Answer:
Step-by-step explanation:
The standard form of a parabola is
![y=ax^2+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc)
If we know the y intercept is (0, 400), that means that when x = 0, y = 400. That allows us to begin by finding c:
and c = 400.
Now to find a and b. Using the fact that the vertex is (1, 405), we know that h is 1 and k is 405. If
and h = 1, then
and
2a = -b so
b = -2a. Save that for a minute or two.
If
and k = 405, then
and
and
405 = 400 - 4a and
5 = -4a so
![a=-\frac{5}{4}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B5%7D%7B4%7D)
We will use that a value now to find the value of b. If b = -2a, then
and
![b=\frac{10}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B10%7D%7B4%7D)
Writing our parabolic equation now:
![y=-\frac{5}{4}x^2+\frac{10}{4}x+400](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B4%7Dx%5E2%2B%5Cfrac%7B10%7D%7B4%7Dx%2B400)
Finding the x-intercepts is just another way of saying "factor this quadratic" so we will begin that by setting the quadratic equal to 0:
and who hates all those fractions more than I do? Probably nobody, so we are going to get rid of them by multiplying everything by 4 to get
Assuming you can throw that into the quadratic formula to solve for the 2 values of x where y = 0, you'll find that the x-intercepts are
x = -16.91647287 and 18.91647287
-2x-3y <12
For this case what you should do is to graph the following straight line:
-2x-3y = 12
Then, the solution will be the shaded region that satisfies the following inequality:
-2x-3y <12
In the shaded region you will find all the solution points.
Answer:
See attached image
Answer:
The answer is
![x = 29 \\ y = 50](https://tex.z-dn.net/?f=x%20%3D%2029%20%5C%5C%20y%20%3D%2050)
Step-by-step explanation:
![(6x - 32) + (2x - 20) = 180 \\ 8x - 52 = 180 \\ 8x = 232 \\ x = 29](https://tex.z-dn.net/?f=%286x%20-%2032%29%20%2B%20%282x%20-%2020%29%20%3D%20180%20%5C%5C%208x%20-%2052%20%3D%20180%20%5C%5C%208x%20%3D%20232%20%5C%5C%20x%20%3D%2029)
By the way can find y
I'm estimating that this is about the 5th or 6th time that I've seen this
question posted on Brainly, and there's STILL not enough information
given to answer it. Maybe several different classes in several different
schools are all using the same textbook, and the book has a big mistake
in (at least) one of the problems.
Answer:
37.5 ( i didn't round cause the answer looked simple already)
Step-by-step explanation:
formula for triangle is base x height divided by 1/2
Base(5) x Height(15) = 75 now divide by 1/2
75 divided by 1/2 = 37.5
(Could i have brainliest if i'm right?)