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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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To factor the polynomial x² - 7x - 18, find two numbers whose sum is -7 and whose product is -18. Begin listing factors of -18, and those numbers' sums.

-2 × 9 = -18; -2 + 9 = 7
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The two numbers are -9 and 2.

The factored polynomial is (x - 9)(x + 2)

Answer:
The missing factor is (x + 2)
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3 years ago
Quadrilateral RSTU, diagonals SU and RT intersect at point V.
max2010maxim [7]

The parallelogram RSTU has a pair of parallel lines ST and RU.

The measure of the angle \angle TUV=48^o

<h3>How to determine the measure of TUV?</h3>

The given parameters are:

m∠SRV= 48° and m∠SVR= 54°

We have the parallel lines of the parallelogram RSTU to be ST and RU.

This means that the transversal between the lines are lines SU and RT.

The above highlights mean that:

SRV= TUV = 48°

By the triangle congruency also:-

\triangle SRV \ \ and \ \ \triangle TUV  are also similar by (AAA) property.

So the angles SRV= TUV = 48° will be equal.

Hence the parallelogram RSTU has a pair of parallel lines ST and RU.

The measure of the angle \angle TUV=48^o

Read more about parallelograms at:

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devante is 26 years younger than Ariana. 2 years ago Arianas age was 2 times devantes age. how old is devante now
lesantik [10]
A= d+26
a-2= 2(d-2)

Substitute for a
d+26-2= 2d-4

Combine like terms
d+24=2d-4

Subtract d from both sides
24=d-4

Add 4 to both sides
d=28

Final answer: 28
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A package of dental floss contains 25 m of floss. How many yards of floss are in the package? If a dental hygienist uses about 1
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Twenty five meters converted to yards is 27.34. For the second bit, 18 inches is 1.5 feet so we divide 27.34 by 1.5. He will be able to floss 18 patients. 
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Which graph represents the function f(x)=-|x|-2 ?
Elden [556K]

Answer:

The graph of given function is shown below.

Step-by-step explanation:

The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.

The given function is

f(x)=-|x|-2              .... (1)

The vertex from of an absolute function is

f(x)=a|x-h|+k          .... (2)

where, a is a constant and (h,k) is vertex of the function.

From (1) and (2) we get

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The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.

The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.

The graph of given function is shown below.

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