math gurus please define the term variable used in math?

Question

as well can you please define ordered pairs? thank you your help is appreciated:)
thank you

Answer 1

A variable is any character in an equation who does not have a fixed value

in y=3x y and x are variables since they change around depending on what the other one equals. 3 is a constant since it always equals 3.

An ordered pair is any set of numbers (x, y) which make a certain equation true.

(2, 4) is an ordered pair fr the equation y=2x

Answer 2

1. A variable is a quantity used in a function for which any desired numerical value, or indeed any other expression or function can be substituted.

Thus H(x) = sqrt (x^2 + 225) defines a function of the variable x.

For x = 4, H(20) = sqrt (400 + 225) = sqrt (625) = 25.

For x = 36, H(36) = sqrt (1296 + 225) = sqrt (1521) = 39.

[ My examples were deliberately chosen to illustrate a function H(x) which could work out the hypoteneuse --- hence the "name" H(x) --- for two Pythagorean triangles whose sides were small multiples of classic Pythagorean triples: 5*(3, 4, 5) = (15, 20, 25) and 3*(5, 12, 13) = 15, 36, 39). ]

2. An ordered pair of numbers (x, y) or (r, θ) is a way of specifying a point in a plane. Here, x and y would be the coordinates of the point (x, y) in a rectangular Cartesian coordinate grid, for example. One can also describe the position of such a point by (r, θ), where r and θ are respectively the value of the radius from the origin, and the angle θ (measured with respect to the original x-axis), in so-called Polar Coordinates.

The connection between these two ways of referring to the same point is:

x = r cos θ and y = r sin θ

This is a transformation in which, GIVEN r and θ, one can easily work out x and y. In other words, it's a transformation (r, θ) --> (x, y).

There is also an inverse transformation (x, y) --> (r, θ), though it doesn't look quite as simple or pretty:

r = sqrt (x^2 + y^2); θ = tan^(-1) (y/x).

These particular examples of an ordered pair of numbers being used to specify a point are by no means unique. There are also MANY other choices which can be made to specify a point in a plane. They include, for example, elliptical or hyperbolic coordinates. In physical problems, the best choice of coordinates often depends upon the particular geometry of the situation being examined.

Live long and prosper

Answer 3

Ordered pairs are used to help you plot points on a graph.
The graph is composed of an x axis and a y axis
The x axis is horizontal and the y axis is verticle(Y has a line going down..so that can help you remember which is which)
Where they intersect(the middle) is called the orgin
Always start at the orgin.
The x axis would look something like this
_______________________________
-5 -4 -3 -2 -1 0(the orgin) 1 2 3 4 5
The y axis is the same, except the numbers get higher as you go up

| 2
| 1
| 0(orgin)
| -1
| -2

Ok, the ordered pair goes as follows
(x,y)
that means you first go left or right to the correct x coordinate, then go up or down to the right y coordinate.
For example, for (1,2), you would first go right one and the go up 2.
X comes before Y in the alphabet, so that can help you remember what goes first.
Good luck!

Answer 4

In addition to what was said above, an ordered pair can be used in a two-dimensional coordinate system to define a position. It does not necessarily have to be in the xy-plane or a rectangular coordinate system. A polar coordinate in the yz-plane would still be an ordered pair.

Answer 5

an ordered pair is a coordinate of a point.
namely an x, and y value.
it tells you where a point is located on the x-y plane..

x is the horizontal axis, and y the vertical..

to plot the point is (3,4)

you go right 3 points, and up 4 points in the first quadrant.

Answer 6

a variable is a quantity which can vary. We talk of dependent and independent variables. In an experiment where we study the effect of temperature on the expansion of a solid or a liquid, temperature would be the independent variable and the volume of the liquid or the length of a long bar would be the dependent variable.