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Dahasolnce [82]
3 years ago
14

What is the distance between C(4,3) and D(7, 7)?

Mathematics
1 answer:
Inessa [10]3 years ago
8 0

Step-by-step explanation:

g it is g

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A circle is centered at M(0,0)M(0,0)M, left parenthesis, 0, comma, 0, right parenthesis. The point B(-4,\sqrt{5})B(−4, 5)B, left
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the plan of a house shows that the first floor will be 13 feet longer than its wide. Which expression represents the area of the
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4 years ago
Find the slope of the line that passes through the points (-19, -4) and (13, -17).​
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m = \frac{-13}{32}

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Read 2 more answers
Match the pairs of equations that represent concentric circles. Tiles
Darina [25.2K]
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.
5 0
3 years ago
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