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.
Answer:
18.75%
Step-by-step explanation:
(round answer if needed)
Answer:
-10x+13
Step-by-step explanation:
Im not 100% sure but i tried!
Answer:
No solution
Step-by-step explanation:
Note how "2x" shows up in both equations. This suggests doing a substitution to solve the system.
Focus first on the first equation. Solving 2x - y = 7 for 2x, we get:
2x = y + 7.
Next, we substitute y + 7 for 2x in the second equation:
y = (y + 7) + 3.
Simplifying this produces:
0 = 10
This is not true and can never be true. Thus, this system has no solution.
Answer:
The answer is True.
Step-by-step explanation:
The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability.
Hope this helps you!
