Free Algebra Answers

Introduction for learning free algebra answers:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The Algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms for learning free algebra answers are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, Learning free algebra answers may be regarded as an extension of Arithmetic.

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Order of the operation for learning free algebra answers:


1. First, we have to evaluate the expressions within the parenthesis.

2. Next,  we have to evaluate the exponents.

3. Next, we have to evaluate the multiplication or division operations.

4. Finally, we have to evaluate the addition or subtraction operations.


Examples for learning free algebra answers:


Example 1:

3(a-2) + 10 = 0

Solution:

3(a-2) + 10 = 0

3a – 6 + 10 = 0

3a + 4 = 0

3a + 4 - 4= 0 – 4 (Add -4 on both sides)

3a = -4

3a / 3 = -4 / 3 (both sides divided by3)

A = -4 /3

Example 2:

5x - 10 = 15x - 20

Solution:

5x - 10 = 15x - 20

5x - 10 + 10= 15x – 20 + 10    (Add 10 on both sides)

5x =15x -10

5x – 15x =15x -15x  - 10 (Add  -15x on both sides)

-10x = -10

-10x / 10 = -10 / 10 (both sides divided by 10)

-x = - 1 which is equal to x=1

Example 3:

10x + 20 = 30

Solution

10x + 20 = 30

10x + 20 - 20 = 30 - 20 (Add -20 on both sides)

10x = 10

10x / 10 = 10 / 10 (both sides divided by 10)

x = 1

Example 4:

Solve the equation   |-25x + 50| -75 = -100

Solution:

|-25x + 50| -75 = -100

|-25x + 50| -75 + 75= -100 + 75(Add 75 on both sides)

|-25x + 50| = -25

|-25x + 50| is same as -25x + 50, now solve for x

-25x + 50= -25

-25x + 50= -25 - 50 (add -50 on both sides)

-25x=-75

-25x /- 25 = -75 / -25 (both sides divided by -25)

x = 1

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Practice problem for learning free algebra answers:


1. 4(x-6) + 15 = 1

Answer: x=2.5

2. 3x - 7 = 15x – 8

Answer: x=0.1

3. 2x + 8 = 3

Answer: x=-2.5

Learn Different Quadrilaterals

Introduction of quadrilateral:  We know that on combining three non-collinear points in pairs, the figure so obtained is a triangle. Now, let us mark four points and see what we obtain on combining them in pairs in some order. Such a figure formed by combining four points in an order is called a quadrilateral. In a quadrilateral, a pair of opposite sides is parallel. I like to share this Slope Intercept Formula with you all through my article.




Definition of Quadrilateral and its types:


Definition of Quadrilateral:   Quadrilateral is a geometrical figure that consists of f our end points called verticals joined to each other by straight-line segments or sides called edges. The quadrilateral are classified depends on the length of side, angle and diagonals of object.

Methods of Quadrilateral:

Parallelogram

Square

Rectangle

Rhombus

Trapezium

Kite

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Types of Description of quadrilateral:


Parallelogram:     Parallel lines are lines are the exactly same distance between two lines that has never cross. A couple of lines of quadrilateral that are parallelograms that you may already know about are squares and rectangles.

Formula:

Area = b × h sq. units (b – Base, h - Height)

Square:    The square is a parallelogram having an angle, equal to right angle and adjacent sides equal. Parallel lines are lines are exactly the same length and height that has never cross.

Formula:

Area = a2    (a - area)

Rectangle:     Parallel lines are the same distance between their two lines and that has never cross. Probably those angles know about a couple of lines quadrilateral that also called as parallel sides and four right angles.

Formula:

Area = l × b sq. units

Where

l – Length

and b – breadth)

Trapezoid:    A quadrilateral should have at least one pair of parallel sides. The quadrilateral one side of opposite sides are parallel if non parallel of opposite sides of a trapezoid are congruent it is called as isosceles triangle.

Formula:

Area = 1 / 2 (a + b) × h sq. units.

Rhombus:     All the four sides of this quadrilateral are equal. Rhombus is a parallelogram having its adjacent sides equal but more of whose angles is a right angles.

Formula:

Area = 1 / 2( d1 × d2) sq. units

Where

d1, d2 are diagonals.

Kite:    A quadrilateral with two pairs of equal sides and hence only one pair of equal angles. The longer one bisects its diagonal. The area of the kite is equal to the product of its diagonals.

Formula:

Area = 1 / 2 * d1 * d2

Where

d1, d2 are diagonals.

Learn Divisor

Introduction to learn divisor:

In learning divisor many students undergo difficulties in it. They find difficulty in multi-digit divisor. To overcome that we should be careful in selecting the numerals, so it may help the students a lot  with the divisor learning–and also from the arithmetic operations used from the divisor. They have to group the numbers when they multiply the numerals with the quotient of the divisor. Please express your views of this topic What is a Divisor by commenting on blog.


Definition of Integers in learn divisor:


The divisor is the digit that the dividend is divided by (in long division). The dividend divided through divisor is known as the quotient (plus a remainder).

One of two or more integers that can be exactly divided into another integer, the number by which a dividend is divided. What does n|m mean? It explains n divides m. For an example 5|10, or 5 divides 10. Do you know when n divides m or when n is a correct divisor of m? I think you do. Understanding List of Composite Numbers is always challenging for me but thanks to all math help websites to help me out.


Let’s see an example on learn divisor:


1)10 divides 20 or 10|20, we know..

The value twenty is divided by ten is written as two x two x five.

The value ten can be written as two x five

20 = 2 X 2 X 5 = 2^2 X 5 and

10 = 2 X 5

2) But 15 does not divides 20,

The value twenty cannot be divide by 15

20 = 2^2 X 5 and

15 = 3 X 5

3) Then why does 10 divide 20 but not 15 ?

We already know, 20 = 2^2 X 5

15 does not divide 20 for the reason that, 15 contains a prime factor ( 3) which is not exist in 20.

Likewise, 14 does not divides 20 as it contains a prime factor (7) which is not exist in 20.

Note that, 14 = 2 X 7

4) Again, 8 does not divides 20. Why?

20 = 2^2 X 5

8 = 2^3

Do you get it? 8 do not include any prime factors which do not exist in 20, then why does 8 not divide 20?

Answer is very easy; just have a close look at the power of 2.

Learn About Algebraic Expressions

Introduction to learn about algebraic expressions:

The Expressions are a central concept in algebra. A variable can take various types of values. Its values are not fixed. Otherwise, a constant has a fixed value. We combine variables and constants with operations this forms the algebraic expressions. For this, we can use the operations of addition, subtraction, multiplication and division. We have already known some simple algebraic expressions like y + 3, p – 5, 4a + 5, 10y – 5a and so on. The above expressions were formed by combining variables with constants.


Learn about Terms of an Expression


When terms have the same algebraic factors, they are like terms. When terms have different algebraic factors, they are unlike terms. For example, in the expression 5xy – 8x + 7xy – 17.

Learn about Like terms:

5xy and 7xy because the factors of 5xy are 5 and x and y. and factors of 7xy are 7 and x and y both factors are same. So these are like terms.

Learn about Unlike terms:

The terms 5xy and –8x, have different algebraic factors. They are unlike terms. Similarly, the terms, 5xy and -17 are unlike terms. Also, the terms –8x and -17 are unlike terms.

Learn about Coefficient of the Term:

The numerical factor is said to be the numerical coefficient or simply the coefficient of the term. The above example the coefficient of x is -8.

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Learn about Kinds of Expressions


Monomial Expression:

An expression with one term is called a monomial. For example, 5pq, 10z,

Binomial Expression:

An expression, it contains two unlike terms is called a binomial. For example,

a + b, b – 5

Trinomial Expression:

An expression, it contains three terms is called a trinomial. For example, the expressions p + q + 17, a b + a +b

Polynomial Expression:

An expression with one or more terms is known as a polynomial. Thus, a monomial, a binomial and a trinomial are all the type of polynomials. For Example: 4x^3+x^2+7x+2

Factoring Quadratic Polynomials

Introduction:

In algebra, the sum of a countable number of monomials is referred as  a polynomial. The way of writing a polynomial as a product of two or more simpler polynomials is referred as factorization.
The process of factorization is also known as the resolution of factors. Factoring quadratic polynomials is one of the basic operations of polynomials. The process of factoring the quadratic expression ax^2 + bx +c is explained below: Looking out for more help on Factor a Polynomial in algebra by visiting listed websites.

Method of factoring quadratic polynomials:


Let us consider the coefficients a, b and c as integers and a is not equal to 0. When the coefficients a, b and c satisfy certain conditions, the quadratic expression ax^2 + bx +c can be factorized.

First, we consider a simpler case with a = 1 and b and c as integers.Now, we have to factorize  x^2 + bx + c. We try to write the integer constant term c as a product of two integers p and q such that p + q = b. If we find solution in our attempt, then

x^2 + bx + c  =  x^2 + (p + q)x + pq

=  (x^2 + px) + (qx + pq)

=  x(x + p) + q(x + p)

=  (x + p) (x + q)

General Rule for factoring quadratic polynomials : If the constant term c of quadratic expression x^2 + bx + c can be expressed as a product of two integers p and q such that the sum p + q is the coefficient b of x, then x^2 + bx + c = (x + p)(x + q).

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Example for factoring quadratic polynomials


An example for factoring quadratic polynomials is given below:

1) Factorize x^2 + 5x + 6.

Step 1 : Possible factorization of 6 is    6 = 1 x 6

6 = 2 x 3

Step 2 : Sum of factors are                      1 + 6 = 7

2 + 3 = 5

Step 3 : Factorization:

Now we need to compare the coefficient of x and the sum of the factors. We find that the sum of the factors 2 and 3 is the coefficient of x. The factorization of quadratic expression is explained below:

x^2 + 5x + 6   =   x^2 + (2 + 3)x + 6

=   (x^2 + 2x) + (3x + 6)

=  x(x + 2) + 3(x + 2)

x^2 + 5x + 6  =  (x + 2) (x + 3)

Continuous Probability Learning

Introduction to continuous probability learning :

Definition: Learning to define continuous probability of an event occurs when the one or more events occurred. Consider any two probabilities A and B. when the event A occur and it depends on the other event which is already occurred then we can say the conditional probability of above two events are P(A | B). Learning  conditional probability of events using the following formula :

`P((A)/(B))=(P(A U B))/(P(A))`

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Learning to solve conditional probability problems 1:


Learning some problems to find the conditional probability.

Pro 1:Consider a population, the probability a men life at least 70 years is 0.70 and is 0.65.if he won’t live more than 80 years. If a man is 70 years old, find the conditional probability that he will survive on 80 years. If A subset of B then P (A U B) = P (A)

Solution:Let us take A is the event that he lives to 70 years and B is the event that he will live at least 80 years.

So given that P (B) = 0.55 and P (A) = 0.70

So Conditional probability P (`(B)/(A)) = ( P (A U B)) / ( P (A))`

The given condition is P (A and B) = P (B) = 0.65

Conditional probability P (`(A)/(B)` ) = `(0.65)/(0.70)`

P (`(A)/(B)` ) = 0.9286

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Learning to solve conditional probability problems 2:

A box contains red and blue marbles. We are choosing two marbles without replacement. Probability of choosing red and blue marbles is 0.45 and choosing the red marbles on the first draw is 0.57. Find the probability if the second marble is blue if the first one is red?

Solution:Probability of choosing red and blue marbles is 0.45

Probability of choosing red in the first draw is 0.57

So probability of choosing second marble ids blue then the probability is

P (`(Blue)/(Red) = ( P ( Red and Blue))/ (P(Red))`

P (`(B)/(R)` ) = `(0.45)/(0.57)`

P (`(B)/(R)` ) = 0.79 = 79 %

How to Learn Geometry

Definition:

Geometry is the defined as the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. However, geometry is used daily by almost everyone. Geometry begins with undefined items, definitions, and assumptions; these lead to theorems and constructions. It is an abstract subject, but easy to visualize, and it has many concrete practical applications. Please express your views of this topic What is a Acute Angle by commenting on blog.


Geometrical objects:

Point

A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point represents position only; it has zero size

Line

A line can be thought of as connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. The symbol ↔written on top of two letters is used to denote that line. A line may also be named by one small letter

Collinear points

Points that are lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are non-collinear points.

Plane

A plane has an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, width, and zero height (or thickness). It is usually represented in drawings by a four-sided. A single capital letter is used to denote a plane. The word plane is written with the letter so as not to be confused with a point . Is this topic How to find Area of a Circle hard for you? Watch out for my coming posts.


Postulates:

Postulate 1: A line contains at least two points.

Postulate 2: A plane has at least three non-collinear points with it.

Postulate 3: If we cross through any two points, there is exactly one line.

Postulate 4: If we cross through any three non-collinear points, there is exactly one plane.

Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.

Postulate 6: If two planes intersect with each other, then their intersection is a line.