Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are inches, then the volume of the box is given by V(x)=x(11-2x)(17-2x)

Answers

Answer 1

Answer:

Step-by-step explanation:

Refer the attached picture for complete question

a) V(x)=x(11-2x)(17-2x)

B(x)=140

Side and volume cannot be negative

So, x> 0

11-2x>0   and 17-2x>0

[tex]x<\frac{11}{2}[/tex] and [tex]x< \frac{17}{2}[/tex]

Domain for V(x) :[tex]0<x<\frac{11}{2}[/tex]

b)For finding the greatest Volume

[tex]\frac{dV}{dx}=0[/tex]

[tex]V(x)=x(11-2x)(17-2x)=4x^3-56x^2+187x[/tex]

[tex]\frac{dV}{dx}=12x^2-112x+187=0\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{112\pm\sqrt{(112)^2-4(12)(187)}}{2(12)}[/tex]

x=7.155 , 2.177

Consider the graph

So, Volume at 7.155 is negative

Thus x≈2 gives the greatest volume

c)

Consider the graph .

It is increasing from [tex]-1 \leq x \leq 2[/tex] and [tex]x \geq 7[/tex]

So, Graph increasing interval is [-1,2] ∪[7,∞)

d)

At the point of intersection, both graph has the same value .

Elena Is Making An Open-top Box By Cutting Squares Out Of The Corners Of A Piece Of Paper That Is 11

Related Questions

What the equation of the line that is perpendicular to the line y = −3x + 5 that goes through point D (9, 2)?

Answers

Answer:

y=1/3-1 ...............

6 lumberjacks can cut down 15 mahogany trees in 2 hours. How much longer will
it take 8 lumberjacks to cut down 35 mahogany trees working at the same rate?
B. 1}hr
c.hr
A. 3hr
D. 21hr​

Answers

9514 1404 393

Answer:

  3.5 hr

Step-by-step explanation:

We assume that "the same rate" means effort per tree is a constant. "Effort" is measured as the product of lumberjacks and hours. Then ...

  (lumberjacks)(hours)/trees = (6)(2)/15 = (8)(t)/35

Multiplying by 35/8, we have ...

  (35/8)(12/15) = t = (3·4·5·7)/(2·3·4·5) = 7/2 = 3.5

It will take 8 lumberjacks 3.5 hours to cut down 35 trees.

can someone help me I need a quick answer. If a base of 5 has an exponent of 2 and is subtracted from a base of 4 that hs an exponent of 3, what is the remaining number?

Answers

Answer:

39

Step-by-step explanation:

4^3 equals 64, and 5^2 equals 25. 64 - 25 = 39.

338 points in 16 games. how many points did they make per game?​

Answers

21.125 (21) points in each game.
just divide 338 by 16.
-hope this helps

write an equation of a line passing through point p(-2, 6) that is parallel to the line x= -5​

Answers

Answer:

x= -2

Step-by-step explanation:

x = -5 is a vertical line, so a line parallel would also have to be a vertical line

It goes through the point ( -2,6)

The x coordinate -2

So a line parallel would be x= -2

Answer:

x= -2

Step-by-step explanation:

Which of the following can be concluded given Z1 a ZT?
4
3/2
5
a

Answers

D alternate exterior angles

Calculate the unit rate for each option of Takis, explain which option is better,
and why?

Answers

Answer: .42 for left bag .22 for right bag

(1st explanation is the left bag and the 2nd in the right bag)
Explanation: If the bag is $1.68 for 4oz of takis and you want to find the unit rate you do 1.68 divided by 4 which equals $0.42 per oz of takis.
2nd Explanation: If its $4.42 for 20 oz of takis do 4.42 divided by 20 which equals $0.22.

Explanation for the teacher (I saw the worst words ever, "why?": The right bag of takis are the best value since the left bag is a little bit less than twice the right bag.

Answer:

they are better because they are cheeper than the other

Solve for f 7a - 3d + 6f = 5

Answers

Answer:

f = 5/6 - 7a/6 + d/2

Step-by-step explanation:

Expand & simplify 4(t+2)+6(t-4)

Answers

Answer:

10t - 16

Step-by-step explanation:

4(t + 2)+ 6(t - 4)

4t + 8 + 6t -24

10t - 16

Expand the first bracket: 4t + 8
Now expand the second bracket: 6t - 24
4t + 8 + 6t - 24
Add all like terms together: 10t - 16

Tara has 3/4 cup of ice cream. How many 1/5 -cup servings are in 3/4 cup of ice cream?​

Answers

Answer:

4/15

Step-by-step explanation:

because 1/5÷3/4=4/15

Find the value of each variable.

Answers

Answer:

19. x = 65

20. x = 12

21. x = 35, y = 85

Step-by-step explanation:

19. 2x -10 = 120

2x (-10 + 10) = (120 +10)

2x/2 = 130/2

x = 65

20. 2x + 4x + 108 = 180

6x + (108 - 108) = (180 - 108)

6x/6 = 72/6

x = 12

21. 2x + 25 = 3x - 10

2x + (25 - 25) = 3x (- 10 - 25)

(2x - 3x) = (3x - 3x) - 35

-x/-1 = -35/-1

x = 35

3x - 10 + y = 180

3(35) - 10 + y = 180

105 - 10 + y = 180

(95 - 95) + y = (180 - 95)

y = 85

An equilateral triangle with side length 4cm is shown in the diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.

Answers

Answer:

4√3cm^2

Step-by-step explanation:

we know that the area of equilateral triangle is √3/4a^2

Irma is just learning to play the Happy Fairies video game. In the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens. Irma had a total of – 5 points. Then, her fairy house fell over in the wind and she got – 3 points. How many total points does Irma have now?

Answers

Answer: -8 points

Step-by-step explanation:

From the question, we are informed that Irma is just learning to play the Happy Fairies video game and that in the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens.

We are told that Irma had a total of –5 points, then, her fairy house fell over in the wind and she got –3 points.

Her total points now will be the addition of -5 and -3. This will be:

= -5 + (-3)

= -5 - 3

= -8

Note that minus multiplied by plus is minus.

Answer: -8

Step-by-step explanation:

Mr. Leto plans to save money to buy a carpet. If he saves $50 each week for 30 weeks, he will have saved the exact amount of money needed to buy the carpet. If Mr. Leto instead saves $75 each week, how many weeks will it take him to save the same amount of money?

Answers

Answer:

Number of new weeks = 20 week

Step-by-step explanation:

Total money saves = $50 x 30

Total money saves = $1,500

Find:

Number of new week

Computation:

Total money saves = Number of money save per week x Number of new weeks

1,500 = 75 x Number of new weeks

Number of new weeks = 20 week

HELP PLEASE ASAP
Which of the following are irrational numbers?
55
53
✓20
71
Submit

Answers

Answer: √20

Step-by-step explanation:

4.47213595 (the 5 repeats)

Kathy ran the 400-meter dash in 60.48 seconds. She ran the 200 meter dash in 28.9 seconds.If she divided her 400-meter dash time in 8 equal time segments, how long would it take cathy to run one of these segments Please HELPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

Kathy would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.

Step-by-step explanation:

Kathy ran the 400-meter dash in 60.48 seconds, so if she now divided that time into 8 equal time segments we have:

[tex] t = 60.48 s [/tex]

By dividing the above equation into 8:

[tex] t = \frac{60.48 s}{8} = 7.56 s [/tex]

Hence, she would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.

I hope it helps you!

Part A: If (6^2)^x = 1, what is the value of x? Explain your answer.

Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer.

Answers

Step-by-step explanation:

A.

[tex](6^2)^x=1\\\\36^x=1\\\\36^x=36^0\Rightarrow x=0[/tex]

Every number to the power of 0 gives us 1

[tex]a^0=1\ \text{for}\ a\in\mathbb{R}[/tex]

B.

[tex](6^0)^x=1\\\\1^x=1\\\\x\in\mathbb{R}[/tex]

1 to the any power gives us 1.

[tex]1^n=1\ \text{for}\ n\in\mathbb{R}[/tex]

Corliss earns an hourly wage, as well as tips, each day he works. His daily earned income, m, after h hours can be represented by the inequality m>11h+35.

He makes at most $11 per hour plus $35 in tips.
He makes more than $11 per hour plus $35 in tips.
He makes at least $11 per hour plus $35 in tips.
He makes less than $11 per hour plus $35 in tips.

Answers

Answer:

He makes more than $11 per hour plus $35 in tips

Step-by-step explanation:

First, you should always look at the sign and identify whether it's greater than, less than, greater than or equal to, or less than or equal to. In this inequality, the sign being shown is greater than: represented by m>11h+3

Here are inequality key words to help better understand the signs:

> : Greater Than, More Than

≥ : More Than or Equal To, At Least, No Less Than, A Minimum of

< : Less Than, Fewer Than

≤ : Less Than or Equal To, At Most, No More Than, A Maximum of

What is the mean height of Bella's corn stalks?

A 69cm

B 75cm

C 78cm

D 80cm

E 81cm

Answers

Answer:

C. 78

Step-by-step explanation:

Add all of them together, then divide by 5 because there are 5 different plants.

C.78 add all together then divided by 5

Can someone send me the answer to the question in the photo? (with solutions)

Answers

Answer:

This is so easy question .

I can do.

Plz help do questions 9 and 10 I will give brainlest

Answers

Answer:

9. B.) c=28h

10. C.) 5x=45y

Step-by-step explanation:

1. 84 cards in three hours 84/3 = 28 cards per hour

2. 2x=18y which means x=9y, x 5 = 5x = 45y

4) Tony pays $245 for a PS4. He decides to sell the PS4 with a 30%
markup. How much is Tony selling the PS4 for?

Answers

Answer:

175

Step-by-step explanation:

trust me .

Answer:

318.5

Step-by-step explanation:

30% of 245 is 73.5

245 + 73.5 = 318.5

Tammy rents an apartment close to her school campus. The amount that she spends on rent is given by the equation r = 355m, where r is the amount spent on rent and m is the number of months she stays in the apartment. What is the constant of proportionality (r to m) for this proportional relationship?
A.

B.

C.
177.5
D.
355

Answers

answer is c because if it's not a and b then the only answers will be c and d and d is the same as the number so it's c

a line is perpendicular to y - 5 = -1/4(x + 8) and goes through the point (-1,2). What is the lines y-intercept?

Answers

Answer:

y = 4x + 6

Step-by-step explanation:

Turn the equation we are given into slope-intercept form.

y - 5 = -1/4(x + 8)

y - 5 = -1/4x - 2

y = -1/4x + 3

The slope of a perpendicular line is the opposite reciprocal of the original line.

-1/4 -> 4/1 -> 4

Find the new y-intercept using the point given.

y = 4x + b

2 = 4(-1) + b

2 = -4 + b

6 = b

Fill in everything we solved for.

y = 4x + 6

Best of Luck!

PLEASE HELP!! MATH FINAL, NO EXPLANATION NEEDED :))

Answers

Answer:

B.

Step-by-step explanation:

When you move right or left it's inside the parentheses and the opposite so right is - and left is + when you move up or down its the same so up is + and down is -.

Answer:

B

Step-by-step explanation:

It's asking for moving right 3 and down 2. To move right three, you have to subtract 3 (It's switched up). This goes inside the parenthesis, because if it was outside of the parenthesis, it would be going up or down. Now, to go down 2, you have to subtract 2 outside of the parenthesis (It's normal). That leaves you with f(x-3)-2. Therefore, the answer is B.

The post office is selling 7 cent stamps and 9 cent stamps. If a package requires 43 cents to mail, how many 9 cent stamps will you need?

Answers

4 9 cent stamps and 1 7 cent stamp

If a package requires 43 cents to mail, the number of 9 cent stamps that will be needed is 41cent  is the value needed.

What is meant by  mathematical equation?

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Identify the question that is being asked. Write the pertinent details in straightforward statements. Give values that need to be discovered symbols. Find the mathematical connections between the assertions.

The most well-known equation in the entire universe is E=mc2. Just like that. It is succinct, elegant, and expresses a phenomenon that is so important that everyone should be aware of it.

Given,

The equation will be:

7x + 9y = 43

7(2) + 9(3) =41

14+ 27 = 41

Since the value that's is gotten not equal to 43  

Therefore  The value is  41 cent  is needed to 9 cent stamps

To learn more about mathematical equation refer to:

https://brainly.com/question/2972832

#SPJ2

PLZ HELP ME HELP PLZ

Answers

Answer:

2000

Step-by-step explanation:

that i the answer becuase you multply

−38÷7/12 another math question.

Answers

Answer:

-0.45238095238

Step-by-step explanation:

-38 divided by 7/12= -0.45238095238

can a triangle have an exterior angle that is obtuse at two vertices? Explain

Answers

Answer:

Yes

Step-by-step explanation:

An obtuse triangle will have two obtuse angle at its exterior.

Take for instance, the angles in the triangle are 100, 40 and 40.

The exteriors would be 80, 140, 140 (this is gotten by subtracting each interior angles from 180).

So, using the above analysis, we can conclude that the statement is possible.

I need helpppp?!!!
What is the slope of the line??
Please give right answer

Answers

Answer: -1/2

Step-by-step explanation:

Slope=rise/run

Up 1 and to the left 2 which makes it a negative

slope = -1/2

to find this, take two points from the graph. I used (0,3) and (2,2). Then find the difference between the y coordinates and x coordinates. So in this case, the difference between 3 and 2 is 1. And the difference between 0 and 2 is two. And remember it is rise over run so that makes it 1/2. And lastly, you know it's negative because the graph is decreasing. hope this helpsss
Other Questions
If A= (-1,-3) and B= (11,-8) what is the length of AB? Select each polynomial expression that could be factored by grouping. plz help me and plz show work 3x + 2y + z = 7 2x + 3y - z = 8 5x + y + 2z = 11 el precio de 25 latas de aceite es de 248 cuntas latas de podrn comprar con 1240? Complete the following organizer to compare Western European and Central European empires.Part 2: Comparing Empires in Eastern Europe and AsiaComplete the following organizer to compare Eastern European and Asian empires.Part 3: Creating Comparative SentencesUse the information you included in the graphic organizers to fill in the blanks and create SAQ comparative sentences. An example has been provided but you will still need to complete each using different countries/empires from your organizer. As you identify similarities and differences between the 10 empires, fill in the two you are comparing on the respective lines, then continue to fill in the blanks to complete the comparative sentences.Note: There are many correct answers for each set of blanks. Which types of rocks can become metamorphic rock?both igneous and metamorphic rockboth igneous and sedimentary rockclastic sedimentary rockclastic or chemical sedimentary rock Cars driving through the tunnel (turns, turn) their lights on. Islam was introduced into West Africa byThe main import of the West African kingdoms was Chromium-48 decays. After 6 half-lives, what fraction of the original nucleiwould remain? Detective is to investigate as advertisement is to the first generation of computers used vaccum tubes .Why were they replaced by the transistors can u guys help with my one question i have left Compare the impacts these two organizations have had on the federal bureaucracy. How has each helped shape the activities and identity of the executive branch? Which do you think has had a greater impact on the bureaucracy? Provide evidence to support your opinion. (4 points) pair 1 What is 40 percent of 50? 1. 202. 303. 404. 10 The temperature at 6:00 am in New York was -7 C. At 2:00 pm thetemperature in New York was 7 C. What was the change in the temperature temperature? Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC Look at the table. Bob ran 3 miles in 18 minutes. Complete the table: Sorry its so long But please help! 20 points Read the story below and complete the assignment at the end.02.02 The Great North American CircusThere was great excitement in Smyrna, especially among the boys. Barlow's Great American Circus in its triumphal progress from state to state was close at hand, and immense yellow posters announcing its arrival were liberally displayed on fences and barns, while smaller bills were put up in the post office, the hotel, and the principal stores, and distributed from house to house.It was the largest circus that had ever visited Smyrna. At least a dozen elephants marched with ponderous steps in its preliminary procession, while clowns, acrobats, giants, dwarfs, fat women, cannibals, and hairy savages from Tibet and Madagascar were among the strange wonders that were to be seen at each performance for the small sum of fifty cents, children half price.For weeks the young people had been looking forward to the advent of this marvelous world of curiosities, and the country papers from farther east had given glowing accounts of the great show, which was pronounced greater and more gorgeous than in any previous year. But it may be as well to reproduce, in part, the description given in the posters:BARLOW'S GREAT NORTH AMERICAN CIRCUS.Now in its triumphal march across the continent, willgive two grand performances,AT SMYRNAon the afternoon and evening of May 18th.Never in all its history has thisunparalleled show embraced a greater variety of attractions,or included a larger number of world-famousacrobats, clowns, bare back riders, rope walkers, trapezeartists, and star performers,in addition to a colossal menagerie, comprisingelephants, tigers, lions, leopards,and other wild animals in great variety.All this and far more, including a hundredDARING ACTS,can be seen for the trifling sum of fifty cents;children half price.COME ONE! COME ALL!Two boys paused to read this notice, pasted with pictures of elephants and circus performers on the high board fence near Stoddard's grocery store. They were Dan Clark and Christopher Watson, called Kit for short.See assignment belowCharacters:Setting: Conflict: Rising action:Climax:Resolution action: Reflection: determine the range of the following graph: