I will explain you and pair two of the equations as an example to you. Then, you must pair the others.
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
The discount given on the cost of the meal is $15
<h3>How to calculate tax on a given price</h3>
According to the question, we are given the following information
The original cost of the meal = $75
Off coupon = 20%
Required
The number of coupons given
coupon amount = 0.2 * 75
coupon amount = $15
Hence the discount given on the cost of the meal is $15
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Answer:
The probability that at lest one job will be missed in 57 second is
=0.819134
Step-by-step explanation:
Poisson distribution:
A discrete random variable X having the enumerable set {0,1,2,....} as the spectrum, is said to be Poisson distribution.
for x=0,1,2...
λ is the average per unit time
Given that, a job arrives at a web server with the probability 0.03.
Here λ=0.03, t=57 second.
The probability that at lest one job will be missed in 57 second is
=P(X≥1)
=1- P(X<1)
=1- P(X=0)
=0.819134
<u>Given</u>:
Time,
t = 20 years
Rate,
r = 4.4%
Price
= $8,375
Now,
The yield will be:
= 
= 
(%)
Time will be:
= 
= 
As we know the formula,
⇒ 
By substituting the values, we get
The face value will be:
($)
Learn more about face value here:
brainly.com/question/14862802
