1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KengaRu [80]
3 years ago
6

PLZ SHOW ALL WORK

Mathematics
1 answer:
lara31 [8.8K]3 years ago
3 0

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
You might be interested in
Multiplying Binomials: (−2h+9)(9h−2) = ?
oee [108]
(−2h+9)(9h−2)

-18h^2 + 4h + 81h - 18

Answer: -18h^2 + 85h - 18
5 0
3 years ago
Explain how to solve -4(1.75 + x) =18
kobusy [5.1K]

Answer:

first change any decimal to a whole. -4(175+x)=18. Then times -4 by 175 and x, -700+ 4x =18. Then add +700 to -700 which equals just 4x ,then add +700 to 18, which is 4x = 718. then divide both sides by 4 and estimate. x= 180

Step-by-step explanation:

8 0
2 years ago
Help me Find the area of
andriy [413]
I believe the answer is 4,523. Correct me if im wrong
3 0
3 years ago
Read 2 more answers
Need help wit home work pl...<br>​
Mariulka [41]

Answer:

Step-by-step explanation:

I will help you just tell me what grade your in and i will help

5 0
3 years ago
5.676524687 in fraction
Ugo [173]

Answer:

5 7/10

Step-by-step explanation:

First, we need to round the number.

5.7

Now that we've rounded the number we can convert it to a fraction based on where the decimal is located.

5.7

   |

   v

Tenths

So, the decimal is in the tenths that means we have to put 7 over 10.

5 7/10

Hope this helps! :)

6 0
2 years ago
Other questions:
  • Please Help I will reward brainliest
    12·1 answer
  • Harper knows he is 50 yards from school. The map on his phone shows that the school is 34 inch from his current location. How fa
    11·1 answer
  • Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. if ashley sold a to
    15·1 answer
  • Please help ASAP.........
    8·2 answers
  • A company that makes cartons finds that the probability of producing a carton with a puncture is 0.03​, the probability that a c
    11·1 answer
  • The circle graph shows Tommy Blox spent the money he earned last summer. If he spent $80 on entertainment, how much did Tommy ea
    6·1 answer
  • Ayo can yall help me plzzz
    5·2 answers
  • Meghan earns $20 for every 5 bracelets she makes. How many bracelets must she make to earn $140?
    11·2 answers
  • How do I figure this out?
    9·2 answers
  • Take some time to fill in your notes, the area that is not shown in this video. Fill in the table with the values you think are
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!