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Helga [31]
3 years ago
6

What is the equation of a circle with center (-3, -1) that contains the point (1, 2)?

Mathematics
1 answer:
Leno4ka [110]3 years ago
7 0
So, we know the center is at -3,-1, ok

hmmm what's the radius anyway?   well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point?  well, is the radius, let's check then.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -3}}\quad ,&{{ -1}})\quad 
%  (c,d)
&({{ 1}}\quad ,&{{ 2}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2}
\\\\\\
r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5

so, what's the equation of a circle with center at -3, -1 and a radius of 5?

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{\quad  k}})\qquad 
radius=&{{ r}}\\
&-3&-1&5
\end{array} 
\\\\\\\
[x-(-3)]^2+[y-(-1)]^2=5^2\implies (x+3)^2+(y+1)^2=25
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The formula to calculate the area of a right triangle is given by:

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Where, “b” is the base (adjacent side) and “h” is the height (perpendicular side). Hence, the area of the right triangle is the product of base and height and then divide the product by 2.

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Given sides of the triangle:

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Answer: 1\dfrac{11}{12}\text{ pounds}

Step-by-step explanation:

The complete question is provided in the attachment.

Given, Amount blueberry jelly beans= 1\dfrac{1}{4} pounds

=\dfrac{5}{4} pounds.

Amount lemon jelly beans = 2\dfrac{1}{3}pounds

=\dfrac{7}{2} pounds

Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans

=(\dfrac{5}{4}+\dfrac{7}{3}) pounds

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Amount of jelly beans she gave away = 1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}

Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away

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She has left 1\dfrac{11}{12}\text{ pounds} of jelly beans.

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Explanation If a figure is rotated around a centre point and it still appears exactly as it did before the rotation, it is said to have rotational symmetry.

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