Ask question

Ask question

All categories

3 years ago

9

The table shows values of a function f(x). What is the average rate of change of f(x) over the interval from x = 5 to x = 9? Sho

w your work.

1 answer:

Snezhnost [94]3 years ago

7 0

F(x) is increasing when x increase. <span />

You might be interested in

A few years ago, when the fuel tank in Sally’s car was completely empty, she paid $63 to fill the tank with 22.5 gallons of gaso

Aloiza [94]

Answer:

2.8

Step-by-step explanation:

ur welcome i hope this helps

8 0

3 years ago

Read 2 more answers

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

5(x-2)-3= 5x-13<br>help me plz

Anna007 [38]

X has infinity solutions.

7 0

2 years ago

The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour

vitfil [10]

Z value is a numerical measurement that describe a value relationship to the mean of a group of values. The standard deviations is 1.25 above the mean is 14,500 hours.

<h3>Given information-</h3>

The mean for the bulb is 12,000 hours.

The standard deviation for the bulb is 2000 hours.

Sample value is 14500.

To find out the how many standard deviation is 14500 mean away from the mean the z value of the mean should be calculated.

<h3>Z value</h3>

Z value is a numerical measurement that describe a value relationship to the mean of a group of values. Z value is the ratio of the difference of the sample value $x$ and mean $\mu$ to the standard deviation. Thus the z value for the given mean $\sigma$ is,

$z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{14500-1200}{2000}$

$z=1.25$

Thus the standard deviations is 1.25 above the mean is 14,500 hours.

Learn more about the z value here;

brainly.com/question/62233

4 0

3 years ago

When constructing an inscribed square how many lines will be drawn

Oksanka [162]

From the research I just did, it seems that 6 lines will be drawn when constructing an inscribed square.

Hope this helped :)

4 0

3 years ago