Mathematics : asked on tdahna0403

25.02.2023

Find the average rate of change from x=4 to x=10 for the equation y=2x-3

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09.07.2023, solved by verified expert

Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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Step-by-step explanation:

The average rate of change of the equation during the interval 4 ≤ x ≤ 10

can be represented in this expression if f(x) is substituted for y:

So, the average rate of change (AOC) is 2.

You also could just figure this out by looking at the slope. Since this is a linear equation, the AOC over any interval will always be the same as the slope, since the slope is constant.

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Mathematics

Find the average rate of change from x=4 to x=10 for the equation y=2x-3

Step-by-step answer

P Answered by Specialist

2

Step-by-step explanation:

The average rate of change of the equation during the interval 4 ≤ x ≤ 10

can be represented in this expression if f(x) is substituted for y:

$\dfrac{f(10)-f(4)}{10-4}$

$=\dfrac{17-5}{6}$

$=\dfrac{12}{6}$

So, the average rate of change (AOC) is 2.

You also could just figure this out by looking at the slope. Since this is a linear equation, the AOC over any interval will always be the same as the slope, since the slope is constant.

Mathematics

Let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

7

To find rate of change, you find the change in the output values compared to the change in the input values and write it as a fraction

$\frac{change \: in \: y}{change \: in \: x}$

f(7) is
${7}^{2} - 3(7) - 4$
49 - 21 - 4

49 - 21 - 4

when x is 7, y=24

f(10) is
${10}^{2} - 3(10) - 4$
100 - 30 - 4

100 - 30 - 4

when x is 10, y=66

the difference in the y values is 42 when the x values change by 3

$\frac{66 - 24}{10 - 7} = \frac{42}{3} = 14$
the average rate of change is 14

Mathematics

Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

4

See attachment for your
Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to

Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to

Mathematics

Let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10?

Step-by-step answer

P Answered by PhD

1

The average rate of change from x= 7 to x=10 is 14

Step-by-step explanation:

We can use the slope formula to find the average rate of change

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Now, we are given f(x) = x^2-3x-4 and x=7 to x=10

Our formula can be rewritten as:

$m=\frac{f(10)-f(7)}{10-7}$

finding f(10) = (10)^2 -3(10) -4

= 100 -30 -4

= 66

and f(7) = (7)^2 -3(7) -4

= 49-21-4

= 24

Now finding m:

m= 66 - 24 / 10-7

m= 42/3

m= 14

So, the average rate of change from x= 7 to x=10 is 14.

Mathematics

Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

4

See attachment for your
Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to

Iwant the best answer possible-let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to

Mathematics

Let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

7

To find rate of change, you find the change in the output values compared to the change in the input values and write it as a fraction

$\frac{change \: in \: y}{change \: in \: x}$

f(7) is
${7}^{2} - 3(7) - 4$
49 - 21 - 4

49 - 21 - 4

when x is 7, y=24

f(10) is
${10}^{2} - 3(10) - 4$
100 - 30 - 4

100 - 30 - 4

when x is 10, y=66

the difference in the y values is 42 when the x values change by 3

$\frac{66 - 24}{10 - 7} = \frac{42}{3} = 14$
the average rate of change is 14

Mathematics

Let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

25

Rate of change is like slope. Change in y/ change in x
First we have to solve for the y.
x^2 -3x -4 when x = 7
7^2 -3(7)-4= 24 (7,24)
x^2-3x-4 when x=10
10^2-3(10)-4= 66 (10,66)

(66-24)/(10-7)
42/3 = 14

Mathematics

Let f(x)=x^2−3x−4 . what is the average rate of change from x = 7 to x = 10?

Step-by-step answer

P Answered by Master

18

So, this is the answers you get from plugging in x = (7 through 10)
x = 7 ... 24
x = 8 ... 36
x = 9 ... 50
x = 10 ... 66

Then you get the rate of changes...

66 - 50 = 16
50 - 36 = 14
36 - 24 = 12

So the average of 16, 14 and 12 (those values added together and then that total divided by the number of values, which is 3) is 14

The average rate of change is 14

Mathematics

Let f(x)=x2−3x−4 . what is the average rate of change from x = 7 to x = 10? question 6 options: 24 14 66 42

Step-by-step answer

P Answered by PhD

5

Just find the slope between the points

basically find (f(10)-f(7))/(10-7)

f(7)=7^2-3(7)-4=49-21-4=24
f(10)=10^2-3(10)-4=100-30-4=66

slope=(66-24)/(10-7)=42/3=14
average rate of change is 14

Mathematics

Let f(x)=x^2−3x−4 . what is the average rate of change from x = 7 to x = 10? enter your answer in the box.

Step-by-step answer

P Answered by PhD

1

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