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liraira [26]
3 years ago
9

What is the equation of a parabola with a focus (-2,4) and directrix y = 0?

Mathematics
1 answer:
Ronch [10]3 years ago
5 0
The general form of a parabola  when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus.  We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus.  Remember that the parabola will hug the focus and run away from the directrix.  The formula would be slightly different if the parabola was opening either left or right.

Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix.  The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2.  We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2)  Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
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Will the following side lengths make a triangle? 7, 5, 4
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Okay too answer this you have to take the two smallest numbers and add them, in this case the answer would be 5 + 4 = 9. The answer has to be greater than the last number, In this case, 7. So the answer is yes.

8 0
2 years ago
two pounds of dried cranberries cost $5.04, 3 pounds of dried cranberries cost $7.56, and 7 pounds of dried cranberries cost $17
yanalaym [24]
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5 0
3 years ago
The board of an internet start up company has sixteen members. if one person is in charge of research and one is in charge of ma
Brilliant_brown [7]

The number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is <u>240 ways</u>. Computed using permutations.

The permutation is the way of choosing a set of objects from a larger set of objects in a specific sequence.

If we are choosing r number of objects, from n number of objects in a specific sequence, then we follow permutation, and it is given as:

nPr = n!{(n - r)!}.

In the question, we are asked to find the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members.

Since the position is to be chosen in a specific order, we will follow permutation.

The number of positions to be chosen (r) = 2.

The number of members (n) = 16.

Thus, the number of ways is given as:

nPr = n!{(n - r)!},

or, 16P2 = 16!{(16 - 2)!},

or, 16P2 = 16!/14! = 15*16 = 240.

Thus, the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is <u>240 ways</u>. Computed using permutations.

Learn more about permutations at

brainly.com/question/4658834

#SPJ4

6 0
2 years ago
Four streets enter a traffic circle at points A B C and D name six arcs formed by the streets.
lilavasa [31]
Arcs are just sections of the circle
so lets say you had a pizza

and you put some points on the crust, the legnth of the crust from point to point is that arc

example
if you put poins A and B, then arc AB is the crust between points A and B

arcs can include other points as well
 and arc AB=arc BA


so
I wil name easy arcs first
arc AB
arc BC
arc CD
ard DA

now ones that include others
arc AC
arc BD

so the arcs you might want to list are
 
arc AB
arc BC
arc CD
ard DA
arc AC
arc DB

5 0
3 years ago
If there are 3 basketballs for every 7 students at Wilder, then how many students are there if the store room has 49 basketballs
Doss [256]

Answer:

113 is correct because 49 divided by 3 is 16.33. 16.33 multiplied by 7 is 113

Step-by-step explanation:

3 0
2 years ago
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