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Darina [25.2K]
2 years ago
10

Given: AB=CB, CD=ED, Prove: AB // DE

Mathematics
1 answer:
Fiesta28 [93]2 years ago
3 0

Hey there mate ;)

The answer for proving your question is sent as image. Please check.

Thank you !

<em>A</em><em>n</em><em>s</em><em>w</em><em>e</em><em>r</em><em>e</em><em>d</em><em> </em><em>b</em><em>y</em><em> </em><em>B</em><em>e</em><em>n</em><em>j</em><em>e</em><em>m</em><em>i</em><em>n</em>

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If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?
kondaur [170]

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here, x_1=-8, y_1=-6, x_2=-4, y_2=-14

$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)

$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)

$P(x, y) =(-6, -10)

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

Here, x_1=-6, y_1=-10, x_2=-8, y_2=-6

r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}

r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}

r=\sqrt{(-2)^{2}+(4)^{2}}

r=\sqrt{20} units

The standard form of the equation of a circle is

(x-a)^{2}+(y-b)^{2}=r^{2}, where (a, b) are center and r is the radius.

Here, center = (–6, –10) and r=\sqrt{20}

(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}

(x+6)^{2}+(y+10)^{2}=20

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

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3 years ago
What is the solution to x 4 – 12x 2 + 10 &gt; 0?
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Answer: The picture contains the answer and the steps

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2 years ago
Someone please help me with this!!
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PEMDAS tells us to use multiplication and division before addition and subtraction.

<u>-5(8) </u>÷ 10 - <u>14 ÷ 7</u> - <u>(-2)(3)</u>

<u> -40  ÷ 10</u> -     2    -   -6

     <u>-4       -    2 </u>     + 6    <em>two negatives make a positive so - - 6  = + 6</em>

           <u> -6              +6</u>

                      0

Answer: 0


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2 years ago
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The answer would be seven point five

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Step-by-step explanation:

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