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koban [17]
3 years ago
8

Show that the equation represents a circle and find its center and radius. x2 + y2 +6y + 2 = 0

Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0

Answer:

Step-by-step explanation:

The general equation of a circle can be expressed as (x-a)²+(y-b)² = r² where (a,b) is the centre of the circle and r is the radius.

To show that the equation x² + y² +6y + 2 = 0 represents a circle, we need to write it in the format above using the completing the square method.

Given x² + (y² +6y) + 2 = 0

First we need to complete the square of the square in parenthesis by adding the square of half of the coefficient of y i.e (\frac{1}{2}*6) ^2 to the equation and adding the constant to the other side of the equation as well.

x² + (y² +6y) + 2 = 0

x^2+(y^2+6y+(\frac{1}{2}*6) ^2)+2 = 0+(\frac{1}{2}*6) ^2\\x^2+(y^2+6y+(3) ^2)+2 = 0+3 ^2\\x^2+(y^2+6y+9)+2 = 0+9\\x^2+(y+3)^2+2 = 9\\x^2+(y+3)^2+2-2 = 9-2\\x^2+(y+3)^2 = 7\\(x-0)^2+(y+3)^2 = 7\\

<em>Hence the equation represents a circle with centre C at (0, -3) and radius of √7</em>

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A store has a 20% sale on everything. An item originally cost 350 AED. What is the sale price? Show your work of how you calcula
slega [8]

Answer:

Step-by-step explanation:

A store has a 20% sale on everything.

So since you are saving 20%, you will only be paying 80% of the original price.

To find the sale price use the following formula:

Sale price = 80% x original price

They told us the original price = 350 AED

This means:

Sale price = 80% x 350

I think it would be easiest to change 80% into a fraction if you don't have a calculator :)

80% = \frac{80}{100}  = \frac{4}{5}

This means that the

Sale Price= \frac{4}{5} x 350 = 280 AED

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3 years ago
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Y_Kistochka [10]

Answer:

let f(x)= y

y = 4x+8

x= 4y + 8

4y = x - 8

y = (x - 8)/4

Hope this helps.

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Please help me <br> Find f(-4)
Katyanochek1 [597]
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3 years ago
a triangle has sides with lengths of 5x, 15 and 17. the perimeter of the triangle is 45 meters. what is the value of x?
Artyom0805 [142]
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Alekssandra [29.7K]

13pi/12 lies between pi and 2pi, which means sin(13pi/12) < 0

Recall the double angle identity,

sin^2(x) = (1 - cos(2x))/2

If we let x = 13pi/12, then

sin(13pi/12) = - sqrt[(1 - cos(13pi/6))/2]

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cos(13pi/6) = cos(2pi + pi/6) = cos(pi/6) = sqrt[3]/2

Then

sin(13pi/12) = - sqrt[(1 - sqrt[3]/2)/2]

sin(13pi/12) = - sqrt[2 - sqrt[3]]/2

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