Answer:
a=-1 goes to the third graph (because it's negative so obviously it's a sad smile)
a=1 goes to the first graph
a=0.25 goes to the second graph
Step-by-step explanation:
The smaller the value of a, the wider the the parabola would be. If the value of a is large then the parabola becomes smol
Answer:
120
Step-by-step explanation:
From 20, choose 3:
₂₀C₃ = 120
Here we use combinations instead of permutations because the order doesn't matter.
The volume formula for a square or a rectangle, even, is V=l*w*h
Here, we are given our volume as 675, now we just have to find everything else, right?! Well, if you have a square, all 4 sides are the same exact length, so the length and the width of our formula are going to be the same so we only have to worry about finding a value for one and then use it twice. If you have a square of side length x and you cut 2 squares out of each side measuring 3 inches each, you are cutting away 6 inches. So the side now reflects a length of x - 6. Which is used for the length and the width in our formula. The height of the box will be 3 inches, or in other words, what you cut away from each corner to make a box in the first place! So our formula will look like this: 675 = (x - 6)(x - 6)3. Easiest thing to do is to divide away the 3 to get 225 = (x - 6)(x - 6). Now expand that by FOILing:

Set it equal to 0 to solve for x, the length and width of each side by moving the 225 over to the other side:

Now you just have to factor this. When you do, you get x values of 21 and -9. But we all know that you cannot have a side length be a negative number so the x value is 21. That's the side length of the original paper before you cut 6 inches away.