Answer:
mean=57
range=19
Step-by-step explanation: there you go
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:
Emily has 20 students and Santiago has 18 students in home rooms
Step-by-step explanation:
to figure out the number in Emily's class we need to answer this question - '15 is 75% of what number'?
we can use:
is/of = %/100
is = 15
of = 'n'
75% = 75/100 or 3/4
15/n = 3/4
cross-multiply to get:
3n = 60
n = 20
So there are 20 students in Emily's home room
Now we find the number of students in Santiago's home room:
the question is - '12 is 2/3 of what number'?
we can write this equation:
12 = 2/3n
multiply each side by 3/2 to get:
36/2 = n
18 = n
18 students in Santiago's home room
The answer is 67
Add all the sides up and you get 67
