are at a constant distance from a fixed point in the plane.

Radius: The distance from the center of a circle to any given point on the circle is known as the radius of a circle

Diameter: Any straight line drawn through the centre and ending at both ways by the circumference is called diameter. Diameter is just the double of radius.

Circumference: The distance around a circle, which is the bounding line is called the circumference.

Chord: A straight line joining any two points on the circumference of a circle is called a chord.

Arc: Any portion of the circumference of a circle is referred as an arc.

I hope the above explanation was useful.

Introduction of Simultaneous Equations

Let us study about Simultaneous Equations,


Simultaneous Equations :
If you have two equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing.


Addition/subtraction method :

To use the addition/subtraction method,

1. Multiply one or both equations by some number to make the number in front of one of the letters (unknowns) the same in each equation.

2. Add or subtract the two equations to eliminate one letter.

3. Solve for the other unknown.

4. Insert the value of the first unknown in one of the original equations to solve for the second unknown.

Example : Solve for x and y.
First multiply the bottom equation by 3. Now the y is preceded by a 3 in each equation.
Now the equations can be subtracted, eliminating the y terms.
Now insert x = 5 in one of the original equations to solve for y.
Answer: x = 5, y = 3

Of course, if the number in front of a letter is already the same in each equation, you do not have to change either equation. Simply add or subtract.
I hope the above explanation was useful.

Measurement Scales

Let us study about Measurement scales,
Different measurement scales allow for different levels of exactness, depending upon the characteristics of the variables being measured. The four types of scales available in statistical analysis are

* Nominal: A scale that measures data by name only. For example, religious affiliation (measured as Jewish, Christian, Buddhist, and so forth), political affiliation (measured as Democratic, Republican, Libertarian, and so forth), or style of automobile (measured as sedan, sports car, station wagon, van, and so forth).

* Ordinal: Measures by rank order only. Other than rough order, no precise measurement is possible. For example, medical condition (measured as satisfactory, fair, poor, guarded, serious, and critical); social-economic status (measured as lower class, lower-middle class, middle class, upper-middle class, upper class); or military officer rank (measured as lieutenant, captain, major, lieutenant colonel, colonel, general). Such rankings are not absolute but rather “relative” to each other: Major is higher than captain, but we cannot measure the exact difference in numerical terms. Is the difference between major and captain equal to the difference between colonel and general? You cannot say.

* Interval: Measures by using equal intervals. Here you can compare differences between pairs of values. The Fahrenheit temperature scale, measured in degrees, is an interval scale, as is the centigrade scale. The temperature difference between 50 and 60 degrees centigrade (10 degrees) equals the temperature difference between 80 and 90 degrees centigrade (10 degrees). Note that the 0 in each of these scales is arbitrarily placed, which makes the interval scale different from ratio.

* Ratio: Similar to an interval scale, a ratio scale includes a 0 measurement that signifies the point at which the characteristic being measured vanishes (absolute 0). For example, income (measured in dollars, with 0 equal to no income at all), years of formal education, items sold, and so forth, are all ratio scales.
Hope the above explanation helped you, now let us study about mathematical modelling.