Equations With No Solution

Equations with no Solution

Intoducion:

There are two types of equation.one is equation with solution and other is equation without solution.in equation with solution we can find the value of variable like x,y,z.but in the equation with no solution we can  not find the value of variable like x,y,z.in the equation with no solution we can get situation like 0=0,4=5,7=8 etc...For equations with solutuion,we can solve the equation by three method.these methods are 1)Elimination method 2)Substitution method 3)Graphing method..by these method we can check that whether a equation has solution or not?

When we solve by Elimination method we have to make the coefficient of one the variable into equal and then add both the equations. Now one of the variables will get cancel and then one of the variables is left out. After that, solve for the left variable. Finally substitute the result of one of the variable in any one of the equation we will get the result for another variable. When we solve by substitution method substitute one of the equation in another and then solve. If we are solving by graphing method draw a graph for both the equation in a single graph. The intersection point of the lines is a solution for the given system of linear equation. So these are method of solving a linear equation.


DESCRIPTION OF EQUATION AND SOLUTION


Equation: . A statement in which values of two mathematical expressions are equal is called an equation sign of equal to is = equation with solution: Here we han find some solution for the given equation

X+5Y=2

X-12Y=10

From the above two equation we can find the value of two variable X, Y

equation with no solution:  a equation from which we cannot find the value of the variable is called any solution of equation.

X+Y=1

2X+2Y=2

From the above equation we cannot find the value of variable X,Y...since both the equations are same.to solve 2 variables we need two different equations. Having problem with Convert a Decimal to a Fraction keep reading my upcoming posts, i will try to help you.


Examples of no solution equation


Problem 1:4x-2+3x=3x+12+4x-14

Solution: 4x-2+3x=3x+12+4x-14

Step 1:  4x+2x-2=3x+4x+12-14

Step2:   7x-2=7x-2

Step 3:  7x-7x=-2+2

Step 4:  0=0

So there is no solution of this equation.

Problem 2:7x-4y+12z+4=5-3y+7x-y+12z

Solution:

Step 1:7x-4y-7x+3y+y+4=-12z+12z+5

Step2:0+4=0+5

Step 3:  4=5

So there is no solution of this equation.

Problem 3:

X+Y=2 (equation 1)

4X+4Y=8(equation 2)

Solution:

Step 1: multiply equation 1 by 4

Step 2: then we will get 4X+4Y=8

Step 3: now subtract this from equation 2

We will get 0=0

So there is no solution of this equation.

Geometry Final Exam

Introduction to geometry final exam:

Geometry is a branch of mathematics deals with the properties of and relationships between planes, points, and figures and examines their properties, measurement, and mutual relations in space with generalizations of these concepts. Plane Geometry is a flat shape of lines, circles, and triangles. Solid Geometry is about solid shapes like spheres and cubes. The group of mathematics, which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles.


Lists of geometries:


The following are the different classifications of geometry involved in geometry final exam.

RIEMANNIAN GEOMETRY:

Riemannian geometry clear as the bough of degree of difference geometry that study smooth manifold, Riemannian manifold with a Riemannian metric with an inner product on the departure space at each point that varied smoothly from one point to another point. It should give in particular local notion of angle, surface area, volume, and length of curve.

ALGEBRAIC GEOMETRY:

Algebraic geometry is mainly used to show the numbers that can be used to describe points in a space or points in a plane and to express geometric relations in algebraic form.

DISCRIPTIVE GEOMETRY:

Differential geometry is mainly used for when the problem of representing three-dimensional objects on a two dimensional surface. Gaspard Monger invented it in the last 18 centuries.

DIFFERENTIAL GEOMETRY:

Differential geometry concepts is mainly used for calculus and are applied to surfaces, curves and other geometric objects

PROJECTIVE GEOMETRY:

Projective geometry is a modern geometry, also branch of mathematics that deals with relation ship between geometric figures and images of the result of projection.

NON EUCLIDEAN GEOMETRY:

A non-Euclidean geometry is study of constructions and shapes it should not map directly to any n-dimensional.

The following sample problems will help you for your final exam. I have recently faced lot of problem while learning Alternate Interior Angles in Real Life, But thank to online resources of math which helped me to learn myself easily on net.


Example problems for final geometry exam:


Example1:

Find the area of square for the side is 4 cm.

Solution:

Area of the square A = 4^2

A = 16 square centimeter.

Example2:

Find the area of sphere for the radius is 3 cm.

Solution:

Area of sphere A = 4 * 3.14 * 3^2

A = 4 * 3.14 * 9

A = 113.04 square centimeter.

Example3:

Find the surface area of cube for the side is 4 inches.

Solution:

Area of cube A = 6 * 4^2

A = 6 * 16

A = 96 square inches.

These example problems will helps for your geometry final exam.

Middle School Math proportions

Introduction to middle school math proportions:

A proportion is called an equation with two ratios on each side (these two ratios are equal). It is denoted by the symbol ‘::’ or ‘=’ to equate the two ratios.  If two ratios are not equal, then the given values are not in proportion. In a proportion, the four terms (quantities) involved. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.

For example proportion:   50: 100:: 2 : 4;

50, 100, 2, 4 are the four terms. 50 and 4 are the extreme terms. 100 and 2 are the middle terms.

Steps to solve proportions:

Solving proportions is the process of setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation.

When one of the four numbers in proportions is unknown, using the cross product we have to find the unknown number. This is called solving the proportions. Letters or Question marks are commonly used in place of the unknown number.

Here, we are going to see some of the middle school math proportions problems.


Example on middle school math proportions


The following are the middle school math proportions problems:

Example problem 1:

In 2005 the number of men enrolled was 194 while women to men enrolled in chemistry are 78: 162 in 2004. How many women were enrolled in chemistry in 2005?

Solution:

Let x is the unknown number of women

78: 162 = x: 194

Cross multiply,

78 * 194 = 162 x

15132 = 162 x

Divide by 162 on both sides

93.4074 = x

So, the women were enrolled in chemistry in 2005 is 93.4074.Approximately it is 93 members. I like to share this Adding Mixed Fractions with you all through my article.



Few more example on middle school math proportions

Example problem 2:

Margret ran 100 meters in 15 seconds. How long did she take to run 1 meter?

Solution:

In 15 seconds Margret ran 100 meters. so x is the unknown.

100/15=1/x

Cross multiply and we get:  100x = 15

Divide both sides by 100 and we get

x = 15/100

x=0.15seconds

So, she takes 0.15 seconds to run 1 meter.

Example problem 3:

In a school, 476 students ride their bicycle to school. If this number is 70% of the school enrollment, then how many students are enrolled?

Solution:

476/y=70/100

Cross multiply and we get:  70y = 47600

Divide both sides by 70 and we get:  y = 680

There are 680 students enrolled in that School.

Expected Value Sum

Introduction to Expected value:

The expected value is nothing but the problem that has many possibilities of occurring  the expected value for the particular problem. Computing of expected value can be clearly explaining you through the probability topic in math, hence the probability has many possibilities of solutions. Thus, the dice and coins play a important role to help you better in expected value.

I like to share this Expected Value of Uniform Distribution with you all through my article.


Expected value Sum - Example Problems:

Problem 1: A perfect cubic die is thrown. Find the probability that

i)an even numbers comes up.

ii)a perfect square comes up.

Solution:

Since a die can result in six outcomes, n(S) =6. All these outcomes are equally likely.

Let A be the event, that an even number comes up.

Then        A = {2, 4, 6}

P(A) = n(A)/n(S)

= 3/6

= 1/2


Let B be the event that a perfect square comes up. Since the only perfect squares in S are 1 and 4,

Therefore B = {1, 4}.

Therefore n(B) = 2,

P(B) = n(B) / n(S)

= 2 /6

= 1/3.

Problem 2:

A box contains 7 red, 3 White and 2 black balls. When a ball is picked up at random from the box find the probability that,

i)it is Red.

ii)it is not Red.

Solution:

The total number of balls in the box is 7 + 3 + 2 = 12

Hence, n(S) = 12.

i)Let A denote the event that the ball drawn is Red.

Since there are 7 Red balls in the box, therefore, n(A) = 7

Therefore  P(A) = n(A) /n(S)

= 7 /12

ii)P (the ball is not Red) = P(A’)

= 1 – P(A)

= 1 – 7 /12

= 5 / 12

We also proceed directly as follows:

When the ball is not Red, it is from the remaining color that’s from the 3 white balls or 2 black balls.

Therefore n(A’) = 3 + 2 = 5.

Hence, P(A’) = n(A’) / n(S)

= 5 / 12.


Expected value Sum - Practice Problems:


Practice Problem: 1

It is found that, when A and B play a game of chess, the odds in favour of A winning the game are 3:5. Find the probability of
i) A winning the game.

ii) A not winning the game.

Answer :

i)     3/8
ii)    5/8
2. An unbiased coin is tossed. Find the probability that

i) A tail turns up,

ii) Both Head and Tail turn up,

iii) Neither Head nor Tail turns up.

Answer:

i)        1/2
ii)       1/2
iii)       0

Definition of Probability

Introduction to Probability Definition:

In math, the probability is one of the important and very simple subjects. Generally the probability is defined as something will be happening. The probability contains sample space, events and experiments. The probability has many types; the two important types are Poisson distribution probability and binomial distribution. Now we will see the definition of probability. I like to share this Law of Probability with you all through my article.

Definition of probability:

Definition of  probability is a possible outcome of a particular process.The part of math that studies the possibility of incidence of random events in order to predict the actions of defined systems.The Probability is a method of expressing knowledge that an action will happen or has occurred.

Formula for Probability:

Probability =` ("Number of probable events")/ ("Total given events")` .

Now we will solve the some of example problems with help of probability formula. Understanding Y=mx+b Calculator is always challenging for me but thanks to all math help websites to help me out.


Example 1:


In a class room 48 students are studying some subjects. In that class room 16 students are studying math subject, 12 students are studying physics subject and 20 students are studying biology subject.What is the probability for,

i. Select the Math students.

ii. Select the biology students.

Solution:

Step 1:

Given:

Total students n(S) = 48.

Studying math students n (A) =16.

Studying Physics students n (B) = 12.

Studying Biology students n(C) = 20.

Step 2:

i. Probability for getting math students:

P (event) = `("Number of favorable math students")/("Total students").`

Number of math students = 16.

Total students = 48.

= `16/48` .

=` 8/24` .

ii. Probability for selecting biology students:

Step 1:

P (event) = `("Number of favorable biology students")/("Total students").`

Here number of biology students = 20.

Total students = 48.

= `20/48`

=`5/12`


Example 2:


The three coins are flip at the same time. What is the probability of getting exacting two tails or three heads?

Solution:

The sample space, when three coins tossed is,

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

A be the event of exacting two tails,

n (A) = {HTT,THT,TTH,TTT} = 4

B be the event of getting exacting three heads,

n (B) = {HHH} = 1

P (A) =`4/8`

P (B) = `1/8`

P (A or B) = P (A) + P (B)

= `4/8` + `1/8` .

=` 5/8` .

= 0.63

The expected value in this probability model is 0.63.

The above information is the definition of probability.

3rd Grade Learning

Introduction for 3rd grade learning:
Third Grade Mathematics is the science of pattern and relationships. It is the language and logic of our scientific world. Mathematical power is the capability to explore, to imagine, to reason logically and to use a diversity of mathematical methods to solve problems - all important utensils for children’s futures. A mathematically great person should be able to:

Reason mathematically.
Communicate mathematically.
Solve problems using mathematics.
Make connections in mathematics and between mathematics and other field. I like to share this Integral Table Exponential with you all through my article.

3rd grade topics:


Where to Look From

Fun with numbers

Give and take

Long and short

Shapes and Designs

Fun with give and take

Time goes on

Who is heavier?

How many times

Play with patterns

Jugs and mugs

Can we share?

Smart charts

Dollars and cents.

Understanding Properties of Limits is always challenging for me but thanks to all math help websites to help me out.

Explanation for 3rd grade learning:


Where to look from?

Viewing of things varies from person to person. This lesson contains about how to look the object.

Fun with numbers:

To have more practice of numbers we have funs like,

Identify number of dots in each circle, Fill in the blanks, counting…

Give and take:

The question will be given and we have to find the answer in fun manner.

Long and short:

There is something given with the diagram. We have to give the answer according to the distance and pattern.

Shapes and design:

Some of the shapes will be given then we have to do some design with the given shapes.

Fun with give and take

Real type of questions will be given then we have to find the answer.

Time goes on

In this we have funny stories with questions that question related to minutes, hours, seconds, number of times, year etc.,

Who is heavier?

In this different type of quantity will be given then we have to find which quantity is heavier.

How many times?

This contains about multiplication with funny pictures.

Play with patterns

We have to find the pattern for the given figures.

Jugs and mugs

Stories of drink related will be given then we have to find the answer with the help of the given story.

Can we share?

This topic contains about the division problem with funny ways.

Smart charts

This contains some real pattern with that we have to find the answer.

Dollar and cents

This topic contains the problem related to Dollar and cents.

Algebra Velocity

Introduction:

Algebra  was popularized in near the beginning ninth century by al-Khowarizmi. The author of the first algebra book was preferred by , Al-jabr wa'l Muqabalah, from which the English word algebra is derived. It remained the standard text in algebra for a long time. The title translates almost to "restoring and balancing, " referring to the primary algebraic method of performing an operation on one side of an equation and restoring the balance, or equality, by doing the same thing to the other side.


Definition:

Velocity  can defined as vector measurement of the rate and direction of movement or, in other terms, the rate and direction of the change in the position of an object. The scalar  magnitude value  of the velocity vector is the speed of the motion. In mathematical terms, velocity is the first derivative of position with respect to time.

More about velocity:

1)  Velocity is a vector quantity.

2)  It is also defined as the distance per unit time, i.e.,  if  s  is distance traveled in time t, then velocity

3)  m/sec,cm/sec,ft/sec,km/hr,miles/hr etc.

4)  Velocity V =  ds / dt

.             Here,

s – Position vector

ds – First derivative of Position vector

t –  time

Please express your views of this topic Formula for Percent by commenting on blog.

Examples:

1. Find the velocity of Ed . it covers a distance of 225 miles in 5 hrs..

velocity   V  = 225 / 5   miles/sec.

velocity   V =45 miles/sec.

2. A submarine descends -120 ft in 6 seconds. What is the velocity of the submarine?
Choices:
A. 30 ft per second
B. - 30 ft per second
C. - 20 ft per second
D. 20 ft per second
Correct Answer = C
Solution:

Step 1:  Velocity = Displacement nt / time .

Step 2:  Since  submarine is descending, the displacement will be negative.

Step 3:  Displacement =120 ft and Time = 6 sec

Step 4:  velocity = -120 / 6 [Substitute the values of displacement and time.]

Step 5:  velocity = 20 [Divide.]

Step 6:  So, The velocity  = - 20 ft / second.


Velocity terms:

Displacement
Distance
Position
Rate
Rate of Change
Speed
Time
These are the various terms involved in velocity.

5th Grade Math Test

Introduction to 5th grade math test:

The given below questions are taken from 5th grade math standard test. All questions on the educational standards test are evaluated by committees.
The committees of educational standards contain content experts, test board, teachers and administrators.
The committee gives some suggestions and advice to teachers for leading the 5th grade students.
Through the test teachers improve the qualities like memory, understand, and remember characteristics of 5th grade students.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. In this article we shall discuss algebra math help. Understanding Math Answers Free is always challenging for me but thanks to all math help websites to help me out.


Example for 5th Grade Math Test


Some of the examples for the 5th grade math test are as follows:

Example 1: This problem demonstrates the proper use of the distributive property.

Solve 4(x + 2 + 9) = 56.

Solution:

Combination of the terms like below, the left side of the equation becomes

4× (x + 2 + 9) ==> 4× (x + 11)

In here we are using the distributive property,

4 × (x + 11) ==> 4 × x + 4 × 11

Carrying out multiplications,

4 × x + 4 × 11 ==> to 4x + 44

The equation now becomes

4 x + 44 = 56.

Subtracting a 44 (adding a -44) to each side gives us

4x + 44 + (-44) = 56 + (-44)

4x + (44 + (-44)) = 56 - 44

4x + 0 = 12

4x = 12

Since the x is multiplied by 4, we divide the value on both sides by 4 to solve for x:

4x = 12

4x ÷ 4 = 12 ÷ 4

(4x)/4 = 3

x = 3.

We get the answer value is X = 3

We can test this solution of the given equation:

4 × (3 + 2 + 9) = 56

4 × 14 = 56

56 = 56 so our answer is correct.

Example 2: Evaluate the following math sum 3(x^2 + 4x) - 3y given that x = 2 and y = -5

Solution:

Given:

x=2

y=-5

3(x^2 + 4x) - 3y   We put 2 in the expression anywhere x appears, and we put -5 in the expression anywhere y appears, and the result is:

3(22 + (4) 2) - 3(-5)

Simplify it (parentheses first), we get:

3(4 + 8) - 3(-5) = 3(12) - 3(-5)

Now after the multiplication step, we get

36    - (-15)

Now, we need to do subtraction, we get

36 + 15

Finally, doing the addition, we get 51

Please express your views of this topic 6th grade math formulas by commenting on blog.


More Example:


Example: Solve x^2 + 5x + 6 = 0 and give the smallest integer of x as final value.

Solution:

x^2 + 5x + 6 = 0

x^2 + 2x + 3x + 6 = 0 (since +6 and +5 is the product and addition value of +2 and +3)

x (x + 2) + 3 (x + 2) = 0

(x + 2) (x + 3) = 0 (taking (x + 2) value as common)

x + 2 = 0, x + 3 = 0

Therefore the value of x = -2 and x = -3.

Exercise: Evaluate the following math sum 3(2x + 5) - 2y given that x = -2 and y = 4. (Answer: -5)

Statistics Help Online

Introduction to statistics help online:

The process of Collection of data with a specific purpose and to answer the question is called Statistics.

Or

Statistics is the process of drawing facts from numerical data. Statistics includes the collection of the data, presentation of the data and interpretation of the data. I like to share this Sample Size in Statistics with you all through my article.


Facts and Definition of statistics help online


Array: Raw data does not provide any useful information but it creates confusion. The data in the above form is called ' Ungrouped data ' . An Array is an arrangement of raw numerical data in the ascending or descending order of magnitude.

Range: The difference between the maximum and the minimum observations is called Range. Please express your views of this topic Decimal Definition by commenting on blog.


Statistical data and collection:
The fact collected for the purpose of investigation is called Statistical data.
There are two types of data:
Primary data
Secondary data

Primary data: The data collected by the investigator for the first time for his own use.
Secondary data: The data collected by a secondary source other than the investigator e.g.
Raw data: The data obtained from the original source but not arranged properly is called “Raw data”

Presentation of Data statistics help online

Presentation of Data: To convert a raw or an ungrounded data into grouped data.

Step 1: Determination of the range.

Step 2 : Fixation of Class Interval: There is not hard and fast rule of determining the number of classes. It is advisable to have total number or classes between 5 and 15.

Step 3: Fixation of Class Size: Divide the range by desired number of classes to determine the approximate size of the class interval.

Step 4 : To find class limits:

Classes should not be overlapping.
There should be no gaps between the classes,
Classes should be of uniform (or same) size.
Open ended classes, for example less than 5 or more than 10 etc. should not be used.

We take each observation from the data one at a time and place a tally mark “ l “ opposite the class to which the item belongs by cutting the numbers from the data.

The counting of tally marks in a particular class tells the frequency of that class. The sum of all the frequencies should be equal to the number of observations.

Kite Geometry

Introduction to  kite geometry:

Geometry is a study of size, shape and properties of objects or figures. English word ‘Geometry’ is derived from the Greek word ‘Geo’ meaning ‘earth’ and ‘metron’ means ‘Measuring’. Euclid who lived in 300 B.C. was distinguished Greek mathematician known as the ‘Father of geometry’

‘Quadrilateral’ is four sides geometric figure which has 4 edges and four angles. Kite is one of the quadrilaterals. Here we are going to see about kite geometry.


Properties of geometry kites:


1. Diagonals:

The diagonals of kite which bisects each other at right angles to form 90 degrees.

2. Area of kite:

The areas of a kite which can be calculated by the following methods .They are

1. The method of using diagonals measurement

Area = (d1*d2)/2

2. The method of using trigonometry

Area = ab sin c

3. Perimeter of kite:

The measurement of each of its sides gives the perimeter of kites.

4. A kite can become a rhombus:

A kite consists of four sides having its adjacent length are same and it looks like rhombus

The adjacent sides of kites are equal in its measurement. The opposite angles are not equal when its length are equal .I have recently faced lot of problem while learning Find the Perimeter of a Polygon, But thank to online resources of math which helped me to learn myself easily on net.


Problems for kite geometry:


Example 1:

The two diagonals of kites are d1 = 12 cm and d2 = 16 cm .Find the area of the kite?

Solution:

The area of kite which can be given as follows,

Area = (d1×d2)/2

= (12 × 16)/2

= 192/2

= 96 cm^2

Example 2.

Find the perimeter of the kite whose sides are 3,3,6,6.

Solution:

The perimeter of the kite can be given as the sum of all the sides.

Perimeter = 2a + 2b

= (2 × 3) + (2 × 6)

= 6 + 12

= 18 cm^2

Example 3:

Find the area of the kite where its sides and angle are 30 and a = 12 cm and b = 15 cm

Solution:

Area = ab sin c

= (12 × 15) sin 30

= 180 sin 30

= 180 × (1/2)

= 90 cm^2

Applied Probability

Introduction of applied probability:

Analysis of random situation, condition, or events is called Probability. Probability is the numerical analysis of impossibility to absolute certainty. Probability is the possibility that something will happen - how likely it is that some event will happen. For example, when picking a one card of diamond from the pack of 52 cards, the probability of picking a diamond card is 13/52, or 1/4.


Formulas for applied probability


Formula 1: Compliment

If AA and A'A' are complements then P(A) + P(A' ) = 1P(A)+P(A' )=1

Formula 2: Addition Rule

P(A OR B) = P(A) + P(B) - P(A AND B)P(A OR B)=P(A)+P(B)-P(A AND B)

Formula 3: Mutually Exclusive

If AA and BB are mutually exclusive then

P(A AND B) = 0P(A AND B)=0 ; so

P(A OR B) = P(A) + P(B)P(A OR B)=P(A)+P(B).

Formula 4: Multiplication Rule

P(A AND B) = P(B) P(A|B)P(A AND B)=P(B)P(A|B)

P(A AND B) = P(A) P(B|A)P(A AND B)=P(A)P(B|A)

Formula 5: Independence

If AA and BB are independent then:

P(A|B) = P(A)P(A|B)=P(A)

P(B|A)= P(B)P(B|A) =P(B)

P(A AND B) = P(A) P(B)

Understanding Partial Fraction Method is always challenging for me but thanks to all math help websites to help me out.

Examples for applied probability:


Applied Probability Problem 1: A die is rolled, find the probability that an odd number is obtained.

Solution:

Let us first write the sample space S.

S = {1,2,3,4,5,6}
Let E be the event "an odd number is obtained" and write it down.

E = {1,3,5}
We now use the formula of the classical probability.

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2
Applied Probability Problem 2: Two coins are tossed, find the probability that two tails are obtained.

Solution 2:

The sample space S is given by.

S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two tails are obtained".

E = {(T,T)}
We use the formula of the classical probability.

P(E) = n(E) / n(S) = 1 / 4

Solve Accuracy

Introduction to solve accuracy:

In mathematics, accuracy is defined as the most important topic. Accuracy is mainly used to find the approximate values. When we divide the two numbers, if the answer comes in decimal points means, then the obtained answer is rounded off to a nearest integer value. The concept of making the approximate numbers is known as the accuracy.  In this article, we are going to solve many examples about the accuracy. I like to share this Subtraction Word Problems with you all through my article.

Explanation to Solve Accuracy

The explanation to solve accuracy is given below the following section,

Example:

The value of the golden ratio is given by 1.61803399

The value of accuracy given for the golden ratio is 1.618

The concept of rounding off the value to its nearest integer is known as the accuracy. Understanding Basic Fractions is always challenging for me but thanks to all math help websites to help me out.

Example Problem to Solve Accuracy

Problem 1: What is the accuracy by solving the division problem, 6589 `-:` 3226

Solution:

Step 1: Given:

6589 `-:` 3226

Step 2: Divide:

6589 `-:` 3226

= 2.0424674

Step 3: Accuracy:

2.0424674

= 2.04 ( The obtained number is rounded off to nearest integer)

Result: Accuracy = 2.04

Thus, this is the obtained answer for solving the accuracy.

Problem 2: What is the accuracy by solving the division problem, 8964 `-:` 3645

Solution:

Step 1: Given:

8964 `-:` 3645

Step 2: Divide:

8964 `-:` 3645

= 2.459259

Step 3: Accuracy:

2.459259

= 2.45 ( The obtained number is rounded off to nearest integer)

Result: Accuracy = 2.45

Thus, this is the obtained answer for solving the accuracy.

Problem 3: What is the accuracy by solving the division problem, 7893 `-:` 4569

Solution:

Step 1: Given:

7893 `-:` 4569

Step 2: Divide:

7893 `-:` 4569

= 1.72751149

Step 3: Accuracy:

1.72751149

= 1.72( The obtained number is rounded off to nearest integer)

Result: Accuracy = 1.72

Thus, this is the obtained answer for solving the accuracy.

Practice Problem to Solve Accuracy

Problem 1: What is the accuracy by solving the division problem, 9785 `-:` 2456

Answer: 3.98

Problem 2: What is the accuracy by solving the division problem, 6987 `-:` 1265

Answer: 5.52

Distance between Houses

Introduction on Distance between Houses:

Distance can be measured by using the units called meter, kilometer, mile, nautical mile etc... Distance is the measure which is used to find the length between the two objects which may be movable object or immovable object. Having problem with Adding Fractions with Common Denominators keep reading my upcoming posts, i will try to help you.

Distance between houses: Through online we can see how to calculate the distance between two houses.

Examples on Distance between Houses:

Example 1:

Distance between two houses is 5 km. convert the distance into a meter.

Solution:

We know that 1 km = 1000 m.

Given:

Distance between two houses is 5 km.

We have to convert 5 km into meters.

So,

5 km = 5 * 1000 m

5 km = 5000 m.

Finally, distance between two houses is 5000 meter.

Example 2:

Distance between house A and house B is 1 kilometer, house B and house C is 3 kilometer. Find the distance between the house A and house C.

Solution:

We know that Distance between house A and house B is 1 kilometer.

Distance between house B and house C is 3 kilometer.

To find the distance between house A and house C, Add all the given distance.

Distance between house A and house C = Distance between house A and house B + Distance between house B and house C.

= 1 + 3

= 4 kilometer.

Distance between house A and house C = 4 kilometer.

Example 3:

Distance between House A and House B is 3 kilometer, distance between house A and house C is 7 kilometer. Calculate the distance between the house B and house C.

Solution:

We know that Distance between house A and house B is 3 kilometer.

Distance between house A and house C is 7 kilometer.

To find the distance between house B and house C, subtract the distance of house AC with house AB distance.

Distance between house B and house C = Distance between house A and house C - Distance between house A and house B.

= 7 - 3

= 4 kilometer.

Distance between house B and house C = 4 kilometer. Please express your views of this topic 9th cbse sample papers by commenting on blog.

Practice Problems on Distance between Houses:

Problem1:

Distance between two houses is 10 km. convert the distance into a meter.

Answer:

10,000 meter.

Problem 2:

Distance between house A and house B is 5 kilometer, house B and house C is 3 kilometer. Find the distance between the house A and house C.

Answer:

8 kilometer.

Root 3 Value

Introduction of root 3 value:

Root is the form of method in the radical, which has been used in mathematics. The radical form has been given as root √. In which the root radical symbol root "√" or otherwise `root(2)(x)` . The numerical significance inside the radical symbol or root symbol called as the radicand. There are many methods available in the rooting analysis they are, square root, cube root, fourth root and its up-to nth root. Here we are going to see about  root 3 value using the formula method and the example problems and practice problems related to the root.

Properties of Roots:

The product of two Variables in the roots which are in different variables in the root, it can be written with in a single root into as a product of those two rooted variables.
`"sqrt(x) xx` =`sqrt((x)(y))`     (By the First property)

The variable at the outside the root symbol, when it gets into root, it turns into a square of that value.
`(x)sqrt(y)` = `sqrt((x^2)(y))` ` (By the Second Property)`

In division, root of the whole division which can be written as a individual roots, as root in numerator with root separately and in denominator with root separately.
`sqrt((x)/(y))` = `sqrt(x)/sqrt(y)`        (By the Third property)

The number without the square value within the root as the result. It is because, When a perfect square value comes out of the root symbol.
`sqrt4` = 2     (By the Fourth Property)

Root 3 Value - Example Problems:

Root 3 value - Problem:

Calculate the root value 3

Solution:

The square root value for 3 is nearly equal value to the square values between 1 and 2, because 12 = 1  and 22 = 4

Step 1: Divide 3 by 1.

`3 / 1 ` = 3

Step 2: Take average for 3 and 1.

` (3 +1) / 2 ` = 2

Step 3: Divide 3  by 2

` 3 / 2 ` =  1.5

Step 4: Take average for the 1.5 and  2

`(1.5 + 2)/2 ` =  1.75

Step 5: Now check the result by taking square for that value.

1.75 2 =  3.0625

If the value is not equal to the requested value then repeat the steps  4, 3 and 5.

Step 6: Divide 3 by 1.75

`3/ 1.75` =  1.71428571

Step 7: Take average for 1.75 and  1.71428571

(1.71428571+ 1.75)/2 = 1.73214285

Step 8: Now check the result by taking square for that value.

1.73214285 2 =  3.00031885

This value is very closer to the given root value `sqrt (3) `

If the value is not equal to the requested value then repeat the steps  4, 3 and 5.Please express your views of this topic Operations on Rational Numbers by commenting on blog.

Root 3 Value - Practice Problems:

Problem 1:

Calculate the root value for 33

Answer: `sqrt 33` =  5.74456265

Problem 2:

Calculate the value for 333

Answer: `sqrt 333` =  18.2482876