Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Using complete sentences, explain the connection between the cutout and the volume of the box.

Answers

Answer 1

Answer: V = (12in - 2*x)*(8 in - 2*x)*x

Step-by-step explanation:

So we have a rectangular cardboard sheet, and we cut four squares of side length x in each corner so we can make a box.

Remember that for a box of length L, width W and height H, the volume is:

V = L*W*H

In this case, the length initially is 12 inches, but we remove (from each end) x inches of the length, then the length of the box will be:

L = 12 in - 2*x

For the width we have a similar case:

W = 8in - 2*x

And te height of the box will be equal to x, then:

H = x

This means that the volume is:

V = (12in - 2*x)*(8 in - 2*x)*x

Here we can see the connection between the cutout and the volume of the box


Related Questions

Solve the equation by factoring: 2x3 - 30x2 + 100x =0​

Answers

Ok so first I am going to multiply the equations that need to be multiplied which will simply the equation down to 6-60+100x=0
My next step is going to be subtracting 60 from 6 which will simply my equation down even further to -54+100x=0
Now I am going to add -54 to both side so that my 100x is my itself which will simply my equation down to 100x=54
Our next step is to divide 100 by both side so that x is left by itself causing our answer to be 0.54!
Hope this helps!
Please tell me if I have made an error, I enjoy learning from my mistakes.
Have a great rest your day❤️

Determine whether the equation has one solution, no solution, or infinite solutions.
Explain your reasoning.
9x + 2 = -4(x + 6)

Answers

Answer:

The equation has 1 solution.

Step-by-step explanation:

Because you don't get the same answer on both sides, this equation does not have infinately many solutions. Because you don't get an invalid answer, such as 1 = 0, this equation doesn't have one solution. When you solve this equation, you'd get something similar to this

9x-2 = -4x-24 (distributive property)

13x-2=-24 (combine like terms)

13x=-22 (additive property of inversion)

x = -22/13

which is a valid, real-world solution.

Anybody just help me

Answers

Answer:

1. 54

2. 63

Step-by-step explanation:


What is the effect of the 3 when y = x² is changed to y = (x – 3)??

Answers

Answer:

3 makes the graph move down 3 units.

Step-by-step explanation:

This is because you are subtracting 3 inside the parentheses. Inside the parentheses are up down changes and outside is left right changes.

Is Figure B a scale copy of Figure A?
2.8
2.8
4
Figure A
10
10
16
Figure B
Choose 1 answer:

Answers

Answer:

no

Step-by-step explanation:

What is the equation of a line when the slope is -1/2 and the y-intercept is 0.

Answers

Answer:

y = -1/2x + 0

y = mx+b

Step-by-step explanation:

Draw a square ABCD with A(0,6), B(4,6), C(0,10), and D(4,10)
Reflect it on the vertical line through 6 on the horizontal axis to get
A'B'C'D'. Write the coordinates of the image.

Answers

Answer:A’(12,6) B’(8,6) C’(12,10) D’(8,10)

Step-by-step explanation:

What is the square root of 49.
a. 7
a.
b. 6
C. 8
2 d. 9

Answers

Answer:

a. 7

Step-by-step explanation:

7x7=49

Answer:

7.

Step-by-step explanation:

7x7=49

I cannot solve this.. i want to solve this

Answers

Can’t see that properly can’t you write it bigger or something

a rectangle has a area of 24 square untis and a side length of 3/4 units. find the other side of the rectangle.

Answers

Area = length x width
24 = 3/4w
Divide both sides by 3/4
32 = w

The other side is 32 units

Julio has a house worth $220,000. He has a $175,000 mortgage. Julio says that in this situation, his asset equity is really only $45,000. Which statement explains whether Julio is correct

Answers

Answer:

the answer is A 100%.....

Will give brainliest

Answers

Answer:

steps attached

Step-by-step explanation:

hellppp 8(–10r+–1)+–r+2

Answers

Answer:

-81r - 6

Step-by-step explanation:

8(-10r - 1) - r + 2

use the distributive property

-80r - 8 - r + 2

combine like terms

-81r - 6

plz mark as brianliest if correct!!!

How many square units is the surface area of the box corresponding to the net?​

Answers

Answer:

64

Step-by-step explanation:

We have two squares of 4x4 units and 4 rectangles of 4x2 units, therefore

[tex]2 \cdot (4 \cdot 4)= 2 \cdot 16 = 32 \text{ squre units}[/tex]

[tex]4 \cdot (4 \cdot 2)= 4 \cdot 8 = 32 \text{ squre units}[/tex]

Total Area is therefore 32 + 32 = 64 square units

Given the table, write and equation for the function, and describe what it does.

ASAP!!!

Answers

Answer:

f(x) = 3x + 1

Step-by-step explanation:

f(x) = 3x + 1

f(1) = 3+1 = 4

f(2) = 3*2 + 1 = 7

f(3) = 3*3 + 1 = 10

f(4) = 3*4 + 1 = 13

it's a linear function with slope 3 and y intercept 1

BRAINLIEST FOR CORRECT

Answers

Answer:

10 windows

Step-by-step explanation:

2.5x2.5=6.25 then you would do 64 divided 6.25 to get 10.24 which would give you 10 whole windows.

if you divide 64 by 2.5 it will give you your answer

For net shown, the 5 in x 2 in . in rectangles represent the bases of a solid .



a . use scratchpad or a piece of paper to highlight the perimeter of the lateral area on the net .



b. use scratchpad or a piece of paper to draw a solid to represent the net .



c. indicate the type of solid . _______





d. the solids surface area is ________ in 2 . ​

Answers

It’s b okkkkkkkkkkkkkkkkkk

Write an equation of a line that is perpendicular to the line y = 2/3x + 5 and that passes through the point (0,0)?

Answers

Answer

y=(2)/(3)x-5

Step-by-step explanation:

answer this question please 3+2(5*6)=?

Answers

Answer:

63

Step-by-step explanation:

NEED HELP ASAP 2 questions WORTH 50

Answers

Answer:

The first question tan(24) = x/12 because tan(x) = opposite/adjacent

so x in radians ≈ -25.618....

x in degrees ≈ 5.342....

For the second question tan(72) = x/20

x in radians ≈ -5.248....

x in degrees ≈ 61.553....

Answer:

for first one

relationship between base and perpendicular is given by tan angle

tan24=p/b

tan24=x/12

x=tan24×12=5.34

Step-by-step explanation:

for second one

relationship between base and perpendicular is given by tan angle

tan72=x/20

x=tan72×20=61.55

Evaluate the expression when a=6 and b=9.
6² – 3a / b
Simplify your answer as much as possible.

Answers

34

Why does my answer need to be 20 characters long :p

What's the volume of the prism?

Answers

Answer:

36

Step-by-step explanation:

Isn’t it 36^3 I think hope this helps

Find the value of x that makes m ∥ n 2x x

Answers

Answer:

Step-by-step explanation:

m/n = 2x/2

but what is the equation u didnt mentiones though

What do you think is the best anime show?

Answers

Answer:

My hero academia

Step-by-step explanation:

Black butler,attack on titan

Answer:

Pokemon

Step-by-step explanation:

Give the other guy the brainliest he deserved it.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Do y'all know how to answer this question?
10. c + 28 = 67 ​

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{c + 28 = 67}\\\\\large\text{SUBTRACT by 28 to BOTH SIDES}\\\\\large\text{c + 28 - 28 = 67 - 28}\\\\\large\text{Cancel out: 28 - 28 because that gives you 0}\\\\\large\text{Keep: 67 - 28 because it helps you solve for your c-value}\\\\\large\text{67 - 28 = 39}\\\\\boxed{\boxed{\large\text{Answer: \bf c = 39}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

C+28=67
C=39
All you do is subtract 28 from its self then 67-28=29 then that gives you C=39

If the sales price is $600 and the commision is $72 then what is the rate of the commission

Answers

Answer:

I am not a fan but I'm a very good i am a fan and the

Answer:

[tex] \frac{72}{600} \times 100 = 12\%[/tex]

so, the rate is 12% of the sales.

What provides the energy to set the water cycle in motion?

Question 2 options:

Rain


Sun


Oceans


Wind


I don't know ... yet!

Answers

It’s from the sun :)


Conor has $200 available to buy software
packages to run updates on his employee
computers. Each software package has a
price of $12, and Conor will pay a sales tax
of 8% of the total price of the software.
What is the maximum number of software?

packages Conor can buy?

Answers

Don’t go to that link it is a virus it’s a bot doing that do not go to that link

HELP!! Select the inequality that match the situation:
A school fundraiser has a minimum target of $500. Faculty have donated $100 and there.are 12 student clubs that are participating with different activities. How much money
should each club raise to meet the fundraising goal?
12x - 100 > 500 12x + 100 > 500 12x - 100 ≥ 500 12x + 100 ≥ 500 12x - 100 < 500 12x +100 ≤ 500

Answers

Given:

A school fundraiser has a minimum target of $500.

Faculty have donated $100 and there are 12 student clubs that are participating with different activities.

To find:

The inequality for the given situation.

Solution:

Let x be the money raised by each club.

Number of clubs is 12. So, total money raised by 12 clubs is 12x.

Faculty have donated $100.

Total funds raised [tex]=12x+10[/tex]

A school fundraiser has a minimum target of $500. It means the total funds raised must be greater than or equal to $500.

[tex]12x+100\geq 500[/tex]

Therefore, the correct option is D.

In ΔFGH, h = 9.6 inches, f = 2.5 inches and ∠G=78°. Find the length of g, to the nearest 10th of an inch.

Answers

Answer:9.4

Step-by-step explanation:

Answer: 9.4

Step-by-step explanation:

S.A.S.→Law of Cosines

a^2=b^2+c^2-2bc\cos A

g^2 = 9.6^2+2.5^2-2(9.6)(2.5)\cos 78

g^2 = 92.16+6.25-2(9.6)(2.5)(0.207912)

g^2 = 92.16+6.25-9.97976

g^2 = 88.43024

g=√88.43024 ≈9.404≈9.4

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