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2 years ago

Find the domain of the rational function.

Mathematics

1 answer:

BigorU [14]2 years ago

5 0

The domain of the given rational function is:

D = {x ∈ R| x ≠ -9}

<h3>How to find the domain of a rational function?</h3>

When given a rational function, we first need to simplify it to its simplest form, (the given rational function is already on the simplest form).

At that point, we identify the domain of the rational function as the set of all real numbers minus the numbers that make the denominator of the rational function to be zero.

In this case, the denominator is:

x + 9

It is zero when:

x + 9 = 0

x = -9

So, the domain of the rational function is the set of all real numbers except for x = -9, it is:

D = {x ∈ R| x ≠ -9}

If you want to learn more about rational functions:

brainly.com/question/1851758

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Solve for x.<br>-4x - 76 < -52<br>

Roman55 [17]

First you add 76 to get

-4x<24

And Then you divide by -4 and sincr its a negative you flip the sign to get

x>-6

That might be wrong Idk

4 0

3 years ago

What is the equation of the line of best fit for the following data? Round the

Svet_ta [14]

Answer:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4$

And the slope would be:

$m=\frac{45.4}{50.8}=0.8937 \approx 0.894$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8$

$\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4$

And we can find the intercept using this:

$b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535$

So the line would be given by:

$y=0.894 x +0.535$

And the best option is:

A. y = 0.894x + 0.535

Step-by-step explanation:

We have the following dataset given

x: 5,6,9,10,14

y: 4,6,9,11,12

We want to find the least-squares line appropriate for this data given by this general expresion:

$y = mx +b$

Where m is the slope and b the intercept

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 44$

$\sum_{i=1}^n y_i =42$

$\sum_{i=1}^n x^2_i =438$

$\sum_{i=1}^n y^2_i =398$

$\sum_{i=1}^n x_i y_i =415$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4$

And the slope would be:

$m=\frac{45.4}{50.8}=0.8937 \approx 0.894$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8$

$\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4$

And we can find the intercept using this:

$b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535$

So the line would be given by:

$y=0.894 x +0.535$

And the best option is:

A. y = 0.894x + 0.535

4 0

4 years ago

15/21 in its simplest form?

garri49 [273]

Answer:

5/7

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

FInd the X- and the Y-intercept of the line.

Maurinko [17]

A. You divide 1 (infront of x) by 12 to get 12. You divide -6 by 12 to get -2 for the y intercept.

6 0

3 years ago

Read 2 more answers

The figure below shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x-axis

german

Answer:

D - The slope from point O to point A is three times the slope of the line from point A to point B.

6 0

3 years ago