Help in finding the slope of a line

Introduction to Finding the slope of a line
Define Slope :
Slope of a line is referred to as the values of the angle that a straight line makes with the positive direction of x-axis in the anticlockwise sense.

Generally , for any straight line equations of the form y = mx + c , m is referred to as slope.This could also help us on periodic function. It is the coefficients of the x term from the equation given.

Keep reading may be in the next session let me help you on algebra formula.

Note on angles of a triangle

Introduction - study about angles of a triangle:
Three-sided shapes that lie in single level surface are triangle. Triangles are a kind of polygons. The abstract of every single one the angles in any triangle is 180º. Triangles can be prepared according to the measurement of its angles. The angle is the diagram is framed by the sharing common end points. Let us study the detailed about the triangle and angle.

Angle - Study about Triangle Angles:
In general angle is the shape in the geometry. They are dissimilar's kinds of the angle is available in the mathematics.

We study detailed about different type of the angle is given below: This could also help us on formula for surface area

Right angle: Exact of the 90 degree is the right angle.
Acute angle: Minor than 90 degree is the acute angle
Obtuse angle: Upper than 90 degree and less than 180 degrees
Straight angle: The 180 degree of the angle dimension is the straight line
Reflex angle: The 360 degree of the angle dimension is the reflex angle
Complete angle: The angle dimension is the 90 degree

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Help with Statistics Variance

Introduction to Statistics Variance calculator:
Calculator is a device, in which the given inputs are processed and the result is manipulated and gives the output for the input given. In the statistics variance calculators, when the given data set is put in the required input field, the calculator keeps processing the given input and gives the required output. Here some of the examples for the statistics variance calculators and steps for calculating the variance manually.

Definition Statistics Variance Calculator:
Definition of variance:
Variance is the measures of the summations of the total squared mean deviation value which is divided by the total number of values subtracted by one. For measuring the statistics variances we have to manipulate the mean value initially.This could also help us on graphing equations
Mean is the average of the given total numbers, total of all the given data set values to that divide it by the total given values in the data set.

Keep reading may be in the next session let me help you with exponents and radicals

Help with simplify equations

Introduction to simplify equations:
In this article let me help you on simplifying equations. An equation is defined as the the equality of two expressions which consists of variables and constants. Equations consist of the expressions that is to be equal to the opposite sides of an equal sign.

The following rules are used to simplify the equations and the equation does not change.
1) Add or subtract any variable or numbers to the both sides of the equation.
2) Multiply or divide any variable or numbers to the both sides of the equation.

Examples of equation: m+10=14, x+22=11, x+25=1,….
Now, we are going to see some of the simplifying equations problems.
Simplifying Equations Problems:

Example problem 1:
Simplify the equation: 7 x + 7 = 91

Solution:
Subtract 7 on both sides of the equation
7x + 7 - 7 = 91 – 7
7x = 84
Divide by 7 on both sides of the equation. This could also help us on right isosceles triangle
7x / 7 = 84 / 7
x = 12
So, the simplified answer is x = 12.

Keep reading may be in the next session let me help you on triangle proof

fractions to decimals chart

Introduction to fraction to decimal chart:
Fractions:
A certain part of the whole is called as fractions. The fractions can be denoted as a/b, Where a, b are integers.

Decimal:
The type of number that has base 10 is called as decimal number. The decimal can also defined as a fraction with the denominator of 10 or multiples of 10.
In this article we are going to see about how to convert the fraction into decimal and a chart for fraction to decimal and some problems on fractions to decimal chart.This could also help us on define independent variable
This is how we learn on polynomial functions. May be in the following lesson i will try to help you more on 4th grade math problems

Help with Fraction Calculator

Today let me help you on help fractions fraction calculator. Fraction calculator includes simple operation for adding, subtraction, dividing or multiplying fractions and returns an answer in a reduced fraction and a mixed number, if it exists.

Adding Fractions

The algebraic formula for addition of fractions is a/b + c/d = (ad + bc) / bd. For example: 2/6 + 1/4 = (2*4 + 1*6) / 6*4 = 14 / 24.
Reducing this fraction we get 7/12.

Subtracting Fractions

subtracting fractions formula is a/b - c/d = (ad - bc) / bd. For example: 2/6 - 1/4 = (2*4 - 1*6) / 6*4 = 2 / 24.
Reducing this fraction we get 1/12. This could also help us on algebra made easy
Multiplying Fractions

The formula for algebraic in multiplying fractions is a/b * c/d = ac / bd. For example: 2/6 * 1/4 = 2*1 / 6*4 = 2 / 24.
Reducing this fraction we get 1/12.

Keep reading may be in the next section let me help you on Fraction Converter

Free math word problems

In this article we are going to study on free math word problems.Since we had studied enough on word problem let me give you a example to understand better.

Solve Online word Problems:
There were 42 apples in each crate. 12 such crates of apples were delivered to a company. 4 apples were rotten and had to be thrown away. The important apples were packed into boxes of 10 apples each. How many boxes of apples were there?

Solution:
Find the total number of apples delivered to a company.
12 × 42 = 504
The total number of apples delivered to company was 504.
Get the number of remaining apples.
504 – 4 = 500
Get the number of boxes of apples. This could also help us on multiplicative inverse property
500 ÷ 10 = 50
There were 50 boxes of apples.

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word math problems

In this article we are going to study on word math problems. Since we had studyied enough on word problem let me give you a example to understand better.

Solve Online word Problems:
There were 42 apples in each crate. 12 such crates of apples were delivered to a company. 4 apples were rotten and had to be thrown away. The important apples were packed into boxes of 10 apples each. How many boxes of apples were there?

Solution:
Find the total number of apples delivered to a company.
12 × 42 = 504
The total number of apples delivered to company was 504.
Get the number of remaining apples.
504 – 4 = 500
Get the number of boxes of apples. This could also help us on triangles types
500 ÷ 10 = 50
There were 50 boxes of apples.

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Note on volume integral

Introduction for volume integral calculus:

Today let me help you go through on volume integral. In this session we see how to find volume of a solid in integral calculus. Volumes are find out for three dimensional solid objects. The volume of a solid is find using the triple integral, the volume of a solid object are find in polar coordinates and spherical coordinates.

The volume of a region for using triple integral we solve with respect to three functions with three limits. Let us see some problems in volume integral calculus. This could also help us on algebra worksheets

Keep reading may be in the next session let me help you on integrals table

Help in math

Introduction to help in Math

Fraction:

* Definition of Fraction is defined as an equal amount of one whole object. It can be represented as " a/b " where 'a' denotes numerator and 'b' denotes denominator and q not equal to zero.
* Example: 1/2 , 3/4.

Multiplication:

* Definition of Multiplication is defined as an arithmetic calculation, which is inversely proportional to the operation of division. By the use of multiplication, two or more numbers can be multiplied. This could also help us on algebra elemental
* Example : 5*6 = 30.

Keep reading may be in the next session let me help you on Trigonometry examples

Quadratic Factoring Calculator

Example Problems for Quadratic Factoring Calculator:

Ex:1 Solve the quadratic equation x² + 4x - 12 = 0 by factoring.

Sol:

Step 1: Given equation

x² + 4x - 12 = 0

Step 2: Rewrite the term '4x' as '6x - 2x'

x² + 4x - 12 = 0

x² + 6x - 2x - 12 = 0

Step 3: Take common terms outside

x(x + 6) - 2(x + 6) = 0

(x - 2) (x + 6) = 0

Step 4: Solve the obtained factor

x - 2 = 0 x + 6 = 0

including on both sides, we get Subtracting 6 on both side, we get

x = 2 x = - 6

Step 5: Solution

x₁ = 2; x₂ = - 6 . This could also help us on ionic equation calculator

Keep reading may be in the next session let me help you on free online tutoring for algebra

online calculus homework

Introduction to Solving online calculus homework problems:
In this article let me help you on online calculus homework.Quantities of comparison varied in a non-linear way is called calculus. It is been given into differential calculus and integral calculus. The calculus differentiation can be referred as rate of change between two quantities. calculus on Integral can be used to find out the direct relationship between two variables.

This has improved one of the major source for students to develop their knowledge. In this lesson we shall discuss about solving online calculus homework problems and precalculus homework online

keep reading may be in the next session let me help you on free math tutoring

Help on Calculus Homework

In this article let me help understand calculus homework.Therefore let me tell you the importance of learning precalculus in mathematics.

Studying on pre-calculus is an important step students must master before they move on to calculus & other forms of higher math. The ideas learned in pre-calculus are essential for careers in engineering, arithmetic, the hard sciences, finance & some design fields. Pre-calculus can be difficult for plenty of students, but there's methods to go about learning it that may help.

This could also help us on solve precalculus answers. Brush up on your algebra. Pre-calculus builds directly from the ideas you learned in algebra I & II, so make definite you are solid on those before you start on pre-calculus. If you have started a pre-calculus coursework & are having trouble, return & review your algebra; a nice review will strengthen your pre-calculus work.

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Note on Homologous Structures

Introduction to examples of homologous structures :

The organs which are similar in structure and origin but dissimilar in function are called homologous organs and this phenomenon is called homology.
Examples of Homologous Organs from Plants and Animals

1. Thorns of bougainvillea and tendrils of cucurbita: The thorns of bougainvillea differ from the tendril of cucurbita in its function but both arise in axillary position as modified branches.

2.Pericarp: The wall of the ovary in flowering plants after fertilization of the ovules become modified in different ways to help in seed dispersal because wing like expansion for wind dispersal in maple ,fibrous and spongy in coconut for water dispersal and succulent in mango for animal dispersal.

3.Vertebrate fore limbs: The forelimbs of vertebrates such as seal, bird,bat ,horse man etc afford a good example for homologous organs. This could help us on hexagon shape
4.Insect mouth parts: In all the insects mouth parts include a labrum, a pair of mandibles, and 2 pairs of maxillae and these help in feeding.


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Interval notation

Interval notation is a method of writing down a set of numbers. Usually, this is used to describe a certain span or group of spans of numbers along a axis, such as an x-axis. However, this notation can be used to describe any group of numbers.

For example, consider the set of numbers that are all greater than 5. If we were to write an inequality for this set, letting x be any number in the group, we would say:

This same set could be described in another type of notation called interval notation. In that notation the group of numbers would be written as:

This could also help us on acceleration formula.

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Examples of Mixtures

Introduction to examples of mixtures:
Mixtures

Mixtures are heterogeneous forms of matter.Mixture contains a combination of two or more elements or compounds mixed together without any chemical bonds.Mixtures can be combined with varying proportions of each substance. It can be separated into individual elements or compounds . Some common examples of the mixtures are soil, air, sea water etc.,There are two types of mixtures. They are

1. Homogeneous Mixture: All the components exist in a single phase and they are uniformly mixed. These mixtures are also called as solution.Potassium sulfide solution is a homogenous mixture.

2. Heterogeneous Mixture: The components exist in more than one phase. They are not uniformly mixed. A mixture of water and oil is heterogeneous in nature. This can also help us on what is a compound?

Properties of Mixtures:

* The composition of a mixture is variable.
* The compounds of a mixture retains its characteristic properties.
* Its components are easily separated

I hope you enjoyed reading on this article. Keep reading may be in the next session let me help you on Arithmetic Reasoning

Help on Unit Circle Chat

Unit circle:
As we had studied enough on circle and its types. Today let me help you on unit circle chat. A unit circle is a circle whose radius = 1 unit and center is ( 0,0). Angles are measured using this chart, angles measure clockwise would have positive values and angles measured in anticlockwise have negative values.

Following are the sample graph of unit circle chat.


On unit circle line inverse trigonometric functions are given as X = Cos and Y = sin
The value of sine is on the y coordinate of unit circle and value of cosine is on the x coordinate of unit circle. Using the unit circle any trigonometric function value can be calculated by using certain formulas. We divide the unit circle into 4 quadrants.

Did i really help you on this? I understand you still need more help on more topics like this. Keep reading and leave your comments so that i can help you particularly on your problems. May be in the next session let me help you on Adjacent Angles

what is a composite number

Introduction:
What is a composite number is a positive integer which is divisible by other number and by itself. When n>0 is an integer , 1composite number is also having more divisors in operation of arithmetic and l.c.m.

Types of Composite Numbers
A composite number with even number of prime factors can distinguish with composite number with odd number of prime factors in real time applications.

1. Example for semi prime number:
Express the following numbers as product of semi prime numbers 6

Solution:
6 = 2 × 3 (2 and 3 are semi prime numbers)

2. Example for spheric prime number:
Express the following numbers as product of spheric prime numbers 8

solution:
8=2×2×2 ( here 2 is spheric number) This can also help us on percent difference formula

The first 105 composite are
4, 6, 8, 9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48, 49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95,96,98,99,100,102,104,105,106,108,110,111,112,114,115, 116,117,118,119,120,121,122,123, 124, 125,126,128,129, 130,132,133,134,135,136,138,140.

Above number shown is a composite numbers example all numbers shown above is a divided by two divisors.some of composite numbers which are

I hope you liked my information on this topic. Keep reading may be in the next session let me help you on Percentage Change Calculator

Identity Property of Addition

Introduction of identity property of addition:

In this section let me help you on identity property of addition. Addition and multiplications are two basic arithmetic processes in mathematics. Addition produce a sum of given numbers where as multiplication produce a produce of given numbers. Identity property of addition and multiplication is the process of producing a result as a same number itself. The element used for this identity property is called identity element. This element is different for addition and multiplication.
Identity Property of Addition and Multiplication:

Statement of identity property of addition:

When a number of any type or variable is added with identity element of addition gives the same number or variables as result. An identity element used for addition is 0.

Example: 0 + 7 = 7 and u + 0 =u. This can also help us on variables in science

Statement of identity property of multiplication:

When a number of any type or variable is multiplied with identity element of multiplication gives the same number or variable as result. An identity element used for multiplication is 1.

Example: 7 × 1 = 7 and u × 1 =u

I hope you liked my information on this topic. Keep reading may be in the next session let me help you on Congruent Angles

Note on Meters to Centimeters

Introduction to meters to centimeters:

In this session let me help you on meters and centimeters.The meter is the basic unit in mathematics. The meter is used for calculating the distance. The symbol of meter is ‘m’.

The kilo meter is a unit of distance end to end in a metric system. It is the usually used measurement unit for expressing distances between geographical places in most of the world

One kilometer = 1000 meter

One meter = 1 * 100 centimeters

One kilometer = 1* 100000 centimeters

Examples for Meters to Centimeters:

This can also help us on mixtures

Example 1:

The Scale A 25 millimeter in one hour. The second scale B 8 millimeters in one ground. What is the difference between the Scale A and B?

Solution:

Here scale A and scale B having the speed in unusual units. Here we need to convert the speed in the equal unit and find the difference between Scale A and Scale B.

Scale A = one millimeter = 0.1 centimeter

So 25 millimeter = 25 * 0.1 = 2.5 centimeter

Scale B = 8 millimeter

Difference = 2.5 - 0.8 = 1.7 centimeter

Keep reading and leaver your comments. May ne in the next session let me help you on Examples on Probability

Factoring Polynomials Calculator

Introduction to learn factor polynomials calculator:

In this let me help you on how to learn factoring polynomials Calculator is used to solve different types of problems. It is a web-based tool designed to solve different problems.Learning factor polynomials through calculators is simple.

Factor polynomials calculator are used to understand the polynomials factorization. Given expression can be factorized by using the greatest common factor. Let us discuss about the learn factor polynomials calculator.

Steps to Learn Factor Polynomials Calculator:

This will also help us on factoring trinomials calculator

The Steps to learn factor polynomials are as follows:

* Given expression can be arranged in the order of powers.

* Expression can be in the form of standard ax2 + bx + c = 0.

* The expression should be factorized.

* Solve the given terms.

Keep reading may be in the next section let me help you on how to calculate pi

Differential Algebraic Equation

In this section let me help you on differential algebraic equation. keep reading and leave your comments. An equation is the combination of two expressions separated by an equal sign. In the equation the both sides of the equal sign has the same value.

For example,

2 + 18 = 4 * 5

Types of Equations

Fundamentals and types of Equations are :

Transcendental Equations

If f(x) is a polynomial in x, then f(x) = 0 is an algebraic equation.

Example; x7 + 5x - 2 = 0.

If f(x) contains algebraic and non algebraic functions namely exponential, logarithmic, trigonometric and inverse trigonometric functions then f(x) = 0 is called transcendental equation.

Example; x + log x + sin x=0. this will also help us on second order differential equations

Transcendental equations may have no root, exactly one root or more than one root.

Algebraic Equations:

Fundamental theorem on Algebra.

Every algebraic equation of degree n ≥ 1 has a root real or complex.

keep reading may be in the next session let me help you on homogeneous differential equations

what are real numbers

In this section let me help you on what are real numbers with the following introduction.
Introduction

The sets of numbers which every student must remember are:
The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecutive integers, Factor, Common factor, Prime numbers, Composite number, Prime factors, Numbers prime to each other, Rule of Divisibility, Fraction, Types of fractions, Simplification of fractions. This can also help us on names of polygons.

Rational Numbers
The rational numbers can be expressed as terminating or recurring decimals.
Decimal fraction has denominator as 10 or a power of 10.
A recurring decimal is denoted by placing dots or a bar over recurring digits.

This is only a brief introduction, keep reading may be in the next lesson let me help you on radius of a circle

Help on Linear Equation

Linear equation represent a straight line and it may be inclined or horizontal. The general format for a linear equation is as follows,

y = mx +b
where,
m = slope of the line (it is a number)

Working of a Linear Graph Solver:

once the enter button is pressed the linear solver accepts the linear equation given by the user and performs the following operations on it.

Step 1: The the given equation is y =ax+c. or x = ay +c.
Step 2: Assume first type y =ax+c. Since the given equation is a function of x, let y =f(x).
Step 3: Therefore f(x) = ax+c.
Step 4: It substitutes various values for ‘x’ and finds the corresponding value of f(x).
Step 5: It tabulates the values as columns x & f(x). The values of x as -2, -1, 0, 1, 2, 3 and for f(x), their corresponding values. will also help on algebra regents.
Step 6: The values in the table are the co-ordinates,
Step 7: It graphs the point and then joins them to give the graph.

This is only the introduction to Linear Equation. Keep reading may be in the next lesson let me help on Trigonometric Function

Help on Substitution Method

In this lesson… let me help you on Substitution Method. Earlier we had learned about types of circle and its importance. Now let me take you through with the introduction to substitution method.

Introduction of Substitution:

The substitution method is also one of the direct parts in algebra. Here we need to substitute the values in one variable. And we need to find the value of another variable.

This also helps us in rules of logarithms.

Example of substitution method:

2x-8y=168.

y=2x.

Solution:

Step1: Here the equation one is 2x-8y=168 and equation two is y=2x.

Step 2: we know that, y value is 2x. So we need to substitute y value is equation one.

Step 3: So, 2x-8(2x) =168.

Step 4:2x-16x=168 (Now we need to find the x value)

Step 5: Therefore, 14x =168.

Step 6: 14 x =168(Now we divide using 14 on both the sides)

Step 7: So the value of x=12.

This was just an introduction to substitution method. Keep reading and may be in the section let me help you with Algebra practice test.

Note on Natural Numbers

In this lesson let me help you understand better on Natural Numbers. First let me help you understand what is all about Natural Numbers.

Definition The name natural number is given for those numbers which come naturally to us. These numbers are all positive integers from 1,2,3,4,5----up to infinity, each succeeding number is greater by its previous number by 1.These numbers are also called counting numbers.

Properties

Algebraic properties

Closure property- For addition and multiplication all natural numbers have closure property. If a and b are two natural numbers, then ( a+ b) and a x b are natural numbers.

Associative property- for all natural numbers like a, b and c a+(b+ c)=(a +b)+c and ax(b x c)=(a x b)x c

Commutatitve property-For all natural numbers (a, b ) a+ b=b+ a and ax b= b x a

Identity property-for every natural number a, a+0=a and ax1=a

Distributive property- Multiplication is done before addition

Example- ax (b +c) = (a x b)+ (a x c)

However, the difference or the ratio of two natural numbers is not always a natural number. For example, 6-4 and 12/4 are natural numbers, but 4-6 and 4/12 are not.

Order

Each natural number corresponds to a position in a sequence. The natural numbers are ordered in an infinite list.

Example: -

1, 2, 3, 4, 5-----that starts at 1, but there is no ending .There is no last natural number.

This is just a brief introduction to natural numbers . Keep reading and leave your comments. May be in the next lesson let me help you go through on types of angels

Exercise on Coefficient of Algebraic Expressions

We just learned about Algebraic Expressions. Now let me hlep you with some sample exercise for you to understand better.
Exercise on Coefficient of Algebraic Expressions:
Following are the sample exercise on coefficient of algebraic expressions. Follow each of them very carfully and try to answer yourself and try to match with the answer which i am giving to you.
1. The coefficient of u in 3u² + 5u is
a) 9
b) 5
c) 3
d) 1
Answer - B) 5

2. Which of the following are like terms?
a) 3x², (2/3) x, ½ x
b) 4xyz², -7xyz, ½ xy
c) 12uv², ¾ v²u, -11v²u
d) None of the above
Answer - c) 12uv², ¾ v²u, -11v²u

1. The sum of 0.2x³ and 5x³ is
a) x³
b) 0.7x³
c) 5.2x³
d) They cannot be added
Answer - c)5.2x³
I hope you enjoyed doing this exercise.. if you still need more exercise on any topic keep reading and leave your comments. In the next lesson.. lets discuss about how to calculate triangle

Steps for solving word problems

Word problem plays an important role in mathematic. Before i take you through on steps for solving word problems. let me help you understand what is word problem and how does it help mathematic.

What is word problem?

In mathematics education, a word problem is a mathematical question written without relying heavily on mathematics notation. Word problems commonly include mathematical modelling questions, where data and information about a certain system is given and a student is required to develop a model.This also plays an important role in algebra word problems.

Steps for solving word problems:-

Now let me help you go through the important steps to be followed in solving word problems before i take you through with the help of examples.

1) The problems are to be thoroughly read

2) The information given is to be listed and what is asked in the problem is to be clearly understood. An equation is to be formed with the information given. While forming equation key words are to be correctly noted for defining the correct operation like addition/subtraction/multiplication/division.

3) The equation is to be solved for knowing the variables.

Key words	Operation
Increased by, more than, combined together, total of, sum , added to	Addition
Key words	Operation
Less than, fewer than, reduced by, decreased by, difference of	Subtraction
Of, times, multiplied by	Multiplication
Per, a, out of, ratio of, quotient of, percent	Division

This was just a brief introduction to word problems. May be in the next lesson let me help you with a example so that you understand word problems in a better way. keep reading and leave your comments. And even if you have any doubts feel free to share with me .. i will be able to help you.

Decimal Number System in Math

Introduction to Math Decimal System:

The concept of math decimal system is also deals with the fractions whose denominators are 10, 100 or 1000 etc. In this section, a decimal can be expressed as a fraction and vice-versa. A math decimal system may contain a whole number part and a decimal part. In a decimal system, if whole number part is not given, we indicate it by writing a zero on the left of the decimal point.In math, decimal value is represented by the point.

Decimal Number System in Math:

In math decimal number system, the value of a digit depends upon its place, or position, in the number. Each place has some value of 10 times the place to its right.

To the left of decimal point are:

Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc

To the right of the decimal point are:

Tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and so on.

Example on Decimal Number System in Math: -

Example :

Write the following as a decimal:

34+

Solution:

34+

=34.23 is decimal form

How do you feel now?...Did i help you understand on number system.. Keep reading and give me your valuable comments or even if you need any help on math...

Understanding Polygons : Types of Polygon

A polygon is a two dimensional plane figure, bounded by line segments called as sides. A polygon can be classified as regular or irregular polygon, based on their sides. If all the sides are equal, then it is called as a regular polygon. An irregular polygon has unequal sides.
Hear are the few types of polygons -

1. Regular polygon,
2. Irregular polygon,
3. Convex Polygon,
4. Concave polygon,
5. Crossed polygon and
6. Equiangular polygon

Polygons can be classified as,
1. Convex and Concave polygon
2. Regular polygon
3. Congruent polygon
These are the types and classification of polygons..... I understand you still require a detailed explanation on all the types of polygons. keep reading.. we will try to learn that may be in the next lesson.

Examples of Congruent Triangles

we just learned on congruent triangles and now let me also help understand better with some examples on congruent triangles.

Examples of Congruent triangles:
The definition of congruent triangles describes only when the triangles are said to be congruent, and here are some examples of congruent triangles.

• If two line segments each measure 20 units, they are congruence segments.
• If two angles each measure 80 degrees, they are congruent angles, even if they are in different locations and facing different directions.
• If two triangles have sides measuring 4, 6, and 8 units, and their equivalent angles are congruent, then the triangles are congruence too
• If two polygons have 20 sides, and the corresponding sides and angles are congruent, then the polygons are congruent too.

I hope you got a good knowledge on congruent triangles. keep reading...... and if you are really keen on leaning math's and need help on any topics then leave your comments. I can help you understand better with my examples....

Note on Congruent Triangles

we were been trying to understand more on number sense and now.. let me help you understand on congruent Triangles.

Introduction:

The triangles are said to be congruent when all the subsequent sides and interior angles are congruent. The triangles will have same shape and size, but one may be a mirror image of other in the definition of triangles

Congruent Triangles:
Probably the most generally used example of congruence is the congruence of two triangles. Congruence in triangles is able to be proven using one of several rules. The rules for the definition of congruent triangles include side-angle-side, angle-side-angle, side-side-side, or angle-angle-side. The below definition gives the meaning of the congruent triangles.

• Side-angle-side – If the two sides and the included angle of one triangle are said to be congruent to two sides and the included angle of another triangle, the triangles are congruent.
• Angle-angle-side – If the two sides and then a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, the triangles are congruent

Now you got an good understanding on congruent triangles. keep reading and leave your comments... may be on the next lesson.. let me share my knowledge on Examples of Congruent Triangles.

procedure to draw hyperbola graph

Dear readers.. as we discussed about properties of hyperbola and now let me help you understand more on the procedure to draw hyperbola graph.

Before we learn on drawing... let me help you on the important steps involved in it

• First we have to plot the intercepts The four points are (a,0), (-a,0) and (0,b), (0,-b)
• Using this four points draw the rectangle
• Draw two lines forming diagonals of the rectangle .It represents the asymptotes of the hyperbola
• Now draw the hyperbola that with the vertices's (a,0) and (-a,0)

Procedure to draw a graph -
Two variables x and y are connected by an equation of the form y = ax2 + bx + c then it is called a quadratic polynomial. We have already seen in Algebra that the equation ax2 + bx + c = 0 is a quadratic equation. This is the reason why we call y = ax2 + bx + c as a quadratic graph. For each value of x the equation y = ax2 + b x + c gives a value of y and we obtain an ordered pair (x, y) of real numbers. The set of all such ordered pairs define the graph of y = ax2 + bx + c called the quadratic graph.

The following procedure is used in drawing quadratic graphs:

• By substituting selected values for x in the equation y = ax² + bx + c, we get corresponding values for y and then we form a table.

• Draw x-axis and y-axis on the graph sheet and choose a suitable scale on the co-ordinates axes. The scale for both the axes are chosen depending on the values of the co-ordinates obtained.

• Plot the points in the Cartesian plane of the graph sheet.

• Join these points by a smooth curve, then we get the required quadratic graph of y = a x² + bx + c

I hope you got an idea on this lesson. Keep reading and i will help you also go through on Different Line Graphs on hyperbola graph

Properties of hyperbola

Introduction to hyperbola learning:

A hyperbola learning is a conic section obtained on slicing a double napped cone by a plane parallel to the axis of the cone.

The locus of a point from a fixed point is at a constant ratio and it is greater than one of its distance from a fixed line is called a Hyperbola.

Standard form of a hyperbola

x²/a² – y²/b² = 1

Learning Properties of hyperbola

Properties of hyperbola is the lines from the foci to any point on a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other, along with hyperbolic functions

The hyperbola is symmetric about x-axis, y-axis and hence the hyperbola is symmetric about the origin.

The hyperbola does not pass through the origin.

The tangent from any point (x₁, y₁) to the hyperbola is xx₁/a² – yy₁/b² = 1

learning the above properties will help to solve many problems

This is only the brief introduction to properties of hyperbola. Let us try to learn more on this topic. may be in the next lesson let me help you go through on Procedure for Draw the Hyperbola Graph.

Rational and Irrational Numbers

In among number theory.... Rational and Irrational Numbers plays an important role... This will help us understand all about number system and its functions in mathematical terms.

Rational Number -

The rational numbers can be expressed as terminating or recurring decimals.
Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digits.

Irrational Number -

Under number theory, numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers

Summary -

1. Problems involving rational numbers are simplified using 'BODMAS' rule.

2. A rational number can be represented in the decimal form.

3. When a rational number is represented as a decimal, it will be either a terminating decimal or a recurring decimal.

4. All rational and irrational numbers can be marked on the number line.

5. Numbers with surds in the denominator are supposed to be simplified by rationalising their denominators

This is only the brief introduction to number theory. After reading this .. i am very sure that .. you would love to learn more and get help on math... keep reading and leave your valuable comments.... may be in the next lesson let me help you go through on Algebra Problems