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inessss [21]
3 years ago
7

What is the average rate of change of f(x), represented by the graph, over the interval [-1, 1]? and my answers are

Mathematics
1 answer:
Alina [70]3 years ago
8 0
Answer: Choice C) 5

-----------------------------------------------------------------
-----------------------------------------------------------------

Explanation:

Step 1) Draw a vertical line through -1 on the x axis. This vertical line crosses through the point (-1,-5) which is a point on the hyperbola.

Step 2) Draw a vertical line through 1 on the x axis. This line crosses the hyperbola at (1,5).

Step 3) Find the slope of the line through the two points (-1,-5) and (1,5) using the slope formula

m = (y2 - y1)/(x2 - x1)
m = (5 - (-5))/(1 - (-1))
m = (5 + 5)/(1 + 1)
m = 10/2
m = 5

The slope of the line is 5. This is the same as saying the average rate of change is 5. The average rate of change is over the interval [-1,1] which is the same as the interval -1 <= x <= 1

Note: writing "<=" without quotes means "less than or equal to".
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Answer before 11:59 plzzz
Alex17521 [72]
0.0392 or 3.92%
The exponential growth formula can find the interest rate.

y - tolat value (P +I) (216)
a - principal (200)
r- rate (unkown)
x - time in years (2 yrs)
Substitute known values

divide both sides by 200

take the square root of both sides

subtract 1 on both sides
r = 0.0392 or 3.92%
5 0
2 years ago
Below is the graph of y= x.<br> Translate it to make it the graph of y=<br> x-1 + 4.
Oduvanchick [21]
  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

<h2>Explanation:</h2>

To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged

Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c

\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

In this case, we have the graph of:

y=x

And we need to translate it to make it the graph of:

y=x-1+4

According to our rules we need:

  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

But y=x-1+4 is the same as y=x+3, so the previous steps can be simplified as:

  • Shifting the graph of y=x 3 unit to the left.

Below are shown those graphs:

  • The blue one is y=x
  • The red one is y=x-1+4

<h2>Learn more:</h2>

Shifting graphs: brainly.com/question/10010217

#LearnWithBrainly

6 0
3 years ago
Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wa
bezimeni [28]
For this case, the first thing we must do is define variables.
 We have then:
 x: number of pens
 y: number of pencils
 We now write the system of inequations:
 x + y  \leq  25&#10;&#10;y  \geq  (x - 3) ^ 2&#10;
 The solution to the system of inequations is given by the shaded region.
 Note: see attached image.

3 0
3 years ago
What two other forms to write 8.517
Lena [83]
8.517 in written form is: 

Eight and five hundred seventeen thousandth

8.517 in expanded form is:

8 + 0.5 + 0.01 + 0.007

<span>Hope I Helped You!!! :-)

Have A Good Day!!!</span>
3 0
3 years ago
Read 2 more answers
A car is traveling at a constant velocity. After two hours the car has traveled 110 miles. After four hours the car has traveled
Likurg_2 [28]
The answer here is 275 miles, because it is going at 55 miles per hour. you can find this out by dividing the miles by the hours. Hope this helps.
3 0
3 years ago
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