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.
Jackie wants to keep her total work time <em>under </em>20 hours, so we can set up a rough inequality right away:
(work time in hours) < 20
Now, it's going to take here 1/2 = 0.5 hours to finish each necklace, an 1 hour to finish each bracelet, so if she's making x necklaces, it'll take her 0.5x hours to make all of them, and if she's making y bracelets, it'll take her 1y = y hours to finish those. Putting the two together, it'll take her 0.5x + y hours altogether to make the necklaces and bracelets. Putting that together with our first inequality, we get the final inequality
0.5x + y < 20
Answer:
25
Step-by-step explanation:
I'm not really sure if this correct its just a guess but here goes.
So as 26x+5 is a vertically opposite angle. So the top angle would be 25x+5.
then we know angles in a triangle add up to 180 degrees so we would add all the angles together. 26x+5+6x-5+20=180. 26x+6x=32x. -5+5=0. 32x+20=180
180-20=160
140/32=5
6×5=30
30-5=25 so angle A is 25?
Please let me know if this is correct and if its not I'm sorry.
12 out of 18. This is because there is 6 red marbles and 18 of them all together. The question states the probability of the red marble NOT being chosen therefore you need to take away 6 from 18 leaving you with 12. I hope this made sense :)
Hi there
Amount financed
89.70−20=69.7
Finance charge
69.7×(0.0123)=0.86
New balance
Previous balance-payment+finance charge+New charge (new transaction)
89.7−20+0.86+32.11
=102.67
Hope it helps