Online Ruler Centimeter

Introduction:

Ruler is a one of the geometry tools. Ruler is mainly used to find the length of the two points or two edges of the particle. Also used to make the line segment in geometry. Without ruler we cannot implement the most fields. Example of carpentry sides, textile sides we must need ruler compare than the other tools. Ruler having  straight line edge for marking the line segment of two edge points. A ruler have the measurement of  marking in centimeter or may be inches. Ruler always starts from zero.


Constructing line segment using online ruler centimeter:


Introduction to online centimeter:

Centimeter means that units of length or distance, Each and every object should have a line segment, these line segments and jointed and make a geometry object shape.

Varies units for finding the length:

• Millimeter
• Meter
• Centimeter
• Kilometer

These all are measuring length of geometry object.

Basic concepts of online ruler centimeter

Structure of the online ruler centimeter

Online ruler centimeter is a one of the instrument of geometry and engineering sidesto ruled the straight lines. Ruler in the form of like as tapes, Straight line edge wood ruler, protractor. Rulers are more types Shorter ruler, Longer ruler, contraction ruler, Desk ruler, Tape ruler etc.

Construct the line segment using  ruler:

To draw a line segment of particular length using ruler:

First we have to position the starting point of line segment on the paper using ruler.

Next we have to draw the given length of line segment( like 8centimeter)

And then point the ending of the line segment.Now plot the line to connected the two points of line segment.

Example for making line segment using online ruler centimeter:


Draw the line segment of 6 centimeter?

Step 1:

Take the ruler and positioned ruler on the paper with a scale of centimeter ruler

Step 2:

Mark the starting point zero point and then mark the ending point 6 centimeter (0 to 6)

Step 3:

Connect the two ending point of line segment AB =6 centimeter

Learn Online Graphing Equations

Introduction :

We can learn how to graph in online.In online we can also get the graph of equations.Learning graphing the equations is very easy, once if we know the procedure to graph the equations.There are many ways to learn is followed in online to draw the graph.In general the graph displays the nature of relationship between the variables. One of the most useful graph that we obtain quite often is the linear  graph. All these ordered pairs (s, p) can be plotted as points in the Cartesian plane where its horizontal axis is the s-axis and the vertical axis is the p-axis. These points now define what is called the learn graph of the relation.

Linear Graphing:


Let x and y be two variables. If they are connected by an equation of the form y = mx + c, then x and y are linearly related. the equation y = mx + c represents a straight line in the Cartesian plane. This is the reason why the relationship between x and y is called linear.

For each value of x, the equation y = mx + c gives a value of y and ordered pair (x, y) of numbers can be obtained. The set of all such ordered pairs defines the graph of y = mx + c, called a learning linear graphing.
In the equation y = mx + c, the number m is called the slope of the line and c is known as the y-intercept. The y-intercept is the value of y when x = 0. Sometimes the y-intercept c is 0. In this situation, the equations of the line is y = mx and we say that the line passes through the origin.

The basic principle behind drawing a linear graph is that only two points are needed to graph a straight line.

Procedure to draw the graph of the equation:


Step 1: By substituting two different values for x in the equation y = mx + c, we get two values for y. Thus we get two points (x1, y1) and (x2, y2) on the line.

Step 2: Draw the x-axis and y-axis on the graph paper and choose a suitable scale on the coordinate axes. The scale for the graph is depends on the coordinates . If the coordinate values are large, then 1 cm along the axes may be taken to represents large number of units.

Step 3: Plot the two points (x1, y1) and (x2, y2) in the Cartesian plane of the paper.

Step 4: draw the line betwwen these two pointst and extend it in both directions of the segment.

Online graphing Example problem:

Draw the graph y = 3x -1.

Solution:

Substituting x = -1, 0, 1 in the equation of the line, we get y = -4, -1, 2 correspondingly. In a graph, plot the points (-1, -4), (0, -1) and (1, 2)

x       -1       0        1

y        -4       -1       2

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Graph of the equation:

Online Calculus Courses

Introduction :

The online calculus courses is common and open to everyone around the world. Students from anywhere can enroll in this online calculus courses. There is no need of class meetings in online calculus courses. Online calculus courses include limits, derivatives, applications of derivatives, integrals and application of integrals. In online calculus courses, students can attend final exam at their home or anywhere around the world. Derivatives and integrals are explained below with its applications to show how online courses helpful to you.

Derivatives and its applications:


In derivatives, we will study the changes in the values of y corresponding to small changes in the values of x where y and x are related to each other by the equation y = f(x).

Application of derivatives:

• Rate of change of quantities
• Errors and approximation
• Rolle's and Lagrange's theorem
• Maxima and minima functions
• Increasing function and decreasing functions
• Tangents and normal
• Optimization
• Graph shape

Example problem:

Find the derivative of the function y = 2x^3 + x^2 + 3.

Solution:

Step 1: Given function

y = 2x^3 + x^2 + 3

Step 2: Differentiate the given function y = 2x^3 + x^2 + 3   with respect to ' x ', to get `(dy)/dx`

`(dy)/dx` = 6x^2 + 2x

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Integrals and its applications:


Integration is the reverse process of that of differentiation. The process of finding derivative of the given function is called differentiation whereas finding the function whose derivative is known is called integration. This function is called as integral of the given function.

Application of integrals:

• To find area under simple curves
• To find areas of circles
• To find areas of parabolas
• To find areas of ellipses
• To find area between the curves
• Average function value
• Volumes of solids of revolution

Example problem:

Find the integration of the function,  f(x) = 3x + 8.

Solution:

Step 1: Given function

f(x) = 3x + 8

`int` f(x) dx = `int` 3x + 8 dx

Step 2: Separate the integral function

`int` 3x + 8 dx= `int` 3x dx + `int` 8 dx

Step 3: Integrate each function with respect to ' x',

`int` 3x + 8 = `(3x^2)/2` + 8x + C

Online Classroom Learning

Introduction :

Math solving is a mechanism of solving math problems. It consists of an in-numerous number of problems for calculation. It consists of many fields related to problem solving methodology. It is related to vector, difference equation, integrals, sets, numerals, and diagrams etc. the online classroom learning article offers you some solved examples and some techniques in mathematics.online is the best tool for learning.Through online we can get instant help at the second.

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Basic operations - online classroom learning:


The following are the basic operations of online classroom learning,

• Addition,
• Subtraction,
• Multiplication and
• Division.

Online Classroom learning - Solved examples:


Example 1:

Solve the equation y +6 = 5.

Solution:

it is easy to solve within one step by grouping like terms

y = 5 - 6

Solution :y = -1

Example 2:

Solve the equation 5y + 5= 25

Solution:

it is easy to solve within one step by grouping like terms

5y + 5 = 25

5y = 25 - 5

5y = 20

Divide by 5

Solution :y = 4

Example 3:

Find the value: 25 y - 10 = 5 y - 5

Solution:

It is easy to solve within one step by grouping like terms

25y - 10 = 5y - 5

25y - 5y = 10 - 5

20 y = 5

Divide by 20

y = 1/4.

The answer is y = 1/4.

Example 4:

Find the sum of 1000 + 5000?

Solution:

1000 + 5000 = 6000.

Answer = 6000.

Example 5:

Solve the equation y +16 = 15.

Solution:

It is easy to solve within one step by grouping like terms

y = 15 - 16

solution :y = -1

Example 6:

Solve the equation 5y + 15= 45

Solution:

it is easy to solve within one step by grouping like terms

5y + 15 = 45

5y = 45 - 15

5y = 30

Divide by 5

solution :y = 6

Example 7:

Find the value: 25 y - 15 = 15 y - 5

Solution:

it is easy to solve within one step by grouping like terms

25y - 15 = 15y - 5

25y - 15y = 15 - 5

5y = 10

Divide by 5

y = 1/2.

The answer is y = 1/2.


Tips - online classroom learning:

The below are the tips for online classroom learning.

at first, solve all the operations with in the parenthesis and braces.
then  the exponents are calculated
next perform the multiplication and division operations
at last do the addition and subtraction.

Online Geometry Calculator

Introduction to Geometry:-

Geometry "Earth-measuring" is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.                                                                                                                                                                            Source: - Wikipedia.

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Online geometry calculator - Example problems:


Online geometry calculator - Problem 1

Calculate the area of rectangle whose side’s measure 12 centimeters and 8 centimeters respectively.

Solution:-

Given

Length – 12 centimeter.

Breadth – 8 centimeter.

The formula used to find the area of rectangle is length * breadth.

Area = length * breadth.

By plugging the given values in to the formula.

We get,

Area   = 12 * 8

The product of 12 and 8 yields 96 so the area of the given rectangle is 96 square centimeter.

Online geometry calculator - Problem 2

Calculate the volume of the cube  whose side measure 12 centimeter.

Solution:-

Given:-

Measure of cube length = 12.

The formula used to find the volume of the cube is `a^3` .

By plugging the value in to formula we get the result as

Volume =  `12 ^3` .

=  1728.

So the volume of given cube is 1728 cubic centimeters.

Online geometry calculator - Problem 3

Calculate the volume of the cylinder which has the height is 12 centimeter and radius of 6 centimeter.

Solution:-

Given:-

Height = 12 centimeter.

Radius = 6 centimeter.

The formula used to calculate the volume of the cylinder is  `pi r^2 h`



`Volume = pi r^2 h`

r– radius of the cylinder

H – height of the cylinder.

By plugging in the given values in to the formula we get

` Volume = pi (6)^2 * 12`

`6^2` can be written as 6 * 6 = 36

Volume = `pi` 36 * 12

The product of 36 and 12 is 432

Volume =` pi` 432.

So the volume of the given cylinder is `432pi`

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Online geometry calculator - Practice Problems:


Problem 1

Calculate the volume of the cylinder which has the height is 2 centimeter and radius of 1 centimeter.

Answer:-

2`pi` .

Problem 2

Calculate the area of rectangle whose side’s measure 14 centimeters and 2 centimeters respectively.

Answer:-

28.

Online Distance Measuring

Introduction to online distance measuring:

Distance is a numerical description of how far apart objects are. In mathematics, a distance function is a generalization of the concept of physical distance.

The distance d between any two points (x1, y1) and (x 2, y2) can be calculated using the following formula,

Distance, d = `sqrt ((x2 - x1)^2 + (y2 - y1)^2)`

If the speed and time is known, then distance d is given by

Distance, d = Speed * Time

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Example problems for online distance measuring:


Measuring distance through online is very simple. In online, if  we enters the data for which the distance is to be measured, it performs the specified operations automatically and generates the required solution for the problem. The example problems are given below which shows online distance measuring with steps in detail.

Example 1:

Using distance formula, calculate the distance between the points (2, 5) and (5, 6).

Solution:

Step 1: Assign variables

x1 = 2     x2 =5

y1= 5      y2 = 6

Step 2: Plug all values in the distance formula

d = `sqrt((x2 - x1)^2 + (y2 - y1)^2)` ........... Distance formula

=  `sqrt(((5 - 2)^2+(6 - 5)^2))`

Step 3: Solve the above equation and find distance

= `sqrt((3)^2+ (1)^2)`

= `sqrt (9 + 1)`

= `sqrt10`

= 3.162

Step 5: Solution

The distance between the points (2, 5) and (5, 6) is 3.162

Example 2:

If a bike runs at the speed of 50kmph and it covers the certain distance in 6 hours, then find out the distance covered by it?

Solution:

Step 1: Given

Speed = 50kmph

Time = 6 hours

Step 2: Formula to find distance

Distance, d = Speed * Time

Step 3: Substitute all values in the formula

d = 50 *6

= 300

Step 4: Solution

Therefore, the total distance covered by the car is 300km

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Practice problems for online distance measuring:


The practice problems are given below which helps you for learning online distance measuring.

1) Using distance formula, calculate the distance between the points (-4, 5) and (- 3, 8).

2) Find out the distance covered by the train if it runs at the speed of 60kmph and it covers the certain distance in 5 hours?

3) Using distance formula, calculate the distance between the points (6, 8) and (1, - 7).

Solutions:

1) d = 3.162

2) d = 300km

3) d = 15.811

What is a Function in Algebra

What is a Function in Algebra

To find the area of a square we need the length of the side. So, we can say that the area of the square depends on the length of the side of the square. It means that if the length of the side changes, the area also changes then we can say that the first is the function of the other. So, we can conclude that the area of the square is the function of and it depends on the length of its side.  So, in mathematics algebraic functions can be defined as, a relationship between two variables something like ‘x’ and ‘y’ , function if there is a rule which assigns to each value of the variable ‘x’ there exists one and only one value of ‘y’. Then we can say that y is a function of x.

It is clear now that a function must be single valued, for instance, y=3x+2. Here to each value of x there is a unique value of y.  All the values which x can assume is called the domain.  These are the values for which the function can be defined. In the function y=3x+2, the domain include all the real numbers which means ‘x’ can be any real number.

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Once the domain is defined, the set of corresponding ‘y’ values for each value of ‘x’ is called the range of the function. For instance, if x=2 in the domain then y=(3.3)+2=11 is the corresponding value in the range.  So, ‘x’ can be called the independent variable and ‘y’ a dependent variable as its value depends on the value of x.
Consider an example of a algebra functions given by, x={-1,0,1,2} where each value is the value of the domain,  the rule being y=x2-1. Let us write the ordered pair of the given function.  Here we need to plug in each of the values of ‘x’ in the given rule to arrive to the corresponding ‘y’ value of the range.  When x=-1 then y=(-1)2-1 = 1-1=0; when x=0 then y=(0)2-1=-1; when x=1 then y=(1)2-1=0; when x=2 then y=(2)2-1=4-1=3. So, when the domain= {-1,0,1,2} the corresponding values of the range={0,-1,0,3} and the ordered pair of the function is (x,y)={(-1,0),(0,-1),(1,0),(2,3)}. So, functions algebra is a well behaved relation which means given an ‘x’ there is exactly one and only one ‘y’.

In the above functions algebra each ‘x’ to each ‘y’ we can see that there is only one arrow coming from each of ‘x’ of the domain and hence it is a function.

Trinomials Solving Online

A trinomial expression is any polynomial expression which has accurately three terms.
The equation or function or expression is in the structure of  ax^2+bx+c =0 where a?0, b, c are constants called as trinomials.
We can say it also as a quadratic function or quadratic equation.
The trinomials are having two roots. When we multiply the two binomials we can get the trinomial.

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STEPS FOR SOLVING TRINOMIALS


Factor out any factors common to all terms. The equation 8x^2 + 12x + 4 has 4 as a common factor, since every term can be divided by 4. Therefore, it can be factored as 4(2x^2 + 3x +1).
The equation x3 +2x^2 + x has x as a common factor. It can be factored as x(x^2 +2x +1).

Look for any other common factors you may have missed. In sometimes, an equation has both a integer and a variable that can be factored out. For example, 4x3 +12x^2 + 16x has both 4 and x as a factor. Factored out, it becomes 4x(x^2 + 3x + 4)

Locate out what type of trinomial equation you have left. If the maximum power of the unsatisfactory part is a squared variable like y2 or 7a2, you can factor it like a quadratic equation.

If you’re maximum power term is a cubed number or higher, you have a higher order equation. By this point, you will most likely not have anything greater than a cubed variable to deal with.
Many trinomial quadratics are easy sums of squares. Using an example from step one: 8x^2 + 12x + 4 = 4(2x^2 + 3x + 1).


EXAMPLES OF TRINOMIALS

1) Factors of trinomials of the form (Ax^2 +Bx +c)

We find two numbers a and b such that ab = C, and a+b = B

3 x^ 2 + 11x + 10

Coefficient of first term is 3, last term is 10

3 x 10 = 30

6x5 = 30, 6+5 = 11

We split middle term 11z = 6x + 5x

3x^2 + 6x +5x +10

3x ( x +2) + 5( x +2)

(3x +5) (x +2)

2)  Factors of trinomials of the form (A x^2 +Bx - C)

We find two numbers a and b such that a (-b) = C, a-b = B

8x^2 +2x - 3

8x^2 +6x - 4x - 3

2x ( 4x +3) -1(4x +3)

(2x - 1) ( 4x +3)

3) Factors of trinomial of the form (Ax^2 - Bx +C)

We find two numbers a and b such that (-a) (-b) = C, -a-b =-B

14 x^ 2 -23x +8

14 x^ 2 -16x -7x +8

2x (7x -8) -1(7x -8)

(2x -1) (7x - 8)

4) Factors of the trinomial of the form (Ax^2 -Bx -C)

We find two numbers a and b such that (-a) (b) = C -a+b = -B

12 x^ 2 -x -35

12x^2 -21x +20x -35

3x (4x - 7) +5(4x -7)

(3x +5) (4x - 7)

Study Online Factors

Introduction to factors:

In online study on factors, it is essential to know the definition of factors.The set of numbers which produce the remainder zero by dividing a particular number. These sets of numbers are called as factors. We can express a number by the multiples of another two numbers called as factors.

For Example,

10= 2 x 5

32=4 x 8

Here 2, 5 are the factors of 10 and 4, 8 are the factors of 32.


Types of Factors and Sample problems:


For the online study on factors, knowing the types of factors is an essential one. The types of factors for online study are as follows:

There are two types of factors,

• Prime Factors
• Composite factors

Online study on Prime Factors:

The numbers that can be expressed as the multiple of one and that number itself are called as prime numbers. The factors of prime numbers are called as prime factors.

Consider the following Examples,

3= 1 x 3 (1, 3 are the prime factors of 3)

5= 1 x 5 (1, 5 are the prime factors of 5)

7= 1 x 7 (1, 7 are the prime factors of 7)

Online study on Composite Factors:

The factors that are not a prime numbers are called as composite factors.

Consider the following example,

24=4 x 6

Here the numbers 4, 6 are not a prime number. Therefore, 4, 6 are called as composite factors of 24.

Example:

Find the factors of 130.
Solution:

130= 1 x  130

130= 2 x  65

130= 5 x  26

130= 10 x 13

So the factors of 130 =1, 2,5,10,13,26,65,130.

Important note: We can express all the numbers except “1” as a product of prime numbers are called as prime factorization.

Consider the following Example,

24 = 4 x 6

= (2 x 2) x (2 x 3)

24 = 23 x 3

Here 2, 3 are the prime numbers. Hence, we conclude that all the numbers can be expressed as a product of prime numbers.

Prime factorization tree:

By using the prime factorization tree, we can get all the prime factors of the given number.

Example:

Find the prime Factors of 124
Solution:

124

/  \

2     62

/  \

2   31

124 = 2 x 2 x 31

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Practice Problems on factors:


Following are the practice problems given for online study on factors.

1. Find the factors of 524.

2. Find the Prime factors of 900

3. Find the composite factors of 1056.

Answer Key:

1. (1, 2, 4, 131, 262, 524)

2.  (2 x 2 x 3 x 3 x 5 x 5)

3. (2  3  4  6  8  11  12  16  22  24  32  33  44  48  66  88  96  132  176  264  352  528  1056)

Study Online Arithmetic

Introduction

Arithmetic is a branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting and many other calculations.

Arithmetic involves the study of the result of combining numbers. It involves in following operation:

Operation                  Symbol

Addition                                +

Subtraction                             -

Multiplication                          X

Division                                     /


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Operations in arithmetic.


Addition

Addition is a mathematical operation that represents combining collections of objects and digits together into a larger collection. It is denoted by plus sign (+).Performing addition is one of the simplest numerical tasks. Addition is written using the plus sign "+" between the terms; that is, in infix notation. The result is expressed with an equals sign.

Example:Add 34 and 14

34+14=48

Addition of 34 and 14 so denoted by (+) sign and result is 48 so denoted by (=) sign

Subtraction

Subtraction is a one of four mathematical operations that represents difference of objects and digits together into a smaller collection. It is denoted by plus minus (-).Performing addition is one of the simplest numerical tasks. Subtraction is written using the plus sign "-" between the terms; that is, in infix notation. The result is expressed with a sign. It’s inverse of addition.

Example:Subtraction of 34 and 21

Given:34 and 21

34-21=13

Subtraction of 34 and 21 so denoted by (-) sign and result is 13 so denoted by (=) sign

The traditional names for the parts of the formula:

C − B= A

Where:C=minuend

B= subtrahend

A=difference

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Multiplication and division of arithmetic problems


Multiplication

Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in arithmetic. It multiplies one number with other and increases or doubles the number.

Denoted by symbol (X or *)

Now  we  study folowing example.

Example:Multiply 2 and 4?

Given: 2 and 4

4X2=8

Division

Mathematics, especially in elementary arithmetic, division is the arithmetic operation that is the inverse of multiplication.

Denoted by symbol (/ or ÷)

a/b=c

Note:b not equal to zero

In the above expression, a is called the dividend, b the divisor and c the quotient

Example:Divide 4 and 2

4/2=2

Solve Online Estimation

Introduction:

Estimation is defined as the method which is used to simply the calculation in easy way. Estimation is the process of values taken for adding and subtracting to change the value into nearest and easier numbers for simplification. In considerations of small values in calculations they are changed to their nearest 10’s and for largest values of calculations they are changed to their nearest 50’s and 100’s.

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Solve Online Estimation – Online Example


Solved Problems:

Example 1: Estimate 84 + 99.

Solution:

84 is changed to the nearest value 80 (i.e. nearest 10’s since it is the smallest value)

99 is changed to the nearest value 100 (i.e. nearest 10’s since it is the smallest value)

80 + 100 = 180

Example 2: Estimate 78 - 62.

Solution:

78 is changed to the nearest value 80 (i.e. nearest 10’s since it is the smallest value)

62 is changed to the nearest value 60 (i.e. nearest 10’s since it is the smallest value)

80 - 60 = 20

Example 3: Estimate 274 + 299.

Solution:

274 is changed to the nearest value 250 (i.e. nearest 50’s since it is the largest value)

299 is changed to the nearest value 300 (i.e. nearest 100’s since it is the largest value)

250 + 300 = 550

Example 4: Estimate 218 - 56.

Solution:

218 is changed to the nearest value 200 (i.e. nearest 100’s since it is the largest value)

56 is changed to the nearest value 50 (i.e. nearest 50’s since it is the largest value)

200 - 50 = 150

Example 5: Estimate 329 - 54.

Solution:

329 is changed to the nearest value 300 (i.e. nearest 100’s since it is the largest value)

54 is changed to the nearest value 50 (i.e. nearest 50’s since it is the largest value)

300 - 50 = 250

Example 6: Estimate 418 - 108.

Solution:

418 is changed to the nearest value 400 (i.e. nearest 100’s since it is the largest value)

108 is changed to the nearest value 100 (i.e. nearest 100’s since it is the largest value)

400 - 100 = 300


Solve Online Estimation - Online Practice


Practice Problems to solve

Problem 1: Estimate 74 + 48

Answer: 120

Problem 2: Estimate 294 – 273

Answer: 50

Quotient Online

Introduction for Quotient:

A quotient is obtained as a result of dividing two integers, where the quotient is the integer part of the result. While dividing two numbers such that 15/3, the quotient would be 5 where the remainder is zero. The quotient has been mainly used to indicate the algebraic structures, sets and spaces where the entities are the equivalence classes of some equivalence relation in a set.

In this article we are going to see some answers for the quotient online.

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Online answers for quotient:


This topic includes some online questions and answers for the quotient.

Example 1: Find the quotient of 1000 / 5.

Solution: As we know already quotient will be obtained by dividing the two given integers.

Given: 1000/5

Here 1000 is referred to as the numerator (dividend) and 5 is said to be the denominator (divisor).

1000/5 = 200

Thus the result of division of two integers 200 is called as the quotient.

Example 2: Find the quotient, remainder of 9/2

Solution: Here 9 is called as the dividend and 2 is the divisor, when the dividend is not exactly divided by the divisor then it yields a remainder.

Given: 9/2

9/2 = 4

4*2 = 8

9-8 = 1.

After the completion of the division process 1 remains which is said to be the remainder.

Here the quotient is four.

Example 3: Find the quotient of 12/4

Solution:

Here 12 is said to be the dividend and 4 is said to be the divisor

When we divide the two integers then we get the quotient.

12/4 = 3

Hence the quotient is 3

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Practice problems for online quotient:


Here there some practice problems given online fir the topic of quotient.

1) Solve the following and find the quotient of 125 / 5

Solution: The quotient is 25.

2)  Find the quotient of 111/10 and also the remainder

Solution: Quotient: 10, Remainder: 1

Solve Algebra Word Problems Online

Algebra, which is derived from the Arabic word al–jabr. In Arabic language, ‘al’ means ‘the’ and ‘jabr’ means ‘reunion of broken parts’. The usage of the word algebra can be understood by a simple example. In the equation x + 5 = 9, the left hand side is the addition (sum) of two parts x and 5. If we add (unite) (–5) to each side of the equation, we get

(x + 5) + (–5) = 9 + (–5) or x + [5 + (–5)] = 9 – 5 or x + 0 = 4 or x = 4.

Here 9 and -5 are reunited to get 4. This type of mathematics is called algebra.

I like to share this algebraic expressions solver with you all through my article.

Problem 1:


The sum of twice a number plus 13 is 75.  Find the number.

Solution:

Given : The sum of twice a number and 13 equals 75.

By using the numbers and a variable that represents something, N in the case (for number),

You can write the equation with the given problem

2N + 13 = 75

By solving the equation we can get the value for variable

2N + 13 = 75     Equation.

- 13 = -13     Add (-13) to both sides.

______________

2N      =  62

N       =  31     Divided both sides by 2.

So, the answer is N= 31

Understanding What is Prism is always challenging for me but thanks to all math help websites to help me out.

Problem 2:


The number which is decreased by 24 is 5 times its opposite. find number.

Solution:

opposite means negative.By the given question we can make an equation and it describes the problem

N - 24 = 5(-N)        Equation.

N - 24 = -5N          Multiplied out.

5N + 24    5N + 24     Add (5N + 24) to

_______________________     both sides.

6N      =       24

N = 4            Divide both sides

by 6 to isolate N

So the answer is N= 4

Practice College Algebra Online

Introduction :

College algebra is one important topic in mathematics. College algebra is used for the known quantities to determine the unknown quantities. In place of numbers, sometimes letters can be used. It includes the different topics such as polynomials, equation, expression, equation of a line, Cramers rule and slope of a line. Let us discuss some practice problems in college algebra through online.


Example problems for practice college algebra online:


Example 1:

Factorize: 45xy -18ya + 60xb -24ab using factor by group

Solution:

Step 1:

Given expression 45xy- 18ya + 60xb -24ab

Step 2:

Given expression in the standard form ax² + bx + c = 0

45xy- 18ya + 60xb -24ab = 0

Step 3:

Groups the terms

45xy- 18ya + 60xb -24ab = 0

(45xy + 60xb) - (18ya – 24ab) = 0

Step 4:

Determine the greatest common factor for the expression given

15x (3y – 4b) – 6a (3y – 4b) = 0

(15x – 6a) (3y – 4b) (3y – 4b) = 0

Solution to the given equation is (15x – 6a) (3y – 4b) = 0.

Example 2:

Find the slope of a line for the given points (4, 6) and (8, 9)

Solution:

For finding the slope of a line, we use this formula

`m = (y_2 - y_1)/(x_2 - x_1)`

Here the given points of (x1 , y1) and (x2, y2) are substituted in the formula.

`m = (9 - 6)/(8 - 4)`

`m = (3)/(4)`

`m = (3)/(4)`

Solution to the slope of a line is m = 3/4.

Example 3:

Find the equation of a line which passes through the line (-3,4) with slope of -3.

solution:

Given:

x1= -3, y1 = 4 and slope m = -3

Equation of a point slope form equation is

y - y1 = m (x - x1)

y - 4 = -3(x - (-3))

y - 4 = -3(x + 3)

y - 4 = -3x -9

y = -3x -5.

Solution to the equation of a line is y = -3x - 5

Having problem with Standard Form of the Equation of a Line keep reading my upcoming posts, i will try to help you.

Practice problem for college algebra online:


Some example practice problems for college algebra online

1). Factorize the given expression by using the factor by group method.

30xy + 40xb - 12ay - 16ab

Solution: (10x – 4a) (3y – 4b) = 0.


2). Solve the system of equation with two variables equations.

x + y = 10                       → (1)
3x - y = 6                       → (2)
Solution of the equation is (x and y) is (4, 6)

3). Find the slope of a line for the given points (5, 6) and (8, 9)

Solution: m = 1

4). Find the equation of a line which passes through the line (-5,6) with slope of -2.

Solution: y = -2x -4

Learn Online Range

Introduction :

Learn online range is the set of values that numbers can have particular starting and ending point of the value that is maximum and minimum value. In between the numbers of maximum and minimum these values said to be with in the range of given set of numbers. For example consider the set of number 1 – 5. learn online range maximum value is 5 and the minimum value said to be 1. The range will be in between the 1, 2, 3, 4, and 5.

Formula for the range = Maximum value – minimum value

I like to share this Function Domain and Range with you all through my article.

Example problem for learn online range:


Example problem :1

A student took 10 math tests in his school. What is the range of the student score in his test?

Test             Marks obtained

1                    56                                                                     

2                    85

3                    55

4                    96

5                    80

6                    65

7                    88

8                    70

9                    75

10                   76

Solution for learn online range:

Given marks are 56, 85, 55, 96, 80, 65, 88, 70, 75, and 76

Order the given test marks

After ordering the given marks: 55, 56, 65, 70, 75, 76, 80, 85, 88, 96

Formula for the range = Maximum value – minimum value

= 96 – 55

= 41

Example problem: 2

A marathon race there is 5 members are participated in the race. They have reached the destination with different timing. Calculate the range of the different timing they have reached the destination in the marathon race.

6.2 hr, 5.5 hr, 4.8 hr, 7.9 hr, 5.0 hr

Solution for learn online range:

Given

6.2 hr, 5.5 hr, 4.8 hr, 7.9 hr, 5.0 hr

Order the given times

4.8 hr, 5.0hr, 5.5hr, 6.2hr, 7.9hr

Formula for the range = maximum time – minimum time

= 7.9 hr - 6.2 hr

= 1.7 hr

Understanding Subtracting Rational Numbers is always challenging for me but thanks to all math help websites to help me out.

Practice problem for learn online range:


1.The Michal family has spent the hotel for their vacation in different place with the different cost. Calculate the range of the cost they have spent in the different place and the cost.

The cost in dollars 200, 300, 100, 500, 600.


2.A football team has scored their goal in the match that has shown. Find the range of the different game.

The goals are 10, 7 , 4, 5, 4

Learn Online Polynomials

Learn polynomials in online very easy. Online polynomials are mathematical expression, which comprises of sum of terms each and every term including a single variable or more variables raised to the powers and it is multiplied by coefficients. A simple online polynomial has only one variable. Polynomials are of different types that is two, three, or more variables. A two-variable polynomial is called bi-variate and three-variable polynomial is called trivariate.


Learning problems on polynomials online:


Learn an Example For Factor Polynomial online:

Factorize 3x3 – 4x2 – 13x – 6.

Solution for factor polynomial:

Sum of the coefficients of all terms: 3 – 4 – 13 – 6 = 20 ≠ 0.

Therefore, learn (x – 1) is not a factor.

Sum of the coefficients of even degree terms = –4 – 6 = –10.

Sum of the coefficients of odd degree terms = 3 – 13 = –10.

Since they are equal (x + 1) is a factor.

By synthetic division,

-1   |      3    -4    -13     -6

|            -3     +7    +6

|____________________

3      -7     -6   | 0

|_____

Remainder is 0.

Therefore the online polynomials (x + 1) is a factor.

Factorizing the quotient,

3x2 – 7x – 6 = 3x2 – 9x + 2x – 6

= 3x (x–3) + 2 (x–3) = (x–3) (3x+2)

Therefore 3x3 – 4x2 – 13x – 6 = (x+1) (x–3) (3x+2)

I like to share this Inequalities Calculator with you all through my article.

Learn sample problems on polynomials online:


Example:

Find out the G.C.D. of the following online polynomials x3 – 9x2 + 23x – 15 and

4x2 – 16x + 12

Solution:

Let f(x) = x3 – 5x2 + 13x – 10 and g(x) = 4x2 – 16x + 12 = 4 (x2 – 4x + 3)



x-5

____________________

x2 – 4x + 3 |      x3 – 9x2 + 23x – 15

|      x3 – 4x2 + 3x

| ___________________

|          – 5x2 + 20x – 15

|          – 5x2 + 20x – 15

| ____________________

0

_____________________

G.C.D. = x2 – 4x + 3

Problem for factorization:

Determine the value of m and learn the factorization, if x + 1 is a factor of x3 + mx2 + 20x + 13

Solution:

Let P(x) = x3 + mx2 + 20x + 13

P(–1) = (–1)3 + m(–1)2 + 20(–1) + 13 = –8 + m

By learn factor theorem since the polynomial (x + 1) is a factor P(–1) = 0 or –8 + m = 0 or m=8