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horrorfan [7]
3 years ago
7

Find the center and radius of this circle x^2+y^2-6x-10y+30=0

Mathematics
1 answer:
Vsevolod [243]3 years ago
5 0

Answer:

The circle's centre is at the position (3, 5), and it has a radius of 2

Step-by-step explanation:

First let's put it in a useful format by completing the squares:

x² + y² - 6x - 10y + 30 = 0

x² - 6x + y² - 10y = -30

x² - 6x + 9 + y² - 10y + 25 = -30 + 9 + 25

(x - 3)² + (y - 5)² = 4

This tells us that the centre position is (3, 5) and the radius is √4, or 2

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If m(x)=x 5/x-1 and n(x) = x – 3, which function has the same domain as (m*n)(x)
Tatiana [17]
<span><u><em>Answer:</em></u>
m(x) has the same domain as (m*n)(x)

<u><em>Explanation:</em></u>
<u>1- For m(x):</u>
m(x) is a fraction. This means that the <u>denominator cannot be zero</u>, otherwise, the fraction would be undefined.
The denominator of m(x) would be zero at x = 1.
This means that the <u>domain of m(x) can be any real number except 1</u>

<u>2- For n(x):</u>
The value of x in n(x) can be any number. This is because there is no value that would make n(x) undefined.
This means that the <u>domain of n(x) is all real numbers</u>

<u>3- For (m*n)(x):</u>
(m*n)(x) = m(x) * n(x) = </span>\frac{x-5}{x-1} *(x-3) =  \frac{(x-5)(x-3)}{(x-1)}
<span>
We can note that the product is also a fraction. This means that the <u>denominator cannot be zero</u>.
The denominator here will be zero at x = 1.
This means that the <u>domain of (m*n)(x) is all real numbers except 1</u>.
<u>This is the same as the domain of m(x)</u>

Hope this helps :)</span>
8 0
3 years ago
Write a polynomial function given the zeros 5, 6+2i, and 6-2i and passes through the point (2, 64)
ivolga24 [154]

Answer:456 thatas the answer

Step-by-step explanation:

6 0
3 years ago
The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of Transportation St
saveliy_v [14]

Answer:

a)0.067

b)0.111

c)0.612

d)$687.28

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $385

Standard Deviation, σ = $110

We are given that the distribution of domestic airfares is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(domestic airfare is $550 or more)

P(x > 550)

P( x > 550) = P( z > \displaystyle\frac{550 - 385}{110}) = P(z > 1.5)

= 1 - P(z \leq 1.5)

Calculation the value from standard normal z table, we have,  

P(x > 550) = 1 - 0.933 = 0.067= 6.7\%

b) P(domestic airfare is $250 or less)

P(x \leq 250) = P(z \leq \displaystyle\frac{250-385}{110}) = P(z \leq -1.22)

Calculating the value from the standard normal table we have,

P( x \leq 250) = 0.111 = 11.1\%

c))P(domestic airfare is between $300 and $500)

P(300 \leq x \leq 500) = P(\displaystyle\frac{300 - 385}{110} \leq z \leq \displaystyle\frac{500-385}{110}) = P(-0.77 \leq z \leq 1.04)\\\\= P(z \leq 1.04) - P(z < -0.77)\\= 0.851 - 0.239 = 0.612 = 61.2\%

P(300 \leq x \leq 500) = 61.2\%

d) P(X=x) = 0.03

We have to find the value of x such that the probability is 0.03.

P(X > x)

P( X > x) = P( z > \displaystyle\frac{x - 385}{110})=0.03

= 1 -P( z \leq \displaystyle\frac{x - 385}{110})=0.03

=P( z \leq \displaystyle\frac{x - 385}{110})=0.997

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 385}{110} = 2.748\\x = 687.28

Hence, the domestic fares must be $687.28 or greater for them to lie in the highest 3%.

7 0
3 years ago
Find the sum of the measures​
jarptica [38.1K]

Answer:

720

Step-by-step explanation:

360/6= 60 (outside angles)

180-60=120 (inside angles)

120x6=720 (sum of inside angles)

6 0
2 years ago
The expression 3P2 represents the number of ways of:?
Vsevolod [243]
The expression 3P2 can also be read as "permutation of 3 taken 2". This represents the number of ways in which the 3 items are arranged with the emphasis on the arrangement of the first two other items. 
5 0
3 years ago
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