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.