check the picture below. So the parabola looks more or less like so.
bearing in mind that the distance "p" is the same from the vertex to the directrix or the focus point, so the vertex is therefore half-way between those two fellows, now, from 3,4 up to y = 8, there are 4 units, and the vertex is half-way, thus is at y = 6, and x = 3, (3, 6) as you see there in the picture.
the parabola is vertical, meaning the squared variable is the "x", and is opening downwards, meaning the "p" distance is negative, so since "p" is 2 units, then p = -2.
![\bf \textit{parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=3\\ k=6\\ p=-2 \end{cases}\implies 4(-2)(y-6)=(x-3)^2\implies -8(y-6)=(x-3)^2 \\\\\\ y-6=\cfrac{(x-3)^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}(x-3)^2+6 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%0A%5C%5C%5C%5C%0A4p%28y-%20k%29%3D%28x-%20h%29%5E2%0A%5Cqquad%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Avertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%0A%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ah%3D3%5C%5C%0Ak%3D6%5C%5C%0Ap%3D-2%0A%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%28y-6%29%3D%28x-3%29%5E2%5Cimplies%20-8%28y-6%29%3D%28x-3%29%5E2%0A%5C%5C%5C%5C%5C%5C%0Ay-6%3D%5Ccfrac%7B%28x-3%29%5E2%7D%7B-8%7D%5Cimplies%20%5Cblacktriangleright%20y%3D-%5Ccfrac%7B1%7D%7B8%7D%28x-3%29%5E2%2B6%20%5Cblacktriangleleft)
Answer:
one sixth of 7.5 pounds is 1.25, so 7.5 minus the rotten 1.25 is 6.25.
Step-by-step explanation:
Answer:
The area of rectangle is 12cm² and the perimeter is 14cm.
Step-by-step explanation:
First, you have to find the length of the rectangle using Pythagoras Theorem :
a² + b² = c²
a² + 3² = 5²
a² = 5² - 3²
a² = 16
a = √16
a = 4 cm
Next, you have to find the perimeter and area of rectangle :
Perimeter = 2(length + breadth)
P = 2(4 + 3)
P = 2(7)
P = 14 cm
Area = length×breadth
A = 4×3
A = 12 cm²
Answer:
$226
Step-by-step explanation:
1. define the variable x
x = # of days to rent the carpet cleaner
2. substitute x for 7 days
c(7) = 30(7) + 16
3. solve
c(7) = 210 + 16
c(7) = 226
For 7 days, Rhonda will have to rent the carpet cleaner for $226.
Answer:
I think the answer is
Step-by-step explanation:
Reason :
Therefore
