The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:
(2) (x - 2)² + (y + 4)² = 16
<h3>What is the equation of a circle?</h3>
The equation of a circle of center 
and radius r is given by:
The circle has center at (2,-4), hence 
.
The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.
Hence the equation of the circle is given by:
(2) (x - 2)² + (y + 4)² = 16
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Answer:
84n-27
Step-by-step explanation:
-9(1-10n)-2(3n+9)
-9+90n-6n-18
-27+84n
I'm afraid it's not 11 (unless you can round the result up, but there is no mention about it).
8 + 13 + 11 + 9 + 13 = 54
54 / 5 = 10,8
Firstly you sum all the numbers and then you divide the result by the amount of the summed up numbers.
Answer:
140
Step-by-step explanation:
The arithmetic series is 5, 7, 9, 11, ........., 23.
First u have to determine the no. of terms that can be done by using
Tₙ = [a + (n - 1)d]
Tₙ-------nth term
a---------first term
n---------no.of terms in the series
d---------common difference
here a = 5,d = 2.
let it contain n terms Tₙ= [a + (n-1)d]
Substitute Tₙ, a, and d in the equation
23 = 5 + (n - 1)2
Subtract 5 from each side.
18 = (n-1)2
Divide each side by 2
(n - 1) = 9
Add 1 to each side
n = 9 + 1 = 10
The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]
Substitute Sₙ, a, n and d in the equation
Sₙ= (10/2)[2(5) + (10-1)2]
Sₙ= (5)[10 + (9)2]
Sₙ= 5[10 + 18]
Sₙ= 5[28] = 140
Therefore the sum of the arithmetic sequence is 140.
The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
<h3>Define the term permutation?</h3>
- The number of potential arrangements for a given set is assessed mathematical terms, but this procedure is referred to as permutation.
- The arrangement's order is essential when using permutations.
For the stated data;
Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.
There are total 9 digits (0 - 9).
There are total 26 letter (A - Z)
Repetitions of letters and numbers given allowed.
Thus, numbers and the letters ca be arranged as;
1st place = 9 ways.
2nd place = 9 ways.
3nd place = 9 ways.
4th place = 26 ways.
6th place = 26 ways.
7th place = 9 ways.
8th place = 9 ways.
Total ways = 9×9×9×26×26×9×9
Total ways = 39917124
Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
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