Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
Answer:
180°
Step-by-step explanation:
Angles that are called straight angles make up a straight line.
A straight line measures 180°.
So, angles on a straight line make up 180°.
Hope this helps.
After plotting the data from the table, with the number of times sick per year as a function of the number of apples eaten per week, I can conclude that there is no definite correlation between the two variables. This is because the data points do not have a good fit with any trend, meaning the R-squared value is low. Thus, the number of apples eaten per week has no significant effect on the number of times the people listed get sick per year.
<h3>Solution and Explanation:</h3>
If 
and 
are directly proportional, then they must have a common scalar.
To find we must first find its scalar. If we let 
be the scalar we can form the equation, 
.
We are given the information that if 
then 
. We can use that in finding the scalar.
Now we can solve for when 
knowing that our scalar is 
.
<h3>Answer:</h3>
when
Answer:
a. (-3,3), (18,-6), (9,15)
Step-by-step explanation:
If the scale factor is 3 and dilation is about the origin, each of the coordinates of the pre-image is multiplied by 3 to get the coordinates of the image.
Multiplying (-1, 1) by 3 gives (-3, 3), which matches choices A and C.
Multiplying (6, -2) by 3 gives (18, -6) which matches choices A and D.
The only viable choice is choice A.
