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Lynna [10]
3 years ago
13

Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5).

Mathematics
1 answer:
mash [69]3 years ago
6 0
If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down.  We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively.  Also, the equation looks like this when it is horizontal: \frac{(x-h) ^{2} }{ a^{2} } - \frac{(y-k) ^{2} }{ b^{2} } =1.  a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3.  We need to find b now, using Pythagorean's theorem.  ( 2)^{2} + b^{2} =( 3)^{2} and b= \sqrt{5}.  Now we have everything we need to rewrite the equation: \frac{(x-4) ^{2} }{4} - \frac{(y-5) ^{2} }{5} =1
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3 years ago
This year the boys’ basketball team won 4 times as many games as it lost. The team played a total of 40 games. How many games di
Salsk061 [2.6K]

Answer:

The team won 32 games.

Step-by-step explanation:

x = games won

y = games lost

z = total games = 40

x = 4y <em>Won 4 times as many games as it lost</em>

x + y = 40 <em>Games won + games lost = Total games played</em>

4y + y = 40 <em>Sub 4y in for x, as established previously</em>

5y = 40

y = 8

x = 4y

x = 4(8)

x = 32

The team won 32 games.

8 0
3 years ago
Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times. Round your answer to the neares
grigory [225]

Answer:

0.0728177272

Step-by-step explanation:

Given :

Number of flips = 80

Probability of landing on tail at most 33 times ;

Probability of landing on tail on any given flip = 1 / 2 = 0.5

This a binomial probability problem:

Hence ;

P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)

Using a binomial probability calculator :

P(x ≤ 33) = 0.0728177272

7 0
2 years ago
Public Service Announcement : For anyone that continues to delete my answers even if their educational/ or correct can STAY MAD.
lozanna [386]

Answer:

You tell them

Step-by-step explanation:

Never stop being postive

6 0
3 years ago
Read 2 more answers
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