Help with triangles and angles

Introduction of understanding triangles:
In this article let me help you on triangles and angles. Triangles is the important geometrical shapes, it is a closed shape with three sides and angles. The triangles are divided into two categories they are based on sides and angles. Comparing sides the triangle consist of three types they are equilateral triangle, scalene triangle, and isosceles triangle.

Comparing angles we consider the triangle as three types they are right angle triangle, acute angle and obtuse angle. In this article, we will understanding triangles with suitable example problem. For more Study material.
Understanding Triangles in Sides
Understanding triangles in sides are classified into three types they are show below.

• Equilateral triangle
• Scalene triangle and
• Isosceles triangle

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Help with algebra worksheet

Introduction to algebra worksheets

Halfway Algebra follows the rules of arithmetic in which letters representing book. The amount is the not changing the see. Mediate Algebra follows the rules of arithmetic operations, and relationships conjunctive the drawing.

Mediate Algebra uses mathematical equations to draw relationships between elements that motley over term; These elements are called as variables.In this worksheets, there are more solved problems. These problems are rattling cooperative to bang nigh work intermediate algebra. This could also help us on statics examples

Let us see gray algebra properties and representative problems , worksheets.

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Equation solver online

Introduction to derive equation of motion:
In this article let me help you on equation solver online. Equation solver describe the behavior of a system or the motion of an object or a particle under the influence of a force as a function of time. These famous equations of motion in elementary Classical

Mechanics are given below:
v= u + at
s =( u + v ) t /2
s = ut + at2/2
v2 = u2 + 2as

The following are the variables used in these equations:

* t is the length of the interval of time and measured in second.
* u is the initial speed of the objects or the speed at the beginning of the time interval, measured in ms-1.
* v is the final speed of the objects or the speed at the end of the time interval, measured in ms-1. This could also help us on homogeneous mixture. This could also help us on linear definition
* a is the accelerations of the object within the time interval t measured in ms-2.
* s is the distance covered or the displacements of the object during the time interval t, measured in metres.

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Algebra 2 book online

Introduction to Saxon algebra 2 help online:

In this lesson let me help you on algebra 2 book online. In algebra 2, there are many symbols are used and the variables are used for the unknown values. In Saxon algebra2 the symbol is used for the variables or the alphabets to denote the number values. In online, the tutor will explain about the Saxon algebra 2 and the students may learn the concepts from the other websites also. Now we see the Saxon algebra 2 through online with the help of tutor.
About the Saxon's Algebra 2 Help Online: This could also help us on parallel line

Let us see about the Saxon's algebra 2 through online with the help of the example problems by the tutor.

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prime number algorithm

In this article let me help you on prime number algorithm. Prime numbers are the numbers which can be divided only by 1 and the number itself.Prime numbers cannot have any other factors except one and the number by itself. The +ve(positive) integers are divided into two such as prime numbers and composite integers.
Totally there is 25 prime numbers between 1 and 100. So remaining are the composite numbers.Now we give the list of prime numbers upto 100.

The numbers are like
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
as the list shows there are 25 prime numbers between 1 to 100. This could also help us on metric system chart.
That twenty five prime numbers are in between 1-100 These numbers cannot be divided by any other number except 1 and the number itself.And the same is called mean mode median and range.

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Solving Proportion Word Problems

Solving Proportion Word Problems:
Solving proportion is the process of setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation.
When one of the four numbers in a proportion is unknown, using the cross product we have to find the unknown number. This is called solving the proportions. Letters or Questions marks are commonly used in place of the unknown number.

Example word problems:
If 3 dollars equals to 1 gallon then find the amounts of gallon for 6 dollars?

Solution:
Let us 6 dollars equal to 'x' gallon. This could also help us on inverse of a matrix
3/1=6/x
By solving this,
3x= 6
3x/3 = 6/3
x=2.

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Note on expression calculator

Introduction to multiplying rational expression calculator:

Today let me help you on expression calculator. In the algebraic expressions the variable does not occur in the fraction or negative index. While using the rational expressions calculator the variable that occur in the fractional notation. The calculator show the error mistake. while in the multiply algebraic expressions the calculator will be mention in the integer it may not occur any fraction or negative variable.

For example 5x²- 3x +2 this is the algebraic expression

This could also help us on linear pairs. An rational expressions of the form A(x) * B(x) where A(x) and B(x) are two polynomials over the set of real numbers and QA(x) ≠ 0 is called a rational expression.

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Decimal Notation

Introduction to Write Decimal notation:
In this section let me help you on decimal notation. Write Decimal notation mean wring the decimal form for fractions, decimal written in words and scientific form to decimal notation and so on. But in general, Decimal notation mean that representing fractions of numbers in tenths (and hundredths, thousandths, etc) rather than in fractions (or in eighths or twelths) if the denominator is a power of ten such fractions are decimal fractions. So in this article we will see about how to write Decimal notations for fractions with examples.

Steps to Write Decimal Notation:
The following are the steps to Write Decimal notations for fractions,
Just divide the numerator by the denominator. We get the answer in decimal form. That is the decimal notion for the given fraction .When the fraction is mixed number, This could also help us on define evolution. Change the mixed numbers into improper fraction (By multiply the whole number with the denominator and add the result with the numerator. Keep the denominator as same.) Divide the improper fraction’s numerator by its denominator

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Noteo n Square shape

Introduction to square shape:
Conservative shapes pictures containing four vertices and the viewpoint activity for conservative is coincident. Oppositeness (word) angles should be coinciding in conservative shapes. Disobedient faces are quasi and change. The honest shapes diagonals are orthogonal to apiece remaining. Diagonals are the assonant in size.



Formulas for Shape Modify Pictures:
The perimeter of a foursquare shapes whose sides fuck size a is
P= 4a
And the country of the conventional pictures is
A= a2. This could also help us on logistic growth
In definitive times, the 2nd quality was stop for in terms of the atlantic of a paddle, as in the above formulas. This led to the use of the cost quadrate to nasty flaring to the 2nd index.
In the peak (x2, y2) = 1 is an equation of row pictures. The x2 or y2, is larger, equals 1. The is circumradius of the conservative.

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solving algebra problems

Lets study on solving algebra problems with the help of following example.

Help algebra one problems 1:

Solving the given algebra sample equation and find out x and y value of the equation.
3x + 4y – 56 = 0
-3x + 7y – 32 = 0
Solution:
To find out the x and y value of algebra 1 linear equation.
3x +43y = 56
-3x + 7y = 32
In the first we are going to add equation (1) and (2). We get
3x + 4y = 56
-3x + 7y = 32
0x + 11y = 88
y = 8 This could also help us on math question solver
Now, we get the y value as 8. In the equation (2) we substitute y = 8, we get
-3x + 7(4) = 32
-3x + 28 = 32
-3x = -24
X = 8

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Note on Fraction Calculator

Today let me help you on 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 mixture

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.

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math word problems solver

In this article we are going to study on math word problems solver. 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 Algebra 2 help
500 ÷ 10 = 50
There were 50 boxes of apples.

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Help on congruent angles

Introduction to congruent angles:

Congruence angles are angles having equal measure. Angle plays a wide role in geometry. Many geometric figures are specified with there angles. Few of them are:

Triangles:- Triangles having all of there interior angle are congruent angles are said to be equilateral triangles.



Triangles:-

(i) Isosceles triangles:- A triangle in which any two of there interior angles are congruent angle is specified as a isosceles triangle. This could also help us on derivative of ln

(ii) Equilateral Triangles:- A triangle in which all of its interior angles are congruent angle is specified as equilateral angles.


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Poisson Distribution Examples

Introduction to the poisson distribution examples:

Today let me help you on poisson distribution examples. The statistics, Poisson distribution is mainly meant for finding out the average of the given functions. The average of the given distribution is found out by using the rate of change of function in which it consists of two values namely , x value known as the event in success and [lambda] value known as the change in average functions. In this article we will illustrate about poisson distribution examples tutorial.
Explanation for the Poisson Distribution Examples:

The formula for the Poisson distribution is given as follows,

* In online, the poisson distribution example problems can be learnt. This could also help us on venn diagram maker
* The online tutors will take the interactive sessions for the students and clear their doubts.
* The practice and solved examples for poisson distribution are shown below,

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Help on Polynomial Long Division

Introduction for long division of polynomials:
In this article let me help you with polynomial long division. Since i had shown you enough summary on polynomials. Let me directly help you with the following examples.

Example Problems for Study about Polynomial Long Division:
Study about polynomial long division - Example:
1) Divide 2x2 – 5x –2 by x -4
Solution:
Step 1: Given Divide 2x2 – 5x -2 by x - 4
Step 2: Take x - 3 and first two digits of given problems 2x2 – 5x
Step 3: Multiply x - 4with 2x then we can get 2x2- 8x.
Step 4: Then minus 2x2- 8x from 2x2 – 5x -1 and change the sign of 2x2- 8x before subtract the polynomial.
Step 5: Then we obtain 0 + 3x - 2
Step 6: After that x - 4 multiply with 3 then we can get 3x - 12.
Step 7: Change the sign then subtract 3x - 12 and x + 3. This could also help you on half angle formula.
Step 8: The solution is: 2x + 3 with remainder 10
2x +3
--------------
x -4) 2x2 – 5x –2

- 2x2 – 8x
----------------
0 + 3x - 2
(-) 3x -12
---------------
0 +10
---------------
Answer is: 2x + 3 with a remainder 10


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Types of Quadrilaterals

Introduction to quadrilaterals:

In this article let me explain on types of quadrilaterals. In Euclidean plane geometry, quadrilaterals are a polygon with four sides (or 'edges') and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") and lateral (meaning "of sides").

Types of Quadrilaterals:

There are two types of Quadrilaterals in geometry.The following are the two types of Quadrilaterals,

* Convex quadrilaterals ( Parallelograms )

* Concave quadrilaterals.

Let us see the types of quadrilaterals briefly in the following section. This could also help us on correlation formula


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John Dalton Atomic Theory

Dalton's atomic theory

In this section let me help you go through on John Dalton atomic theory. Dalton included in his theory some important new concepts. He said that the atoms of any one element are identical in all respects and in particular they have exactly the same mass. Furthermore, different elements have atoms of different mass, the mass of its atoms being a characteristic of each element. Dalton also stated that when chemical combination occurs, small whole numbers of atoms join together.

Except for the slight modification which became necessary when isotopes were discovered, this theory is still accepted today. The various points are, however, more familiar as the basic chemical laws of conservation of mass, constant composition, and multiple proportions.

It was during the third decade of the 19th century that Dalton arrived at his atomic theory. At that time it was virtually impossible to make accurate measurements because the apparatus available was still quite primitive. It is all the more remarkable, therefore, that Dalton's theory has withstood the test of time. This could also help us on probability mass function

Another valuable contribution which Dalton made to chemistry was his idea for representing chemical compounds visually. A distinctive circular symbol was used to denote the atoms of each element – hydrogen was a circle with a dot in the middle, while a circle with one vertical line through it denoted a nitrogen atom.

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Help on Geometric Progression

Introduction:

In this section let me help you on geometric progression. Solving online progression is very interesting since we can find the nth term of the particular sequence in much easier way. In this article we shall learn about steps involved in progressions solving. Moreover we will see in detail about different types involved in progression.

There are three types of Progression in math,

* Arithmetic progression
* Geometric progression
* Harmonic progression

Let us see these progression and their properties in the following section.
Arithmetic Progression. This can also help us on linear programming

Definition:

It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number.

The General form of the arithmetic sequence is,

a, a+d, a+2d, a+3d………..

Here a is the first number and d is the common difference.

To find the nth term of an arithmetic progression we can use the following formula,

an=a+ (n-1) d

Properties of Arithmetic Progression:

* When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

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Note on Frequency Polygon

Introduction to Frequency Polygon:

A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that together with the X-axis they form a polygon

Frequency polygons are useful for comparing distributions.This is achieved by overlaying the frequency polygons drawn for different data sets. The figure below provides an example. This will also help us on kinematics equations. The data come from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target

was a large rectangle. Time to reach the target was recorded on each trial.

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Fundamental Theorem of Calculus

Introduction to Fundamental Theorem of Calculus :

In this section let me try to help you on fundamental theorem of calculus. Calculus originated to solve mainly two geometric problems : the first is studied by a limit process known as differentiation and the second by another limit process known as integration.

Integral calculus is the study of the definition, properties and applications of two real concepts: the indefinite integral and definite integral.

The indefinite integral is the antiderivative. the definite integral inputs a function and outputs a function a number. The technical definition of the definite integral is the limit of a sum of areas of rectangles, called Riemann sum, as propounded by Riemann. This will also help us on normal distribution table

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved.

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Definite Integral Calculator

Definite integral calculus:

Definite integral calculator is same as the integral calculus calculator but it is mainly for finding the integral which is covered by a specific intervals. That is it has upper limit value and lower limit value.

For this definite integral calculus calculator first the given expression should be integrated as integral calculator and then the limits should be applied. The final output can be derived by substituting the upper limit – lower limit.

Integral calculator:

Integral calculus calculator is mainly for finding the indefinite integral of the given expression by getting an input value.

Consider an expression x then the integral calculus gives the calculator is, This will also help us on integral table

Example:

Find the integral calculus calculator of the function f=10x3.

Solution:

Given,

Function f=10x3

We know the integration of xn is

Therefore [int 10x^3] =10 [intx^3] =10 [x^4/4]

= [5/2x^4]

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what is measurement

In this lesson let me help you understand more on what is measurement and how it is measured in our day today life. keep reading
Everything that we use in our daily life is ultimately governed by principles of physics. All gadgets we use everyday at home, bicycles and cars, all different types of machinery and instruments, work on principles of physics. Hence to understand even the elementary working of these things, the study of physics is essential.
For understanding the relationships between matter and energy, measuring them is very essential. There are thousands and thousands of different things around us. There are different kinds of forces around us and there are different kinds of energies that we come across every day. Thus there would be millions and millions of physical quantities and energies that could be measured. Yet you would be surprised to know that there are only six basic units from which all other units are derived. This also helps us on water pollution statistics. These basic units are the units of length, mass, time, electric current, temperature and luminous intensity. Out of these only three fundamental or basic units of measurements are used in mechanics.
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Note on Continuous Function

Definition of Continuous Function:

In study of probability, a Random Variable X is assumed as a continuous variable, if it can take all possible values within certain given limits. That is X is a continuous its values cannot be put in one to one associated with N.

A nonstop probability function f(x) is a function that satisfies the following properties:

• It is non-negative for all real X.
• The probability function of integral is one.
• Constant continuous probability functions are known as probability definition function (pdf).
• Since regular probability function are defined for uncountable number of
  points over an interval, the probability at a single point is always zero.

The probabilities are measured between intervals। That Is, the area under the curve stuck between two distinct points define the probability for that interval.This can also help us on how to simplify radicals.

P(a ≤ x ≤ b) = P(a ≤ X < b) = P(a < x ≤ b) = P(a < x < b)

Discrete Probability function is referred to as probability mass function.

Continuous probability functions are known as probability density function

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Sample Problems on Radicals

Introduction for radical:

The opposite operation to the exponent is known as radical. A radical is an expression which contains the square roots, cube roots etc. For example the expression √49 can also be called as square root of 49 or root of 49. Radicals have the same property of the numbers.

Examples for Radical:

Following are the examples of radicals.

Example 1 for radical problem:

Simplify the radical: √ (49) / (√36)

Step 1: Factors of 49 = 7 × 7

√ (49) = √ (7 × 7)

= √7²

Step 2: Square root of 7² = 49

Step 3: Factors of 36 = 6 × 6

√ (36) = √ (6 × 6) = √6²

Step 4: √6² = 6

Step 5: so, √ (49) / √36) = 7 / 6

The answer of the given radical is 7 / 6

Even Rules of Radicals helps us understand better in doing all the problems.

Example 2 for Radical Problem:

Simplify the radical: 3√8 × √12

Step 1: Find the factor of 8 = 2 × 2 × 2

Step 2: Take cubic root of 8 = 2

Step 3: Find the factor for 12 = 2 × 2 × 3

Step 4: Take square root of 12 = 2 √3

Step 5: so, 3√8 × √12 = 2 × 2 √3

The answer for the given radical is = 4√3

This was just a sample examples on this topic. keep reading and leaver your comments. if you like this. May be in the next session lets study on dividing radicals

Help on Probability

In this lesson let me share with you on what is probability and its importance to mathematics.

Introduction to Probability:

In our day to day life, we come across many uncertainties of events. We wake up in the morning and check the weather report. The statement could be 'there is 60% chance of rain today'. This statement infers that the chance of rain is more than that having a dry weather. We decide upon our breakfast from a statement that "corn flakes might reduce cholesterol". What is the chance of getting a flat type on the way to an important apartment? And so on.

How probable an event is? We generally infer by repeated observation of such events in long term patterns.

Probability is the branch of mathematics devoted to the study of such events and this study also will help us on probability problems.

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Note on Closure property of integers under addition

In this lesson let me help you go through on closure property of integers under addition. Before i go more deep on this let me help you understand on what is all about integers.

What is integers?
The negative numbers, zero and the natural numbers together are called integers.
For example -8, -2, 0,2,8

Now we will discuss about the closure property of integers:

If a and b are two integers, then a+ b is also an integer. In other words, the sum of any two integers is also an integer or, integers are closed for addition.

Verification : In order to verify this property, lets us take any two integers and add them. We find the sum is always an integer.

Consider the following :

Integer(a) Integer(b) Sum(a+b)

5 7 (5+7)=12

[Here we observe that 5 is an integer as well 7 is also another integer and now if we add these two integers then the sum 12 is also an integer].

Integer(a) Integer(b) Sum(a+b)

-8 5 {(-8+5)}=-3

[Here we observe that -8 is an integer as well 5 is also another integer and now if we add these two integers then the sum -3 is also an integer].

Integer(a) Integer(b) Sum(a+b)

8 -10 {8+(-10)}=8-10=-2

[Here we observe that 8 is an integer as well -10 is also another integer and now if we add these two integers then the sum -2 is also an integer].

This was just a brief introduction to the topic . Keep reading and leave your comments. May be in the next lesson let me help you go through more on properties of logarithms.

Solved Problem on Cyclic Quadrilateral.

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Introduction to Cyclic Quadrilateral.

A Quadrilateral whose all four vertices lie on the circumference of the same circle is called a Cyclic Quadrilateral. As all the vertices are on same circle, so they are called Concyclic. Thus, a Cyclic Quadrilateral can be circumscribed. The circumcenter may or may not lie in the interior of the Quadrilateral

Sample problems on cyclic Quadrilateral.

Let me help you go through few solved problems on Cyclic Quadrilateral.

Problem: 1

The Cyclic Quadrilateral ABCD,

Solution

In the Cyclic Quadrilateral ABCD,

80 +

Similarly,

120° +

Hence,

Problem: 2

ABCD is a Quadrilateral circumscribed by a circle with center O. The diagonal AC is also the diameter of the circle. Find

Solution:

Since AC is the diameter

therefore,

Now,

90° +

Hence,

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Note on Trigonometry Fuctions

Studying about trigonometry is always interesting since it contains major parts of math factions in it. Before we go more deeply on Trigonometry Functions.. Let me show you what is trigonometry.

What is Trigonometry:-

Trigonometry is noun, trigonometric is adjective: the first part of the word from Greek trigon"triangle". The second part of the trigonometry is from Greek Merton "a measure." The Indo-European root is probably me- "to measure." trigonometry is the literally the measuring (of angles and sides) of triangles. Historically speaking, the triangular approach to trigonometry is ancient where’s the circular approach now taught in our schools is relatively recent

Applications of Trigonometry:-

There are enormous number of uses of the trigonometry and trigonometric functions. For instance of the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are the fundamental to the theory of periodic functions such as those that describe sound and light waves

Trigonometric Functions:-

A common use of the mnemonics is remember facts and relationships in trigonometry

For example, the sine, cosine, and tangent ratios is a right triangle can be remembered by representing them as strings of letters, as in SOH-CAH-TOA.

Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

The memorization of this mnemonic can be aided by expanding into a phrase such as "SomeOfficers Have Curly Auburn Hair Till Old Age" Any memorable phrase constructed of words beginning with the letters S-O-H-C-A-H-T-O-A will serve.

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How do Solve Proportions

Before we learn about how to solve proportions.. let me help you go through cross multiplication to solve proportion. this will help you understand better about proportion..

A proportion is an equation which states that two ratios are equal.

When the terms of a proportion are cross multiplied, the cross products are equal.

Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.

    21      3     --  =  --            70     10     21 * 10 = 70 * 3       210 = 210 

If one term of a proportion is not known, cross multiplication can be used to find the value of that term.

     x      3     --  =  --            70     10     x * 10 = 70 * 3       10x = 210            10x   210     --- = ---     10    10            x = 21 

This was just a sample problems on proportion.... keep reading and leave your valuable comments .. may be in the next lesson.. let me help you go through deeply on Algebra , number system, and matrix. I feel these are the major and simple topic which we need to know before we learn anything about math,,, Keep reading and leave your valuable comments... to help you better.

Types of Angles

Studying about angles are very interesting since it comes with diagrams and more easy to explain and learn as well. let me show you few types of angles with the diagram..

Acute angle:

An angle whose measure is less than 90 degrees. The following is an acute angle.
Right angle:

An angle whose measure is 90 degrees. The following is a right angle.

Obtuse angle:

An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees. The following is an obtuse angle.



Straight angle

An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line. The following is a straight angle.



Reflex angle:

An angle whose measure is bigger than 180 degrees but less than 360 degrees.The following is a reflex angle.

Adjacent angles:

Angle with a common vertex and one common side. <1 src="http://www.basic-mathematics.com/images/Adjacentangle.gif" border="0" alt="Adjacent-angle-image">

Complementary angles:

Two angles whose measures add to 90 degrees. Angle 1 and angle 2 are complementary angles because together they form a right angle.

Note that angle 1 and angle 2 do not have to be adjacent to be complementary as long as they add up to 90 degrees



Supplementary angles:

Two angles whose measures add to 180 degrees. The following are supplementary angles.

Vertical angles:

Angles that have a common vertex and whose sides are formed by the same lines. The following(angle 1 and angle 2) are vertical angles.



When two parallel lines are crossed by a third line(Transversal), 8 angles are formed. Take a look at the following figure



Angles 3,4,5,8 are interior angles

Angles 1,2,6,7 are exterior angles

Alternate interior angles:

Pairs of interior angles on opposite sides of the transversal.

For instance, angle 3 and angle 5 are alternate interior angles. Angle 4 and angle 8 are also alternate interior angles.

Alternate exterior angles:

Pairs of exterior angles on opposite sides of the transversal.

Angle 2 and angle 7 are alternate exterior angles.

Corresponding angles:

Pairs of angles that are in similar positions.

Angle 3 and angle 2 are corresponding angles.

Angle 5 and angle 7 are corresponding angles

Example Problems for Word Problems

Introduction to word problems:

In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are also referred to as story problems and may vary in the amount of language used.

Problems on Word Problems

Hear by ... let me show your a example on word problems ... so that it is little easy for you to understand better.

Example:

The sum of thrice a number plus 60 is 330. Determine the number.

Solution:

The word is means equals. The word and means plus.
Rewrite the word problem
the sum of thrice a number and 60 equals 330.
Write the problem into an equation.

3M + 60 = 330

Solve the above equation using the variable.

3M + 60 = 330 (Given Equation)
3M + 60 – 60 = 330 - 60 (Both side subtracted by – 60, we get)
3M = 270
M = 90 (Both sides Divided by 3, we get the result)
Solution to the given word Problem is 90.

This was just a sample problems on word.. Keep reading and leave your valuable comments.. and let me know if you are particular in learning any topic in math, i will be able to help you with that all.

Polynomial Matrices

In this lesson let try to understand more on A polynomial matrices or matrix polynomial is a matrix whose elements are univariate or multivariate polynomials.

Properties of Polynomial Matrices
Following are the properties of polynomial Matrics and its functions

• A polynomial matrix in excess of a field with determinant equivalent to a non-zero constant is called uni modular, and have an inverse, which is also a polynomial matrix.
• Note, that the simply scalar uni modular polynomials are polynomials of degree 0 - nonzero constants, for the reason that an inverse of an arbitrary polynomial of high degree is a rational function.
• The roots of a polynomial matrix in excess of the complex numbers are the points in the complex plane wherever the matrix loses rank.

Example 1
An example the 3x3 polynomial matrices



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This is how we solve problems on plynomial Matrices. Hope this lesson is more useful to you. Keep reading.... and leave your comments if you wish to share anything to me . May be in the following lesson we shall dicuss on Various topics involved in the algebra ii