What is the average rate of change of f(x) = 2x^2 - x - 4 over the interval -4 < x < 2?

Answers

Answer 1

The average rate of change of f(x) = 2x^2 - x - 4 over the interval -4 < x < 2 is -5.

To find the average rate of change of a function over an interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.

The given function is f(x) = 2x^2 - x - 4.

Let's calculate the function values at the endpoints of the interval: -4 and 2.

For x = -4:

f(-4) = 2(-4)^2 - (-4) - 4 = 32 + 4 - 4 = 32.

For x = 2:

f(2) = 2(2)^2 - 2 - 4 = 8 - 2 - 4 = 2.

Now, we can calculate the difference in the function values: f(2) - f(-4) = 2 - 32 = -30.

Next, we calculate the difference in the x-values: 2 - (-4) = 6.

Finally, we can calculate the average rate of change by dividing the difference in the function values by the difference in the x-values:

Average Rate of Change = (f(2) - f(-4)) / (2 - (-4)) = -30 / 6 = -5.

For more such questions on  rate of change

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Related Questions

How can you find the length of an arc

Answers

Start by dividing the arcs central angle in degrees by 360. Then, multiply that number by the radius of the circle. Finally, multiply that number by 2 x pi to find the arc length.

a vehicle traveled at a speed of 54 kilometers per hour for 3 hours. find the distance traveled

Answers

Answer:

162

Step-by-step explanation:

54x3

Evaluate the algebraic expression x^2 - 20 for x = 7 and for x = 9

Answers

Answer:

29

61

Step-by-step explanation:

x^2 - 20

x = 7 and 9

Evaluate

___________

We know the values of x, let's substitute them with the x in the problem :

(7)^2 - 20

49 - 20

29

(9)^2 - 20

81 - 20

61

help please!! (math)

Answers

Answer:

It's gonna be C and good luck!

the answer is C lovely

Complete the remaining columns in the chart by calculating the missing values for each category. Round your percentages to the nearest tenth of a percent. (16 points)

Answers

Answer:

yearly cost for housing expenses = $11,400, average monthly cost for food = $650

yearly clothing cost = $900,

average monthly cost for transportation= $500,

Yearly cost for insurance & medical= $14,400

yearly cost for emergency fund = $600

average monthly college saving = $50

Step-by-step explanation:

Yearly housing = monthly cost * 12 = 950 * 12 = 11400

Food, monthly = 7800 /12 = 650

Clothing, yearly = 75 * 12 = $900

Monthly transport = 6000 / 12 = $500

Insurance and medical = 1200*12 =14400

Emergency fund = $50 * 12 = $600

College saving = $600 / 12 = $50

find the product of (x-3)^2

Answers

Answer:

x^2 - 6x + 9

Step-by-step explanation:

(x-3)^2

(x-3)(x-3)

x^2 -3x -3x + 9

x^2 - 6x + 9

^2 means (x - 3) times itself twice.

(x - 3)(x - 3)             multiplying polynomials- Firsts, Outs, Inners, Lasts (FOIL)

                                 Firsts (x* x)   Outs (x*-3)   Inners (-3 * x)   Lasts (-3*-3)

xx -3x -3x +9            Combine like terms.

      -3x -3x             Adding/subtracting integers- same signs means you add          

                                     and keep the sign.

x^2 -6x + 9              

Which expression is equivalent to 4(9 + 7)?

Answers:
A. 36 + 7
B. 13 + 11
C. 36 + 28
D. 13 + 7

Will mark brainliest!!

Answers

the answer for this is C

Answer:

c 36+28

Step-by-step explanation:

the answer is c 36 + 28

34.8 x 7 what is the answer?

Answers

Answer:

243.6

Step-by-step explanation:

34.8x7=
243.6
Hope this helps have a nice day! :)

Please Help. Im stuck on this question and i cant figure it out

Answers

Answer:

Where is it?

Step-by-step explanation:

Where is the question exactly?

Camille's birthday party will cost $32 if she invites 16 guests. How many guests can there be, at most, if Camille can afford to spend a total of $48 on her birthday party? Assume the relationship is directly proportional.

Answers

Answer:

I think its gon be 24 guests

Answer:

24 people can be there at most :)

Step-by-step explanation:

$32 divided by 16(guests) is $2

so its $2 per person

so 48$ divided by $2 is 24

So Camille can invite 24 people at the cost of 48$ being her total at most :)

2-(3x+5)=5-2x

i have too answers but need the right one lol​

Answers

Answer:

x = -8

Step-by-step explanation:

2 - (3x + 5) = 5 - 2x

Subtract 2 from each side.

-(3x + 5) = 3 - 2x

Apply the negative sign in front of the parentheses.

-3x - 5 = 3 - 2x

Add 5 to both sides.

-3x = 8 - 2x

Add 2x to both sides.

-x = 8

We can't have a negative x value, so we'll need to multiply each side by -1.

x = -8

Hopefully, this helped and wasn't too confusing!

Answer:

Solution given;

2-(3x+5)=5-2x

2-3x-5=5-2x

-3-5=3x-2x

x=-8 is your answer

9e + 4=-5e + 14 + 13e

Answers

Answer:

e= -10/9

Step-by-step explanation:

Answer:

e = 10

Step-by-step explanation:

1.) We need to manipulate the equation to get e by itself.

2.) To solve the equation, do the following steps;

9e + 4 = −5e + 14 + 13e

9e + 4 = 14 + 8e (Combine like terms)

9e + 4 − 8e = 14 + 8e − 8e (Subtract 8e from each side)

e + 4 = 14 (Combine like terms)

e + 4 - 4 = 14 - 4 (Subtract 4 from each side)

e = 10 (Combine like terms.

3.) Answer: e = 10.

Now lets check our work. To check your work, do the following steps;

9e + 4 = −5e + 14 + 13e

9e + 4 = 14 + 8e

9(10) + 4 = 14 + 8(10)

90 + 4 = 14 + 80

94 = 94

By doing those steps we can confirm the answer, e = 10, is true.

What is the slope of the line below asap plzzzzzzzzzzzzzzzzzzzzz quick

Answers

Answer:

w of king akinf arro

Step-by-step explanation:

Remember to do run (x) then jump (y).


This is where you find two parts of the line that hit a corner and find the x and y for them.


The question already tells us this. Remember that the x always goes first and that if the line is going down (left to right), the slope is a negative.


Answer: -2/3


Answer:

A driver was going more then 15 miles per hour over the speed limit when he received a speeding ticket. If the driver's speed was 75 miles per hour, what was the speed limit, m, on the road where he was driving.

I need help with this ASAP!

Answers

Answer:

60

Step-by-step explanation:

You just subtract 75 - 15, and you get 60. I hope this helps :)


2/3x + 1/4 = 46/6x - 1/3

Answers

Answer:

x = 1/12

Step-by-step explanation:

2/3x + 1/4 = (8x+3) /12   (create equivalent fractions with a denominator of 12)

23/3x - 1/3 = (23x - 1) /3            *(46/6x = 23/3x)

8x + 3  =  23x - 1

    12            3

now cross-multiply:

3(8x + 3) = 12(23x - 1)

24x + 9 = 273x - 12

9 = 252x - 12

21 = 252x

x = 21/252 which reduces to 1/12

Which is the graph of y = 3sqrt/X+1 - 2?

Answers

Look at the graph i sent you.

Graph of : y = 3sqrt(x+1) - 2

what is the degree of the following polynomial 2x^3

Answers

Answer:

3

Step-by-step explanation:

Whatever the highest exponent is determines the degree.

A number n increased by 4 is -19

Answers

Answer:

n=23

Step-by-step explanation:

4-23=19

meme

Answer:

-23

Step-by-step explanation:

-23+4= -19


Can I get help on this math problem makes makes no sense

Answers

(2,-1) The intersecting point is the point where the two lines meet.

simplify this equation: 2^-4 (2√3)^2

Answers

Answer:

download photo math you can take pictures of math problems and will solve them.

7. What is the slope of the line that passes through the points (14, -18) and (5, -12)?​

Answers

Answer:

slope =[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope, or [tex]m[/tex]. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point, and the [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point. So, substitute the x and y values of the points (14, -18) and (5, -12) into the formula and solve:

[tex]m = \frac{(-12)-(-18)}{(5)-(14)}\\m = \frac{-12+18}{5-14}\\m = \frac{6}{-9} \\m = -\frac{2}{3}[/tex]

Thus, the slope is [tex]-\frac{2}{3}[/tex].

102 = 1.2 x w
what is w?

Answers

Answer:

122.4

Step-by-step explanation:

Just Divide.

Answer:

85

Step-by-step explanation:

1x2 x 85 = 102

Calcuate the 2 unit rates for the following 150 gallons in 50 seconds. this answer has 2 answers. please help the teacher is going to ask me for this question!!!​

Answers

3 gallons per second
Or
1/3 second per gallon

Just do 150 gal over 50 seconds
Or reverse it to 50 sec over 150 gallons

So you get 3 gallons occur each 1 second or the it takes 1/3 of a second for each 1 gallon to flow

encuentra el MCM de 12 y 24

Answers

【Rep.】The least common multiple of 12 and 24 is 24.

                             [tex]\red{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

   [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 24}\\ \ 6 \ \ \ 12\\ \ 3 \ \ \ \ 6\\ \ 3 \ \ \ \ 3\\ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ \: \end{matrix} \end{gathered}$}[/tex]

                                 [tex]\sf{L.c.m.(12,24)=2\times2\times2\times3}[/tex]

                                       [tex]\sf{L.c.m.(12,24)=2^{3}\times3 }[/tex]

                                       [tex]\boxed{\boxed{\sf{L.c.m.(12,24)=24}}}[/tex]

{ Pisces04 }

You travel 36 miles north and then 15 miles east. How far are you from your starting point?

Answers

Answer:

21 is the correct answer because

MATH HELP!! ASAP!!! MARKING BRIAINLIEST!!

Answers

Answer:

18 meters.

Step-by-step explanation:

The ratio is 1cm:2m, so for every centimeter, you multiply it by 2 and convert it to meters. So, 9 cm time 2 equals 18 and then add meters, so 18 meters.

(hope this helps :P)

Help me with number 2 plz. Its vertex

Answers

Ok I would help you but you have bad music taste

Answer:

x=4, x= -1

Step-by-step explanation:

Write your problem:

[tex]x^{2}[/tex] - 4 = 3x

Subtract 3x from both sides:

[tex]x^{2}[/tex] - 4 - 3x = 3x - 3x

Simplify:

[tex]x^{2}[/tex] - 3x - 4 = 0

Sovle with quadtric formula:

.....

NEED HELP ASAP
A quarterback’s pass-completion percentage is 70%. Eight of his passes are randomly selected. What is the probability that 6 of them were successful passes?

0.06
0.08
0.12
0.30

Answers

Answer:0.08

The answer is b i always got your back

Step-by-step explanation:

Answer:

.30

Step-by-step explanation:

Write an equation in slope intercept form (y=max+b) for the line passing through the points. Show your algebraic solving steps.

(-2, -1) and (2,3)

Answers

Find the gradient first

m = (y2-y1)/(x2-x1) = 3-(-1)/2 - (-2) = 4/4 = 1

then find the equation of the... slope ._.

y - y1 = m(x - x1)

y - (-2) = 1(x - 3)

y + 2 = x - 3

y =x -3 - 2

y = x - 5

So the equation is y = x - 5


Explain how to solve the equation 21 = m +14. What is the value of m?
Enter your explanation and answer in the space provided.

Answers

Answer:

m = 7

Step-by-step explanation:

21 = m + 14

21 - 14 = m

m = 7

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