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2 years ago

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Prove that the two circles shown below are similar. Circle A is shown with a center at 3, 4 and a radius of 5. Circle C is shown

with a center of 0, negative 1 and a radius of 2.

1 answer:

MaRussiya [10]2 years ago

8 0

Answer:

Is there a picture to go with it?

Step-by-step explanation:

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Line Equation from Two Points

Verdich [7]

Hi!

We can use <u>point-slope form </u>to solve this.

$y-y_{1} =m(x -x_{1})$

$y_{1}$ <em> and </em> $x_{1}$ <em> will be from one of the points.</em>

<u>First, we have to find </u> $m$ <u>, the slope. We can use the slope equation to get this.</u>

$\frac{y_{1} -y_{2} }{x_{1} -x_{2} }$

<em>Plug in your points:</em>

$\frac{4-0}{8-(-8)} =\frac{4-0}{8+8} =\frac{4}{16} =\frac{1}{4}$

Your slope is $\frac{1}{4}$

<u><em>Now plug points and slope into point-slope equation. We will use (8, 4).</em></u>

$y-4=\frac{1}{4} (x-8)$

Now, if you want to get it into y = mx + b form, you have to solve for y:

$y-4=\frac{1}{4} (x-8)$

$y-4=\frac{1}{4} x-2$

$y=\frac{1}{4} +2$

Your equation is $y=\frac{1}{4} +2$

<u><em>For more information on how to get the equation of a line when given two points, see here:</em></u>

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1 year ago

The value of $y$ varies inversely as $\sqrt x$ and when $x=2$, $y=4$. What is $x$ when $y=1$?

Dovator [93]

$x=3$ I think that’s it... try that

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Read 2 more answers

Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

BlackZzzverrR [31]

Answer:

$\boxed{\sf a = 9 }$

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

$\sf\longrightarrow 3x - 2y +7=0$

$\sf\longrightarrow 6x +ay -18 = 0$

Step 1 : <u>Conver</u><u>t</u><u> </u><u>the </u><u>equations</u><u> in</u><u> </u><u>slope</u><u> intercept</u><u> form</u><u> </u><u>of</u><u> the</u><u> line</u><u> </u><u>.</u>

$\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}$

and ,

$\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a}$

Step 2: <u>Find </u><u>the</u><u> </u><u>slope</u><u> of</u><u> the</u><u> </u><u>lines </u><u>:</u><u>-</u>

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

$\sf\longrightarrow Slope_1 = \dfrac{3}{2}$

And the slope of the second line is ,

$\sf\longrightarrow Slope_2 =\dfrac{-6}{a}$

Step 3: <u>Multiply</u><u> </u><u>the </u><u>slopes </u><u>:</u><u>-</u><u> </u>

$\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1$

Multiply ,

$\sf\longrightarrow \dfrac{-9}{a}= -1$

Multiply both sides by a ,

$\sf\longrightarrow (-1)a = -9$

Divide both sides by -1 ,

$\sf\longrightarrow \boxed{\blue{\sf a = 9 }}$

<u>Hence </u><u>the</u><u> </u><u>value</u><u> of</u><u> a</u><u> </u><u>is </u><u>9</u><u> </u><u>.</u>

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