The Ellipse and Circle

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Pre algebra online solver is an algebraic equation solving in step by step. Algebra is division of mathematics in that, letters are replaced by numbers. An algebraic equation stand for the scale, what is finished on the one side of a scale with a number is also completed to the other side of the scale. In this article we shall discuss for pre algebra online, also get more help with algebra 2 homework online

Solve the given samples pre algebra equation and find out x value of the equation.
3(3x - 2) + 4x = 2(4x + 5) – 11x
We are going to find the x value of the given pre algebra equation.
In the first we are going to multiply the term – 4x in both sides of the equation. We get
3(3x - 2) + 4x - 4x = 2(4x + 5) – 11x - 4x
3(3x - 2) = 2(4x + 5) – 15x
9x – 6 = 8x + 10 – 15x
In the next step grouping the same terms in the above equation, we get
9x – 8x + 15 x = 10 + 6
16x = 16
X = 1
The value of the x in a given equation is 1.

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Planets are the largest objects in the solar system except for the sun. Unlike the sun, the planets do not produce their own energy. They reflect the heat and visible light produced by the sun. The four planets near the Sun - Mercury, Venus, Earth and Mars are called terrestrial (earth-like) planets because they are somewhat similar in size and composition to the earth. They appear to consist chiefly of iron and rock. The terrestrial planets and Pluto are the smallest planets. The earth has one satellite, Mars has two, and Pluto has one. Mercury and Venus have no satellites.

Also learn about grams to kilograms

The outer planets - Jupiter, Saturn, Uranus and Neptune are called the giant planets or Jovian planets. They are mainly made up of hydrogen, helium and ice. Compared to the terrestrial planets, they contain little iron and rock. Each of the giant planets has several satellites. They also have rings around them. However, only Saturn's large, bright rings can be easily seen through a small telescope.

Introduction to multiplying matrices
The rectangular arrangement of some numbers in some rows and columns is called matrix.
The scientist Sylvester defined matrix is a rectangular array or arrangement of entries or elements displayed in rows and columns put within a square bracket or parenthesis. The entries or elements may be any kind of numbers like real or complex, polynomials or other expressions. learn more on dividing polynomials Matrices are denoted by the capital letters like A, B, C.... The matrices use algebraic operations like addition, subtraction, multiplication and division. Let us see how to multiply the matrices in this article.
Any matrix A is denoted by A_mxn (m by n), where m is the number of rows and n is the number of column in the matrix A and consists of m x n elements.

A_mxn =

The number of rows and number of columns m x n (m by n) gives the size of the Matrix.

For example: A = has 2 rows and 3 columns, so the size of matrix A is 2 x 3 (2 by 3).

Leraning Geometric Sequence

A sequence is a collection of numbers is called as terms, arranged in some particular order. There are several types of sequences; one of the most frequent sequences is the geometric sequence and series.
In mathematics, a geometric sequence is otherwise known as a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, if the sequence is 1, 4, 16, 64... here the common ratio is 3 in the geometric progression. Similarly 10, 5, 2.5... is also a geometric sequence with common ratio ½ .
The addition of all the terms in geometric sequence is known as a geometric series.

The Ellipse and Circle

Definition of  Ellipse and Circle
Ellipse
The locus of a point in a plane whose distance from a fixed point bears a constant ratio, less than one to its distance from a fixed line is called ellipse. An ellipse is the set of all points (x, y) in the plane such that the sum of the distances from (x, y) to two fixed points is some constant. The two fixed points are called the foci, which is the plural of focus.







Circle
A circle is the locus of a point which moves in such a way that its distance from a fixed point is always constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle.
Geometric Construction

The geometric construction of an ellipse can easily be accomplished with some very simple tools: a piece of string, a pencil, two pins, and a piece of paper. Simply stick the two pieces of string into the piece of paper using the two pins. Pull the string tight (using the pencil) until a triangle is built with the pencil and the two pins as vertices. Now, keeping the string pulled tight, move the pencil around until the ellipse is traced out.







 Example: Consider the equation Given our comments above, this equation yields an ellipse. We see that and and the graph of this ellipse is the following:

Consider the equation     



Given our comments above, this equation yields an ellipse. We see that
a=5
and
b=3

and the graph of this ellipse is the following:

Polynomial Graphs: End Behaviour

Polynomial Graphs

When we are  graphing (or looking at a graph of) polynomials, it can help to already have an idea of what basic polynomial shapes look like. One of the aspects of this is "end behavior", and it's pretty easy. Look at these graphs:






















As you can see, even-degree polynomials are either "up" on both ends (entering and then leaving the graphing "box" through the "top") or "down" on both ends (entering and then leaving through the "bottom"), depending on whether the polynomial has, respectively, a positive or negative leading coefficient. On the other hand, odd-degree polynomials have ends that head off in opposite directions. If they start "down" (entering the graphing "box" through the "bottom") and go "up" (leaving the graphing "box" through the "top"), they're positive polynomials; if they start "up" and go "down", they're negative polynomials.

All even-degree polynomials behave, on their ends, like quadratics, and all odd-degree polynomials behave, on their ends, like cubics.