Answer:
Not sure about the first one.
For the second question: d. reflect over x-axis, reflect over y-axis, then translate 2 units up
Step-by-step explanation:
It is reflected over both axis and then moved up 2 units.
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:
The sample proportion is 0.36635
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
The sample proportion is the halfway point betwen those two bounds, that is, the sum of those bounds divided by 2.
In this problem, we have that:
Lower bound: 0.2931
Upper bound: 0.4396
What is the sample proportion?
(0.2931 + 0.4396)/2 = 0.36635
The sample proportion is 0.36635
