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2 years ago

Give the equation for a circle with the given center and radius. Center at (2, -9), radius = 3

Mathematics

1 answer:

olga2289 [7]2 years ago

8 0

Answer:

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (2, - 9) and r = 3, thus

(x - 2)² + (y - (- 9))² = 3², that is

(x - 2)² + (y + 9)² = 9 → B

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The functions $f$ and $g$ are defined as follows: \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}

CaHeK987 [17]

Answer:

The answer is "domain and range are different".

Step-by-step explanation:

Given:

$f(x) = \sqrt{\frac{x+1}{x-1}}\\\\g(x) =\frac{\sqrt{x+1}}{\sqrt{x-1}}\\$

Solve f(x) to find domain and range:

for element x: R:

⇒ $x \leq -1 \ \ \ and \ \ \ x > 1$ range:

$for \ \ f(x) \times element : 0 \leq f(x)< 1 \ \ \ or \ \ f(x)>1$

$g(x) =\frac{\sqrt{x+1}}{\sqrt{x-1}}\\$

Solve for domain:

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So, the value of the method f(x) and g(x) (range and domain) were different.

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2 years ago

Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.

Ghella [55]

Answer: The required inequality is $x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$ and its solution is $x>8.$

Step-by-step explanation: Given that Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.

Also, Heloise has written $\frac{1}{4}$ as many articles as Mustafa has and Gia has written $\frac{3}{2}$ as many articles as Mustafa has.

We are to write an inequality to determine the number of articles, m, Mustafa could have written for the school newspaper. Also, to solve the inequality.

Since m denotes the number of articles that Mustafa could have written. Then, according to the given information, we have

$x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$

And the solution of the above inequality is as follows :

$x+\dfrac{1}{4}x+\dfrac{3}{2}x>22\\\\\\\Rightarrow \dfrac{4x+x+6x}{4}>22\\\\\\\Rightarrow 11x>88\\\\\Rightarrow x>\dfrac{88}{11}\\\\\Rightarrow x>8.$

Thus, the required inequality is $x+\dfrac{1}{4}x+\dfrac{3}{2}x>22.$ and its solution is $x>8.$

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