Answer:
The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)
Step-by-step explanation:
Focus: F=(3,1)=(xf, yf)→xf=3, yf=1
Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:
f(x)=[1 / (4p)] (x-h)^2+k
where Vertex: V=(h,k)
The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:
Vertex is the midpoint between (3,5) and (3,1):
h=(3+3)/2→h=6/2→h=3
k=(5+1)/2→k=6/2→k=3
Vertex: V=(h,k)→V=(3,3)
p=yf-k→p=1-3→p=-2
Replacing the values in the equation:
f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3
f(x)=[ 1 / (-8) ] (x-3)^2 + 3
f(x)= - (1/8) (x-3)^2 + 3
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The equation of the given line is expressed as
3x - 6y = 30
Rearranging it so that it will look like the slope intercept form, it becomes
6y = 3x - 30
Dividing both sides by 6, it becomes
6y/6 = 3x/6 - 30/6
y = x/2 - 5
Looking at the equation, slope, m = 1/2
If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2
To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute
x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes
- 9 = 1/2 * 4 + c
- 9 = 2 + c
c = - 9 - 2
c = - 11
By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be
y = x/2 - 11
First we have to assume that each quarter touched each other. Hence the area of the table not covered by the coins (A) is equal to the total area of the table (At) minus the total area of the coins (Ac). Coins are circle, so
and r =24.26mm. The area of one coin is then 1848.98mm^2. Hence the equation is A = At - xAc where x is the number of coins.
Answer:
289
Step-by-step explanation:
Hope this helps
<u>Complete Question</u>
The line plot shows the amount of green ooze (in cup) carried by ten contestants. Find the amount each contestant would carry if the total amount carried (5 cups) was redistributed equally among all the contestants.
Answer:
1/2 Cup
Step-by-step explanation:
This is a Line Plot in which:
- 1/4 had two Xs
- 3/8 had two Xs
- 1/2 had two Xs
- 5/8 had three Xs
- 7/8 had one Xs
Total
If this amount was redistributed equally among the ten contestants:
Each contestant would carry (5/10) cups =1/2 cup.
