Variable in Math Form

Introduction to variable in math form:

The varied values are denoted as variable using symbols in math form. It also represent the constant that is non varying value. The modern mathematics and engineering is use this variables for determine the unknown values. In math form, the variables are present in some theories. The variables are most commonly used in geometry and algebra.

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variables in function form


Function:

The functions are expressed by ideas with one or more variables. The variables function has ordered pairs. For example sum(a + b) = a  + b, here sum is denoted as function and a and b are variables of function. We can denote the function as f( x, y ). This is function of two variables.

Types of variables in math form:

A variable is varied based on problem and it is considered as characteristic of measurement. In math form different kinds of variables are used. They are quantitative and qualitative variables, independent and dependent variables.

Quantitative and qualitative variables in math form:

Quantitative variables are categorical data that is it denote the values of experiment. The ordinal, interval or ratio scale is measured by quantitative variables.

The qualitative variables are define the quality of math form and the nominal scale is used for measurement. For example favorite color, subjects are define the qualitative variables.

Independent and dependent variables:

The independent variables are also called as former variables and experiment is influence the independent variables in math form. The dependent variables are denoted as factors.

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More about math variables


Examples for variables:

Derive the math form  by using variables:

Problem 1: Find the unknown value  for the following math form:

X + 20 =10

Answer: This is simple example for variables.

X = 10 – 20

X = -10.

Problem 2: Find the values for following expressions:

2x + y = 4

X + y = 2

Answer:

2x + y =4 ----- (1)

X + y = 2 ------(2)

8x + 4y = 16 --- (1) x 4

4x + 4y = 8 -----(2) x 4

----------------

4x         = 8

X     = 8/4 = 2.

Sub x value in (1), 4 + y = 4

Y = 4 -4 =0

The x and y values are (2, 0).

Exercise problems in math form:

1. Find the value of y for 20 +y = 50.

Answer: y = 30.

2. Solve the following form and find the unknown value:

Answer:

60 + x = 75

X = 75 – 60

X = 15.

How to Understand Math

How to understand math (Introduction):
Math is also called as mathematics. Compare to other subject math is tough subject to understand this math subject; we want to listen the class care fully. Mathematics is separated into different sub titles shown here:

Number theory
Mensuration
Sets and functions
Algebra
Applied mathematics.
Geometry
Analytical geometry
Trigonometry
Practical geometry
Statistics
In this topic we discuss how to understand math with examples as problems are shown below:

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Easy Understand math Problems with Answers:


Problem 1:

Given the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.

-15x - 10 - x + 3 = -16x - 20 +13

Group like terms.

-16x - 7 = -16x - 7

Add 16x + 7 to both sides and write the equation as follows

0 = 0

Hence this statement is true for all values of x and therefore all real numbers are solutions to the given equation.

Problem 2:

Given the line

5x - 5y = 7

Re-write the equation in slope intercept form y = mx + b and identify the value of m the slope.

-5y = -5x + 7

y = x - ` 7/5`

The slope is given by the coefficient of x which is 1.

Problem 3:

To find the eqn of the line through the points (-1, -1) and (-1, 2), we use the slope m.

m = `(y_2 - y_1)/(x_2-x_1)` = `(2 - (-1)) / ((-1) - (-1))` = `3 / 0`

The slope is defined that means the line is perpendicular to the x axis and its equation has the form x = constant. Since all points have equal x coordinates with -1, the equation is given by:

x = -1

Problem 4:

Given the equation

2x - 4y = 10

To find the x intercept we set y = 0 and solve for x.

2x - 0 = 10

Solve for x.

x = `10 / 2`

= 5

The x intercept is at the point ( 5 , 0).

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Easy Understand math Practice Problems with Answers:


1. Find the statement is equal or not equal: 7(-4x - 3) - (x - 4) = -8(2x + 6) + 11

Answer: Not Equal.

2. To find the equation of the line through the points (-8, -6) and (-6, 2), we first use the slope m.

Answer: Slope m =1/4

3. Solve: 8x - 2y = 3

Answer:  The x intercept is at the point (3/8 , 0).

Math Work Problem Solver

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 in this topic we are going to discuss about introduction of math problem solver with work, examples of math problem solver with work and practice math problems using solver with work (Source: Wikipedia).

Is this topic Definition of a Function hard for you? Watch out for my coming posts.

Math Work Problem Solver Example: 1


In a room there are 54 mans and 6 woman’s. The chief wants to select a man or women to represent the room in a function. In how many ways can the chief make this selection?

Solution:

Here the chief performs either of the following two jobs:

(i) Selecting a man among 54 mans. (or)

(ii) Selecting a woman among 6 woman’s

The first of these can be performed in 54 ways and the second in 6 ways.

Therefore, by fundamental principle of addition either of the two jobs can be performed in (54 + 6) = 60 ways

Hence, the chief can make the selection of either a man or a woman in 60 ways.


Math Work Problem Solver Example: 2


A room has 8 doors. In how many ways can a man enter the room through one door and come out through a different door?

Solution:

Clearly, a person can enter the room through any one of the eight doors. So, there are eight ways of entering into the room.

After entering into the room, the man can come out through any one of the remaining 7 doors. So, he can come out through a different door in 7 ways.

Hence, the number of ways in which a man can enter a room through one door and come out through a different door

= 8 × 7 = 56.


Math Work Practice Problem Solver:

1. A college has 15 doors. In how many ways can a man enter the room through one door and come out through a different door?

Answer: 210.

2. In a town there are 5000 mans and 4000 woman’s. The government staff wants to select a man or women to represent the room in a function. In how many ways can the govt staff make this selection?

Answer: 9000.

Online Algebra ii Test

Introduction :

An online algebra ii is also one kind of  mathematics . An online algebra ii explains the main properties of algebraical expressions and relations. This online algebra ii  explains the quantity, letters and other symbols. It indicates variables, equations, objects, polynomials, and expression etc. An online algebra ii, math test II solves lessons Pre-algebra, an online algebra I, an online algebra II, and Geometry. Fundamentally , Algebra involved from the properties and processes of arithmetic which begins with the four processes: addition, subtraction, multiplication and division of numbers.


Definition on online algebra ii test:


Numerals, some literal numbers are made by algebraical symbol. Which expression denotes one number or one quantity. That is, just like the sum of 4 and 2 is one quantity, which result is 6, The sum of X and Y is one quantity, that is, X + Y. Similarly divide b,√b , a*b, a – b are algebraic expressions each of these represents one quantity or one number. Some signs and mathematical symbols are used in the algebraic expression.

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Examples of online algebra ii test


Solve the online algebra ii test equations:
Example 1 on online algebra ii test:

Problem 1:

Solve the equation:

4(-2x - 1) - (x - 2) = -3(3x + 4) + 12

Solution to Problem 1:

Given the equation

4(-2x + 1) - (x + 2) = -3(3x + 4) + 6

Multiply factors.

-8x - 4 - x - 2 = -9x - 12 +6

Group like terms.

-9x - 6 = -9x - 6

Add 9x + 6 to both sides and write the equation as follows

0 = 0

For x value will be true for all statement x and therefore all real numbers are solutions to the given equation.

Simplify the expression 3(a -2) + 3b - 3(a -b -2) + 4

Problem 2:

Given the algebraic expression

3(a -2) + 3b - 3(a -b -4) + 4

Solution:

Multiply factors.

= 3a - 6 + 3b -3a + 3b + 12 + 4

Group like terms.

= 6b + 10.

Problem 3:

Simplify: 6c + 4d – 5d + 7c + d = 0

Solution:

Step 1: Group together the like terms:

6c + 4d – 5d + 7c + d = 0
(6c + 7c) + (4d – 5d +d) = 0

Step 2: Then simplify:

13c   = 0

Answer: 13c = 0.

Problem 4:

Simplify: 4(c – 3) + 2 = 7

Solution:

Step 1: Remove the brackets

4c – 12 + 2 = 7

Step 2: Isolate variable a

4c = 12 – 2 + 7
4c = 17
c=17/4 = 3.4

Answer: c = 3.4

Grade 8 Math Problems

Grade 8 Math Problems

Introduction to 8th grade math:

In this article you learned how to do 8th grade math. In 8th grade math covers the following topics:

Algebra
Linear algebra
Fraction
Quadratic equation
Algebraic expression
Area of triangle and parallelogram
Polynomial
Probability
In this content we discuss about the algebraic expression and quadratic equation with suitable example problems.


Example problems on 8th grade math:


Simplify the algebraic equation.

x^2 - x = 0

Solution:

Let us take the equation is
x^2 - x = 0

Take the common factor x outside
x (x - 1) = 0

So the product x (x - 1) to be equal to zero, then we get

x = 0 or x - 1 = 0

Solve the above simple equations to obtain the solutions.
x = 0
or
x = 1

Hence the answer is x=0 and x=1

Example problems on 8th grade math:

Solve x^2-15x-100

Solution:

Let P (x) = x^2-15x-100

Step 1: The given polynomial is in the form of ax^2+bx+c =0

a = 1; b =-15; c =-100

Multiply the coefficient of x^2 and the constant term,

1*-100 =-100 (product term)

Step 2: Find the factors for the product term

-100---- > -20*5 = -100 (factors 20 and -5)

-15 ---- >-20+5 =-15 (-15 is the coefficient of x)

Step 3: Divide the coefficient of x as -15

x^2-15x-100=0

x^2+5x-20x-100=0

Step 4: Taking the common term x from the first two terms and -20 from the next two terms

x(x+5) -20(x+5) =0

(x-20) (x+5) = 0.

Now set (x+5) =0; x=-5

(x-20) =0; x=20.

The roots are x=20 and -5.

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Example problems on 8th grade math:


Solve the algebraic expression

4(x -2) + 2y - 3(x -y -4) + 5

Solution:

Given algebraic expression is
4(x -2) + 2y - 3(x -y -4) + 5

Multiplying the integer with above terms

4x - 8 + 2y -3x -3y + 12 + 5

Combine like term
4x-3x +2y -3y -8+12+5

x –y +9

Hence the answer is x-y+9

Study Online Model

Introduction to study online model:

Nowadays, studies are getting more advanced and fast paced in change. One needs to keep up his/her level to the expected level in whichever stream of education chosen by him/her. Apart from learning in school, there are various ways to get help in homework, assignments, test preparations, etc. A study online model is a way of studying online. In it you get live help on any topic you need help with or on any thing related to it, like projects, homework, etc. Thus, you get a live session in which, like a teacher teaches in the class room, you get that at home and at any time you need help; the major advantage is that one gets the full attention of the tutor, as only one student and tutor are connected through a session. I like to share this Proportions in Math with you all through my article.


Benefits of study online model:


The concept of a 'study online model' helps us to understand the theory and to solve sums relating to the topic at our own pace and ease. This is because the advantage of a 'study online model' is that we get the chance to grasp a single concept at a time and thus divide the topic to be learnt into 'basic building blocks' according to our calibre. There is no time limit to cram up the subject and one can look back at any concepts any time which may need a bit of a revision during the course of study. There are ample of rich and versatile example questions along with their solutions to refer to. A study online model has an advantage that the online content has more scope of being 'accurate', or more properly, 'updated', owing to the high speed of change on the net. This also helps those students that lag behind in studies. You can always rework and rework any part of the subject not understood properly and thus clear away any trace of hesitation with the subject to be learnt.

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The increasing scope of studying online model


From the point of view of clashing of education and daily life, a study online model is the best type of gaining education as it gives us the most flexibility which one can expect during studying. One can study at any time during the day and night and get flash backs at any concept left over or not understood properly. Thus, the 'study online model' is one of the key educational models developed in the 21st century and will play a major role in the education of all – children or adults.

A study online model helps you to develop essential skills as a person given the opportunity to critically analyse his own level can effectively correct mistakes – and furthermore, if at any time any help is needed, it is there - 24 x 7.

Online Numeric Test

Introduction to online numeric test:

Online numeric test is the process of finding appropriate solutions to the problem displayed online.  The student needs to have a clear step by step approach to solve the problems presented online fast and accurate. This lesson deals with some sample problems for online tests. I like to share this Numerical Differentiation with you all through my article.


Math - online numeric test:

In online numeric test maths there are thousands of methods to find a solution for a problem by using different methods and various formulae. the most basic operations of study online calculating are given as below:

Addition,
Multiplication,
Subtraction and
Division
Steps to do online numeric test:
The basic steps of math solving from online numeric test are

At first, perform all the operations enclosed in the brackets

Then calculate the exponents

Next perform the multiplication and division operations

At last do the addition and subtraction.

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Online numeric test - 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

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

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

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.

Quadratic Equations with Square Roots

Introduction :

In mathematics, a quadratic equation is one of a polynomial equation of the second degree. The general form is

ax^2+bx+c=0

Where x represent a variable, and a, b, and c, are the constants, with a ? 0. (If a = 0, the equation becomes a linear equation.). The constants a, b, and c, are called, the quadratic coefficient, the linear coefficient and the constant term or free term. The word "quadratic" comes from quadratus; it is the Latin word for "square." Quadratic equations can also be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula.

Source: wikipedia


Example problems on Quadratic equations with square roots:

Example 1:

Determine all real solutions to the equation

Sqrt (x + 1) = 4

Solution:

Given equation is
sqrt (x + 1) = 4

Squaring on both sides, then the above equation becomes
[sqrt (x + 1)]^2 = 4^2

Simplify the above equation
x + 1 = 16

Solve for x.
x = 15

NOTE: Because we squared both sides not including putting any conditions, extraneous solutions may be introduced, checking the solutions is necessary.

Check the left side (LS) of the given equation when x = 15

LS = sqrt (x + 1) = sqrt (15 + 1) = 4

Check the right Side (RS) of the given equation when x = 15

RS = 4

When x = 15, the left and the right sides of the given equation are equal: x = 15 is a solution to the given equation.

Example 2:

Determine all real solutions of the equation

Sqrt (3 x + 1) = x - 3

Solution:

Given equation is
sqrt ( 3 x + 1) = x - 3

Squaring on both sides, then the above equation becomes
[sqrt ( 3 x + 1) ]^2 = (x - 3)^2

Simplify the above equation
3 x + 1 = x^2 - 6 x + 9

Rewrite the above equation in factor form.
x^2 - 9 x + 8 = 0

The above form is a quadratic equation with 2 solutions
x = 8 and x = 1


Practice problems on quadratic equations with square roots:


1) Determine the real value of the given quadratic equation with square roots.

Sqrt (2 x + 15) = 5
Answer: x = 5

2) Determine the real value of the given quadratic equation with square roots.

Sqrt (4 x - 3) = x – 2

Answer: x = 7

Write Number Sentence

Number:
A number is described as a mathematical thing, which is used for calculating and counting. The system of mathematical function involves one or more numerical as input and produce its related mathematical output. This operation consists of arithmetic function for example online addition, online subtraction, online multiplication, and online division.

There are variety of numbers are used in arithmetic operation. Some of them as follow,

Natural numbers
Integers
Rational numbers
Real numbers
Complex numbers
Computable numbers
Prime number

Rules:


General rules for to write the number with sentence as follows,

Rule: 1 If the value of given number is above 9, then writing the number for it.

Examples: 1) I have 11 books.

2) There are three balls.

Rule: 2 if a line has number either above the value of 9 or below the value of 9, then writing integers for all numbers or writing in words for all numbers.

Examples: 1) They have 10 rupees and 40 paise

2) The hall contains six doors and twenty windows.

Rule: 3 the simple fractions are writing by the use of hyphens.

Examples: 1) One-half of the value is found

2) One-fourth of problems are solved.

Rule: 4 the mixed fractions are writing in numerical or writing the first word of a sentence.

Examples: 1) There are 7 ¼ water.

2) Five and one-fifth percent of acid mixed with them

Rule: 5 the maximum amount of numbers are rounding by writing in words

Examples: 1) He can earn up to five million dollars.

2) Town has 44 million people

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Examples:


1) Write the following numbers in sentence: (66, 100)

Solution:

66 – Sixty six
100 – A hundred
2) Write the following fractions in sentence: (1/2, 1/4)

Solution:

1/2 – A half
1/4 – A quarter
3) Write the following roman in sentence: (X, XII)

Solution:

X – Ten
XII – Twelve
4) Write the following decimals in sentence: (6000.14, 0.003)

Solution:

6000.14 - Six thousand and fourteen hundredths
0.003 - Three thousandths
5) Write the following mixed numbers in sentence: (1 ½, 5 ¾)

Solution:

1 ½ - One-half
5 ¾ - Five and three-fourth

Online Slope Factor

Introduction :

Learning online slope factor is very simple and interesting. All linear equation has a slope factor which is attached with its x component. In general slope factor is represented by a symbol 'm'. Linear equation can be expressed as a relation between x and y with unit power. We can see linear equation in following forms:

ax + by + c = 0      ....................(1)

ax + by = c            .....................(2)

y = mx + b            ......................(3)

The equation y = mx + b is known as slope intercept form. where m is called slope factor and b is called y intercept. We can convert any linear equation in slope intercept form and then we can calculate slope factor. Slope factor is nothing but coefficient of x in the slope intercept form equation.

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eq 1 can be rewritten as: by = -ax -c   or y = (-a/b) -c/b

Therefore slope m = (-a/b)

Similarly, we can see that for eq 2 also slope m = (-a/b)


Learn to find the slope factor online

Slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

m=(y2-y1)/(x2-x1)

Through differential calculus, one can calculate the slope of the tangent line to a curve at a point.

The concept of slope applies directly to grades or gradients in geography and civil. Through trigonometry, the grade m of a road is related to its angle of incline theta by

m=tan(theta).

If we have two points then find the slope  using 1st formula.

If we give any equation then we can find dy/dx=function(x) where substitute x value the we get slope.

If we have any angle then we have to use slope(m)=tan(teta) where teta is the angle.

Examples to learn online slope factor


Example1: Find the slope of 4x + 3y = 5.

Solution: Converting it into slope intercept form we get,

y = (-4/3)x + 5/3, comparing it with y = mx + b we get,

Slope m = -4/3


Example 2: Find slope of line passing through (0,0) and (2,3).

Solution: Slope m = (y2-y1)/(x2-x1)

m = (3-0)/(2-0)

or slope m = 3/2

Learn Online Linear

A statement in which two quantities are equal is called an equation.

Introduction to learn online linear:

An equation of the form `ax+b=0, a!=0` is called a linear equation in the variable x.When the degree of the variable on both sides equal to one, then it is a linear equation. It has more than one variable.

Linear equation is the equation of the form y = mx + b. The above equation involves two variables namely  x and  y. Linear equation is a type of algebraic equation, which consists of all variables of degree one and constants. Examples of linear equations are

`5x = 10`  Linear equation of one variable

`4x+7y = 10` Linear equation of two variables

`3x +7y+9z = 11` Linear equation of three variables

Solution of linear equation: Any value ( or values) of the variable (or variables) which when substitued in an equation makes its both sides equal is called a solution (or root ) of the equation.


Types of linear equation:


Conditional Equation:
If the linear equation has the real roots, it is called conditional.

Ex:

2x + 5 = 7

7x + 3 = 10

Unconditional Equation:
If the roots are not real, it is called unconditional.

Ex:

5x + 8 > 1

4x + 4 < 1

Quadratic Equation:
Quadratic is  the second degree of the polynomial equation

Ex:

4x2 + 2x + 4 = 9

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Example problems on linear equations:


Ex 1: Solve the given equation 5x + 6 = 81

Sol:

Step 1:Given equation:   5x + 6 = 81

Step 2:Subtracting in both in 6:    5x + 6 - 6 = 81 - 6

Step 3:Simplification:      5x = 75

Ans:                   x  = 15

Ex 2 : Solve the given equation 8x + 5y = 90 and where is y = 2

Sol:

Step 1: Given equation:        8x + 5y = 90

Step 2:Substitute in y=2:   8x + 5(2) = 90

Step 3:Simplification:       8x + 10=90

8x = 90 -10

8x = 80

Ans:                x = 10

Ex 3 : Solve the given Equation: 9z + 25 = 4z + 65

Sol:

Step 1: Given equation:    9z + 25 = 4z + 65

Step 2:Subtracting both sides from 25:    9z + 25 - 25 = 4z + 65 - 25

Step 3:Simplification gives:        9z = 4z + 40

Step 4:Subtracting both sides 4z:  9z - 4z = 4z - 4z + 40

Step 5:Simplification gives:      5z = 40

Ans :    z = 8

Ex 4 :Solve 5x^2 + 2x - 3 = 0 for x.
Sol:

Step 1: Factor:   (5x - 3)(x + 1) = 0

Step 2:Simplification:   5x - 3 = 0, x + 1 = 0

Ans:  5x = 3,  x = -1

Ex 5: Solve: 4x + 9 > 97

Sol:

Step 1 Given equation:   4x + 9 > 97

Step 2  Simplification:     4x > 97 - 9,  then 4x > 88

Ans :   x > 22

Completing The Square Solve Online

Introduction:

Complete squaring is an application of algebra . this means the given equation is having solution, it means each equation is having one or more solutions. now a days technology is also uses in mathematics and the students is learning in online. the tutors would explain step by step for the students.

In this content we learned about the complete square problems. I like to share this Types of Triangle with you all through my article.


Complete Square Method Problems:


Example:

Solve the equation for x x^2 + 8x + 15 = 0
Solution:
There are three terms in this equation. One is constant (15) and the others contain variables (x^2 and 8x).

in this problem we do  factor the equation by determining what two numbers multiplied together gives a result of 15 when added give a sum of 8.

The factored equation looks like this:


(x + 3)(x + 5) = 0 (a)

the rule is First, Outside, Inside, Last (FOIL) method,

x^2 + 5x + 3x + 15 = 0 ----> x^2 + 8x + 15 = 0 (b)

We convert equation (a) into its terms and set each term equal to zero:

(x + 3) = 0 (c)
(x + 5) = 0 (d)

Now, solve each for x:

x + 3 = 0

subtract 3 from each side

x = -3

x + 5 = 0

subtract 5 from each side

x = -5

solutions are that x is equal to -3 or -5.

substitute x values in equation( 1 )

start with -3:

(-3)^2 + 8(-3) +15 = 0
(9) + (-24) + 15 = 0 This is a true statement so -3 is a solution.

Next,  -5:

(-5)^2 + 8(-5) + 15 = 0
(25) + (-40) + 15 =0 This is also a true statement so -5 is a solution.

So answer is x =  -3

and  x =   -5

Example2:Solve the equation for 2x^2 - 3x + 1 = 0

Solution:

2x^2 - 3x + 1 = 0

2x^2 - 3x = -1

x^2 - (3/2)x = -1/2

2a = 3/2

a = 3/4

a^2 = 9/16, so we add 9/16 to both sides:

x^2 - (3/2)x + 9/16 = -1/2 + 9/16 = 1/16

(x - 3/4)^2 = 1/16

x - 3/4 = +/- 1/4

x = 3/4 +/- 1/4

x = 1, 1/2

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Practice Problems:


Solve the equations for competing square
1)x^2 - x - 1 = 0
2)x^2-6x=16

Free Online Algebra Calculators

Introduction of free online algebra calculators:

Algebra is the part of mathematics which always deals with the study of operations such as addition, subtraction, multiplication and division. Algebra includes variables, constants, polynomials, exponents, terms and expressions. Basic operation of algebra is to balance the expression on both sides. This article free online algebra calculator briefly tells you the operations of algebra with various examples. I like to share this Polynomial and Rational Functions with you all through my article.


Examples of free online algebra calculators:


For free online algebra calculators consider the following examples.

Ex 1:   Simplify the expression:

10(a-5) + 7b-4(2a -3b+5) +15

Sol :        = (10a-15) + 7b-4(2a -3b+5) +15.

= 10a-15 + 7b -8a+12b-20+15.

= 10a-8a+7b+12b-15-20+15.

= 2a+19b-20.

Ex 2 :      Solve the equations:

x + 2y + 3z = 14, 3x + y + 2z = 11, 2x + 3y + z = 11

Sol :     Let the given equations be

x + 2y + 3z = 14  `|->` (1)

3x + y + 2z = 11  `|->` (2)

2x + 3y + z = 11  `|->` (3)

Consider the equations (1) and (3)

(1) `rArr` x + 2y + 3z = 14

(3) × 3 `rArr` 6x + 9y + 3z = 33

Subtract (1) –(3):

–5x – 7y = –19

5x + 7y = 19          `|->` (4)

Consider the equations (2) and (3)

(2) `rArr` 3x + y + 2z = 11

(3) × 2 `rArr` 4x + 6y + 2z = 22

Subtract (2) – (3):

–x – 5y = –11

x + 5y = 11              `|->` (5)

Consider the equations (4) and (5)

(4) `rArr` 5x + 7y = 19

(5) × 5 `rArr` 5x + 25y = 55

Subtract (4) – (5):

–18y = –36;                             i.e. y = 2

Substitute y = 2 in (5) we get

x + 5(2) = 11; x + 10 = 11;   i.e. x = 1

Substitute x = 1, y = 2 in (3) we get

2(1) + 3(2) + z = 11; 2 + 6 + z = 11 ; z = 3

The solution is x = 1, y = 2, z = 3.

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Practice problems for the free online algebra calculators:


Consider following problems for practice.

Pro 1 :  Solve the expression:  5(2a-3b+5c+7) + 21a – 3c + 34 + 12b.

Answer: 31a-3b+22c+69

Pro 2 :  Solve: 3x – 3y + 4z = 14; –9x – 6y + 2z = 1; 6x + 3y + z = 5

Answer: x = 1, y = –1, z = 2

These are the problems under the free online algebra calculators.

Algebra Calculator Online

Introduction to websites to learn algebra calculator online:-

In this article, we are going to learn

"what is the definition of algebra?"

"Where the algebra calculators are available online?"

"How to learn algebra from the calculators online?"


Definition of algebra:


Algebra is a  a branch of Mathematics in which the letters (generally alphabets) are used to represent members or numbers of a particular set. I like to share this learning pre algebra with you all through my article.


Websites which help us to learn algebra calculator online:


Here are a list of websites that help us to learn algebra online , the topics which can be covered using this calculator are also discussed here.

www.easycalculation.com:

This website will provide the calculator on Matrices (which is a concept of algebra). This will allow us to do the matrix addition, matrix subtraction, matrix multiplication, matrix inverse including determinant and ad joint of matrices.

www.algebrahelp.com:

This will provide us a calculator which can be used to solve equations.

www.myalgebra.com:

This is also one of the websites from which we can learn slgebra online. This website provides a calculator which allows us to enter the algebra problem and gives us the solutions.

www.quickmath.com:

This is an automated service which can be used to answer the common math problems online. This can be thought as an online calculator which can solve the equations and calculus problems automatically and instantly.

www.mathway.com:

This is an online Math problem solver which provides step by step solutions for the problems in  algebra concepts like basic maths and pre - algebra.

www.math.com:

This will provide us a basic calculator.

www.math-videos-online.com:

This is also one of the websites which provides online calculators and  helps us to learn algebra online.

This will provide graphic calculator, fraction calculator, compound interest calculator, factoring calculator, prime number calculator, greatest common factor calculator and least common multiple calculator.

www.calculatorsoup.com:

This will provide calculators to learn many algebra concepts online like cube roots, cubic polynomials, exponents, fifth roots, fourth roots, fractional exponents, radicals, radical exponents, square roots, quadratic equations etc.


Some other websites that help to learn algebra calculator online:


Other than the online calculators to learn algebra mentioned above, there are some other websites which are listed below.

www.univie.ac.at

www. solvemymath.com

www. myalgebra.com

www. sciencecentral. com

etc.

Factorization Solve Online

Introduction :

Factorization solve online guides you to understand the rules of factorization. To understand factorization, factorization solve online gives ample of time to grasp the concept. You can any time access online content and solve your doubts. Through factorization solve online you can 'by heart' the rules of factorization. Factorization solve online not only makes you clear all doubts regarding the subject, but also makes easy to remember it.

I like to share this Factorization of Polynomials with you all through my article.

What are the factors of 42? The answer is the factors of 42 are 6 and 7. Can 6 and 7 be factorized further? We will say yes because 6 = 2 x 3.. So now we can write 42 = 7 x 3 x 2. Here, 7, 6, 3 and 2 are called the factors of 42 because they can be multiplied by one another to get 42.

Similarly, to find the factors of an algebraic expression, we shall write it as a product of two or more algebraic expressions.

For example,

X(Y  +  Z) = X * (Y + Z)     -> Here the product of X and (Y + Z) is X(Y  +  Z). So X and (Y  +  Z) are called the factors of X(Y  +  Z). But if X(Y  +  Z) is written as XY  +  XZ, then XY and XZ are not the factors of X(Y  +  Z), because we do not get X(Y  +  Z) on multiplying XY and XZ.


An example of solve factorization online


What are the factors of 30?                                                                                                                                                                                       30 = 3 x 10 = 3 x 5 x 2

Similarly, factors of 2XY are:

2XY = 1 and 2XY

2XY = 2 and XY

2XY = 2X and Y

2XY = X and 2Y

2XY = 2, X and Y

Therefore the factors of 2XY are 2, X, Y, 2X, 2Y, 1 and 2XY itself. This is the example of factors of a monomial.

Factorization of binomials:

15x²y³ + 12x³y

Here for the constant numbers 12 and 15, the common factor is 3, so we write the binomial as

3(5x²y³ + 4x³y)

and the common variables are x and y. The exponents of x are 2 and 3out of which take x²(the least value of the exponent) out. So we will write                                                                                                                                                                                                                              3(5x²y³ + 4x³y) as                                                                                                                                                                                                                   3x²(5y³ + 4xy)

Similarly, the exponents of y are 3 and 1. Take the least exponent out. Thus, the expressions becomes

3x²y (5y² + 4x)


Another factorization example (solve online)


Let us look at another example:

20 a²b³ + 32 a³b²

The common factor of 20 and 32 is 4.

So 4(5 a²b³ + 8 a³b²)

Now looking at the variables, the common variable 'a' has exponents 2 and 3, and the common variable b has exponents 3 and 2. As we did in the previous sum, take out the variables carrying the least exponents, that is b² and a², to get

4a²b²(5b + 4a)

This is a completely factorized expression.

Online Algebra Terms

Introduction to algebra terms:

Online learning is a modern way of learning, which comprises of several advantages. The major advantage of online learning is that we can learn with comfort by staying in our home itself. Online learning will help us to improve our skills and knowledge level in a rapid manner. There are enormous amount of websites are available to learn in online. Online learning not only helps the students to improve their knowledge but also pay way for getting various information's related to a particular topic or subject. In math, various branches exist. Algebra is a main branch of mathematics. Algebra is a vast area in which various terms and definitions exists. Learning algebra terms finds it necessity in solving the problems. In this article, we are going to discuss few algebra terms, which are used in common.


Algebra terms:


Equation:

If the algebraic expressions contain equal sign, then it is referred as an equation.Let us consider 2x+y=6 as an equation since it has an algebraic expression with equal sign.

Degree of polynomial:

Degree of polynomial is the highest degree of any term present in the given polynomial.Let us consider x^2+2x+5 as a polynominal with the degree of 2

Direct variation:

Direct variation is the relationship between two given variables in which one of the variables will be a constant multiple of the other variable.

Domain:

Domain is the set of values of the independent variables for which a given function can be defined.

Factorial:

Factorial is the product of a given integer and all its smaller positive integers.

Focus:

Focus is a unique point, which is used to define and construct a conic section. I have recently faced lot of problem while learning Parallel and Perpendicular Planes, But thank to online resources of math which helped me to learn myself easily on net.


Additional algebra terms:


Function:

Function is a relation in which each and every element of the domain value  will have the corresponding range value.

Imaginary numbers:

If the complex numbers has no real parts, then it is referred as imaginary numbers.Here, `+-ib`

Leading coefficient:

The coefficient of the leading term in a given polynomial is referred as the leading coefficient.Let us consider 2a3 +6a here the leading coefficient is 2

Monomial:

A polynomial with a single term is referred as a monomial.Here 2x is a monmial since it has a single term.

Midpoint:

If the point lies halfway between the two given points, the point is known as midpoint.

Combinatorics:

The process of counting the number of elements in very large sets is known as combinatorics.

Common ratio:

In a geometric sequence, the common ratio is the ratio of a term to the previous term.

Teach Online and Get Paid

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Uses of teach online and get paid:

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