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dusya [7]
2 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]2 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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nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. in the first part of the race, her av
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Total distance 5 km; at 5km / 0.65 h =

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5 0
3 years ago
$1000 is invested at 2.9% annual interest for 6 months.<br> a. Simple Interest b. Compound Interest
kirza4 [7]

Answer:

a. Simple interest = $174

b. Compund interest = $1187.1

Step-by-step explanation:

Given the following data;

Principal, P = $1000

Interest, R = 2.9%

Time, T = 6 months

a. To find the simple interest;

S.I = (PRT)/100

S.I = (1000*2.9*6)/100

S.I = 17400/100

S.I = $174

b. To find the compound interest;

A = P(1 + \frac{r}{100})^{t}

Substituting into the formula, we have;

A = 1000(1 + \frac{2.9}{100})^{6}

A = 1000(1 + 0.029)^{6}

A = 1000(1.029)^{6}

A = 1000(1.1871)

A = $1187.1

8 0
3 years ago
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