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.
Answer:
The answer is below
Step-by-step explanation:
The question is not complete. A complete question is in the form:
A letter is chosen at random from the letters of the word EXCELLENT. Find the probability that letter chosen is i) a vowel ii) a consonant.
Solution:
The total number of letters found in the word EXCELLENT = 9
i) The number of vowel letters found in the word EXCELLENT = {E, E, E} = 3
Hence, probability that letter chosen is a vowel = number of vowels / total number of letters = 3 / 9 = 1 / 3
probability that letter chosen is a vowel = 1/3 = 0.333 = 33.3%
ii) The number of consonant letters found in the word EXCELLENT = {X, C, L, L, N, T} = 6
Hence, probability that letter chosen is a consonant = number of consonant / total number of letters = 6 / 9 = 2 / 3
probability that letter chosen is a consonant = 2/3 = 0.667 = 66.7%
Answer:
3.92$
Step-by-step explanation:
Given that the die-cast has been represented by 3/16 in to 1 foot, We are are required to calculate for the actual measure of a toy measuring 6.5 inches wide and 8.5 inches long;
the actual width will be given by:
(6.5÷3/16)×1
=34.66666667
=35 feet
The actual length will be given by:
(8.5÷3/16)×1
=45.333
=45 feet
Answer:
Step-by-step explanation:
Factor the sum of cubes
a³ + b³ = (a+b)(a² - ab +b²)
= 2a² - 2ab + 2b²
a³ + b³ + 6ab = 2a² + 4ab + 2b²
= 2(a² + 2ab +b²)
= 2(a+b)²
= 8
