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dusya [7]
3 years ago
9

Convert the circle to standard form.

%20%20%2B%2018x%20%2B%209y%20-%2036%20%3D%200" id="TexFormula1" title=" {9x}^{2} + {9y}^{2} + 18x + 9y - 36 = 0" alt=" {9x}^{2} + {9y}^{2} + 18x + 9y - 36 = 0" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
lara31 [8.8K]3 years ago
7 0

Answer:

(x + 1)² + (y + 1)² = (√6)²

Step-by-step explanation:

Group the x- and y- terms together:

9x^2 + 18x + 9y^2 + 9y = 36

Factor out the coefficient 9:

x^2 + 2x + y^2 + y = 4

Complete the square of x^2 + 2x and then do the same for y^2 + 2y:

x^2 + 2x + 1 - 1 + y^2 + 2y + 1 - 1 = 4

Rewrite x^2 + 2x + 1 as the square of the binomial x + 1:

(x + 1)^2 + (y + 1)^2 - 2 = 4

Collect the constant terms on the right side:

(x + 1)^2 + (y + 1)^2 = 6

Rewrite 6 as (√6)^2:

(x + 1)² + (y + 1)² = (√6)² is the equation in standard form (x - h)² + (y - k)² = r²

Completing the square is done as follows:  x^2 + 2x

Start with x^2 + 2x

1.  Take half of the coefficient of x, which results in 2/2, or 1

2.  Square this result and add it to, and subtract it from x^2 + 2x

     x^2 + 2x + 1 - 1

3.  Rewrite the first three terms as the square of a binomial:  

     x^2 + 2x + 1 - 1 = (x + 1)² - 1.

Do the same for y² + 2y.

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Answer:

31, 32, 33

Step-by-step explanation:

x + x + 1 +x + 2 = 96

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x = 31

31 is the first number, so since they’re consecutive, the second two numbers are 32 and 33.

6 0
3 years ago
there are 3 times as many adults as children at a book fair what is the ratio of people at the book fair​
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Step-by-step explanation:

There are 3 adults per 1 child at the book fair. I think this is right but im not 100% sure :)

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Which function is the inverse of ſx) - 2x+ 3?
Sonbull [250]

If f^{-1}(x) is the inverse of f(x), then

f\left(f^{-1}(x)\right) = x

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