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sweet [91]
3 years ago
12

A certain circle can be represented by the following equation. x^2+y^2+6y-72=0 What is the center of this circle ?

Mathematics
1 answer:
jek_recluse [69]3 years ago
8 0

Answer:

(0, -3)

Step-by-step explanation:

Here we'll rewrite x^2+y^2+6y-72=0 using "completing the square."

Rearranging x^2+y^2+6y-72=0, we get  x^2 + y^2 + 6y                = 72.

x^2 is already a perfect square.  Focus on rewriting y^2 + 6y as the square of a binomial:  y^2 + 6y becomes a perfect square if we add 9 and then subtract 9:

x^2 + y^2 + 6y + 9  - 9              = 72:

x^2 + (y + 3)^2 = 81

Comparing this to the standard equation of a circle with center at (h, k) and radius r,

(x - h)^2 + (y - k)^2 = r^2.  Then h = 0, k = -3 and r = 9.

The center of the circle is (h, k), or (0, -3).

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8 0
3 years ago
. Mr. Perez owns a house on a lot shaped like a square. The perimeter of the lot is 60 feet. What is the length and the width of
pantera1 [17]
Hi there!

If we know the perimeter of the lot, it's pretty easy to find the length and width. Since we know that the lot is a square, we know that all sides are the same. And there are four sides on a square. Using this information, we can get an equation: 60 = x + x + x + x. Then, we need to simplify and solve the equation: 60 = 4x | x = 15 feet. Therefore, the length and width of the lot is 15 feet.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
7 0
3 years ago
Exactly a year ago, the volume of Arlington lake was 1,620,757 liters. Right now, it’s volume is 382,403 liters greater. How man
UkoKoshka [18]

Answer:

2,003,160

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We can see the key word greater and know to add.

If someone mixes 36 liters of orange juice and 45 liters of soda water, how many batches would they make?

1,620,757 + 382,403 = 2,003,160

3 0
2 years ago
Read 2 more answers
(Essay Question 7 Points)
Irina18 [472]

Well I don't know.
Let's think about it:

-- There are 6 possibilities for each role.
    So 36 possibilities for 2 rolls.
    Doesn't take us anywhere.

New direction:
-- If the first roll is odd, then you need another odd on the second one.
-- If the first roll is even, then you need another even on the second one.
This may be the key, right here !

-- The die has 3 odds and 3 evens.

-- Probability of an odd followed by another odd = (1/2) x (1/2) = 1/4
-- Probability of an even followed by another even = (1/2) x (1/2) = 1/4

I'm sure this is it.  I'm a little shaky on how to combine those 2 probs.

Ah hah ! 
Try this:

Probability of either 1 sequence or the other one is (1/4) + (1/4) = 1/2 .

That means ... Regardless of what the first roll is, the probability of
the second roll matching it in oddness or evenness is 1/2 .

So the probability of 2 rolls that sum to an even number is 1/2 = 50% .

Is this reasonable, or sleazy ?


4 0
3 years ago
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'
MArishka [77]

The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.

From the graph:

The two points are (-4, -2) and (4, 5)

The line equation passing through two points:

[y - 5] = (5+2)/(4+4)[x - 4]

y - 5 = 7/8[x - 4]

8y - 40 = 7x - 28

8y = 7x + 12

Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

6 0
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