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2 years ago

A circle centered at the origin contains the point (0,-9). Does (8, sqr 17) also lie on the circle?

Mathematics

1 answer:

Reptile [31]2 years ago

7 0

Check the picture below.

since the circle is centered at the (0,0) origin, and a point on it is at (0, -9), its radius is simple the distance between those two, or r = 9.

if the second point is also on the circle, it must also be 9 units away from the origin.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{\sqrt{17}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(8-0)^2+(\sqrt{17}-0)^2}\implies d=\sqrt{8^2+(\sqrt{17})^2} \\\\\\ d=\sqrt{64+17}\implies d=\sqrt{81}\implies d=9~~\textit{\Large \checkmark}$

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Rufina [12.5K]

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sveta [45]

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<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

$\rm x=y+z$

Plug this value in the equation (2) and (3):

$\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2$

After solving we get:

z = -1

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Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

Learn more about the linear equation here:

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blagie [28]

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3 years ago

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2 years ago

Read 2 more answers

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 280 engines

DENIUS [597]

Answer:

The value of the test statistic is $t = -2.09$

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 6.6$

The alternate hypotesis is:

$H_{1} \neq 6.6$

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation(square roof of the variance) and n is the size of the sample.

In this problem, we have that:

$X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280$

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}$

$t = -2.09$

The value of the test statistic is $t = -2.09$

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3 years ago