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3 years ago

What is the greatest common factor of the terms in the polynomial 8x4 - 4x3 - 18x2

Mathematics

1 answer:

uysha [10]3 years ago

3 0

Answer:

2x^2

Step-by-step explanation:

The coefficients of the terms in this expression are 8, 4, and 18.

The largest number that you can divide all of them with and get a whole number is 2.

So, 2 is part of our greatest common factor.

These terms also have the variable x. The exponent of the smallest x term is 2, so x^2 is the other part of our greatest common factor.

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Consider the given data. x 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 8 10 12 12 Use the least-squares regression to fit a straight

levacccp [35]

Answer:

See below

Step-by-step explanation:

By using the table 1 attached (See Table 1 attached)

We can perform all the calculations to express both, y as a function of x or x as a function of y.

Let's make first the line relating y as a function of x.

y as a function of x

(y=response variable, x=explanatory variable)

$\bf y=m_{yx}x+b_{yx}$

where

$\bf m_{yx}$ is the slope of the line

$\bf b_{yx}$ is the y-intercept

In this case we use these formulas:

$\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}$

$\bf b_{yx}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum x^2$ with $\bf (\sum x)^2$

Performing our calculations we get:

$\bf m_{yx}=\frac{(83)(95)^2-(95)(923)}{10*1277-(95)^2}=176.6061$

$\bf b_{yx}=\frac{10*923-(95)(83)}{10(1277)-(95)^2}=0.3591$

So the equation of the line that relates y as a function of x is

In order to compute the standard error $\bf S_{yx}$ , we must use Table 2 (See Table 2 attached) and use the definition

$\bf s_{yx}=\sqrt{\frac{(y-y_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{yx}=\sqrt{\frac{39515985}{10}}=1987.8628$

Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.

So now we have:

x as a function of y

(x=response variable, y=explanatory variable)

$\bf x=m_{xy}y+b_{xy}$

where

$\bf m_{xy}$ is the slope of the line

$\bf b_{xy}$ is the x-intercept

In this case we use these formulas:

$\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}$

$\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum y^2$ with $\bf (\sum y)^2$

Remark: If you wanted to draw this line in the classical style (the independent variable on the horizontal axis), you would have to swap the axis X and Y)

Computing our values, we get

$\bf m_{xy}=\frac{(95)(83)^2-(83)(923)}{10*743-(83)^2}=1068.1072$

$\bf b_{xy}=\frac{10*923-(95)(83)}{10(743)-(83)^2}=2.4861$

and the line that relates x as a function of y is

To find the standard error $\bf S_{xy}$ we use Table 3 (See Table 3 attached) and the formula

$\bf s_{xy}=\sqrt{\frac{(x-x_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{xy}=\sqrt{\frac{846507757}{10}}=9200.5856$

In both cases the correlation coefficient r is the same and it can be computed with the formula:

$\bf r=\frac{\sum xy}{\sqrt{(\sum x^2)(\sum y^2)}}$

Remark: This formula for r is only true if we assume the correlation is linear. The formula does not hold for other kind of correlations like parabolic, exponential,..., etc.

Computing the correlation coefficient :

$\bf r=\frac{923}{\sqrt{(1277)(743)}}=0.9478$

5 0

4 years ago

How do I graph a x intercept of 4 and a y intercept of -1

Verdich [7]

Answer:

Down below

Step-by-step explanation:

I can not exactly show a graph, but the equation will be y=1/4x-1, since:

Points: (4,0) (0, -1)

Slope: (0+1)/(4-0)= 1/4

Slope intercept form: y=mx+d

7 0

3 years ago

I will give brainliest if correct! <3

stellarik [79]

Answer:

Step-by-step explanation:

77÷7=11 I know Trust me

8 0

3 years ago

Ep-8 if grounded aboard a small powerboat, which is a method to help free yourself?

andreyandreev [35.5K]

Grounding on boats is something like a mystery to most of the people. They think that the factory hooked it up like that and therefore the installation must be correct. But that's something which will not work every time.
Thus if you are grounded aboard a small powerboat then place everybody aboard in the center of the boat and try to kedge your boat off the obstruction.

5 0

3 years ago

What's 8,000,000+300+9 in standard form

igomit [66]

This is your answer 8,000,309

5 0

4 years ago

Read 2 more answers