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2 years ago

What is the equation of a circle whose radius is 16 units and center is at (2,-5)?

Mathematics

1 answer:

STatiana [176]2 years ago

8 0

Answer:

The general equation of the circle is
$( {x - a})^{2} + ({y - b})^{2} = {r}^{2} \\ therefore \: we \: \: have \: \\ ( {x - 2})^{2} + (y - ( - 5)) {}^{2} = ({16})^{2} \\ ({x - 2})^{2} + ( {y + 5})^{2} = 256$
HOPE THIS HELPS!

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Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

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$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

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3 years ago

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Step-by-step explanation:

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2 years ago

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leva [86]

Answer:

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Step-by-step explanation:

The expression that needs to be made in this question refers to the total number of people that signed the petition. To calculate this we need to add the total number of signatures that both you and your friend were able to acquire. Once we do this we simply combine like terms in order to simplify the expression as much as possible.

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