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Ket [755]
3 years ago
5

Write the equation of the circle with center (0,0) and (-1,-3) a point on the circle

Mathematics
2 answers:
saw5 [17]3 years ago
6 0

Answer:

Equation of given circle :-  x² + y² = 4

Step-by-step explanation:

The equation of the circle with center (0, 0) and radius r is given by,

x² + y² = r²

It is given that, a  circle with center (0,0) and (-1,-3) a point on the circle

To find the radius of circle

radius r = √[(0 - - 1)² + (0 - -3)²] =√(1 + 3) =√4 = ±2

r = 2

<u>To find the equation of circle</u>

x² + y² = r²

x² + y² = 2²

x² + y² = 4

Nataly_w [17]3 years ago
5 0

Answer:

\left(x\right)^2+\left(y\right)^2=10

Step-by-step explanation:

Given that center of the circle is at (0,0) and it passes through a point (-1,-3).

Now we need to write the equation of the circle with given center and point on the circle.

So let's plug given values into standard formula of the circle

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

there (h,k) gives center of the circle then h=0, k=0

So we get equation :

\left(x-0\right)^2+\left(y-0\right)^2=r^2

\left(x\right)^2+\left(y\right)^2=r^2 ...(i)

plug the given point (-1,-3) that is x=-1 and y=-3 into (i)

\left(-1\right)^2+\left(-3\right)^2=r^2

1+9=r^2

10=r^2

plug above value into (i)

\left(x\right)^2+\left(y\right)^2=10

Hence final answer is \left(x\right)^2+\left(y\right)^2=10

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2 years ago
true or false If x represents a random variable with mean 114 and standard deviation 40, then the standard deviation of the samp
Goshia [24]

Answer:

\mu = 114, \sigma = 40

We also know that we select a sample size of n =100 and on this case since the sample size is higher than 30 we can apply the central limit theorem and the distribution for the sample mean would be given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard deviation for the sampling distribution would be:

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So then the answer is TRUE

Step-by-step explanation:

Let X the random variable of interest and we know that the true mean and deviation for this case are given by:

\mu = 114, \sigma = 40

We also know that we select a sample size of n =100 and on this case since the sample size is higher than 30 we can apply the central limit theorem and the distribution for the sample mean would be given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

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6 0
3 years ago
Help me with this please
alina1380 [7]
If you assign variables to the problem, it can make things a lot simpler. Lets say chairs are x and tables are y. Therefore you have:
2x+6y=40 
5x+3y=25
Now you can isolate the variable of one equation and put it into another (it doesn't matter which. I'm going to manipulate the top equation to plug into the bottom one).
2x=40-6y 
x=20-3y
Now I plug into bottom equatioin:
5(20-3y) + 3y=25
100-15y+3y=25
100-12y=25
-12y=-75
y=$6.25
Now you can plug in y in either equation to get x. 
2x+6(6.25)=40
37.5+2x=40
2x=2.5
x=1.25
So it costs $6.25 for each table and $1.25 for each chair. If you think about it, it would make sense for the table to cost more for the chair. 
6 0
3 years ago
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