<span>Naming of rays Rays are commonly named in two ways: By two points. In the figure at the top of the page, the ray would be called AB because starts at point A and passes through B on it's way to infinity. Recall that points are usually labelled with single upper-case (capital) letters. There is a symbol for this which looks like this: AB This is read as "ray AB". The arrow over the two letters indicates it is a ray, and the arrow direction indicates that A is the point where the ray starts. By a single letter. (I have not seen this done.) The ray above would be called simply "q". By convention, this is usually a single lower case (small) letter. This is normally used when the ray does not pass through another labeled point.</span>

6 0

3 years ago

How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these simila

jeyben [28]

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

$\frac{a}{b} =c$

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If $a = x^{2}$ and $b = x$ , then:

$c = \frac{x^{2}}{x}$

$c = x$

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If $a = 3\cdot x^{3}$ and $b = x$ , then:

$c = \frac{3\cdot x^{3}}{x}$

$c = 3\cdot x^{2}$

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If $a = 10^{2x}$ and $b = 3\cdot 10^x$ , then:

$c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}$

$c = \frac{1}{3}\cdot 10^{2\cdot x -x}$

$c = \frac{1}{3}\cdot 10^x$

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If $a = 5\cdot e^{x}$ and $b = -3\cdot e^{x}$ , then:

Example

$c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}$

$c = -\frac{5}{3}$

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

$5\cdot a^2\cdot x -9$

7 0

3 years ago

The long side of a box is 6 inches. That is 3 times the length of the short side. How long is the short side? PLEASE HELP NEED A

Montano1993 [528]

Answer:

2 inches

Step-by-step explanation:

If the long side is 6 inches and it's 3x the length of the short side, then you need to divide the long side into 3 parts because the short side is 1/3 the length of the long side. This means that the short side is 2 inches.

5 0

3 years ago

Read 2 more answers