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Stolb23 [73]
3 years ago
11

Match the pairs of equations that represent concentric circles. Tiles

Mathematics
1 answer:
Darina [25.2K]3 years ago
5 0
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.
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Answer:

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General Formulas and Concepts:

<u>Algebra I</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

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Which of the following best defines 2 2/3?
inna [77]

Answer:

A. \sqrt[3]{4} = Cube root of 4.

Step-by-step explanation:

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Using exponent property \sqrt[n]{a^m} =a^{\frac{m}{n}, we will get,

2^{\frac{2}{3}}=\sqrt[3]{2^2}

2^{\frac{2}{3}}=\sqrt[3]{4}

Upon looking at our given choices, we can see that option A is the correct choice.

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If f(x)=×^2+7x-5 and you divide by x-2, What is the quotient and remainder?
katrin [286]

Answer:

The quotient is : x+9

The remainder is : 13

Step-by-step explanation:

The question requires you to perform the long division method;

This will be;

x-2\sqrt{x^2+7x-5}

start with the x term in x-2 and the first term in the function, x², to get x then multiply the x with x-2 to get x²-2x and perform the operation below;

x-2√x²+7x-5 -----------to first get x and then multiply x*[x-2]⇒x²-2x

    -  x²-2x+0 ------------perform subtraction of like terms

---------------------

            9x-5  ----now divide this answer by x-2 ,starting with x and 9x

----------------------This will give , 9 then multiply  9 by x-2 to get 9x-18 and perform the subtraction operation as;

             9x-5

      -      9x-18

------------------------

                     13

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What is the correct slope intercept form of the equation y + 16 = 3(x - 0) ?
Sindrei [870]

slope intercept form is just solve for y

y+16=3(x-0)

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4 = a

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So the other base length is 5

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