Match the pairs of equations that represent concentric circles. Tiles
1 answer:
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.
You might be interested in
Is it 2x +7= -3? If so the answer is -5
for converting km to meters
1 km = 1000 m
5807 km = 1000 × 5807 m
= 5807000m ...
for converting cups to gallons
1 cup = 0.0625 gallons
2144 cups = 0.0625 × 2144 gallons
= 134 gallons
So first you need to by the chain saw and the chipper for $380. It should only take you about 9 hours to assemble it. And lets say that the 31 hours you were looking for the best of the best chain saw and chipper.
Answer:
<h2>
Average speed is 15km/h </h2>
Step-by-step explanation:
Step one:
given data:
total distance =7.5km
time taken= 30 min= 0.5 hours
we know that the average speed is the average distance divided by time taken
Step two:
mathematically expressed as
speed=distance/time
substituting we have
speed=7.5/0.5
speed=15km/hour
Hence the average speed is 15km/h