Math Solved Problems

Bernoulli distribution

2011-07-29T04:51:00.000-07:00

Let's learn about binomial distribution in statistics.

Binomial distribution is first adopted by John Bernoulli, and therefore it is also named as Bernoulli distribution. Any trial that has two outcomes, one success and one failure is called a Bernoulli distribution.

Next time i will help you with some other concepts such as statistics formula. For more help you can also connect with an online tutor and get your required help not just in statistics but on other subjects such as biology tutoring and so on.

Do post you comments.

Converting Fractions to Decimals

2011-07-26T22:11:00.000-07:00

Let's learn about convert fractions to decimal in today's session.

Fractions can be represented for three identifications: ratio, percentage and decimals. Today's learning is based on converting fractions to decimals. Here is the way to perform it: 3/2 is a fraction and in order to convert this fraction into decimal, 3 has to be divided by 2. Therefore, the answer is 1.5.

One can also get help from converting fractions to decimals calculator online for answers. Similarly students can avail to adding fractions calculator, subtracting fractions calculator and so on. Also one can try out online tutoring and get practice problems on any concept like pre calculus problems and also avail to the tutors help in solving them.

Do post your comments.

Z SCORE TABLE

2011-01-24T20:34:00.000-08:00

The Z Score table is a table to list normal distribution as a standard normal distribution.

A standard normal distribution table shows a cumulative probability linked with a particular z score. Table rows are whole number and tenths place of the z score table. Table columns are the hundredths place. The cumulative probability which is generally from minus infinity to the z score is displayed in the cell of the table.

According to the Probability theory, the Normal distribution is basically used to describe real-values that cluster around a single mean value. The graph has a typical 'bell-shape'. That is the values peak at a particular point and return back to the least values.
The Normal distribution is given by the following formula:

where, u (mu) is the Mean
sigma square is the Variance

WORKING WITH INEQUALITIES

2011-01-18T23:02:00.000-08:00

The study of inequalities is an important topic under Math. It deals with comparison of 2 values how the relative size or order of two objects, or about whether they are the same or not.
It includes various symbols like:

< - lesser than
> - greater than
= -equal to
greater than or equal to
lesser than or equal to etc.

Students should under the comparisons and learn to draw conclusions out of them. It is therefore important for students to understand the concepts clearly.
Inequalities have the following properties:

Transitivity
Reversal
Addition
Subtraction
Multiplication
Division properties

Students can learn how to solve problems on Inequalities step by step by observing the solved examples or take the help of the online Inequalities calculator to solve the problems.

adjoint of a matrix

2010-09-22T23:10:00.001-07:00

Let us learn about adjoint of a matrix & its properties

1. A.(adj A) = (adj A). A = |A| I

2. adj (AB) = (adj B) . (adj A).

Non-singular Matrix & Singular Matrix

A square matrix A is called non-singular if its determinant value is non-zero.

That is a square matrix A = [aij]nxn is called non – singular if lAl # 0.

A square matrix A is called singular if |A| = 0.

In our next blog we shall learn about red square direct I hope the above explanation was useful.Keep reading and leave your comments.

11th grade

2010-09-15T23:47:00.000-07:00

Let us learn about important topic of 11th grade math.

Number System
Algebra 1
Algebra 11
Pre Calculus
Calculus
Statistics
Geometry
Trigonometry
Advanced Trigonometry

11^th grade student should Challenge themselves academically.

11^th grade student should decide what they want out of each specific session

In our next blog we shall learn about fleming's right hand rule I hope the above explanation was useful.Keep reading and leave your comments.

square root of 25

2010-09-14T00:18:00.000-07:00

Let us learn about square root of 25

The square root of 25 is 5. 5 Squared = 5² = 5 × 5 = 25

A divisor of a quantity when squared gives the quantity. Best example, the square roots of 25 are 5 & −5 because 5 × 5 = 25 & (−5) × (−5) = 25.

A square root symbol (√) of a number x is a number r so that r² = x, or, in other words, a number r whose square is x. Every positive number x has 2 square roots. 1 of them is √x, which is positive, and the other - √x, which is negative

In our next blog we shall learn about rounding calculator I hope the above explanation was useful.Keep reading and leave your comments.

i need help with my homework

2010-09-09T00:14:00.000-07:00

Hi Friends!!!

When was the last time you heard your children say, 'I need help with my homework'? Even if a learner is struggling, she or he might not ask for help. The family involvement in a student’s education can be of overwhelming importance, but is often neglected. By learning how best we can assist with homework & create the proper learning environment for his or her child, a parent can promote educational success & a lifelong love of learning. In this way, Families may need to do their own homework. Parents can find further blogs & information about important of homework

Homework is the perfect method to build responsibility in children. Homework is an opportunity to . . .

Practice always new learning.
Review learned concepts everyday.
Develop student’s interest & responsibility.
Instill good & best study habits.
Support parent & student communication.

In our next blog we shall learn about physics problem I hope the above explanation was useful.Keep reading and leave your comments.

skill tutor

2010-09-01T23:51:00.000-07:00

Let us learn about skill tutor of math subject

Math Tutoring involves working with learners on specific math skills. This work can take place in ongoing one-on-one session or small-group sessions. Tutors, learners & school-day tutor’s work together to identify skills or areas where learners need help, & design activities & review sessions to build specific math skills.

Math tutor should know how to use black board & whiteboard to teach math. How to include fun activities while teaching math subject.

Math Skills Tutor is designed for learners to supplement classroom instruction with online practice. Learners receive Skills Tutor guidelines & can complete the lessons & quizzes from school or home. Since Skills Tutor is individualized, learners can precede their own pace & target specific skills. Math skills Tutor have lessons for kindergarteners through adults in reading, science, writing, math & career skills.

In our next blog we shall learn about free math problem solver I hope the above explanation was useful.Keep reading and leave your comments.

convert circumference to diameter

2010-08-31T00:16:00.000-07:00

Let us learn how to convert circumference to diameter

If we draw several circles & measures the circumference & diameter of each, we shall find each case that

Diameter circumference = 3.14 or 722

We denote 722 or 3.14 by the symbol pie.

Therefore,

Circumference of a circle = π x diameter of the circle

= 2π x radius (r) of the circle.

Therefore, 2 x π x radius

&, Radius = circumference/ 2π

Diameter = circumference/π

In our next blog we shall learn about 50 ml equals how many ounces I hope the above explanation was useful.Keep reading and leave your comments.

Prime Factorization worksheets

2010-08-29T23:50:00.000-07:00

Let us learn about Prime Factorization worksheets

Prime Factorization is the method of find which prime numbers that need to multiply together to get the original number. The method of find this number is called prime factorization or integer factorization. Prime number does not have any factors apart from itself & 1, but 1 is not a prime number.

Prime number is nothing but which doesn’t have factors other than itself & 1, but 1 is not regarded as a prime number. A factor which is prime number is said to be as a prime factor.

To Find prime factorization of a number first divide all its factors until every remaining integer that is prime. Secondly result of prime numbers is the prime factorization of the real integer. Best example: 36

36 = 2 × 18 = 2 × 2 × 9 = 2 × 2 × 3 × 3

The prime numbers 30 are thus 2, 3, 5, 7, 11, 13, 17, 19, 23, & 29. A factor which is a prime number is said to be as prime factor. All the numbers can be expressed as a product of prime numbers.

In our next blog we shall learn about Prime Factorization calculator I hope the above explanation was useful.Keep reading and leave your comments.

5th grade math help

2010-08-27T22:32:00.000-07:00

Let us learn about 5th grade math help

2nd grade math builds upon the skills learned in the 1st grade. In 2nd grade, homework becomes slightly harder, causing many learners to look toward their parents for homework help. Read on to learn more about the math topics taught in 2nd grade classrooms & how you can help your kid to succeed.

Mastering measurements can be a daunting task for learners in grade 4th. But helping them learn can be as fun & as easy as baking a cake!

If you are a 5th grader's parent curious about your kid's mathematical abilities, this article is especially for you! Read on for help in understanding the math skills your child should have acquired by the end of the 5th grade

A 5th grade student should be able to recognize numbers up to 100,000 & able to place them in order & compare them to other numbers. By the time your kid completes grade 5, they should be able to count by 3's, 4's, 6's, 7's, 8's, 9's, 10's, 11's and 12's up to 144. Your child should have a firm grasp of multiplication & division with all the numbers up 12 & should be able to add, multiply, subtract & divide with decimals & fractions.

Lessons in measurement also continue during the 5th grade. Before entering the 6th grade, your child should be able to make appropriate apply of units such as feet, yards, millimeters, inches, centimeters, meters, kilometers & miles. Your children should have a grasp of reading & writing with dates & time, as well as the ability to apply money correctly.

Basic algebra skills await your kid in the 5th grade. They'll learn about the order of operations in a mathematic problem, how to complete mathematic problems with multiple operations, & how to find a missing value from given equation involving multiple operations.

In our next blog we shall learn about 4th grade math help I hope the above explanation was useful.Keep reading and leave your comments.

primary resources maths

2010-08-27T02:40:00.000-07:00

Let us learn about primary resources maths

Using your imagination which teaching math subject.

Students are far more likely to remember the innovative rather than the mundane, so a tutor's imagination can be vital if pupils are expected to engage well with a subject. tutors should aim to get across to learners the fact that numbers are everywhere, & relate to pretty much everything, whether dealing with quantity, time, weight or sound. In this way classroom tutoring methods can be built on by using traditional mathematics subjects to a variety of topics & sub topics. Ideally, mathematics subject lessons should be a chance for pupils to engage with technical & inventive skills, ideas by linking the subject with a wide range of oral, written & even physical activities. At Key Stages one & two, this is particularly important as younger students — mainly those aged three to seven Key Stage one — will still be grappling with their oral & mental abilities to work with numbers & shapes, & to decipher specific patterns & calculations.

In our next blog we shall learn about fraction calculator I hope the above explanation was useful.Keep reading and leave your comments.

whole number definition

2010-08-26T02:12:00.000-07:00

Let us learn about whole number definition

The number without fractions, negative number or a positive number, including zero, that does not contain a decimal or fraction

The set of familiar numbers (0, 1, 2, 3, 4, & so on) sometimes called natural numbers or counting numbers. When they are said to be as counting numbers but zero is not included.

An integer equal to or greater than zero; one of the numbers 0,1,2,3…

The term whole number is 1 that you’ll find often in mathematics. You may also see the natural number or term integer used in the same manner. Essentially the meaning of a whole number is based around what it doesn’t contain. A whole number can’t be a fraction of a number, a percentage, or have a decimal. If you have a number like 21.32, it has a whole number portion (21). But in itself & this number is not a whole number because it includes a fraction (.32).

Natural numbers also referred to as counting numbers. They’re really the first numbers student learn. They include zero, though it has some distinctive properties, & every number that is not fractional below & above zero. The sequence 1, 2, 3, 4… is a whole number sequence. Similarly 0, -1, -2, -3, -4 are natural numbers.

In our next blog we shall learn about zero product property I hope the above explanation was useful.Keep reading and leave your comments.

4 grade math

2010-08-25T03:19:00.000-07:00

Let us learn about "The 4 grade math Board Games Book"

The 4 grade math Board Games Book provides a great selection of math games specially for kids for instant use by tutor, parents & home schoolers. Colorful boards give a selection of 32 different games covering addition, multiplication, subtraction, fractions, decimals & much more & also free bonus puzzles with every book.

The 4 grade math problem is that kids aren't really interested in doing the same thing again & again until they get good at it. Therefore, tutors & parents need to be clever when it comes to getting kids to practice math problems. That's why tutors created a new book that gives kids math practice the fun way.

In our next blog we shall learn about fraction adding I hope the above explanation was useful.Keep reading and leave your comments.

algebraic expressions worksheets

2010-08-24T03:28:00.000-07:00

Let us learn about algebraic expressions worksheets

A algebraic expressions worksheets is a sheet of paper, or on a computer, on that problems are worked out or solved and answers recorded. A algebraic expressions worksheets of document used for keeping a proof of work done or scheduled

A algebraic expressions worksheets of paper used for making a rough plan or preliminary notes. Tutors should feel free to use & distribute our materials for educational purposes, so long as the copyright & footer information are left intact. Students will often use algebraic expressions worksheets to review what has been taught in class. A algebraic expressions worksheets generator is a software program that generates problems, particularly in mathematics. Such software is often used by tutors to make classroom materials & tests. A algebraic expressions worksheets t of paper on which work records are kept. A algebraic expressions worksheets t of paper on which preliminary notes or computations are set down.

Simplify the expression

2(a -3) + 4b - 2(a -b -3) + 5

2a-6+4b-2a+2b+6

Combining like terms

2a-2a+4b+2b+6-6

=6b

In our next blog we shall learn about a line segment I hope the above explanation was useful.Keep reading and leave your comments.

isosceles triangle

2010-08-18T00:32:00.000-07:00

Hi Friends!!!

Can you identify which is isosceles triangle from given figure.

A triangle in which two sides and two angles are equal is called an isosceles triangle.

The base of the triangle is always its unequal side. Base angles of triangle are in equal measurement. Here, angles ∠ABC and ∠ACB are often the same. 3rd angle should be a 90^o known as "right isosceles triangle". Perpendicular length between topmost vertex & base = Altitude

Learn to construct isosceles triangle as shown in figure.

In our next blog we shall learn about animalia I hope the above explanation was useful.Keep reading and leave your comments.

decimal to fraction calculator

2010-08-17T02:25:00.000-07:00

Hi Friends!!!

How many of you like using calculator? Even a hardest math problem can be easily solved using calculator.

Now let us solve problem on decimal to fraction calculator

Change 0.20 using decimal to fraction calculator.

Correspond 0.20 as a Fraction, except to the decimal attempt of the symbol, the .20, means.

Since there are 2 digits in 20, the really finish figure is the "100th" decimal base.

So we can conscionable say that .20 is the equal as 20/100.

The fraction 20/100 is not low to minimal status. We can bound these fractions to minimal position by segmented on both the numerator and denominator by 20.

20 is the Greatest Common Factor and Greatest Common Divisor of the numbers 20 and 100.

So, this fraction low to worst cost is 1/5

Answer: 0.20 can be written as,

The fraction = 1/5.

In our next blog we shall learn about nucleoplasm I hope the above explanation was useful.Keep reading and leave your comments.

Area of the Quadrilateral

2010-08-16T00:02:00.000-07:00

Let us learn how to find the area of a quadrilateral.

A quadrilateral is a polygon with four sides. the parts of a quadrilateral are its sides, its four angles, and its two diagonals. a diagonal is a straight line joining two alter ac and db are the diagonals. the area of a quadrilateral can be found by dividing it into triangles and summing the areas of the triangles. however, the altitudes of the triangles are usually difficult to calculate un- less the quadrilateral has at least one pair of parallel sides.

how to find the area of a quadrilateral ?

calculate the area of a quadrilateral: a diagonal of a quadrilateral is 10m and perpendiculars to the opposite vertices are 9.5 m and 12 m. find the area of the quadrilateral.

area of a quadrilateral problems: d = 10m, h₁ = 9.5 m, h₂= 11m

a = 1/2 d (h₁ + h ₂)

=1/2x 10 x (9.5 + 12)

= 5 x 21.5

= 107.5 sq. m

area of quadrilateral = 107.5. sq m.

I hope the above explanation was useful.Keep reading and leave your comments.

online homework help free

2010-08-14T04:15:00.000-07:00

Hi Friends!!!

Don't cry my friend, there are many website which provides you online homework help free. Why can't you try instead of crying.

You can get free homework help from expert tutors. who are expert in free homework help.

Now a day we can education in fraction of second. Online tutoring made this possible for every learner to learn, to extract knowledge with a minute. So students never get frustrate and boor from studies. Try to utilize available help from online tutors. You can find many online subject tutors like geometry tutor, trigonometry tutor, calculus tutor, math tutor, Pre algebra tutor, algebra tutor, statistics tutor, precalculus tutor so on.

I hope the above explanation was useful.Keep reading and leave your comments.

Mathematics truth

2010-08-13T05:16:00.000-07:00

Welcome to free math tutor online,
Let me put it another way. There are two kinds of truth; I'll call
them mathematical truth and real-world truth. Mathematical truth means
that a statement is consistent with the assumptions of a particular
mathematical system. examples on math forum; In a sense, people created that system, and they
can tell absolutely whether the statement is true within that system.

(However, Kurt Goedel threw a monkeywrench in the works earlier in
this century. He proved that any sufficiently rich mathematical system
must include statements that are true but that cannot be proved within
that system. We can't tell what these statements might be. This is
mind-boggling!) read more on math tutors online.

Math construction

2010-08-13T02:48:00.000-07:00

Welcome to math tutor online free,
This is a very clever construction to solve what seems to be a simple problem. One would like simply to slide the line BC along so that one end coincides with the point A. But there is no motion in the geometry of Euclid. There is something like motion used in proposition I.4, but nothing is actually moved there. The only basic constructions that Euclid allows are those described in Postulates 1, 2, and 3. more examples on online math forum; Euclid then builds new constructions (such as the one in this proposition) out of previously described constructions. So at this point, the only constructions available are those of the three postulates and the construction in proposition I.1, and Euclid uses all four here.

Another, different, expectation is that one might use a compass to transfer the distance BC over to the point A. It is clear from Euclid's use of postulate 3 that the point to be used for the center and a point that will be on the circumference must be constructed before applying the postulate; postulate 3 is not used to transfer distance. Sometimes postulate 3 is likened to a collapsing compass, that is, when the compass is lifted off the drawing surface, it collapses. read more on math forum.

Math axioms

2010-08-13T02:18:00.000-07:00

Welcome to online math tutor,
These common notions, sometimes called axioms, refer to magnitudes of one kind. The various kinds of magnitudes that occur in the Elements include lines, angles, plane figures, and solid figures. The first Common Notion could be applied to plane figures to say, for instance, that if a triangle equals a rectangle, and the rectangle equals a square, then the triangle also equals the square. examples on math forum; Magnitudes of the same kind can be compared and added, but magnitudes of different kinds cannot. For instance, a line cannot be added to a rectangle, nor can an angle be compared to a pentagon.

On the face of it, it seems to say that if two things are identical (that is, they are the same one), then they are equal, in other words, anything equals itself. But the way it traditionally is interpreted is as a justification of a principle of superposition, which is used, for instance, in proposition. Using this principle, if one thing can be moved to coincide with another, then they are equal. more examples on online math help.

online statistics help

2010-08-13T01:29:00.000-07:00

Hi Friends!!! Let us learn about online statistics

Statistics is the rhetorical bailiwick of making good use of denotative accumulation relating to groups of individuals or experiments. It deals with all aspects of this, including not only the group, psychotherapy and explanation of such assemblage, but also the intellection of the collecting of collection, in status of the plan of surveys and experiments.

A statistician is someone who is specially shafted versed in the distance of thinking essential for the winning coating of statistical analysis. Of times specified grouping eff gained this experience after play utilize in any of a signal of comic. There is also a discipline titled mathematical statistics, which is involved with the divinatory basis of the soul.

The language statistics can either be singular or descriptor. When it refers to the penalty, "statistics" is single, as in "Statistics is an art." When it refers to quantities deliberate from a set of aggregation, statistics is descriptor, as in "These statistics are dishonorable.

Sir Ronald A. Fisher, he is a father of statistics. He is good statistic tutor during his period and he encouraged free statistics tutoring in order to help students.

In our next blog we shall learn about Pre algebra I hope the above explanation was useful.Keep reading and leave your comments.

Orthogonal in Geometry

2010-08-13T00:20:00.000-07:00

Welcome to online math tutor,

The word "orthogonal" is frequently used in mathematics as a synonym for "perpendicular."

This is the first mention in the Elements of magnitudes being equal. There are several different kinds of magnitudes in the Elements besides angles. examples on math forum; Lines, plane figures, and solids are also kinds of magnitudes. Some of the assumptions about magnitudes are stated later as "common notions" C.N., which are often called "axioms."

One thing that magnitudes of the same kind can be is "equal," as the angles in this definition can be. Nowhere does Euclid explicitly state what it means for angles to be equal, or for that matter, for lines, plane figures, or solids to be equal, although much can be determined by the way he uses equality. more examples on online math forum.

Straight line element

2010-08-12T23:46:00.000-07:00

Greetings from online math tutoring,

This statement indicates, at least, that the term "straight line" refers to a kind of line. It is hard to tell what else it means, if anything. find more examples on math forum;Various commentators have interpreted in a variety of ways. The definition of plane surface in I.Def.7 uses a similar language that is equally opaque.

There are a some postulates that come a little later in Book I and give meaning to straight lines. I.Post.1 says that a straight line can be drawn between any two points, I.Post.2 says that a straight line can be extended, and the remaining postulates use the concept of straight line in one way or another. more help on math tutors online.

Undefined terms

2010-08-12T23:01:00.000-07:00

Welcome to math tutor online for free,

Math in itself is not intrinsically connected to the real world. It is
possible, and perfectly okay, to develop a mathematical system that
doesn't relate to anything in the real world. online math forum; It is, as you say,
necessary to have "undefined terms" describing entities in the system,
and "postulates" (unproven facts relating those entities).

But these
are not so much matters of faith as "rules of the game." They are
rules that we must adhere to if we are going to prove theorems within
the particular mathematical system. read more on math forum.

Millenium years

2010-08-12T22:19:00.000-07:00

Welcome to free math tutor,
The problems with that are numerous. First, since our years are
actually enumerated as "the 1999th year of our lord," it seems we
actually started counting at the year 1, i.e. "the first year of our
lord." That's essentially the argument of people who say the
millennium begins next year.

Did we actually start counting like this, from the year 1? Of course
not - the present-day Gregorian calendar, which is reasonably accurate
and reliable, wasn't adopted until the year 1582 AD (for
English-speaking countries). examples on math forum; Before that, people used the Julian
calendar, which had been in use since about 4 A.D. and was
recalibrated in about 527 A.D. to count years from the birth of
Christ. Previously it counted from the founding of the Roman Empire.
To perform this recalibration Roman scholars did the best they could,
but modern scholars seem to think they were off by a few years.
more examples on free math help.

pre algebra homework online

2010-08-12T00:14:00.000-07:00

Our topic for today is pre algebra homework online

Pre algebra is a branch of mathematics. Pre algebra covers everything in our day to day life. Pre algebra homework help covers the four basic operations such as addition, subtraction, multiplication and division. Pre algebra homework help covers the most important terms, such as variables, constant, coefficients, exponents, terms and expressions. Also Pre algebra homework help teach us to use the symbols and alphabets in the place of unknown values, to create the expressions and equations. Therefore, students are getting Pre algebra homework help very interactively and efficiently.

Example Problems - online pre algebra homework

Example 1:

Solve the equation x + 232 = 235 for x.

Solution:

x + 232 = 25 (add -232 on both sides. So we get,)

x + 232 – 232 = 235 – 232

x = 3

In our next blog we shall learn about pre algebra homework I hope the above explanation was useful.Keep reading and leave your comments.

breadth definition

2010-08-11T01:28:00.000-07:00

Let us learn about breadth definition

Length may be distinguished from height which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length. Breadth is one of the dimention used to measure a object. We will use this dimension in rectangle alone. While we make any piece of something we have to consider the breadth.We will know about definition of breadth and some worked example corresponding to bredth.

Breadth definition:

From this diagram the breadth is the plane from one side to another side .And it will be measured perpendicular to length.

Example Problem to Kno about Breadth

Worked example:

Area of rectangle:

In rectangle two opposite sides are equal .Those two sides are called length,breath.To find out the area of rectangle multiply the length and breadth

Area of rectangle= lengthX Breadth

In our next blog we shall learn about balancing chemical equations practice I hope the above explanation was useful.Keep reading and leave your

mathematicians math

2010-08-09T23:30:00.000-07:00

Welcome to math tutors online,

Mathematicians don't do mathematics because they get paid to do
it, or because they think it will somehow be useful. examples on free math; In almost every
case, they are motivated by one of two things: fun or beauty.

I know that can be hard to believe, given the way math classes are normally
taught in schools, but it's true, and just what makes mathematics fun
and beautiful is the kind of thing that you can learn by reading
biographies.

Learn more on online math forum.

Real world math problems

2010-08-09T22:21:00.000-07:00

Welcome to math tutors online,
While we're on the topic, there's another point that I think is
important to make, which concerns the popular idea that mathematics
should be made 'relevant' by showing how it can be used to solve 'real
world' problems.

If I take some silkworms and put them in a warm place with plenty of
mulberry leaves to eat and no predators to eat them, they'll make
silk. Now, I can take that silk and use it to make all kinds of
things - scarves, boxer shorts, surgical thread, parachutes, or
whatever - but the silkworms don't care about any of that. They make
silk because it's what they know how to do.
If you need more help in math go through math forum.

Math freeze on tests

2010-08-09T21:53:00.000-07:00

Greetings from math tutors online,
As for why kids so often "freeze on tests," my own feeling is that
it's because they aren't fooled at all by the pretense that the tests
are being given to help them figure out what they need to learn.
Adults deny it, but kids know that every test is another opportunity
for society to decide who is going to end up on top, and who isn't.

math online tutors ; Tests are competitions, kids know that, and so they freeze - for
exactly the same reason that they'd freeze if they were forced to do
something trivially easy (like toss a piece of paper into a trash can
five feet away), with the promise that they'd be flogged in public for
screwing up. learn more on online math forum.

What is Math

2010-08-06T00:18:00.000-07:00

Welcome to free math help online,

Mathematics is normally called as "math" or "maths". It is the lessons for learning patterns, numbers, and shapes.

The four basic operation of help in math are Addition, subtraction, multiplication or repetitive addition and division or repetitive subtraction. The main branches of mathematics are algebra, geometry and calculus, precalculus, prealgebra.

In this piece of writing, we are going to see some solved and practice problems in math forum.

area of a quadrilateral

2010-08-05T23:34:00.000-07:00

Let us learn about area of a quadrilateral

A quadrilateral is a polygon with four sides. The parts of a quadrilateral are its four sides, its four angles, and its two diagonals. In ABCD quadrilateral diagonal is a straight line joining two alters AC and DB are the diagonals. Area is usually measured in square units such as square inches, square feet or square meters.

Formula for Finding Area of Triangle and Quadrilateral

Formula for area of triangle:

Area of triangle is the base times of height by two.

Area of each triangle =1/2 (base × height)

Area of Quadrilateral: If two sides of the quadrilateral are not parallel, you need to calculate the area of a quadrilateral then here is the formula:

1) Area = Square Root of {(s-a) (s-b) (s-c) (s-d) -1/4(ac+bd+pq) (ac+bd-pq)}

Where a,b,c and d are the four sides of the quadrilateral with a and c and b and d as the opposite sides, p and q are diagonals, and s = (a+b+c+d)/2.

The quadrilateral is dividing it into two triangles and summing the areas of the triangles.

2) The area of the quadrilateral ABCD = Area of ABD + area of BDC

= ½ x base x altitude + ½ x base x altitude

=1/2 d (h1 x h2)

In our next blog we shall learn about analogy example I hope the above explanation was useful.Keep reading and leave your

factors of 60

2010-08-05T00:31:00.000-07:00

The factors of 60 are 1, 3, 5, 6, 21, and 60.

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization.

In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x² − 4 factors as (x − 2) (x + 2). In all cases, a product of simpler objects is obtained.

In our next blog we shall learn about "linear programming examples" I hope the above explanation was useful.Keep reading and leave your comments.

linear algebra tutorial

2010-07-31T04:03:00.000-07:00

Let us learn about linear algebra

Linear algebra is a division of math concerned with learns of vectors, with families of vectors recognized vector spaces and by purpose to input one vector also output another, according to definite rules. These functions are identified linear chart and are frequently signify by matrices. Linear algebra is essential to made easy for modern math and its applications. If you are interested in linear algebra tutorial then click on the given link.

An elementary function of linear algebra is to the resolution of systems of linear equations in some indefinite. More difficult applications are everywhere, in areas as different as abstract algebra and efficient analysis. Linear algebra has an existing representation in systematic geometry and made easy for common in operator theory. It has wide applications in the usual math. Nonlinear arithmetical form can frequently be approximated through linear ones.

Linear Equations - Linear Algebra in three Dimensions:

The following are the linear equations types from linear algebra in three dimensions.

System of linear equations
Determinant
Minor
Cauchy-Binet formula
Cramer's rule
Gaussian elimination
Gauss-Jordan elimination
Strassen algorithm.

In our next blog we shall learn about power rule

I hope the above explanation was useful.Keep reading and leave your comments.

coordinate plane graph paper

2010-07-26T02:53:00.000-07:00

Let us learn about "coordinate plane graph paper"

A graph is a stylized picture. It shows how a first set of numbers is acted upon by a rule to create a second set of numbers. Just as the Impressionists used points to paint a picture, mathematicians use points to produce their graph. Though an Impressionists' points blurr to create the picture, the mathematician's points are drawn as accurately as possible. A mathematician's blank canvas is a coordinate plane.

In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links.

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

Student should always have touch math worksheets and it will help students learn better.

I hope the above explanation was useful.Keep reading and leave your comments.

Learn Multiplication Tables

2010-07-23T22:22:00.000-07:00

In this session let us study about multiplication tables,

Multiplication is the arithmetical operation of calculating one value with another value. This is a one kind of operations in basic arithmetic. Multiplication is nothing but the repeated addition. For example: 7 x 7 = 49, so it represents 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49, therefore for adding the number 7 simultaneously 7 times. Multiplying bigger numbers like 6589 x 54 is a bit difficult than the simpler one. Now we are going to see how to multiply big numbers.
Multiplication Table.

By using the multiplication table, it will be easy for us to solve big numbers. The multiplication table is

I hope the above explanation was useful, now let me explain Sector formula

Factors of 35

2010-07-21T23:50:00.000-07:00

Hi Friends, Good Afternoon!!!

In our previous blog we learned about Factors of 28.

Like concepts presented throughout the Montessori classroom, even those more abstract concepts of Mathematics have been made concrete for the children in our classrooms. Beginning with simple number concepts like understanding quantity and identifying numerals, the Math materials include advanced presentations in cubing numbers, factors, fractions, and mathematical operations.

Factor Tree can be started by taking Different factors . The factor trees can be different but we will see that the Prime Factorization will remain same.

Find the prime factor of 35.

Solution:-

The given number is 35 we need to find the prime factor of the 35

Step 1:-

Divide the given number by 5.

35/5 = 7 remainder (0).

7 is one of the prime factors of 35.

Step 2:-

The answer in the last step is 5, is a prime number.Therefore, 5 is also one of the prime factors.The prime factorization of 35 is 5.

I hope the above explanation was useful.Keep reading and leave your comments.

What are the law of exponents

2010-07-21T22:28:00.000-07:00

Let us study about Law of exponents,

The following laws of exponents.

Law 1 a^m * aⁿ= a^(m+n)
Law 2 ( a^m)ⁿ = a^mn
Law 3 (ab)^m = a^m b^m
Law 4 = a^m-n
Law 5 a⁰ = 1.
Law 6 a¹ =a

All exponents operations are executed only by using the above laws.

I hope the above explanation was useful, now let us study about trigonometric table.

Formula for volume of a cylinder

2010-07-21T04:07:00.001-07:00

Hi Friends, Good Afternoon!!!

Let us learn about "Formula for volume of a cylinder"

The cylinder has two parallel faces in its structure. The height of the cylinder is perpendicular to the two bases. The cylinder has a round base and a perpendicular height. First we have to Multiply pi and the constants. Then multiply the constant values with the given height of the cylinder. The volume of the cylinder formula depends on the area of the cylinder. The formula for surface area of the cylinder can be written as,

Surface area of cylinder = 2 *pi * r² + 2 * pi * r * h

Volume of Cylinder (formula)

The formula for volume of the cylinder depends on the area of the cylinder. The area of the cylinder can be written as, A = pi * r². Here, pi is the constant value and r is the radius of the cylinder. To find the volume of the cylinder we have to multiply the height of the cylinder to the area of the cylinder. The formula for the volume of cylinder can be written as,

Volume of cylinder = pi * r² * h.

Here, pi is the constant variable, r is the radius of the cylinder and h is the height of the cylinder. The constant variable pi is equal to (22 / 7) or 3.14.

Note: A cylinder looks like a round pipe. A new pencil, electric poles are examples of a cylinder.

A cylinder has 3 faces, 1curved face and 2 flat faces. It has 2 curved edges.

In our next blog we shall learn about " exponential form"

I hope the above explanation was useful.Keep reading and leave your comments.

Define Vertices

2010-07-20T04:35:00.000-07:00

Let us study about Vertices definition,

Vertices in general refer to the point where two line segments meet. It is also defined as the point where two sides meet. It is like corners in 2D and 3D shapes. Vertices are the plural form of the word vertex. It is available only in shapes. It is not available in circle and oval. The vertex forms an angle since it is the meeting point of two lines or sides. And the angle is called as interior angle, so vertex got the name as corner point of angle.

Definition of Vertices:

The plural of vertex is also known as vertices. The vertex is defined as the point of intersection of lines or the point opposite the base of the figure. A point two or more straight lines intersect each other. Basically it means corner or points where meet lines. The square has four corners. Each corner is called as vertex of the square.

I hope the above explanation was useful, now let me help with Integer definition.

Integrated Algebra Regents

2010-07-19T03:08:00.000-07:00

Hi Friends, Good Afternoon!!!

Let us learn about "integrated algebra regents"

Introduction to Integrated algebra regents 2010 Examination:

The integrated algebra includes the fundamental concepts of algebra like simple expressions , linear equations, rational and radical expresssions. Algebra, Geometry, and Trigonometry are included in the parts of integrated algebra regents examination. The integrated algebra regents exam gives the clear idea of solving different types of questions.

Integrated Algebra Regents 2010 Examination 1:

Integrated algebra regents question 1:

Given:
Q = {0, 1, 2, 4, 6}
W = {0, 1, 2, 3}
Z = {1, 2, 3, 4}
What is the intersection of sets Q, W, and Z?
(1) {1, 2} (3) {1, 2, 3}
(2) {0, 2} (4) {0, 1, 2, 3, 4, 6}

Integrated Algebra Regents: Integrated Algebra II and Trigonometry are the part of papers of Global Regents examination is held in New York State after two year Global History and Geography course.

If you like to learn about "trigonometry table" click on given link.

If students want to get brief information about Integrated Algebra Regents then please click on links given above.

Introduction to Interquartile range

2010-07-17T03:11:00.000-07:00

Introduction to interquartile range for a given set of date:

The range is the smallest of all the measures of dispersion. It is defined as the difference between the two extreme observation of the distribution. In other words, range is the difference between the greatest ( maximum ) and the smallest (minimum) observation of the distribution.

Range = Xmax - Xmin

Where Xmax is the greatest observation and Xmin is the smallest observation of the variable values.

In case of the grouped frequency distribution or the continuous frequency distribution, range is defined as the difference between the upper limit of the higher class and the lower limit of the smallest class.

I hope the above explanation helped you...

Multiplication of Two Binomials

2010-07-15T02:17:00.000-07:00

my dear friends...i enjoy writing for you guys everyday and therefore i just think of the topics that i can share with all of you. Let us learn about "Binomial"

An algebraic expression which contains two terms is called a binomial

Pupils can come out with further examples and Please look in to examples for Binomial

Now let us learn about "Multiplication of Two Binomials"

Rule: Multiply each term of one binomial with each term of Another binomial and simplify by adding the like terms. While multiplying binomial even the signs have to be multiplied.

Example: Find the product of 3a + 7b and 5a + 2b

Solution: Multiplying each term of one binomial with each term of another binomial and adding the like terms, we get:

3a + 7b

X 5a + 2b

15 a² + 35 ab [Multiplying (3a + 7b) by 5a]

+ 6 ab + 14 b² [Multiplying (3a + 7b) by 2b]

15 a² + 41 ab + 14 b² [Adding like terms] [ab=ba]

The product is 15a² + 41 ab + 14b² Answer

How to simplify a radical

2010-07-15T01:50:00.000-07:00

Let us study how to simplify a radial.
A problem like may look difficult because there are no two numbers that multiply together to give 24. However, the problem can be simplified. So even though 24 is not a perfect square, it can be broken down into smaller pieces where one of those pieces might be perfect square. So now we have .

Simplifying a radical expression can also involve variables as well as numbers. Just as you were able to break down a number into its smaller pieces, you can do the same with variables. When the radical is a square root, you should try to have terms raised to an even power (2, 4, 6, 8, etc). When the radical is a cube root, you should try to have terms raised to a power of three (3, 6, 9, 12, etc.). For example

I hope the above explanation helped you.

Division of a Monomial by a Monimal

2010-07-15T00:43:00.000-07:00

Good Afternoon!!! my dear friends...i enjoy writing for you guys everyday and therefore i just think of the topics that i can share with all of you. Today i have come up with a familiar concept "Division of a Monomial by a Monimal".

Dividing a Monomial by a Monomial:

Steps to be followed are:

Step1: Arrange the monomials in fractional form, keeping

the dividend as numerator and the divisor as

denominator

Step2: Divide numerical coefficients

Step3: Divide literal coefficients

Step4: Divide the signs

(i) + ÷ + = +

(ii) + ÷ - = -

(iii) - ÷ - = +

(iv) - ÷ + = -

Step5: Multiply the results

Example: Divide – 32p²qr³ by - 4pqr

Solution: We have,

– 32 p²qr³ ÷ (- 4pqr)

= – 32p²qr³ [Arranging the monomials in fractional form]

- 4pqr

= 8 p²qr³ [Dividing numerical coefficients and signs]

pqr [- ÷ - = +]

= 8 p r² [Dividing literal coefficients]

= 8pr² [Multiplying the results]

The quotient of – 32 p²qr³ ÷ (- 4pqr) is 8pr² Answer

The example above has the steps mentioned above.Let me know how informative you found this post and if you want to share some ideas let me know.

How to do ratios

2010-07-15T00:11:00.000-07:00

Let us study how to do ratios,
A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12.
We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

Examples:
Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange.

1) What is the ratio of books to marbles?
Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 7/4.
Two other ways of writing the ratio are 7 to 4, and 7:4.

2) What is the ratio of videocassettes to the total number of items in the bag?
There are 3 videocassettes, and 3 + 4 + 7 + 1 = 15 items total.
The answer can be expressed as 3/15, 3 to 15, or 3:15.

I hope the above explanation was useful.

slope of a line

2010-07-12T22:17:00.000-07:00

Let us study about Slope of a line,

The slope of a line is the ratio of the change in y over the change in x.

Simply put, find the difference of both the y and x coordinates and place them in a ratio.
Pick two points on the line. Because you are using two sets of ordered pairs both having x and y values, a subscript must be used to distinguish between the two values.

This is the formula for finding the slope of a line.
m is the variable used for the slope.

I hope the above explanation was useful.

Pie Chart

2010-07-07T02:17:00.000-07:00

Let us study about Pie chart,
If knowing about a “part of the whole” is an important consideration, then a pie chart is a good choice for showing particular data. A pie chart may also display each category's percentage of the total. Using data from Table 1 , we get the pie chart shown in Figure 1 .

Figure 1

Pie chart presentation of the expenditures of a college undergraduate for the past year.

The parts of the circle (or pie) match in size each category's percentage of the total. The parts of the pie chart are ordered from highest to lowest for easier interpretation of the data. Pie charts work best with only a few categories; too many categories will make a pie chart confusing.
I hope the above explanation was helpful.

Proper Fraction

2010-07-01T03:14:00.000-07:00

Let Us Learn About Proper Fraction

If the numerator of the fraction is less than its denominator then such a fraction is called a proper fraction.

for example 3/4, 7/12, 15/23, 71/100........

The base number has always been larger than the top number. The top number, which tells you how many part you have, is called the numerator. The base number, which tells you how many equal part the strip is divided into, is called the denominator. If the top number is lesser than the bottom number we always have what is called a proper fraction. Proper fraction are always less than one value.

Example for Proper Fraction: we multiply the given proper fraction numbers 5/6 and 3/4?

Sol : Step1: we take this problem multiply the given values

Step2: proper fraction multiplication method just multiply the values directly

Step3: 5/6 x ¾

Step4: finally we get the answer for this problem

= 5/6 x 3/4

= 15/24

We divide 3 on both sides

= 5/8

In our next Blog we shall learn about Improper Fraction

Keep reading and leave your comments.

Functions of Acute Angles

2010-06-27T22:10:00.000-07:00

Let us study about Acute angles,
The characteristics of similar triangles, originally formulated by Euclid, are the building blocks of trigonometry. Euclid's theorems state if two angles of one triangle have the same measure as two angles of another triangle, then the two triangles are similar. Also, in similar triangles, angle measure and ratios of corresponding sides are preserved. Because all right triangles contain a 90° angle, all right triangles that contain another angle of equal measure must be similar. Therefore, the ratio of the corresponding sides of these triangles must be equal in value. These relationships lead to the trigonometric ratios. Lowercase Greek letters are usually used to name angle measures. It doesn't matter which letter is used, but two that are used quite often are alpha (α) and theta (θ).

Angles can be measured in one of two units: degrees or radians. The relationship between these two measures may be expressed as follows:

The following ratios are defined using a circle with the equation x2 + y2 = r2 and refer to Figure 1 .

Figure 1

Reference triangles.

Hope the above explanation helped you.

Explain Line segment

2010-06-17T05:06:00.000-07:00

Let us learn about Line Segment,

A line segment is a connected piece of a line. It has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment. This is line segment CD (Figure 1).

Figure 1

Line segment.

It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.) Note that CD is a piece of .

Postulate 7 (Ruler Postulate): Each point on a line can be paired with exactly one real number called its coordinate. The distance between two points is the positive difference of their coordinates (Figure 2).

Figure 2

Distance between two points.

Hope the above explanation helped you.

Define complex number

2010-06-17T03:30:00.000-07:00

Let us learn about complex numbers,
A complex number z can be expressed as:

Where,
is the imaginary unit. Both x and y are real numbers. They are called the real and imaginary parts of z, respectively.

The complex number z can also be expressed in exponential and polar forms:

where,

In the above equations, r is called the modulus of z and teta is the argument or phase angle of z. It can easily be shown that:

Hope the above explanation helped you.

Definition of Trigonometry

2010-06-11T03:22:00.000-07:00

Let us understand what is Trignometry,
Definition of Trigonometry: Trigonometry considers the properties of angles and certain ratios associated with angles, and applies the knowledge of these properties to the solution of triangles and various other algebraic and geometric problems. Incidentally trigonometry considers also certain time-saving aids in computation such as logarithms, which are generally employed in the solution of triangles. Briefly stated,

Trigonometry is the science of angular magnitudes and the art of applying the principles of this science to the solution of problems.

The word Trigonometry comes from two Greek words, trigonon = triangle, and metron = measure. The method was originated in the second century B.C. by Hipparchus and other early Greek astronomers in their attempts to solve certain spherical triangles. The term trigonometry was not used until the close of the sixteenth century.

Before we get into the basic definitions of Trigonometric Functions, let us look at the basic definition of a function.
Hope the above explanation helped you..

Tangent to a Circle

2010-06-08T02:22:00.000-07:00

To understand the existence of the tangent to a circle at a point, let us perform
the following activity:

Activity : Take a circular wire and attach a straight wire AB at a point P of the
circular wire so that it can rotate about the point P in a plane. Put the system on a table
and gently rotate the wire AB about the point P to get different positions of the straight
wire [see Fig.].
In various positions, the wire intersects the
circular wire at P and at another point Q1 or Q2 or
Q3, etc. In one position, you will see that it will
intersect the circle at the point P only (see position
A′B′ of AB). This shows that a tangent exists at
the point P of the circle. On rotating further, you
can observe that in all other positions of AB, it will
intersect the circle at P and at another point, say R1
or R2 or R3, etc. So, you can observe that there is
only one tangent at a point of the circle.
Hope the above explanation helped you, now let us learn about line intersecting circle.

Math Relations

2010-06-04T04:46:00.000-07:00

Let us learn about math relations,
Consider the two sets P = {a, b, c} and Q = {Ali, Bhanu, Binoy, Chandra, Divya}.
The cartesian product of
P and Q has 15 ordered pairs which
can be listed as P × Q = {(a, Ali),
(a,Bhanu), (a, Binoy), ..., (c, Divya)}.
We can now obtain a subset of
P × Q by introducing a relation R
between the first element x and the
second element y of each ordered pair
(x, y) as
R= { (x,y): x is the first letter of the name y, x ∈ P, y ∈ Q}.
Then R = {(a, Ali), (b, Bhanu), (b, Binoy), (c, Chandra)}
A visual representation of this relation R (called an arrow diagram) is shown
in Fig.
Definition 2 A relation R from a non-empty set A to a non-empty set B is a subset of
the cartesian product A × B. The subset is derived by describing a relationship between
the first element and the second element of the ordered pairs in A × B. The second
element is called the image of the first element.
Definition 3 The set of all first elements of the ordered pairs in a relation R from a set
A to a set B is called the domain of the relation R.
Definition 4 The set of all second elements in a relation R from a set A to a set B is
called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range ⊆ codomain.
Hope the explanation helped you, now let me explain about math functions.

Cartesian Products of Sets

2010-06-04T03:46:00.000-07:00

Let me explain about Cartesian Products of Sets,
Suppose A is a set of 2 colours and B is a set of 3 objects, i.e.,
A = {red, blue}and B = {b, c, s},
where b, c and s represent a particular bag, coat and shirt, respectively.
How many pairs of coloured objects can be made from these two sets?
Proceeding in a very orderly manner, we can see that there will be 6
distinct pairs as given below:
(red, b), (red, c), (red, s), (blue, b), (blue, c), (blue, s).
Thus, we get 6 distinct objects (Fig).
Let us recall from our earlier classes that an ordered pair of elements
taken from any two sets P and Q is a pair of elements written in small
brackets and grouped together in a particular order, i.e., (p,q), p ∈ P and q ∈ Q . This
leads to the following definition:
Given two non-empty sets P and Q. The cartesian product P × Q is the
set of all ordered pairs of elements from P and Q, i.e.,
P × Q = { (p,q) : p ∈ P, q ∈ Q }
If either P or Q is the null set, then P × Q will also be empty set, i.e., P × Q = φ
From the illustration given above we note that
A × B = {(red,b), (red,c), (red,s), (blue,b), (blue,c), (blue,s)}.
Again, consider the two sets:
A = {DL, MP, KA}, where DL, MP, KA represent Delhi,
Madhya Pradesh and Karnataka, respectively and B = {01,02,
03}representing codes for the licence plates of vehicles issued
by DL, MP and KA .
Hope the above explanation helped you, now let me explain on Basic property of Cartesian Products.

Distance between Two Points

2010-06-04T02:50:00.000-07:00

Let us learn about Distance between Two Points in three-dimensional system.

Let P(x1, y1, z1) and Q ( x2, y2, z2)
be two points referred to a system of
rectangular axes OX, OY and OZ.
Through the points P and Q draw planes
parallel to the coordinate planes so as to
form a rectangular parallelopiped with one
diagonal PQ.
Now, since ∠PAQ is a right
angle, it follows that, in triangle PAQ,
PQ2 = PA2 + AQ2 ... (1)
Also, triangle ANQ is right angled triangle with ∠ANQ a right angle.
Therefore AQ2 = AN2 + NQ2
... (2)
From (1) and (2), we have
PQ2 = PA2 + AN2 + NQ2
Now PA = y2 – y1, AN = x2 – x1 and NQ = z2 – z1
Hence PQ2 = (x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2

Therefore PQ = This gives us the distance between two points (x1, y1, z1) and (x2, y2, z2).

In particular, if x1 = y1 = z1 = 0, i.e., point P is origin O, then OQ =

which gives the distance between the origin O and any point Q (x2, y2, z2).
Hope the above explanation helped you, now let me explain you to find Distance in graph.

Area of a Triangle

2010-06-02T04:49:00.000-07:00

Let us learn about Area of a Triangle.

First of all let us understand what is Area of a Triangle ?

Let ABC be any triangle whose vertices are A(x1, y1), B(x2, y2) and C(x3, y3). Draw AP, BQ and CR perpendiculars from A, B and C, respectively, to the x-axis. Clearly ABQP, APRC and BQRC are all trapezia
Now, from Fig. it is clear that
area of Δ ABC = area of trapezium ABQP + area of trapezium APRC
– area of trapezium BQRC.
You also know that the
area of a trapezium = 1/2 (sum of parallel sides)(distance between them)
Therefore,

Thus, the area of Δ ABC is the numerical value of the expression
Hope the above explanation is clear about area of a triangle.

Distance Formula

2010-06-02T03:23:00.000-07:00

Let me explain Distance Formula with an example,
Let us consider the following situation:
A town B is located 36 km east and 15
km north of the town A. How would you find
the distance from town A to town B without
actually measuring it. Let us see. This situation
can be represented graphically as shown in
Fig. You may use the Pythagoras Theorem
to calculate this distance.
Now, suppose two points lie on the x-axis.
Can we find the distance between them? For
instance, consider two points A(4, 0) and B(6, 0)
in Fig. The points A and B lie on the x-axis.
From the figure you can see that OA = 4
units and OB = 6 units.
Therefore, the distance of B from A, i.e.,
AB = OB – OA = 6 – 4 = 2 units.
So, if two points lie on the x-axis, we can
easily find the distance between them.
Now, suppose we take two points lying on
the y-axis. Can you find the distance between
them. If the points C(0, 3) and D(0, 8) lie on the
y-axis, similarly we find that CD = 8 – 3 = 5 units
(see Fig.).
Next, can you find the distance of A from C (in Fig.)? Since OA = 4 units and
OC = 3 units, the distance of A from C, i.e., AC = 32+42 = 5 units. Similarly, you can
find the distance of B from D = BD = 10 units.
Hope the above explanation helped you to know about Distance Formula.

Sequences

2010-06-01T03:30:00.000-07:00

First let me explain sequences with an example

Let us consider the following examples:
Assume that there is a generation gap of 30 years, we are asked to find the
number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person
might have over 300 years.

Here, the total number of generations
The number of person’s ancestors for the first, second, third, …, tenth generations are
2, 4, 8, 16, 32, …, 1024. These numbers form what we call a sequence.

Now let me give more examples and explain types of sequences.

Inequalities

2010-06-01T02:11:00.000-07:00

Let us learn about Inequalities.

First of all let us understand what is Inequalities ?
A number a is greater than a number b if a−b is positive. In symbols
this is written as a > b.
Thus 2 > 1 because 2 − 1 = 1 is positive,
3 > −1 because 3 − (−1) = 4 is positive,
BUT −1 > 2 is false because −1 − 2 = −3 is negative.
Example 1 Prove or disprove the following inequalities.

(a)

(b)

Solution :

(a) As a decimal, 1/4 = 0.25 and so 0.4 − 1/4 = 0.4 − 0.25 = 0.15,
which is positive. Thus 0.4 > 1/4 is true.
(b) Here (0.7)2 = 0.7 × 0.7 = 0.49. As a fraction 1/2 is 0.5. In this
case, (0.7)2−1/2 = 0.49−0.5 = −0.01, which is negative. This means
that the inequality (0.7)2 > 1/2 is false.

Hope the above explanation helped you, now let me give you more examples.

Quadratic Equations

2010-05-24T00:18:00.000-07:00

Questions on Quadratic Equations

Let us learn about Quadratic Equations.

First of all let us understand what is Quadratic Equations?

Quadratic equation is an equation with second degree. It has to possible results. The roots of the quadratic equation are as follows,

   - b + √(b² -4ac)
X = -------------------
        2a
The solutions of the quadratic equation ax2 + bx + c = 0, where a, b, c ∈ R,

Let us solve Example on Quadratic Equation which will help us to understand concept better.

Complex Numbers

2010-05-23T22:48:00.000-07:00

Let Us Learn What Is Complex Numbers?

Complex Numbers: Let us denote −1 by the symbol i. Then, we have i2 = −1 . This means that i is a solution of the equation x² + 1= 0

A number of the form a + ib, where a and b are real numbers, is called a
complex number, a is called the real part and b is called the imaginary part
of the complex number.

Example for complex numbers as follows.

If x and y are any real numbers, then x+iy is called a complex number.

Various Forms Of The Equation Of A Line

2010-05-21T03:47:00.000-07:00

The general equation of a line can be reduced into various forms of the equation of a line.

The Following are the different forms of the equation of a line.

* Slope-intercept form
* Intercept form
* Normal form

Slope-intercept form If B ≠ 0, then Ax + By + C = 0 can be written as

Intercept form If C ≠ 0, then Ax + By + C = 0 can be written asIf C = 0, then Ax + By + C = 0 can be written as Ax + By = 0, which is a line
passing through the origin and, therefore, has zero intercepts on the axes.

Normal form Let x cos ω + y sin ω = p be the normal form of the line represented
by the equation Ax + By + C = 0 or Ax + By = – C. Thus, both the equations are
same and therefore,

Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.

Horizontal And Vertical Lines

2010-05-21T02:47:00.000-07:00

Let Us Define Horizontal And Vertical Lines

What is Horizontal Line?
A line parallel to x-axis is a horizontal line. In the above figure line y = b is a horizontal line

What is Vertical Line?
A line parallel to y-axis is a vertical line. In the above figure line x = a is a horizontal line

Horizontal and vertical lines If a horizontal line L is at a distance a from the
x-axis then ordinate of every point lying on the line is either a or – a.

Therefore, equation of the line L is either y = a or y = – a.

Choice of sign will depend upon the position of the line according as the line is above or below the y-axis. Similarly, the equation of a vertical line at a distance b from the x-axis is either x = b or x = – b

Straight Line

2010-05-21T01:58:00.000-07:00

Let Us Define What Is Straight Line, Inclination Of The Line, Slope Of Line.

What is Straight Line?
A line in a coordinate plane forms two angles with the x-axis, which are supplementary.

A line traced by a point moved in a same direction then the shortest space among two points is named as straight line
_______________________
What is inclination of the line?
The angle (say) θ made by the line l with positive
direction of x-axis and measured anti clockwise
is called the inclination of the line. Obviously
0° ≤ θ ≤ 180°

We observe that lines parallel to x-axis, or
coinciding with x-axis, have inclination of 0°. The
inclination of a vertical line (parallel to or
coinciding with y-axis) is 90°.

What is slope of line?
If θ is the inclination of a line
l, then tan θ is called the slope or gradient of
the line l.

The slope of a line whose inclination is 90° is not
defined.

The slope of a line is denoted by m.
Thus, m = tan θ, θ ≠ 90°

It may be observed that the slope of x-axis is zero and slope of y-axis is not defined.

Solving Linear Equation using Substitution Method

2010-02-05T01:44:00.000-08:00

Substitution Method is another method of solving any linear equation. To understand much better we shall go through an example and also graphical representation showing how to solve linear equation using substitution method.

Let us Consider the following system of linear equations:
x - y = -2
x - y = 1.

Using the method of substitution, we subtract the second equation from the first to obtain: 0 = -3. This is a false statement and the system, therefore, has no solution. If we look closer at the lines we see that they satisfy the condition

a₁/a₂ = b₁/b₂

and are therefore parallel(as can be shown below). They do not intersect explaining why the system of linear equations has no solution.

What if the two equations represent the same line?

Consider the equations

x - y = 1
2x - 2y = 2

Multiply the first equation by 2 to put the equations in the form
2x - 2y = 2
2x - 2y = 2

Now subtraction gives 0 = 0, which is true no matter what values x and y may have! This time the two equations represent the same line, since both can be written in the form y = x - 1.

Any point on this line has coordinates which will satisfy both equations, so there are an infinite number of solutions!

In general, two equations represent the same line if one equation is a multiple of the other. That is a₁/a₂ = b₁/b₂ = c₁/c₂

There are then three possibilities for a pair of simultaneous linear equations:

(i) Just one solution (the usual situation - both lines are unique and not parallel to each other)
(ii) No solution ( the lines are parallel a₁/a₂ = b₁/b₂)
(iii) Infinitely many solutions (the equations represent the same line, a₁/a₂ = b₁/b₂ = c₁/c₂

Factors and roots of a Equation

2009-12-01T02:35:00.000-08:00

In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.We also have factoring calculator to find factors.

The aim of factorization is usually to reduce something to "basic building blocks," such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.Similarly we can find roots of simultaneous quadratic equations

The opposite of factorization is expansion. This is the process of multiplying together factors to recreate the original, "expanded" polynomial.Let's see equations reducible to quadratic form in the following example.

Question:-

Find the factors and roots for

8x³-12x²-2x+3 = 0

Answer:-

Let us rewrite the equation as

8x³-2x-12x²+3 = 0

by Taking 2x as common from from first 2 terms we get

2x(4x²-1)-12x²+3 = 0

by taking 3 as common from last 2 terms we get

2x(4x²-1)-3(4x²-1)=0

By taking (4x²-1) as common we get

(2x-3)(4x²-1)=0

4x²-1 can be written as (2x+1)(2x-1) using a²-b² formula

(2x-3)(2x-1)(2x+1)=0

So factors are (2x-3)(2x-1)(2x+1)

To find the roots we solve each term separately for x we get

x=3/2,1/2,-1/2 (Roots)

Rules of multiplying Positive and Negative numbers

2009-09-16T00:56:00.000-07:00

Multiplying negative and positive integers can be confusing and frustrating for students. Learning different strategies can help a student to remember the rules and apply what they learned.let's see some rules from number theory tutorial.

Rules of multiplying negative and positive numbers.

we have used prime numbers up to 100 in the following examples.

1)When we have two positive numbers .we multiply them and the answers to math problems
is a positive number

example : 5 x 4 = 20

2)When we have two negative numbers ,we multiply them and product is a positive number

example: -5 x -4 = 20 (not -20)

3)When we have one negative and another positive number,we multiply them and the product is negative

example: -4 x 5 = -20 or 4 x -5 = -20

Many students can memorize the rules with funny sayings or examples. They can think about the positive integers as "good" people and negative integers as "bad" people like criminals.
P x P = P; When GOOD (P) things happen to GOOD (P) people, that's GOOD (P)
N x N = P; When BAD (N) things happen to BAD (N) people, that's GOOD (P)--(It's good when criminals go to jail.)
N X P = N; When BAD (N) things happen to GOOD (P) people, that's BAD (N).
P X N = N; When GOOD (P) things happen to BAD (N) people, that's BAD (N). --(It's bad when criminals can escape.)

Solving the equation by completing the square method

2009-08-25T22:00:00.000-07:00

In elementary algebra practice, completing the square is a technique for converting a quadratic polynomial of the form

to the form

In this context, "constant" means not depending on x. Evaluate the expression inside the parenthesis is of the form (x − constant). Thus one converts ax² + bx + c to

and one must find h and k.

Question:-

Solve the equation by completing the square method

x²-8x+12=0

Answer:-
now we solve this quadratic equation by completing the square method

x²-8x = -12

x²-8x+(8/2)²=(8/2)²-12

x²-8x+16=16-12

(x-4)²=4

taking the square root on both sides,or we can use square root calculator

√(x-4)²=√4

x-4 = ±2

x-4 = +2 or x-4 = -2

x=6 or x=2

so the answers are x=6 or 2

Solving Algebraic Expression using Factorizing Method

2009-08-17T21:40:00.000-07:00

Topic : Factorizing Method

Factorization is an important method of solving any given algebraic expression and finding the roots of a variable in the given equation. Method includes taking out any common factor in the expression.

For example: If you are asked to factorize x² + x,
Since x is a common term we can simplify the given expression as
x (x + 1)

Question: Solve the numeric and algebraic operations
given below


    - 7
--------------
(x - 5)(x + 3)

Answer:


      - 7
= --------------
 (x - 5)(x + 3)

We can factorize the denominator,
x² - 2x -15
- 5 * 3 = - 15
- 5 + 3 = - 2


      - 7
= --------------
 (x - 5)(x + 3)

if x = 5
Then the fraction is -7/0

if x = - 3
Then the fraction is -7/0

The excluded values are x = 5 and x = 3

A word problem on speed

2009-08-11T03:28:00.000-07:00

Speed is the rate of motion, or equivalently the rate of change of distance.

Speed is a scalar quantity with dimensions length/time; the equivalent vector quantity to speed is velocity. Speed is measured in the same physical units of measurement as velocity, but does not contain the element of direction that velocity has. Speed is thus the magnitude component of velocity.

In mathematical notation, if an object traveling at constant speed moves a distance $x$ in time $t$ , its speed, denoted by $v$ , is simply given by

Let's see how to find speed

Question:-

If George travels 12 miles and his car averages 50 miles per hour, how long will it take George to complete the distance? Express this situation in an equation, making "t" the variable for time.

a. 12 x t = 50

b. 50 x t = 12

c. 50 ÷ 12 = t

Answer:-


Distance =12 miles

speed =50 miles per hour

Time=t

      Distance
speed= --------
        Time

plug in value and we get

         12  
50 x t = ---- x t
          t

 50t=12

So the choice 'B' is correct.

For more help on this ,you can reply me.

Solving Linear Equation Using Graphical Representation

2009-08-03T22:26:00.000-07:00

Linear equation can have one or more variables. Common form of a linear equation in the two variables

x

and

y

is y = mx + b, where m and b designate constant.

And mx - y + b = 0 represent a equation of straight line. Any linear equation can also be solved using graphical representation of straight line as shown below.

Problem : Solve and graph 2x + y = 8

Solution : Given equation is 2x + y = 8

So y = 8 - 2x

To plot a graph let us consider a range of x values and calculate respective y values.

x	- 3	- 2	- 1	0	1	2	3	4
y	14	12	10	8	6	4	2	0

Graph representing above data,

Scale : on x axis 1cm = 1 unit
on y axis 1cm = 2 units

How do you solve word problems with percentage

2009-07-15T22:55:00.000-07:00

Topic:- percentage

a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred").Percentages are used to express how large one quantity is, relative to another quantity.

let us consider the example below:

Question:-

A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25. A computer software retailer used a markup rate of 40%.
Find the selling price of a computer game that cost the retailer $25.

Solution :-

The markup is 40% of the $25 cost, so the markup is:

(0.40)(25) = 10

Then the selling price, being the cost plus markup, is:

25 + 10 = 35

The item sold for $35

For more help on this ,Please reply me.

How to solve logarithms

2009-07-01T03:18:00.000-07:00

Topic:-Logarithm

The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.

Here is some natural logarithm basics

The logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 10³ = 1000, so log₁₀1000 = 3, and 2⁵ = 32, so log₂32 = 5.

This math help contains a example problem as well.


Question:-

3 log ⁴+2logx⁵-1/3log(x+3)

Answer:-

3 log 4+2logx⁵-1/3log(x+3)

 log 4³+log(x⁵)²-log(x+3)^1/3

 log 64 + log x¹⁰ - log(x+3)^1/3

    
                  64 x¹⁰
           log -------------
                 (x+3)^1/3

For more help on this ,please reply me

problem on Permutation Combination

2009-06-25T01:07:00.000-07:00

Topic: Permutation Combination

what is Permutation : Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.

what is Combination: Combination means selection of things. The word selection is used, when the order of things has no importance.

Here is a simple question on how to find permutation and combination.

Question:-

Find the 5 digit numbers with distinct digits

Solution:-

10 digits are there in total

0,1,2,3,4,5,6,7,8,9

To make 5 digit numbers ,we have to pick 5 different digits such that 1 st one not 0

So ,1 st digit has 9 options

2 nd has 8 options (including 0)
3 rd has 8 options(leaving out the 1 st and 2 nd)

4 th has 7 options (leaving out 1 st 2nd and 3 rd)

5 th has 6 options (leaving out 1 st 2 nd 3 rd and 4 th)

So ,the total number =9*9*8*7*6

=27216

27216 is the answer.

For more help ,please reply me.

Using Shell or Disc Method to Find Volume of the Solid

2009-05-15T01:56:00.000-07:00

Disc method and Shell(cylinder) method of integration are the two different methods of finding volume of solid of a revolution, using rectangular coordination system the functions are defined in terms of x in the below problem.

Topic : Disc or Cylinder Method of Finding Volume of the Sphere.

Problem : Use the disc or shell method to find the volume of the solid generated by revolving the regions bounded by the graphs of the equations about the y axis. y=x³, y=0, x=2

Solution :

Volume of a Solid by rotating about y-axis is given by:

V = 2π_a∫^bp(x)h(x) dx
here p(x)=x³, h(x)=x
when y = 0, 0 = x³ or ³√0 = x or x = 0
So a = 0 and b = 2
Plugging in all the values in the formula, we get

V = 2π₀∫²(x)³.x dx

= 2π₀∫⁸(x)⁴ dx

= 2π[x⁵/5₀]²

= 2π[(2)⁵/5 - (0)⁵/5]

= 2π[32/5]

= 64π/5

So this how the volume of Solid of revolution is determined when the equations about the y axis.
For more help write to our calculus help.

Problem on Logarithm and Solving for the value of x

2009-05-03T23:34:00.000-07:00

Logarithmic Expression are solved using Logarithmic rules/identities and find unknown value of a variable x.

Topic : Solving for x using Logarithm

Below problem explains use of logarithmic identities/properties and also quadratic equation.

Problem : log 3 (x + 11) + log 3(x + 5) = 3, Solve for x

Solution :

We have the property of log as

log a + log b = log (ab)

So, log 3 (x + 11) + log 3(x + 5) = log (3(x + 11)3(x + 5)) = log 9(x² + 16x + 55)

Thus we have ; log 9(x² + 16x + 55) = 3

as we have the base of given logarithmic expression 10,

So 9(x² + 16x + 55) = 10³ (by the definition of logarithm identity)

9x² + 144x + 495 = 1000

9x² + 144x + 495 - 1000 = 0

9x² + 144x - 505 = 0

x = -144 ±√[144² - 4 (9)(-505)] / 2(9)

= -144 ±√[20736 + 18180] / 18

= -144 ±√[38916] / 18

= -144 ± 197.27 / 18

Thus either x = 2.96 or -18.96

But as log of a negative number is not defined, we discard x = -18.96

hence the answer is x = 2.96

If you have any queries please write to us.

Question on Calculating Surface Area of a given Cone

2009-04-05T23:26:00.000-07:00

Topic : Surface Area

Question : Find the Surface area of cone with base radius of 10 inches and height of 12inches.

Solution :

A Simple Problem to Find Value of x

2009-04-02T05:46:00.000-07:00

Topic : Solve for x

Question : Solve (x-7)(x+5) > 0

Solution :
The product is greater than 0 implies that either both (x-7) and (x+5) are positive or both are negative

because + X + = +
and - X - = +

1) x - 7 > 0
add 7 on both side
so x>7
and x+5 <>
to this add -5 on both side
x < -5
So x >7 and x < -5 implies x>7

2)x - 7 > 0
add 7 on both side
so x>7
and x+5 < 0
to this add -5 on both side
x < -5
So x <7>
Thus we got x>7, x < -5
In interval rotation, it will be (-∞,-5) U (7,∞)

Question on Non Negative Real Values

2009-03-30T04:53:00.000-07:00

Topic : Non Negative real Numbers
Question : For how many non-negative real values of x is √[144 - ³√(x)] an integer?

Solution :
The root of an integer that is not a square number cannot be an integer.

It is given that x is a non-negative real number. So x takes only the positive values.

Therefore the values within square root will be the square numbers less than or equal to 144 so that √[144 - ³√(x)] is an integer.

The possible values within the square are :
144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0

The possible values of ³√(x) are:
(144-144), (144-121), (144-100), (144-81), (144-64), (144-49), (144-36), (144-25), (144-16), (144-9), (144-4), (144-1), (144-0)

0, 23, 44, 63, 80, 95, 108, 119, 128, 135, 140, 143, 144

Therefore the possible non-negative real values of x for which √[144 - ³√(x)] an integer are:
0, 23³, 44³, 63³, 80³, 95³, 108³, 119³, 128³, 135³, 140³, 143³, 144³

Therefore for 13 non-negative real values of x, √[144 - ³√(x)] is an integer.

Question on Number of Mangos in a Basket

2009-03-24T22:46:00.000-07:00

Topic : Number of Mangos in a Basket

Question : A mango seller describes the number of mangoes in his basket as :
IF the mangoes are grouped in twos, then 1 mango remains
IF the mangoes are grouped in threes, then 2 mangoes remain
IF the mangoes are grouped in fours, then 3 mangoes remain
IF the mangoes are grouped in fives, then 4 mangoes remain
IF the mangoes are grouped in six, then 5 mangoes remain
IF the mangoes are grouped in sevens, then no mangoes left.
Find the number of mangoes in the basket.

Solution :
The least number of mangoes would be 119.
but if the question is to find the number of mangoes then119,539,959,1379,1799,2219,..... all qualify for the answer... as shown below.
Let n denote the number of mangoes in the basket.
then since n leaves remainder 1 when divided by 2, hence
2 divides n+1
since n leaves remainder 2 when divided by 3, hence
3 divides n+1
since n leaves remainder 3 when divided by 4, hence
4 divides n+1
since n leaves remainder 4 when divided by 5, hence
5 divides n+1 since n leaves remainder 5 when divided by 6, hence
6 divides n+1
since 2,3,4,5,6 divide n+1 hence
the LCM of 2,3,4,5,6 = 60 divides n+1
hence n+1 = 60k for some positive integer k . [ we need to find k now]
also since 7 divides n hence
60k leaves remainder 1 when divided by 7, hence
60k=1(mod 7) , which gives
4k=1(mod 7), which gives
k=2(mod 7).
Hence k = 2,9,16,23,30,37......
Hence n+1=60k gives
n = 119,539,959,1379,1799,2219,.....
hence the least number of mangoes would be 119.
but if the question is to find the nuber of mangoes then
119,539,959,1379,1799,2219,..... all qualify for the answer.

Note :
The number of mangoes = LCM (2,3,4,5 and 6) - 1 = 120 - 1 = 119 and the sequence is = 120N - 1 where N is any whole number.

Problem on Integrating a Trignometric Value

2009-03-20T00:06:00.000-07:00

Topic : Integration

Question : Integrate (tanˉ¹ x)³ / 1+ x²

Solution :

Steps to Integrate an inverse of trignometric value is as follows

Question on Probability in a Class Room

2009-03-16T21:16:00.000-07:00

Topic : Probability

Question : In a class of 72 students, 44 are girls and,of these, 12 are going to college. Of the 28 boys in the class, 9 are going to college. If a student is selected at random from the class, what is the possibility that the person chosen is not going to college

Answer :
Not going to college means complement that students goes to college
So 1 is the probability that student goes to college
and no of students going to college is given by 9+12/72 = 7/24
= 1 - 7/24 = 24-7 / 24 = 17/24

Question to Find Square root of a Negative Number

2009-03-11T05:12:00.000-07:00

Topic : Square Root of a negative Number

Question : Find the Square Root of -64

Solution :
√-64 = √64 * √-1 , where ‘i’ is the imaginary unit
= √(8*8) * i (√-1 = i and i² = -1)
= 8i

Question on Finding unknown value in a Geometrical Figure

2009-03-05T01:28:00.000-08:00

Topic : Internal Opposite Angles are Equal

Question : Find the unknown angle in the geometrical figure.

Solution :

Line L is parallel to line M
N is the traversal

5x – 28 = 3x + 12
5x - 3x -28 = + 12

->2x - 28 = + 12
-> 2x – 28 +28 = +12 +28 (adding +28 on both sides)

-> 2x/2 = +40/2 (dividing both sides by 2)
-> x = 20

Question on Solving the Inequalities

2009-02-27T01:04:00.000-08:00

Topic : Inequalities

Question : Solve the Inequality "2x-2<8"

Solution :
Case 1 :
"2x-2<8" face="arial">"2x<8+2"
"2x<10" face="arial">dividing both sides by 2
"x<5">
Case 2 :
"-2x+2 < face="arial">"-2x < face="arial">"-2x < face="arial">dividing both sides by 2
"x < - 3""

Hope Answer did the needful.