Which statements are correct about the average rate of change for the function f(x) = x2 + 9x + 18 ?

Answers

Answer 1

Answer:

Presumably this is a multiple choice question, and without seeing the potential answers, we can't tell you which ones are correct.

A few things can however be said about this function:

1) It describes a parabola that extends upward infinitely.  We can see this because it's in the classic format ax² + bx + c, and all terms are positive.

2) We can find the x-intercepts by solving for zero.  In this case we can do that by factoring it:

x² + 9x + 18 = 0

x² + 3x + 6x + 18 = 0

x(x + 3) + 6(x + 3) = 0

(x + 6)(x + 3) = 0

So the x intercepts occur at (-6, 0) and (-3, 0)

3) we can find its vertex by taking its derivative and solving for zero:

f'(x) = 2x + 9

0 = 2x + 9

x = -4.5

We can then plug that coordinate into the original function to find the y coordinate:

f(x) = x² + 9x + 18

f(-4.5) = 20.25 - 40.5 + 18

= -2.25

So the vertex is at (-4.5, -2.25)

4) As mentioned, the derivative of f(x) is f'(x) = 2x + 9.  The integral is:

x³ / 3 + 9x² / 2 + 18x + C


Related Questions

change 5 feet 10 inches to centimetres

Answers

Answer:

177.8

Step-by-step explanation:

There are 30.48 centimeters per foot so multiply 30.48 by 5. And there is 2.54 centimeters in a inch so multiply 2.54 by 10. And then add the totals together to get 177.8

You move right 3 units. You end at (5, 2). Where did you start?

Answers

Answer:

8,2

Step-by-step explanation:

ANSWER:
You started at (2,2)

EXPLANATION:
you subtract the 5 by 3 because moving to the right affects the x axis, and (x,y), so the 5 is what is being affected

Please answer the questions attached below

Answers

Answer:

Step-by-step explanation:

The parallelogram is two congruent triangles. Area of blue triangle is ½·2·2 = 2 units²

Area of parallelogram = 4 units²

:::::

area of blue parallelogram = 4×9 = 36 units²

:::::

area of green parallelogram = 3×5 = 15 units²


Use the figure to find the Volume.

Answers

Answer:

12π un^3

Step-by-step explanation:

Use the fomula: V= πr2 h

The radius is 2 and the height is 3.

I really don't know how to explain this but I can try, with a self- explanatory steps including the formula .

The work is in the screen shot goodluck.

Hope this helped!

Stay Safe!

Free Brainliest

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ


ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ













ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ


ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ













ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ


ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ















ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ















ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ














A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box.


A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall.

Answers

Answer:

Search for space diags

Step-by-step explanation:

you will find answer

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 480000 CM ^3

Explanation:

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

NEED HELP MY GRADE DEPENDS ON ITT!!!!!!!! I will mark brainliest answer.

find the value of f and g in the figure below.

Answers

Answer:

DONT PRESS THAT LINK

Step-by-step explanation:

simplify by distributive property 8-3(7m-3p)​

Answers

56m-21m+9p-24p

35m-15p

Draw arches over the numbers and just multiply the values. The arches help keep track of it.

A farmer knows that a grocery store will reject a shipment of his vegetables if more than 4% of the vegetables contain blemishes. He inspects a large truckload of tomatoes to determine if the proportion with blemishes (p) exceeds 0.04. He selects an SRS of 150 tomatoes from the more than 2,000 tomatoes in the truck. Suppose that 8 tomatoes sampled are found to have blemishes. Which of the assumptions for inference about a proportion is violated, if any?

a. Large Counts: np > 10
b. Large Counts: n(1 – p) > 10
c. The sample is a random sample of the entire population.
d. 10% condition: the sample size is less than 10% of the population.
e. There do not appear to be any violations.

Answers

Answer:

Assumption A is violated

Step-by-step explanation:

x = number of blemishes = 8

n = sample size = 150

proportion = x/n = 8/150 = 0.0533

1. large counts: np> 10

= 150 * 0.0533 >10

= 7.995 > 10

this assumpton is obviously violated. 7.995 is not greater than 10

2. Large Counts: n(1 - p) > 10

150(1-0.0533)>10

150-7.995 > 10

142.005> 10

there is no violation. The assumption is satisfied

3. This assumption is satisfied. this is because the tomatoes were selected using simple random sampling.

4. 10% of the population = 0.1 * 2000 = 200

the sample size = 150

150 < 200

this assumption is satisfied

The diameter of a circle is 3 meters. What is the circumference?

Answers

Answer:

C≈9.42m

Using any of this formulas

C=2πr

C=2πrd=2r

Solution:

C=πd=π·3≈9.42478m

siny dy/dx=cosy (1-xcosy)

Answers

Step-by-step explanation:

hope it helpe...............

I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS

Answers

Answer:40 inch
Explanation: the radius is half of the circumference therefore the answer is 40 inches considering the radius is 20 inches.

Help plz need the answer asap

Answers

Answer:

The video is blocked but you can type your question on here1

Step-by-step explanation:

g The distribution of the monthly amount spent on childcare in a Midwestern city has a mean of $675 and a standard deviation of $80. A random sample of 64 families in this city paying for childcare is selected. Find the probability that the sample mean is less than $650. (Round the result to 4 decimal places.)

Answers

Answer:

0.0062 = 0.62% probability that the sample mean is less than $650.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of $675 and a standard deviation of $80.

This means that [tex]\mu = 675, \sigma = 80[/tex]

A random sample of 64 families in this city paying for childcare is selected.

This means that [tex]n = 64, s = \frac{80}{\sqrt{64}} = 10[/tex]

Find the probability that the sample mean is less than $650.

This is the pvalue of Z when X = 650.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{650 - 675}{10}[/tex]

[tex]Z = -2.5[/tex]

[tex]Z = -2.5[/tex] has a pvalue of 0.0062

0.0062 = 0.62% probability that the sample mean is less than $650.

The probability that the sample mean is less than $650 is 0.62%.

The z score is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\sigma=standard\ deviation,\mu=mean,n=sample\ size\\\\\\Given \ \mu=675,\sigma=80,n=84, hence:\\\\For\ x<650:\\\\z=\frac{650-675}{80/\sqrt{64} } =-2.5[/tex]

From the normal distribution table:

P(x < 650) = P(z < -2.5) = 0.0062 = 0.62%

The probability that the sample mean is less than $650 is 0.62%.

Find out more at: https://brainly.com/question/15016913

In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows:

$1,589, $593, $1,223, $869, $423, $1,720, $708, $1,425, $922 and $308.

a. What is the mean and median change in the cost? (Explain how you obtain your answer.)
b. What is the five-number summary of the change in the cost? (Explain how you obtain your answer.)
c. What is the standard deviation of the change in the cost? (Explain how you obtain your answer.)
d. The middle 50% of the change in the cost is spread over what value? (Explain how you obtain your answer.)
e. What is the coefficient of variation of the change in cost? (Explain how you obtain your answer.)
f. What are the (absolute values of) the Z scores of the change in cost?

Answers

Answer:

1. mean = 980 median = $895.5

2. 308, 593, 895.5, 1425, 1720

3. 491.7978

4. 895.5

5. 50.28%

Step-by-step explanation:

1. mean $1,589+$593+$1,223+$869+$423+$1,720+$708+$1,425+$922+$308/10

= 9780/10

= $978

median

We first arrange the values in ascending order

308,423,593,708,869,922,1223,1425,1589,1720

number of observation is even so we pick the 2 values in the middle and divide by 2

= 869+922/2

= $1791/2

$895.5

2. five number summary of change

the botom half of th dta set = 308,423,593,708,869

minimum value = 308

n = 5

median = 593 = q1

from 1, q2 = median = $895.5

the upper half of data

922,1223,1425,1589,1720

n = 5

median = $1425

maximum value = $1720

the five number summary of change in cost is therefore

308, 593, 895.5, 1425, 1720

3. standard deviation

[tex]s =[\sqrt{x-barx} ]^{2} \frac{1}{n-1}[/tex]

bar x is the mean = 978

($1,589-978)²+ ($593-978)²+ ($1,223-978)²+ ($869-978)+ ($423-978)²+ $1,720-978)²+($708-978)²+ ($1,425-978)²+ ($922-978)²+ ($308-978)²

= 2176786

=[tex]\sqrt\frac{1}{10-1} {2176786} \\\sqrt{ \frac{2176786}{9}[/tex]

= [tex]\sqrt{241865.1}[/tex]

= 491.7978

4.  middle 50% is spread over the median, which is 895.5

5.  coefficient of variation

= s/bar x * 100

= 491.7978/978 * 100

= 49179.78/978

= 50.28%

6. z score = x - mean/s

x = 1589

= 1589-978/491.7978

= 1.2424

for x = 593

593-978/491.7978

= -0.7828

= 0.7828

for x = 1223

1223-978/491.7978

= 0.4982

for x = 869

869-978/491.7978

= -0.2216

= 0.2216

for x = 423

423-978/491.7978

= -1.1285

= 1.1285

x = 1720

1720-978/491.7978

z = 1.5088

for x = 708

708-978/491.7978

= -0.5490

= 0.5490

for x = 1425

1425-978/491.7978

= 0.9089

for x = 922

922-978/491.7978

= -0.1139

= 0.1139

for x = 308

308-978/491.7978

= -1.3624

= 1.3624

Help math plzshnsndnfjc

Answers

Answer:

11 inches

Step-by-step explanation:

So first I don’t typically go with fractions so I broke 2 3/4 down into a decimal which is:

2.75

Then the index card is

4 by 2.75

Then you multiply the sides

4 x 2.75

= 11 inches

Question 7 of 10
When you multiply a function by -1, what is the effect on its graph?
A. The graph flips over the yaxis.
O B. The graph flips over the line y= X.
O C. The graph flips over the xaxis.
SUBMIT

Answers

it should be C, im not 100% sure though.

Answer:

the answer is c because it is over xaxis

Muhammad Amanullah buys 4 apples for $1.12.
At the same price, how many apples can he buy for $2.52?

A-5
B-6
C-7
D-8
E-9

Answers

Answer: E) 9

Step-by-step explanation:

1.12/4 = 0.28

2.52/0.28 = 9

Answer:

9

Step-by-step explanation:

To find how much each apple costs, you have to divide the price by how many apples he brought.

1.12/4 = 0.28

Each apple costs $0.28

Now, you have to divide 2.52 by 0.28.

2.52/0.28 = 9

He can buy 9 apples at the same price with $2.52.

The relationship between the height of a tree and the time snice the tree was planted?

Answers

Answer:

Answer: It´s correlated. Step-by-step explanation: The graph shows that the height of the tree increases as time passes, meaning that the more time that a three has been planted the more height it has, so there´s a direct correlation between the time passing and the height of the tree.

What is the value of y in the equation 3(3y-12)=0

Answers

Answer:

y = 4

Step-by-step explanation:

use the distributive property

9y - 36 = 0

     +36  +36

9y = 36

divide by 9

y = 4

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

answer the questions, please I will give you 10 points

Answers

A) 3 times 7x makes it a normal number of 21.
B) using PEMDAS you must multiply 5 times 5 to put 5 to its own power, then multiply by 2 to get 50, then add 4 getting 54.
C) 9 times 5y gets the normal number of 45, then subtract that from 80, you get 35.

Question here

I need help with this

Answers

cool can i have brainliest

Answer: nice the answer is ummmm I don’t know

Step-by-step explanation:

Quadrilateral GHIJ is dilated by a scale factor of 22 to form quadrilateral G'H'I'J'. What is the measure of side H'I'?

Answers

Answer:

[tex]H'I = 48[/tex]

Step-by-step explanation:

Given

See attachment for complete question.

From the attachment, we have:

[tex]GH=16.5[/tex]

[tex]HI =24[/tex]

[tex]IJ = 17[/tex]

[tex]JG =32.2[/tex]

[tex]k = 2[/tex] --- Scale factor

Required

Find H'I

The corresponding side of H'I is HI.

So:

H'I is calculated as:

[tex]H'I = k * HI[/tex]

This gives:

[tex]H'I = 2 * 24[/tex]

[tex]H'I = 48[/tex]

Answer I to j is 42

Step-by-step explanation:

Can someone help please

Answers

Answer:

Angle 2 = 34 degrees

Angle 4 = 34 degrees

Step-by-step explanation:

Angle 7 = Angle 1

180 - 146 = 34 degrees

so Angle 2 and 4 are 34 degrees, since they are congruent.

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Help rn ahhhh please

Answers

Answer:

117π or 367.56634047

Step-by-step explanation:

Volume = π × r² × h          (r=radius and h=height)

Volume = π × 4² × 13

Volume = π × 9 × 13

Volume = π × 117

Volume = 117π

I'll give points and brainalist for answer / explanation

Answers

Answer:

D. 28.26 in²

Step-by-step explanation:

Area of a circle= πr²

r= 3

π= 3.14

A= (3.14)(3)²

A= 28.26 in²

HELP PLEASE BRAINLYIST
Examine the diagram. It is not drawn to scale.
Wh at is the m angle 3?
Х
m angle 3=

Answers

Answer:

isn't it just 50°

Step-by-step explanation:

180=a straight line.

you are given 75° and 55°

75+55=130

180-130

Answer:

105

Step-by-step explanation:

Chupapi

Some loser deleted my answers

That's why it says 1 answer and 1.5k people helped

Prove that a+b/2≥√ab

Answers

Start by squaring both sides got remove the sqrt
[(a+b)/2]^2 ≥ ab
(a^2 +2ab +b^2 )/4≥ ab
Multiply both sides by 4
a^2 +2ab +b^2 ≥ 4ab
Subtract 2ab from both sides
a^2 + b^2 ≥ 2ab
Subtract 2ab from both sides
a^2 - 2ab + b^2 ≥ 0
Use quadratic equation to solve where a = 1 and b = -2b
2b ± sqrt[(-2b)^2 - (4x1xb^2)]/(2x1)
2b ± sqrt[4b^2 - 4b^2]/2
(2b ± 0)/2
a = b
Substituting for b in the equation a^2 + b^2 ≥ 2ab
2a^2 ≥ 2a^2

helppppppppppppppppppppppp

Answers

Answer:

E = N × C

for

E: earnings

N: number sold

C: cost

she will make:

50 × 1.25 = $62.5

Cayle the cat 3.1.4 Suppose I am conducting a test of significance where the null hypothesis is my cat Cayle will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.002. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals

Answers

Answer: hello the options related to your question is missing attached below are the missing options

answer : Neither the 95% nor the 99% intervals will contain 0.25  ( B )

Step-by-step explanation:

Given that ;

H0 : = 0.25

Ha : ≠ 0.25

p-value = 0.002

also 95% and 99% confidence intervals are constructed

p value = 0.002        i.e. < 0.01  ∝ < 0.05 ∝

This means that we reject null hypothesis in both cases when  (∝ =0.05 and ∝ = 0.01 )

Hence The true statement about my confidence intervals is :

Neither the 95% nor the 99% intervals will contain 0.25

It costs $6 per hour for a park to water the grass. How much will it cost to water the grass for
7/3
hours?

Answers

$43.8, do 7.3 (if that’s how long it was) times $6, giving you 43.8

Answer:

I think the answer is $14 hope this helps!

Step-by-step explanation:

Other Questions
Which sentence does NOT use a colon correctly? A. Warning: This bridge is slippery when wet. B. To make a simple bean dip, mix refried beans with: salsa, spices, and chopped onion. C. The time of Mr. Parks drawing class has been changed from 3:00 to 3:30. Joe buys 6 adult tickets and 4 child tickets for the movies. Each adult ticket cost $9. Each child ticket cost the same amount. Joe pays with a $100 bill and gets $22 in change. How much does each child ticket cost? 3. Marie n'pas cours demain.a. ab. ontC. asd. avons Type a sentence with the following parts of speech in the order they are given. 3. NOUN CONJUNCTION PRONOUN VERB CONJUNCTION VERB PREPOSITION ARTICLE NOUN. INTERJECTION i need help with dis math HELP HAVING A BAD DAYRoger can finish his math homework in 6 hours. Trish can finish the same homework in 5 hours. What part of the homework will Roger and Trish finish if they work together for x hours?I WILL REWARD BRAINLIEST FOR THE CORRECT ANSWER Memos and EmailsEmailOk so here's the thing: 90% of the emails I get from students look like texts. When I was a grant writer, if I sent an email like that, I would have been in my boss's office so fast. SO let's learn proper etiquette for sending emails. 1) Start with a salutation. Hello, Hi, Dear _____, Hi _______, Greetings! any of these work. Make sure your initial email has these. If you don't know the person personally, use Mr., Mrs., Ms., or the new Mx. and their last name. 2) Body: The body has to be right to the point and formal. Most work emails are all business. You can say something like "I hope your Monday is going well!" but beyond that, get to the point. 3) End it well. Best is a good way to go if you don't know the person. Sincerely is good too. It's all personal preference. Just make sure you end it. Also, ALWAYS include your last name. I get so many emails that say "Jackie" or whatever short name people go with, and I have 5 classes. Let's do some math here. Your job is to create an email that you, as the CEO, are sending to one or more of your staff. One is preferable. Set up an issue you wish to address with that person (I really don't care what it is). Make it at least 100 words. Memo An intra-office memo is very important for giving widespread information to your employees. For this piece, you will create a big problem that your employees created, and then send them a memo explaining how you fixed it and how to prevent it from happening again. Use your imagination. Play with this. Make it funny. I want to laughCan someone give me an example Multiplying and dividing radical expressions and leaving them in factored form. I am trying to find the best and easy way to get the factored form correctly. This is my problem: 3x+8 over 36-2x / 27x^2+72x over 3x^2-27. What is circuit training?O Exercise at a high level with no breaks Exercise consistently for a long timeExercise with different activites and sets 3Ba(C2H3O2)2 + 2K3PO4 Ba3(PO4)2 + 6KC2H3O2If 4.36 mol of potassium phosphate react, how many grams of barium phosphate are produced? Do mutations in body cells contribute to genetic variation?(1 point)A) No, the causes of body cell mutations are outside the body and cannot alter DNA.B) Yes, the mutations can be passed on to offspring and contribute to variation in the population.C) Yes, these body cell mutations lead to mutations in the gametes.D) No, the mutations cannot be passed to offspring and only affect the individual. What was the bloodiest battle in ww2?(I dont need help Im just asking for fun) if the circumference of a circle is 52 cm, what is the radius? round to the nearest tenth. PLESE HELP I DONT HAVE THAT MUCH TIME :( Answer all of these questions and you will get the brain list 109Ryan and Daniel are both packing boxes at a factory. Ryan can pack three boxes every hour. The number of boxes Daniel can pack inx hours is represented by the equation below.y = 45Which of the following correctly describes the two functions?OA. The number of boxes that can be packed by Ryan and Daniel each increases over time. Daniel's function has a greater rate ofchange than Ryan's function indicating that Daniel can pack more boxes per hour.0.The number of boxes that can be packed by Ryan and Daniel each decreases over time. Daniel's function has a greater rate ofchange than Ryan's function, indicating that Daniel can pack fewer boxes per hour.OC.The number of boxes that can be packed by Ryan and Daniel each increases over time. Ryan's function has a greater rate ofchange than Daniel's function, indicating that Ryan can pack more boxes per hour.The number of boxes that can be packed by Ryan and Daniel each decreases over time. Ryan's function has a greater rate ofchange than Daniel's function, indicating that Ryan can pack fewer boxes per hour.OD.10ResetSubmitSubmit8 of 10 AnsweredSession Timer: 21:09Session Score: 38% (318)- 15 The grocery store has 2 1/3 times as many cashiers in late afternoon than in the morning. If there are 21 cashiers at 10:00 am, how many would there be at 4:00 pm? Cmo se llama lo que queda delimitado por la sangra y el punto aparte? What do you have to pay attention to when it comes to the nuances of words as a reader?(1 point) the context the metaphors the audience the definitions misdemeanors do not use a pre-trial hearing or grand jury.?A.trueB.false Please answer this :/