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Tatiana [17]
3 years ago
11

10 increased by the quotient of a number and 2 is -15

Mathematics
1 answer:
IrinaVladis [17]3 years ago
5 0

x/2 + 10 = -15

Subtract 10 from both sides:

x/2 = -25

Multiply both sides by 2:

x = -50

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The equation for the ellipse given is 4x^2+9y^2-16x+18y-11​
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d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

\dfrac{(x - h)^2}{a^2}  + \dfrac{(y - k)^2}{b^2} = 1

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) =  25 + 11 = 36

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\dfrac{4\cdot (x - 2)^2}{36}  + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}

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c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

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