What are the center and radius of the circle defined by the equation x2 + y2 -6 x + 10y + 25 = 0

Mathematics

2 answers:

Natasha_Volkova [10]3 years ago

5 0

Answer:

(3,-5), radius 3

Step-by-step explanation:

levacccp [35]3 years ago

4 0

To determine the center points and the radius of the circle, we can either graph the equation or write it in a form where the center and the radius can be easily be seen. For this, we use the second method. The form should be:

(x - h)^2 + (y-k)^2 = r^2

(h,k) represent the center and r the radius

We do as follows:
<span>x2 + y2 -6x + 10y + 25 = 0
</span>x2 -6x + y2<span> + 10y = - 25
x2 - 6x + 9 + </span> y2 + 10y + 25 = -25 + 9 + 25 = 9
(x - 3)^2 + (y + 5)^2 = 3^2

Therefore, the center is at ( 3,-5) and the radius is 3 units.

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The number of text messsages that teenagers send per month is normally

ki77a [65]

Answer:

$z=\frac{4415-3400}{450}=2.26$

And the explanation of this number is:"The number of text messages for Kendra it's 2.26 deviations above the mean"

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Calculate the z score

Let X the random variable that represent the number of text messages per month, and for this case we know the distribution for X is given by:

$X \sim N(3400,450)$