Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places.


f(x)=x^2+6x, where x goes from 5 to 7.

Answers

Answer 1

Answer:

The average rate of change of the function in this interval is of 18.

Step-by-step explanation:

The average rate of change of a function [tex]f(x)[/tex] in an interval from a to b is given by:

[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]

In this question:

[tex]f(x) = x^2 + 6x[/tex]

Where x goes from 5 to 7.

This means that [tex]b = 7, a = 5[/tex]. So

[tex]f(7) = 7^2 + 6(7) = 49 + 42 = 91[/tex]

[tex]f(5) = 5^2 + 6(5) = 25 + 30 = 55[/tex]

The rate of change is:

[tex]A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18[/tex]

The average rate of change of the function in this interval is of 18.

Answer 2

The rate of change of a function over a given interval is required.

The average rate of change is 18

Rate of change

The given function is

[tex]f(x)=x^2+6x[/tex]

The interval is between [tex]x=5[/tex] to [tex]x=7[/tex]

Finding the corresponding [tex]y[/tex] values

[tex]y=5^2+6\times 5=55[/tex]

[tex]y=7^2+6\times 7=91[/tex]

The two points are

[tex](5,55),(7,91)[/tex]

The slope is

[tex]m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{91-55}{7-5}\\\Rightarrow m=18[/tex]

Learn more about rate of change:

https://brainly.com/question/8728504


Related Questions

What is the slope of a line perpendicular to the line whose equation is x-y=6

Answers

Answer:

1

hope this helps!!:)

Step-by-step explanation:

X^9/7 convert from exponent form to radical form

Answers

Answer:

[tex]x^{\frac{9}{7}} = \sqrt[7]{x^9}[/tex]

Step-by-step explanation:

You can solve this by realising that the denominator of a fractional exponent can be expressed as the base of a radical.

Note also that the order does not matter.  You could also express it as

[tex]\sqrt[7]{x}^9[/tex]

The reason this works is that you're effectively breaking the exponent into fractions.  The first answer is the equivalent of:

[tex](x^9)^{1/7}[/tex]

and the second would be:

[tex](x^{1/7})^9[/tex]

In both cases, the exponents would be multiplied, giving the same result.

please help on the last question im gonna do 40 points

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i believe number 5 is c and number 6 is f

Find the unknown angle measure by solving for the given variable.

Answers

Answer:

10 1/2

Step-by-step explanation:

Question Progress
Homework Progress
23/ 47 Marks
8296
Expand and simplify (x + 2)(x + 1)
Expanding and Simplifying - Double Set of Br View One Minute Version
Overview

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(x+2)(x+1) = x^2 + x + 2x + 2

simplify it
x^2 + 3x + 2

The translation that moves a figure down 4, to the right 2 is
1. (x + 4, y - 2)
2. (x - 2, y + 4)
3. (x + 2, y - 4)
4. (x - 4, y + 2)

Answers

I think it is the 3 on

Please answer soon ty!

Answers

Answer:

A

Step-by-step explanation:

4.22

If f(x)= x/2-2 and g(x)= 2x^2+x-3, find (f+g)(x).

Answers

Answer:

2x^{2} + \frac{3}{2} x - 5

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

(f+g)(x)= [tex]\frac{x}{2} -2[/tex] + [tex]2x^{2} +x-3[/tex] = [tex]2x^{2} + \frac{3}{2} x - 5[/tex]

Algebraic Expression Evaluate the expression 9x + 2 when × = 3

HELP ME​

Answers

Answer:

The value of 9x+2 when x=3 is 29

Step-by-step explanation:

Algebraic Expressions

We are given the expression

9x + 2

And it's required to evaluate the expression when the value of x is 3.

It can be done by substituting x by 3:

9*3 + 2

=27 + 2

=29

The value of 9x+2 when x=3 is 29

An employee was hired at a wage of $12 per hour. After a raise, she now earns $13.17 per hour.

Answers

Answer:

ok keep going more questions cause ido t get it what u trying to ask

What’s the question? Is it supposed to be how much she gained in her raise? If so, she gained $1.17 in her raise.

PLEASE HELP!
If Southbrook Middle School has 850 students, then how many students participate in the various number of sports: I download a picture with the question. Thank You!

Answers

Answer:

102 Non-Participation

357 One sport

238 Two sports

153 Three sports

Step-by-step explanation:

−1/5(x−4)=−2 Please help me fast

Answers

Answer:

x=14

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−1/5(x−4)=−2

(−1/5)(x)+(−1/5)(−4)=−2(Distribute)

−1/5x+4/5=−2

Step 2: Subtract 4/5 from both sides.

−1/5x+4/5−4/5=−2−4/5

−1/5x=−14/5

Step 3: Multiply both sides by 5/(-1).

(5/−1)*(−1/5x)=(5/−1)*(−14/5)

pls help asap will give brainliest!!!

Answers

Answer:

step two added the 9 to each side :)

Solve and show all steps


PLSSS ASAP I NEED HELP TYSM!!!!

Answers

Answer:

n < 6

Step-by-step explanation:

I multiplied the entire equation by 3 to remove the fraction. This got me:

12 + n < 18

I then subtracted 12 (inverse operations) to get:

n < 6

I hope this helps!

Answer:

n=1

Step-by-step explanation:   n/3=3+4 is less than 6

List the number from least to greatest.

Answers

Answer:

1. $1430

2. $930

3. $1070

4. 105

   96

  -20

  -76

  -560

What is the volume of the figure Enter the answer in the box

Answers

Answer: 1360

Step-by-step explanation: I saw it on brainless

please help ASAP 25 pts + brainliest, please show or explain answer

Answers

Answer:

B. .60

Step-by-step explanation:

With reference angle A

perpendicular (p) = 6

hypotenuse (h) = 10

Then

Sin A

= p/h

= 6 / 10

= 0.6

Answer:

Option B

Step-by-step explanation:

We know that

[tex] \sin( \alpha ) = \frac{side \: opposite \: to \: \alpha }{hypotenuse \: of \: triangle} [/tex]

where [tex] \ alpha [/tex] is an angle of a triangle.

In the triangle given above , [tex] \ alpha = angle A [/tex]. So,

[tex] \sin(a) = \frac{6}{10} = 0.60[/tex]

what is the difference between online school and in-person
pls just write some down for a project thanks :)

Answers

Answer:

The difference between online school and in person school is that online is online and inperson is in person.

Step-by-step explanation:

Answer:

Online-School is worse and In-person is better bc when your at home your not face to face with the teacher and you can get bad grades and when your at school you can get better grade and online- school is hard bc you have lots of homework and it complicated but have a great day

Step-by-step explanation:

Combine the two expressions found in parts C and D to relate a, c, A, and C. Rewrite the expression as an equality between two ratios. Show your work.

Answers

Answer:

BD = c sin A and BD = a sin C.

Therefore, a sin C = c sin A.  

Divide both sides by sin A × sin C to get A/sin A = C/sin C

Step-by-step explanation:

Consider the two functions below. Which one of these functions is linear? What is its equation? Enter any answers to two decimal places.

Answers

Only A is a linear function because B is not a straight line.
Slope m=(y2-y1)/(x2-x1)=(10-5)/(6-3)=5/3

5=5/3*3+b

b=0

Y=5/3x

Help pls! 37 points.

Answers

Answer:

7 squares

Step-by-step explanation:

Key skills: Counting, Averages

1) Based on what I counted, there are 11 columns, and 53 squares. If you want an average of 5 squares per column and you have 12 columns, the total number of squares you want is 60.

2) Since there are already 53 squares present, you need 60-53 = 7 squares more.

Hope you understood and have a nice day!!

answer:

should be 7 squares.

Ariana went shopping for a new video game. The listed price of the video game was
$36, but the price with tax came to $37.08. Find the percent sales tax.

Answers

Answer:

I think it should be around 0.03%

Step-by-step explanation:

hope that helps:)))

Answer:

3%

Step-by-step explanation:

What percentage of the students surveyed eat no more than 3 whole servings of fruits and vegetables daily

Answers

Answer:

Step-by-step explanation:

The missing histogram file is attached in the image below.

From the graph, deduce that:

the servings of fruits and vegetable                     number of students

0                                                                             1

1                                                                             4

2                                                                             5

3                                                                             10

4                                                                             8

5                                                                             3

6                                                                             0

7                                                                             1

Thus, the percentage of students surveyed that eat more than 3 whole servings is:

= starting from 4 = (8+3+0+1)/32 = 0.375

How to solve:

5 1/2 + x/6 ≤ 3 1/3

Answers

Answer:

x≤-91

Step-by-step explanation:

plz help me!?!?

and thank u

Answers

Answer:

-4.8+2.5-7.8

= -10.1

Step-by-step explanation:

Asphere has a radius of 27 inches. A horizontal plane passes through the center of the sphere.
Part 1 out od 2
Describe the cross section formed by the plane and the sphere.

Answers

9514 1404 393

Answer:

  circle of radius 27 inches

Step-by-step explanation:

Anywhere a plane cuts a sphere, the cross section is a circle. When the plane includes the center of the sphere, the circle has the same radius the sphere has.

The cross section is a circle of radius 27 inches.

Solve for x x/12+6=8

x=​

Answers

Answer:

X=24

Step-by-step explanation:

X/12 + 6 = 8

we can multiply the equation to 12 to make it simple. We get:

X + 72 = 96

So X = 96-72=24

an oil tank loses 32% of its contents every hour. Peter says the tank will have lost 95% of its original contents by the end of the sixth hour. Is peter correct

Answers

Answer:

it lose 90 percent in 3 hours so peter is incorrect

Step-by-step explanation:

Solve x4 - 11x2 + 18 = 0.

Answers

Answer:

x=√2, x=-√2, x= 3 and x=-3

Step-by-step explanation:

We need to solve the equation x^4 - 11x^2+18=0  

We can replace x^4 = u^2 and x^2 = u

So, the equation will become

u^2 -11u+18 = 0

Factorizing the above equation:

u^2 -9u-2u+18 =0

u(u-9)-2(u-9)=0

(u-2)(u-9)=0

u=2, u=9

As, u = x^2, Putting back the value:

x^2 =2 , x^2 =9  

taking square roots:

√x^2 =√2 ,√x^2=√9  

x=±√2 , x = ±3

so, x=√2, x=-√2, x= 3 and x=-3

Answer:

The second answer is correct.

Step-by-step explanation:

Mark brainliest if correct please

Luis solves the following system of equations by elimination.
5s+ 3t = 30
2s+3t=-3
What is the value of s in the solution of the system?

Answers

the value of s is 11
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