Check the picture below. So the parabola looks more or less like so.
let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.
Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \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=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20this%20one%7D%7D%7B4p%28y-%20k%29%3D%28x-%20h%29%5E2%7D%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-2%5C%5C%20k%3D5%5C%5C%20p%3D-1%20%5Cend%7Bcases%7D%5Cimplies%204%28-1%29%28y-5%29%3D%5Bx-%28-2%29%5D%5E2%5Cimplies%20-4%28y-5%29%3D%28x%2B2%29%5E2%20%5C%5C%5C%5C%5C%5C%20y-5%3D-%5Ccfrac%7B1%7D%7B4%7D%28x%2B2%29%5E2%5Cimplies%20y%3D-%5Ccfrac%7B1%7D%7B4%7D%28x%2B2%29%5E2%2B5)
The bottom left angle is 180 -80=(100)
So the remaining 2 angles are equal 80
As all angles in a triangle are equal to 180
X+5 + x - 5 =80
Simplify
2x=80
X=40
Soo one of the angles are 40-5 which is (35)
And the other is 40+5 which is (45)
So sean is not correct
~sorry sean teehee
Answer:
The circle has an area of about 1385 square mm.
Step-by-step explanation:
Let's recall that circles have an area that can be found with the following formula:
where r is the radius of the circle.
Now, focus your eyes on the circle. We are shown that the diameter of this circle is 42 mm, but we only want the radius. Since the radius is half the diameter, the radius is 21 mm. Now, we can solve for the area of the circle.
So, to the nearest whole number, the area of the circle is 1385 square mm.
Answer:
4.5 minutes
Step-by-step explanation:
first convert 3/4 to a decimal so you can multiply it which would be .75
so then .75 times 6=
4.5
Answer: Carlos is correct
Step-by-step explanation:
2x^5-250x^2
The first step is to factorize out 2x^2
2x^2(x^3-125)
This can be rewritten as
2x^2(x^3-5^3),
Recall, difference if cube (a^3-b^3)
= (a-b)(a^2 +ab + b^2)
from our equation,
a= x
b = 5.
So the difference of cubes will be
2x^2[(x-5) (x^2 + 5x + 5^2)]
=2x^2[(x-5) (x^2 + 5x + 25)]
Carlos followed these steps. So he is correct. Carlos is correct because he correctly factored the GCF, identified a and b, and applied the difference of cubes method.
Amber is incorrect because 125 is equal to b3, not b.
Bernie is incorrect because x2 is not the GCF of the polynomial. The GCF is 2x^2.
