Jae is constructing an open box from a piece of cardboard that is 9 in. Wide and 12 in. Long. Jae cuts squares of equal size from each corner of the cardboard, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x.

Answers

Answer 1

Answer:

The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].

Step-by-step explanation:

Geometrically speaking, the volume of the open box ([tex]V[/tex]), measured in cubic inches, is described by the volume of a right parellelepiped. That is:

[tex]V = w\cdot l \cdot h[/tex] (1)

Where [tex]w[/tex], [tex]l[/tex] and [tex]h[/tex] are the width, length and height of the open box, respectively, measured in inches. Please notice that width of the open box is the width of the piece of cardboard ([tex]w'[/tex]), measured in inches, minus two times the side of the cut squares ([tex]x[/tex]), measured in inches, length of the open box is the length of the piece of cardboard ([tex]l'[/tex]), measured in inches, minus two times the side of the cut squares and the height of the open box is the side of the cut squares. That is:

[tex]w = w' -2\cdot x[/tex] (2)

[tex]l = l' - 2\cdot x[/tex] (3)

[tex]h = x[/tex] (4)

By applying (2), (3), (4) in (1), we expand and simplify the volume function:

[tex]V = (w'-2\cdot x)\cdot (l'-2\cdot x)\cdot x[/tex] (5)

If we know that [tex]w' = 9\,in[/tex] and [tex]l' = 12\,in[/tex], then the equation above is:

[tex]V = (9-2\cdot x)\cdot (12-2\cdot x)\cdot x\,\,\,[in^{3}][/tex]

[tex]V = (108-24\cdot x-18\cdot x+4\cdot x^{2})\cdot x\,\,\,[in^{3}][/tex]

[tex]V = (108-42\cdot x +4\cdot x^{2})\cdot x \,\,\,[in^{3}][/tex]

[tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex]

The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].


Related Questions

El precio del saco de arroz es a 2 como el precio del saco de azúcar es a 3; si el producto de ambos precios es numéricamente 3 456, calcula el precio del saco de azúcar.

Answers

Answer:

El precio del saco del azúcar es de 72.

Step-by-step explanation:

Sean [tex]x[/tex], [tex]y[/tex] los precios del saco de arroz y el saco de azúcar, respectivamente. A continuación, traducimos cada oración relevante en ecuaciones matemáticas:

(i) El precio del saco de arroz es a 2 como el precio del saco de azúcar es a 3:

Aquí se menciona una igualdad entre expresiones racionales, es decir:

[tex]\frac{x}{2} = \frac{y}{3}[/tex]

[tex]3\cdot x -2\cdot y = 0[/tex] (1)

(ii) El producto de ambos precios es numéricamente 3456:

[tex]x\cdot y = 3456[/tex] (2)

Ahora resolvemos el sistema de ecuaciones, despejamos [tex]x[/tex] en (1):

[tex]x = \frac{2}{3}\cdot y[/tex]

Y la aplicamos en (2):

[tex]\frac{2}{3}\cdot y^{2} = 3456[/tex]

[tex]y^{2} = 5184[/tex]

[tex]y = 72[/tex]

El precio del saco del azúcar es de 72.

Find the slope of the line passing through the two points.

(12, 1), (36, 42)

Answers

Answer:

m=41/24

Step-by-step explanation:

The slope of the line passing through the points (12, 1), (36, 42) is m=41/24.

Answer:

To find slope, we need to use the slope formula*.

42 - 1/36 -12 = 41/24

m = 41/24

PLEASE ITS ALREADY LATE AND I NEED TO TURN IT TODAY
Example 1 Fatima works as an intern at a construction company earning $10 per hour. Her office is open 8
hours per day, 5 days a week. Analyze Fatima's potential earnings for the 12 weeks she interns at the
company this summer.
A. Write a function rule to model
the situation
B. Identify the independent
variable
C. Identify the dependent
variable
f(x) =

Answers

Answer:

4800

Step-by-step explanation:

I attached a picture of the work.

We need to made a function that will help us solve this

f(x)=dx; d = $ per hour, x = # of hours

step 1) identify d (in this case, the money made per hour) which = 10

f(x)=10x

step 2) identify x (# of hours total) which = 480

f(x)=10(480)

step 3) solve the equation

f(x)=4800

independent variable:

the number of hours

dependant variable:

the amount of money made after 12 weeks

P(-2, -3) and Q(2, 7)

Answers

Answer:

The slope is 10/4

Step-by-step explanation:

Please help. I’ll give brainliest

Answers

Answer:

x > -5

Step-by-step explanation:

Monica weighed 135 pounds before she started a 3 week diet for her cruise. She lost 18 pounds in the first 2 weeks then gained 5 pounds back the last week. Choose the answer below that correctly identifies how much Monica weighed when she left for her cruise.
A.
112 pounds
B.
104 pounds
C.
140 pounds
D.
122 pounds

Answers

Answer:

D.

Step-by-step explanation:

135 - 18 = 117 + 5 = 122

Answer:

D. 122 pounds

Step-by-step explanation:

135-18=117

117+5=122

Tell me a fun fact about horses I will give brainliest to whoever tells me one I don’t know (I have been riding for 12 years) so I know a lot about horses also don’t answer this just for the points or else you will get reported

Answers

Answer:

Horses can sleep both lying down and standing up.

Step-by-step explanation:

Help plz:))) I’ll mark u brainliest

Answers

X=6 ^ like they said
(Give me thanks ) :)

Please help i need submit it in 10 mins! show work! i will mark brainliest!

Answers

Answer:

C and D is the answer.

Step-by-step explanation:

If m∠5 = x°, according to the Corresponding Angle Theorem, m∠9 will equal the same, and because 9 and 12 are vertical angles, both of these will be the same measure.

help please there is actually a question this time

Answers

Answer:

D...

Step-by-step explanation:

Thats on mine and got it right

La regla de Ruffini es un procedimiento que nos permite dividir fácilmente un polinomio cuando el divisor es un binomio de la forma (x ± a). *


Verdadero

Falso

Answers

Answer:

si como estas chico

Step-by-step explanation:

help me please i will give out brainliest!

Answers

Answer:

A

Step-by-step explanation:

Can anyone do it I'll give you brainiest

Answers

Answer:

64°

Step-by-step explanation:

? + 86 + 90 + 84 + 36 = 360

? = 360 - 86 - 90 - 84 - 36

? = 64

therefore, the missing angle = 64°

Find the hypotenuse
84 + 36 + x = 180
x = 60
80 + 60 + x = 180
x = 40
The value of ? Is 40

David uses 1/2 cups of apple juice for every 1/8 cup of carrot juice to make a fruit drink. Write the number of cups of apple juice David uses for 1 cup of carrot juice.

Answers

Answer:

4 cups of apple juice for 1 cup of carrot juice

Step-by-step explanation:

Solve this problem 48-2(8+2)

Answers

28 is the correct answer:)

Can somebody please help me solve problem 16 .

Answers

Answer:

i think it`s $35

Step-by-step explanation:

Because 80 divided by 2 = 40 and the problem says to subtract 5 so I believe the answer is $35.

The rectangle below has an area of 12y^2+21y^512y 2 +21y 5 12, y, squared, plus, 21, y, start superscript, 5, end superscript. The width of the rectangle is equal to the greatest common monomial factor of 12y^212y 2 12, y, squared and 21y^521y 5 21, y, start superscript, 5, end superscript. What is the length and width of the rectangle? \text{Width} =Width=start text, W, i, d, t, h, end text, equals

Answers

Answer:

This means that the width = 3y²

The length = 4y+7y³

Step-by-step explanation:

Given

Area of the rectangle = 12y^2+21y^5

Width of the rectangle is the greatest common monomial of 12y^2 and 21y^5

First let us get the greatest common monomial of 12y^2 and 1^5

12y^2 = (3  * y * y) * 4

21y^5 = (3 * y*y)*y*y*y* 7

Hence the greatest common monomial is 3 * y * y = 3y²

Factor out 3y² from the area function;

12y^2+21y^5

3y² (4y+7y³) = Area of the rectangle

Length * Width = 3y² (4y+7y³)

On comparing both sides of the equation

This means that the width = 3y²

The length = 4y+7y³

Answer:

4y^2

Step-by-step explanation:

how would you solve p-11=-14

Answers

Answer:

Step-by-step explanation:

all you would need to do is add 11 to both sides, and then you would get your answer.

the product of two consecutive integers is 72. find the integers

Answers

Answer:

the integers are 8 and 9

Step-by-step explanation:

consecutive means one right after the other. 9 is right after 8. and its product is 72, well 8x9 is 72.

1) Dave is 9 years older than his brother.
Dave is also 9 years younger than twice
his brother's Ige. How old is each?

Answers

Answer:

Dave is 27. His brother is 18.

Step-by-step explanation:

Dave is 9 years older than his brother, so if his brother is 18, he is 27. If you doubled the brother's age (18) you would get 36. Then you subtract 36 by 9 and get 27. <3

If x + 12 = 40,
what is the value of x + 7
please help

Answers

35 because 40-12= 28 and 28+7=35

Mr. Ash owns a tree, which is 42 feet tall. He estimates that this tree is 75% as tall now as it will be when fully grown. How tall will the tree be when it is fully grown?

Answers

Answer:

73.5 feet

Step-by-step explanation:

The length of a tree =42 feet

Mr. Ash estimates that this tree is 75% as tall now as it will be when fully grown.

We need to find the length of the tree when it is fully grown. It means we need to find the 75% of 42 and adding 42 to it as follows :

[tex]T=75\%\times 42+42\\\\=\dfrac{75}{100}\times 42+42\\\\=73.5\ ft[/tex]

So, the tree will be 73.5 feet tall when it is fully grown.

What is the scale factor from triangle A to triangle B??

Answers

Answer:

3

Step-by-step explanation:

i believe this should be the answer, simply because 15÷5 is 3. if you were to find x, you would multiply the scale factor value by the first triangle

- 9j + -11 = 61
What is this?

Answers

Answer:

j= - 8

Step-by-step explanation:

- 9j + -11 = 61

        -9j = 61 + 11

        -9j = 72

            j = - 8

Which of the following relations has a domain of {-4, -2, 1}?

Group of answer choices

{(1, 2), (-2, 3), (4, 6)}

{(1, 2), (-2, 2), (-2, 4), (-4, 4)}

None of the other answers are correct

{(-1, 2), (4, 3), (-2, 6), (-2, 3)}

{(1, 2), (-2, 2), (-2, 4), (4, -4)}



Answers

Answer:

{(1, 2), (-2, 2), (-2, 4), (-4, 4)}

Step-by-step explanation:

Plz mark as Brainliest!

Write an
equation for the line in the given form.
slope is -3 and (6,8) is on the line; standard form
Yo

Answers

Answer:

Step-by-step explanation:

Negative3 is6,8

Answer:

Negative3 is6,8

Step-by-step explanation:

i know it

What is the solutions set for -4x - 10< 2?

Answers

The correct answer is x is greater than -3

who good with graphs

Answers

Not me I suck at them

travels only on Saturdays and Sundays and has miles this month. Travels every weekday and has miles this month. If they each travel about the same number of miles each​ day, who travels more miles per day for this​ month?

Answers

Complete question :

William travels only on Saturdays and Sundays and has flown 400 miles this month. Jason travels every weekday and has flown 500 miles this month. Who travels more miles per day for this month

Answer:

WILLIAMS ; 50 miles per day

Step-by-step explanation:

Given that :

Williams travel times = Saturdays and Sundays

Total distance traveled = 400 miles

Jason travel times = Every weekday

Total distance traveled = 500 miles

Number of weeks in a month = 4

Hence, saturdays and Sundays = 4 * 2 = 8 days

Weekdays = 5 * 4 = 20 days

Miles traveled per day:

Williams :

Total distance / number of days

= 400 miles / 8 days

= 50 miles per day

Jason :

Total distance / number of days

= 500 miles / 20 days

= 25 miles per day

50 > 25

Hence, Williams travel more miles per day than Jason

What is the binary number for 15​

Answers

Answer:

111

Step-by-step explanation:

notice that 1000 in binary is 16, as 1000 in binary would be 2^4 = 16. If you subtract 1 from 1000 in binary, you get 111.

If this helped please give brainliest.

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