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3 years ago

A circle has the equation x2+y2−14x−18y+105=0.

Mathematics

1 answer:

kolezko [41]3 years ago

8 0

Answer:

The answer to your question is the last option

Equation in standard form = (x - 7)² + (y - 9)² = 5²

Center = (7, 9)

Radius = 5

Step-by-step explanation:

Equation

x² + y² - 14x - 18y + 105 = 0

- Grouping property

(x² - 14x ) + (y² - 18y ) = -105

- Complete perfect square trinomials

(x² - 14x + 7²) + ( y² - 18y + 9²) = -105 + 49 + 81

- Factor

(x - 7)² + (y - 9)² = 25

or (x - 7)² + (y - 9)² = 5²

Center = (7, 9)

Radius = 5

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3 years ago

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Consider this rational equation. 1 x 1 x − 2 = 1 4 use the least common denominator to simplify the rational equation into a sta

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By using least common denominator, the rational equation can be expressed into a standard form quadratic equation as x^2 - 10x + 8 = 0.

In this question,

The rational equation is,

$\frac{1}{x}+\frac{1}{x-2}=\frac{1}{4}$

The standard form quadratic equation can be expressed as

$ax^{2} +bx+c=0$

The above rational equation can be expressed into a standard form quadratic equation by using least common denominator method as,

⇒ $\frac{1}{x}+\frac{1}{x-2}=\frac{1}{4}$

⇒ $\frac{(x-2)+x}{(x)(x-2)}=\frac{1}{4}$

⇒ $\frac{2x-2}{x^{2} -2x}=\frac{1}{4}$

⇒ $4(2x-2)=x^{2} -2x$

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Hence we can conclude that by using least common denominator, the rational equation can be expressed into a standard form quadratic equation as x^2 - 10x + 8 = 0.

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1 year ago

The stock of company a gained $0.76 throughout the day and ended at a value of $38.76. By what percentage did the stock rise

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Answer:

Its either 1.98 percentage or 51.

Step-by-step explanation:

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