Math Problems Solved Website

Introduction to math problems solved website:
         
                     Math is one of the important branches related to science it deals with logical quantity, numbers, shapes and structures of object. In this article math problems solved website we are going to see about Example math problems through website.Generally website is defined as the collection of colorful images, attractive video clips and some of the related web pages.  Through the websites  the student directly receive the help form the tutor.

Solved Example math problems with help of website:


 Example math problems with help of website:

Example problem 1:

Find the area of the rectangle Its Length is 13.7cm and width is 3.7?

Solution:

Given data:

Width =13.7cm

Height =3.7cm

Solved area of rectangle:

Area of the rectangle=`("Length")xx("Width")`

Area of the rectangle=`13.7xx3.7`

                                  =187.69cm^2

Example problem 2:

Solved the expression 6x-4x=50

Solution:

Solved the x value:

Given expression: 6x-4x=40

Subtract the term

6x-4x=50

2x=50

Divide both sides by 2

`(2x)/2=50/2`

X=25

Value of x=25


Solved Example math problems with help of website:


Example problem 3:

 Set A :{ 2, 4, 6, 8, 7, 10}, B :{ 3, 5, 1} Find A U B =?

Solution:

Given data:

A :{ 2, 4, 6, 8, 7, 10}

B :{ 3, 5, 1}

Here we have to perform union operation for set A and set B

A U B= A :{ 2, 4, 6, 8, 7, 10} U B :{ 3, 5, 1}

Here combined the all item of both sets (A&B)

A U B= {2, 4, 6, 8, 7, 10} U {3, 5, 1}

A U B= {2, 4, 6, 8,7,10, 3, 5, 1}

Arrange the items

A U B= {1, 2, 3, 4, 6, 7, 8, 10}

Example problem 4:

Angle of quadrilateral is 145^0, 75^0, 55^0.Find the fourth angle of the quadrilateral?

Solution:

Steps for finding fourth angle:

Let us consider as x is a unknown angle

Total angle of quadrilateral is 3600

145+75+55+x=3600

275+x=360

x =360-275

x =85

Fourth angle of quadrilateral is 850

Learn Online Simple Math Problems

Introduction to learn online simple math problems:

Basic math problems contains simple problems of addition, subtraction, measurement, number sense, multiplication, functions, adding and subtraction of decimals, fractions & mixed numbers, division, algebra, decimals . In this article we shall learn about online simple math problems.

Online assist students to learn the concepts promptly and without difficulty, learning online make students believe the subjects effortless and enjoyable.


Example Problems: learn online simple math problems


Example 1: adding the positive numbers: (+7) + (+27) =?

Solution: The sum of two positive numbers will be a positive numbers.

(+7) + (+27) = +34

Solution is 34.

Example 2: adding the positive numbers: (+120) + (+12) =?

Solution: The sum of two positive numbers will be a positive numbers.

(+120) + (+12) = +132

Solution is 132.

Learn online simple math problems:

Addition of negative numbers:

Example 1: Subtracting the negative numbers: (-5) + (-7)

Solution: The sum of two negative integers will be a negative integer.

(-5) + (-7) = -12

Solution is -12.

Example 2: Adding the negative numbers: (-8) + (-25)

Solution: The sum of two negative numbers will be a negative number.

(-8) + (-25) = -33

Solution is -33.

Example 3: Find the value form the expanded form 9× 10000 + 8× 1000 + 7 × 10

Solution:   9 × 10000 + 8 × 1000 + 7 × 10

= 90000 + 8000 + 70

=> 98070.

Learn online simple math problems- multiplication problems:

Example 1:

Multiply the two numbers: 4` xx` 8

Solution:

Here 4 is multiplicand

8 is multiplier

Answer is 32.

Example 2:

Multiply the two numbers: 5 `xx ` 8

Solution:

Here 5 is multiplicand

8 is multiplier

Answer is 40

Numbers using words - Learn online simple math problems:

Example problem 1:

Write a number using words: 68

Solution:

=68

8 is ones place

6 is tens place.

= 60+8 = sixty + eight

So that 68 is become in a word, sixty eight.

Example problem 2:

Write a number using words: 72

Solution:

=72

2is ones place

7 is tens place.

= 70+ 2= seventy + two

So that 72 is become in a word, seventy-two.


Practice Problems Learn online simple math problems:


Problem 1:

Sum of positive integers: (+9) + (+37)

Result: 46

Problem 2:

Sum of negative integers: (-5) + (-36)

Result: -41

Problem 3:

Multiply the two numbers: 3 * 10

Result: 30

Problem 4:

Write a number using words: 58

Result: fifty eight.

These are the examples for learn online simple math problems.

Preparation for Arithmetic Problems

Introduction of preparation for arithmetic problems:
The earliest and mainly elementary division of mathematics is the arithmetic or arithmetics.  The arithmetic is approximately used by everyone, for assignments ranging from simple day-to-day counting to advanced science and business operations.

It presents the study of quantity, mainly as the effect of combining values. Generally the arithmetic properties contain the operations of addition, subtraction, multiplication and division with the smaller values of numbers. Let we see about the answers for solve arithmetic problems.

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Preparation for arithmetic problems:


Let we discuss about preparation for arithmetic problems.

Addition (+):

Addition is one of the most significant and fundamental process in arithmetic. The addition process is performed for joins two or more values. Addition can be represented using the symbol +(plus sign) that is, infix notation. This symbol is present among the two values. The outcome is articulated with an = (equal sign).

Preparation for addition problem:

Examples:

1 7 1
6 4 2  (+)

________

8 1 3

________

6.78
9.76  (+)

________

16.54

________

1145+383= 1528
743+0=743
4 7
5 0  (+)

______

9 7

______

Subtraction (-):

Subtraction is also a one of the fundamental process in arithmetic. It is reversible processes for additions that is, if we begin with any value and adds any value and then subtract the similar value we added, we back to the value we started with. The symbol used to represent the subtraction is – (minus sign) in infix notation.

The below format defines the subtraction,

y - z = x

here c- minuend, b-subtrahend, x- difference.

Preparation for subtraction problem:

108
9 7  (-)

________

1 1

________

1 2 3
0  (-)

______

1 2 3

______

(-171)-(171)=0
5-43= -38
25-20= 5

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More Preparation for arithmetic problems:


Multiplication (*,.,×):

Multiplication is one of the four fundamental process in arithmetic.  Multiplication is the process of  determining the value or quantity (product) get by the frequent addition of a particular value or quantity (multiplicand) a particular number of times (multiplier)

Preparation for multiplication problem:

3 × 5 = 15 (or) 3+3+3+3++ = 15.
120 * 0=0
-7*13= -91
20*5=100
-3*-9=27
Division (÷ or /):

The division process is used to finding how many times quantity is contained in another; the opposite of multiplication.

Preparation for division problem:

Divide 645 by 4
Solution:

645/4=161.25

-18/2= -9
0/32=0
-47/-47=1

Solve Online Area Math Problems

Introduction :

Here we are going to see the article as solve online area math problems; generally Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3-dimensional solid is the total area of the exposed surface, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of surfaces.

(Source: Wikipedia)

I like to share this Area of a Triangle Using Trig with you all through my article.

Example 1- solve online area math problems:


Suppose the sides of the triangle are given as 6cm, 8cm and the angle of the triangle is 30 degree find the area of the triangle?

Solution:

Here the sides of the triangle is given as 6cm, 8cm and the angle of the triangle is 30 degree

If the sides of the triangles are given means we use the below formula to find the area of the triangle

`(1/2)xxaxxbxxsinc`

Now we plug the a, b and angle in the above equation

So the area of the triangle is `((1/2) xx6xx8xxsin30)`

We know that sin 30 =`1/2`

Area of the triangle is` (1/2) xx48xx1/2`

`1/4xx48=48/4=12`

So the area of the triangle is 12cm^2

Example 2- solves online area math problems:

If the length of the parallelogram is 8cm and width of the triangle is 13cm find the area of the parallelogram?

Solution:

Area of the parallelogram =`("length") xx ("width")`

Here the length of the parallelogram is 8cm and width of the parallelogram is 13cm

Area of the parallelogram is `8xx13=104cm` 2


Example 3- solves online area math problems:


If the diagonals of the rhombus are 18cm and 14cm find the area of the rhombus?

Solution:

The diagonal of the rhombus is 18cm and 14cm.

We know that the area of the rhombus is` (1/2)xxaxxb,` here a, b are the diagonals value

Area of the rhombus is` ((1/2) xx18xx14) = (252/2)`

So the area of the rhombus is 126.

Example 4- solves online area math problems:

Calculate the area of the circle whose radius is 9cm?

Solution:

We know that the area formula for the ellipse is `pi` r^2

Here the value of pi is 3.14 and r=9cm

We plug these values in the above formula means we get the area of the circle

`3.14xx9xx9=3.14xx81=254.34cm^2

Learn Numbers Online for Kids

Introduction to learn numbers online for kids:

When we search online for learn about numbers we have getting the following topics. These topics are helping us to understand the basic number systems and some interesting schemes and practices on numbers. There are many kinds of numbers in mathematics. Normally numbers are the back bone of mathematics. Let us see about Learn numbers online for kids. I like to share this Perfect Square Numbers with you all through my article.


Learn numbers online for kids:


Learn numbers online for kids – square numbers:

In the division of arithmetic the square numbers are expression to be as the numbers that are shaped as the product value when the similar numbers got multiply twice as r * r = p, where ‘p’ is said to be as the square digit and ‘r’ is said to be as square root of ‘p’.
Illustration of square numbers is1, 4, 9, 16, 25……
Learn numbers online for kids – cube numbers:

In the division of arithmetic the cube numbers are expression to be as the numbers that are created as the product value when the similar numbers got multiplied thrice as r * r * r = p, where ‘p’ is said to be as the cube number and ‘r’ is said to be as cube root of ‘p’.
The examples for cube integers are 1, 8, 27, 64……


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Some more details about learn numbers online for kids:


Learn numbers online for kids – triangular numbers:

In the division of arithmetic the triangular numbers are expression to be as the numbers that are created as the added value when the consecutive numbers are added to the resulted number as r,  (r+2) = p, (p+3) = q, (q+4) = s…..
Example for triangular numbers is 1, 3, 6, 10, 15, 21, 28, 36, 45……….
Learn numbers online for kids – prime numbers:

In the division of arithmetic the prime numbers are expression to be as the numbers that are said to have only two factors as they get divisible by the multiplication table ‘1’ and its similar number multiplication table.
Example for prime numbers is 2, 3, 5, 7, 11, 13, 17, 19…….

Solve Online Math Education

Introduction to solve online math education

In this article we will see about math tutoring.  Tutorvista is an educational websites. Whenever you need you can use tutorvista website. In this website you can see tutoring for kindergarten to college level.  Here you can get help for maths terms, Exam practices test, problem solving and online test and our tutor will helps you. You will get math tutoring from the home. Following preparations are really exercising your brain it helps for your math study. Let us see some example math problems and solving methods.


Math problems:


Problem 1: Solve online math education

Nancy wants to buy a scooter that costs $120. She has saved $40 so far. How much more money does Nancy need?

Let us see how to solve this math test problem.

Solution:

Step 1:    A scooter cost is = $120

But Nancy has   = $40    we find how much more money does Nancy need.

Step 2:    Let x as money does Nancy need so

40 + x = 120

Step 3: If we subtract 40 we can cancel out the plus 40 so let us have go to at subtracting 40 from both sides

40 -40 + x = 120 -40

Step 4: remove combine terms like 40 – 40 = 0

0 + x = 80

Step 5: Therefore Nancy need $ 80 for buy a scooter.

Probelm2: Solve online math education

Which sign goes in the blank?  8 ___ 8 – 2

Let we show how to solve this math question.

Solution:

Step 1: remember, Subtracting from a number makes it smaller.

Step 2:   8 must be bigger than 8 – 2 .

Step 3: Therefore 8 > 8 – 2.

Probelm3: Solve online math education

Write place value 569.

Let we show how to solve this math question.

Solution:

The "9" is in the Units position, meaning just 9 (or 9 "1"s),

The "6" is in the Tens position meaning 6 tens (or sixty),

The "5" is in the Hundreds position, meaning 5 hundreds.

5  6  9

|    |   |_______ one’s place

|     |_________ Ten’s places

|____________ Hundreds

Probelm4: Solve online math education

When counting by twos, what comes after 16?

Solution:

Step 1: count by twos

12   14   16  17   18   20

Step 2: when counting by twos, 18 comes after 16.

Step 3: therefore 18 is correct answer.


Practices problems:


1) When counting by four, what comes after 20?  Answer: 24

2) Add this numbers 5 + 8 + 2 =?          Answer: 15

3) Write place value 102.                 Answer:  1 Hundred | 0 tens | 2ones.

Basic Maths Solved Sample Test

Introduction to basic maths solved sample test:

In maths, integers are the basic needs. With the integer simplification, calculations and elimination are the operations handled in mathematics. In math we can search and learning about the basic operation called arithmetic operation which includes addition, subtraction, multiplication and division. And also math includes many topics like algebra, linear equation, slope of the line and many more. Sample test deals with some of the basic topics with solved maths test problems. Here we have some solved basic maths sample test problems.

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Basic maths solved sample test:


The basic math is involved in arithmetic operations like addition, subtraction, multiplication, and division. Some of the solved sample test problems are,

Addition: Addition ids the process of adding two terms like, 8 + 9 = 17 or 2x +7x = 9x

Subtraction: Subtraction id the process of having the difference between two terms like, 5 - 2 = 3 or -3x + 9x = 6x

Multiplication: It is the process which involves multiplying like, 2 xx 5 = 10 is by 2 + 2 + 2 + 2 + 2 = 10 adding five times 2.

Division: Its performed like, (8 / 2) = 4.

Example for basic maths solved sample test 1: Add 5 + 3

Solution:

= 5 + 3

= 8

Example for basic maths solved sample test 2: subtract 9 - 3

Solution:

= 9 - 3

= 6

Example for basic maths solved sample test  3: Solve `5xx6`

Solution:

` 5`
` 6 xx`
----------
` 30`
------------
Answer: `30`

Example for basic maths solved sample test 4: Divide 40/5

Solution:

Dividing the number 40 by 5 is,

40
5 (/)
-----------
8
-----------
Example for basic maths solved sample test 4: Solve the given terms

a)      15 +81 =? – 8

Solution:

15 + 81 =? – 8

96 =? – 8

96 + 8 = 104

So the answer is 104

Answer: 15 + 81 =104 – 8

b)      50 – 35 = 6 + ? + 7

Solution:

50 – 35 = 13 + ?

15 = 13 + ?

15 –13 = ?

So the answer is 2

Answer:  50 – 35 = 6 + 2 + 7

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Basic maths solved sample test problems:


Example for basic maths solved sample test 1: Add 55 + 13

Answer: 68

Example for basic maths solved sample test 2: subtract 9 - 3

Answer: 6

Example for basic maths solved sample test 3: Solve `6 xx15`

Answer: 90

Example for basic maths solved sample test 4: Divide 50/10

Answer: 5

10th Grade Math Sample Tests

Introduction to mathematics:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. (Source: Wikipedia)

Topics under 10th grade math:

Linear and non linear equations
Quadratic equations
Standard form of line equations
Slope intercept form
Trigonometry
Geometrical areas and volume
Here, we see about linear equations, quadratic equations, and trigonometry.

Please express your views of this topic system of linear equations examples by commenting on blog.

Example problems for 10th grade math sample tests


10th grade math sample test example problem 1:

Solve the linear equations 2x - 3y = 6 and x + 2y = 10

Solution:

The given linear equations are 2x - 3y = 6 and x + 2y = 10

2x - 3y = 6 ------- (equation 1)

x + 2y = 10 ------- (equation 2)

Multiply the equation 1 by 2, we get

4x - 6y = 12 ------ (equation 3)

Multiply the equation 2 by 3, we get

3x + 6y = 30 ------- (equation 4)

Add the equation 3 and equation 4, we get

7x = 42

Divide by 7 on both the sides, we get

x = 6

Substitute the value of x in the first equation, we get

18 + 6y = 30

Subtracting the above equation by 18 on both the sides, we get

6y = 12

Divide by 6 on both the sides, we get

y = 2

Answer:

The final answer is x = 6, y = 2

10th grade math sample test example problem 2:

Solve the linear equation 3x - y = 24, x = 3y using substitution method.

Solution:

Given equations are 3x - y = 24 and x = 3y

3x - y = 24 ---------- (1)

x = 3y ---------- (2)

Substitute the equation 2 in equation 1, we get

9y - y = 24

8y = 24

Divide the above equation by 8 on both the sides, we get

y = 3

Substitute the value of y in equation 2, we get

x = 3 (3)

x = 9

Answer:

The final answer is x = 9, y = 3.

10th grade math sample test example problem 3:

Find the value of (sin 30° + cos 45°)

Solution:

Given (sin 30° + cos 45°)

We know that,

sin 30° = 0.5

cos 45° = 0.707

Substitute the above values in the given, we get

(sin 30° + cos 45°) = 0.5 + 0.707

= 1.207

Answer:

The final answer is 1.207

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Practice problems for 10th grade math sample tests


10th grade math sample test practice problem 1:

Solve the linear equations 5x + y = 36 and x - 3y = 4

Answer:

The final answer is x = 7, y = 1.

10th grade math sample test practice problem 2:

factorize the given quadratic equation x2 - 13x + 22 = 0

Answer:

The final answer is x = 11 and x = 2

10th grade math sample test practice problem 3:

Find the value of (cos 60° + tan 45° + sin 90°)

Answer:

The final answer is 2.5

What is a Difference in Math

Introduction to what is a difference in math:

In math, the subtraction of two terms are called as difference and give the difference value. What is a difference in math is use the different method in different branch. For example, if we want to know the difference between the 20 and 10 means subtract the numbers and get the difference as 10.Here we see about different types of difference method with example.

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Explanation for what is a difference in math


What types of methods are used in difference in math:

Normal arithmetic subtraction
Finite difference
Percent difference
Set theory difference
Normal arithmetic subtraction:

This normal subtraction is performed based on sign of numbers.Some conditions are used in subtraction.

If we subtract the two negative numbers means the difference is carry the negative sign and add the numbers. For example, subtract the -10 and -5 and get the difference as -5.
If we subtract the two positive numbers means determine the difference from large number. For example, find the difference between 55 and 30 and get the difference as 25.
In math subtraction, the ‘-‘ is used for representation.
Finite difference:

The differential equation subtraction is performed by finite difference. The math expression for finite difference is f(x + b) – f(x + a). There are forward, backward and central difference.

Other math difference:

Percent difference – The subtraction of two percentage is used in quality assurance.

Set difference – The representation of set difference is B\A that is elements of B is not in A. The formula for set difference is B \ A = { x = B | x = A }.

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Examples for what is a difference in math:


Problem 1: What is the difference between 1000 and 570.

Answer:

Difference of these numbers is 1000 – 570 = 430.

Problem 2: What is the difference between given sets?

X = { 4, 5, 6 } and Y = { 5, 6, 7 }.

Answer:

The set difference is { 4 }.

Exercise problem for difference in math:

1. What is the difference between 58% and 25%?

Answer: The difference of percent is 33%.

2. What is the difference between 88 and 44?

Answer: Difference is 44.

Scalene Triangle Math

Introduction :

A two dimensional geometric shape with three sides and angles is called as a triangle. If no sides and angles are equal in a triangle, then it is said to be as scalene triangle. i.e. a scalene triangle is formed by three different sides and angles. Here we are going to learn the math properties of scalene triangles.

Elements of a scalene triangle

Three angles:

`angle` ABC or `angle` B
`angle` ACB or `angle` C
`angle` CAB or `angle` A  and
Three sides:

AB
BC
CA
Types of scalene triangles in math

Acute scalene triangle
Obtuse scalene triangle
Right scalene triangle

Properties of scalene triangle in math

Definition

A scalene triangle is a triangle containing three unequal sides that all are of different lengths.Most triangles drawn at random would be scalene triangles.

Properties of Scalene triangles

A scalene triangle has no congruent sides.
no angles in a scalene triangle are equal.
Perimeter of a scalene triangle is given as
P = x + y + z where x,y,z are the sides of the triangle

a scalene triangle has no line of symmetry ( a line that divides the entire figure into two exact halves).
Calculation of area of a scalene triangle
Area of scalene triangle( that is a triangle with all different sides) can be calculated with the help of the following formula,

Area = `sqrt(s(s-a)(s-b)(s-c))`
where s = `(a+b+c)/(2)`  is the semi-perimeter, or half of triangle's perimeter.

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Example problems for scalene triangles in math

Example 1

Find the area of a scalene triangle with side lengths 4ft, 6ft, and 8ft respectively

Solution

Area = `sqrt(s(s-a)(s-b)(s-c))`

S = `(a+b+c)/2`

Here, a = 4ft

b = 5ft

c = 8 ft

So, s = `(4+5+8)/2`

= `17/2`

= 8.5

Area = `sqrt(8.5(8.5-4)(8.5-5)(8.5-8))`

= `sqrt(8.5xx 4.5 xx 3.5 xx 0.5)`

= `sqrt(66.937)`

= 8.181

So the area of the given scalene triangle = 8.181 square ft

Example 2

Find the perimeter of a scalene triangle with side lengths 4ft, 5ft and 8ft.

Solution

Perimeter of a scalene triangle = a + b + c

Here, a = 4, b = 5, and c = 8

Perimeter = 4 + 5 + 8

= 17 ft

So the perimeter of the given scalene triangle is 17 ft.

Math Solving Tips

Introduction :

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. (Source: wiki)

Essential to math study are,

1) A good foundation in basic math principles,

2) The ability to analyze relevant information, and

3) An understanding of the purpose of symbols and formulas and what they represent.


Math Solving Tips


Tips 1:

Learning math requires studying 8–10 hours per week for a 3 credit class – and at least 30 minutes daily.

Tips 2:

Seek help early! Utilize available resources. Then make a commitment to yourself to keep up to date.

Tips 3:

If problems with math (particularly with word problems and concepts), explore reading comprehension as a possible cause. An LSS counselor can help plan an approach to finding solutions.

Math Solving Tips Background Steps:

Step1:

A common cause of math study problems is failure to master elementary math principles.

Step 2:

If you’re not sure what your deficiencies are, seek a diagnostic tool, ask your professor, or take the chapter quizzes from a math text one level below your current class.

Step 3:

If you score below 80%, you should work on that skill. Then do one or more of the following:

Drill the weak areas from a lower level text. The library has many textbooks. Work simple, fundamental problems to check your understanding

Spot review, using math texts that you can refer to as needed

Get a tutor.

Resolve that in the future you’ll avoid giving superficial treatment to your math study.

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Example problems for math Solving Tips :

Step 1:

Fundamental to math study is problem solving, a two-step process involving analysis and computation.

Step 2:

The most essential process in problem-solving is analysis.

Step 3:

Simply having the ability to compute results is not sufficient; you must be able to analyze what you’re doing.

Step 4:

When solving math problems, follow the steps below for maximum understanding and accuracy:

Read the problem carefully

Reread and analyze the problem, noting what’s given, what’s implied, and what’s to be found

Translate the information into mathematical symbols or into your own words

Make a tentative sketch of the problem

Analyze the information you have and set up an equation

Make an educated guess at the answer

Solve the equation, one step at a time, using accepted mathematical procedures

ALWAYS check for errors by checking your answer:

against your educated guess

against the actual answer when available

by inserting the answer into the problem

by re-working the problem, using the same or an alternate method

by checking the solution against the information in the original problem

Take ar Test Online

Introduction to take ar test online:

Arithmetic or arithmetic’s is the oldest and most elementary branch of mathematics, used by almost everyone. Professional mathematicians sometimes use the term arithmetic when referring to more advanced results related to number theory, but this should not be confused with elementary school arithmetic. Arithmetic operation includes addition, subtraction, multiplication and division. Let us take school arithmetic tests for online. (Source: Wikipedia)


Questions to take ar in online


Now take a test for ar in elementary school.

Question 1: Solve the following: 24,508 + 24,862 – 3562 + (3562 *4).

Question 2: From the following number find the prime numbers: 10, 15 and 30.

Question 3: From the following series find the composite and prime numbers: 11, 12, 14, 16, 17, 23, 33, 37.

Question 4: Multiply the following: 15, 672 + 14,578 – 2562 + (2562 *2)

Question 5: Find the common factors 14 and 16.

Question 6: Solve for y/4 =15.

Question7:

There are 40 orange trees in a garden. There are 225 oranges in each tree. Find the total number of oranges in the garden.

Question 8:

Mani has 24 chocolates and Knish has 37 chocolates. Find the total number of chocolates did the Mani and Knish has.

Question 9:

Solve by `x/6` = 20.

Question 10:

Multiply: 5/12 x  6/5


Solutions for ar tests in online


Answer to take ar tests online:

Solution 1:

Given 24,508 + 24,862 – 3562 + (3562 *4)

Step 1:

First multiply the 3562 *4= 14248

Step 2:

Add the positive terms 24,508 + 24.862 + 14248 = 63618

Step 3:

Subtract 3562 from 63,618.

63,618 – 3562 = 60056

Answer: 24,508 + 24,862 – 3562 + (3562 *4) = 60056

Solution 2:

Given 16, 15 and 30

16 is divisible by 1, 2, 4 ,8, 16

15 is divisible by 1, 3, 5, 15

60 is divisible by 1, 2, 3, 5, 6, 10, 15, 30

Therefore the given numbers are not prime number.

Answer: There is no prime numbers.

Solution 3:

Given 11, 12, 14, 16, 17, 23, 33, 37

11 is divisible by 1, 11.

12 is divisible by 1, 2, 3, 6, 12.

14 is divisible by 1, 2, 7, 14

16 is divisible by 1, 2, 4, 8, 16.

17 is divisible by 1, 17

33 is divisible by 1, 3,11, 33.

37 is divisible by 1, 37.

Therefore, 11, 17 and 37 are prime number and 12, 14, 16, 33 are composite.

Answer: Prime numbers: 11, 17, 37; Composite numbers: 12, 14, 16, 33.

Solution 4:

Given 15, 672 + 14,578 – 2562 + (2562 *2)

Step 1:

First multiply the 2562 *2= 5124

Step 2:

Add the positive terms 15, 672 + 14,578 + 5124 = 35374

Step 3:

Subtract 2562 from 35374.

35,374 – 2562 = 32812.

Answer: 15, 672 + 14,578 – 2562 + (2562 *2) = 32812.

Solution 5:

Given 14 and 16.

1, 2, 7, 14 are the factors of 14

1, 2,4, 8, 16 are the factors of 16

Therefore, common factors of 14 and 16 are 1, 2.

Answer: Common factors of 14 and 16 are 1, 2.

Solution 6:

Given y/4 =15.

y = 15 * 4 (multiply by 4 on both sides)

y=60.

Answer: x=60.

Question 7:

Solution:

Number of oranges trees in a garden   = 40

Number of mangoes in each tree        = 225

Total number of oranges in the garden = 225 x 40

2 2 5

X 40

_________

9 0 0 0

__________

the total number of oranges in the garden is 9000

Answer: 9000

Solution 8:

Number of chocolates in Mani = 24

Number of chocolates in Knish = 37

Total number of chocolates = 24 + 37

2 4

+ 3 7

_______

6 1

_______

Answer: 61

Solution 9:

Given x/6 =20.

x = 20 * 6 (multiply by 6 on both sides)

y=120.

Answer:20

Solution 10:

Given 5/12 x  6/5

(5 x 6) / (12 x 5) = (30/60)

Answer: 5/12  x  6/7 = (30/60)

How to Decompose in Math

Introduction for decompose:

Decompose a number can be used to separate a product of prime factors. A sum of partial fractions can be stated by decomposing a fraction. A product of two or more matrices with particular properties can be attained when decompose a matrix into lesser. For instance the decomposition of 42 is 7 × 6. Let us discuss about decompose numbers in this article. The procedure of separating number into their components and dividing a number into lesser element is known as decomposing.

Example Problems for how to decompose in math:


How to decompose in math - Example 1:

How do you add normally without using paper and pen in hand?

27 + 31

Solution:

Step 1:

Initially add the tens: 20 + 30 =50.

Step 2:

After that add the ones: 7 + 1 = 8.

Step 3:

Add the total of tens and the total of one’s jointly in the step 1 and step2.

50 + 8 = 58

Answer is: 58

How to decompose in math - Example 2:

How do you add usually without using paper and pen in hand?

36 + 58

Solution:

Step 1:

Initially add the tens: 30 + 50 = 80.

Step 2:

Then add the ones: 6 + 8 = 14.

Step 3:

Add the tens once again,

80 + 10 = 90.

Step 4:

Add the totals of tens and the totals of one’s jointly in the step 2 and step3.

90+ 4 = 94

Answer is: 94

How to decompose in math - Example 3:

How do you subtract normally without using paper and pen in hand?

45 - 22

Solution:

Step 1:

Initially subtract the tens: 40 - 20 = 20.

Step 2:

After that subtract the ones: 5 - 2 = 3.

Step 3:

Add the total of tens and the total of one’s jointly in the step 1 and step2.

20 + 3 = 23

Answer is: 23

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Example Problems for how to decompose in math:


How to decompose in math - example 4:

Decompose a number 37, 482.

Solution:

Step 1:

Decompose the number with simple components such as,

37, 482 = 30000 + 7000 + 400 + 80 + 2.

Step 2:

(3 * 10, 000) + (7 * 1000) + (4 * 100) + (8 * 10) + (2 * 1).

Step 3:

Then, whenever we decompose 37, 482 we will obtain 3 ten thousands, 7 thousands, 4 hundreds, 8 tens and 2 ones.

How to decompose in math - Example 5:

Decompose a value 8, 74, 375.

Solution:

Step 1:

Decompose the value with simple component such as,

8, 74, 374 = 8, 00,000 + 70,000 + 4,000 + 300 + 70 + 5.

Step 2:

(8 * 100,000) + (7 * 10,000) + (4 * 1000) + (3 * 100) + (7 * 10) + (5*1).

Step 3:

So, whenever we decompose 8, 74, 374 we will obtain 8 hundred thousands, 7 ten thousands, 4 thousands, 3 hundreds, 7 tens and 5 ones.

Online Substitution Help

Online substitution help:

This algebra session introduces the technique of solving systems of equations by substitution method. Substitution method is a method of solving a system of equations wherein one of the expressions is solve for one variable in conditions of the other variables. In this article discuss about online substitution help.

(Source – Wikipedia)


Online substitution help-Example 1:


To solve for substitution method for online help:

Equation 1    3x + 2y = 2
Equation 2    y + 8 = 3x

Solution:

Step 1: The equation of the coefficient of a variable is 1.

Select the equation 2 and isolate variable y
y = 3x – 8   equation 3

Step 2: From equation 3, the equation y is the same as 3x – 8

So, substitute the variable y in equation 1 with 3x – 8
3x + 2 (3x – 8) = 2

Step 3: Distributive property using to remove the brackets.

3x + 6x – 16 = 2

Step 4: The Combine like term is

9x – 16 = 2

Step 5: The Isolate variable x is

9x = 18

x = 18/9

x = 2

Step 6: x=2 Substitute in equation 3

y = 3 (2) – 8
y = 6 – 8 = – 2

The substitution solution is x = 2 and y = -2

Step 7: subtitle x = 2 and y = -2 in equation and check you solution

3 (2) + 2 (–2) = 6 – 4 = 2

Answer: x = 2 and y = –2

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Online substitution help-Example 2:


Use the substitution method to solve the equation
5x + 3y = 26 equation 1
x - 3y = 4   equation 2

Solution:

Step 1: 5x + 3y = 26              [Equation 1]

Step 2: x - 3y = 4                 [Equation 2.]

Step 3: Rearang the equation 2  x = 3y + 4

Step 4: subtitle the value in 5(3y + 4) + 3y = 26

Step 5: The group link teams is 18y + 20 = 26

Step 6: subtute the 20 on the both side equation 18y = 6

Step 7: divided by 18 on the both sides 18y/18 =6/18

y =1/3

Step 8: subtute the values in equation 2

x = 3y + 4= 3(1/3) + 4

Step 9: simplify the equation of x = 3y + 4= 3(1/3) + 4

x = 5
Step 10: The substation solution is (5, 1/30 ).

Online substitution help-practice problem:

Problem 1: Using substitution method, evaluate the equation x - 5` sqrt (x)` = - 6

Solution: The substitution solution is x= 4 and x= 9

Problem 2: Using substitution method, evaluate the equation x - 6 `sqrt (x) ` = - 9

The substitution solution is 9

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                                     /


I like to share this Arithmetic Mean Formula with you all through my article.

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.

Is this topic Infinite Limits hard for you? Watch out for my coming posts.

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

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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

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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

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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