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zlopas [31]
3 years ago
13

the equation of a circle in general form is x squared + y squared + 20x + 12 y + 15 equals 0what is the equation of the circle i

n standard form ​
Mathematics
1 answer:
Marrrta [24]3 years ago
4 0

Answer: (x+10)^2+(y+6)^2=121

Step-by-step explanation:

The equation of a circle in the general form is:

 ax^{2}+by^2+cx+dy+e=0

The equaton of  a circle in standard form is:

(x-h)^2+(y-k)^2=r^2

Where the center is at <em>(h, k)</em> and <em>r</em> is the radius

To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:

1- Given the equation in general form:

x^{2}+y^2+20x+12y+15=0

2- Complete the square:

-Group the like terms and move the constant to the other side.

- Complete the square on the left side of the equation.

- Add the same value to the other side.

Then you obtain:

(x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121

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Lcm of (x-2)(x+3) and 10(x+3)^2
Arte-miy333 [17]
Least common multiple: factor them, then see what they have in common and what is leftover and multiply those expressions:

(x - 2)(x + 3)          10(x + 3)(x + 3)
Common: (x + 3)
Leftover: (x - 2), (10), (x + 3)
Common · Leftover is: (x + 3) · (x - 2) · (10) · (x + 3) = 10(x - 2)(x + 3)²

Answer: LCM is 10(x - 2)(x + 3)²


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xeze [42]

Answer: 45

Step-by-step explanation:

5 0
3 years ago
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(8.218+9.93)+(17.782+0.07)
Licemer1 [7]
First, using the order of operations(PEMDAS), you would solve what is inside the parenthesis. 
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(</span>18.148) + (17.852)
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Now, all you would have to do is add the two sums. 
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</span>
The answer would be 36. 

I hope this helps!

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Maura drives to work, a distance of 30 miles in 40 minutes. she takes the same route to return home. if her average speed on the
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Well to solve this firstly we should calculate her average speed while she was going to work. Which comes out to be 45 miles per hour.

Now if her average speed while going home is half as fast as while coming to work was, the answer would be 22.5 miles per hour. So the average speed for the total journey would be the average for these two values. As the distance was same for both the journeys we can simply do 45 + 22.5 / 2 = 33.75 mph.

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