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.
FACTOR ALL OF THE EQUATIONS INTO "y = (x-h)^2 + k," AND THE EQUATION'S VERTEX IS (h,k)
10. y = (x+2)^2 - 11 --> (-2, -11)
11. y = -(x-4)^2 + 32 --> (4, 32)
12. y = 3(x-1)^2 - 5 --> (1, -5)
13. y = -2(x+2)^2 + 5 --> (-2, 5)
14. y = 2(x+1)^2 - 1 --> (-1, -1)
15. y = -5(x-1)^2 + 8 --> (1, 8)
16. y = 3(x-3)^2 - 26 --> (3, -26)
17. y = (x+5)^2 - 32 --> (-5, -32)
18. y = -(x-3)^2 + 10 --> (3, -10)
Answer:
√20
Or
2√5
Step-by-step explanation:
It is very easy just substitute
It will be:
Answer:
How many ounces of fish per gram of protein?
Step-by-step explanation:
Answer:
The Answer is C: Yes, △EFG~ △KLM by SSS or SAS
Step-by-step explanation:
SSS is for side-side-side
Both triangles have all three sides given, so the SSS similarity theorem is one way to prove these triangles are similar.
SAS is for side-angle-side
Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.
Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS
(I also just answered this question on the assignment and got it correct)
