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.
The Correct option is 36.60
Step-by-step explanation:
The key to solving this question lies
around measurement
conversion,specifically converting
grams into its equivalence in
kilograms.
1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg 1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg
70 grams=0.07 kg
Julie pays=$600*0.009=$5.4
Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-
$5.4) than Julie paid
Option is wrong because that was Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-
$5.4) than Julie paid
Option is wrong because that was
what Julie paid
Option D is wrong because that was
what Jacques paid
Option B is obviously wrong
Answer:
512
Step-by-step explanation:
8 x 8 x 8 = 512
2/3 n = -12 Write equation
(3/2) 2/3n = -12/1 (3/2) Isolate n
n = -36/2 Simplify
n = -18 Answer
Answer:
O length = 11 inches width = 12.5 inches
Step-by-step explanation: