Where p is the distance the focus is above the vertex, the equation of a parabola with vertex (h, k) can be written as
... y = 1/(4p)·(x -h)² +k
The vertex is halfway between the focus and directrix. The focus of your parabola is on the y-axis at y=6, and the directrix of your parabola is at y=-6, so the vertex of your parabola is on the y-axis at y=0. That is, the vertex is
... (h, k) = (0, 0).
The distance p from the focus at y=6 to the vertex at y=0 is 6 units, so
... p = 6.
Filling these values into the equation gives
... y = 1/(4·6)·(x -0)² +0
... y = (1/24)x²
4) angle wpr is equal to angle arp because of alternate interior angles (remember WRAP is a parallelogram)
So:
x + 12 = 2x - 37
49 = x
Now plug in x = 49 for all four angles.
angle ARP = 61
angle WPR = 61
angle WRP = 29
angle APR = 29
So the two corners are both 90 degrees. We can easily see that the other two corners are also 90 degrees, thus this parallelogram is also a rectangle.
Answer:
3x=-x-60
Step-by-step explanation:
The z-score is the number of standard deviations away from the mean. We first subtract the actual score from the mean, then divide the difference by the standard deviation. In this case, our actual score is 13, so we subtract from the mean of 16, then divide by the SD of 2
(13 - 16) / 2 = -1.5