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astraxan [27]
3 years ago
8

Help, this is a course challenge

Mathematics
1 answer:
tankabanditka [31]3 years ago
8 0

Answer:

Step-by-step explanation:

                    Statements                         Reasons

1. m∠BAC = m∠DAC = 51°                 1). Given

2. AB = AD = 4                                  2). Given

3. AC = AC                                        3). Segments are the same length as

                                                              themselves.

4. ΔABC ≅ ΔADC                            4). Side - Angle - Side property of

                                                             congruence.

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Answer:

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3 years ago
What is the equation for a circle with a center at (-2,-4) that passes through the point (3,8)?
Margarita [4]
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so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points }&#10;\\\\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&&(~ -2 &,& -4~) &#10;%  (c,d)&#10;&&(~ 3 &,& 8~)&#10;\end{array}\qquad&#10;%   coordinates of midpoint &#10;\left(\cfrac{ x_2 +  x_1}{2}\quad ,\quad \cfrac{ y_2 +  y_1}{2} \right)&#10;\\\\\\&#10;\left( \cfrac{3-2}{2}~~,~~\cfrac{8-4}{2} \right)\implies \left( \frac{1}{2}~,~2 \right)\impliedby center

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&&(~ -2 &,& -4~) &#10;%  (c,d)&#10;&&(~ 3 &,& 8~)&#10;\end{array}~~~ &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;d=\sqrt{[3-(-2)]^2+[8-(-4)]^2}\implies d=\sqrt{(3+2)^2+(8+4)^2}&#10;\\\\\\&#10;d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13\qquad\qquad \qquad  \stackrel{radius}{\frac{13}{2}}

\bf \textit{equation of a circle}\\\\ &#10;(x- h)^2+(y- k)^2= r^2&#10;\qquad &#10;center~~(\stackrel{\frac{1}{2}}{ h},\stackrel{2}{ k})\qquad \qquad &#10;radius=\stackrel{\frac{13}{2}}{ r}&#10;\\\\\\&#10;\left( x-\frac{1}{2} \right)^2+(y-2)^2=\left( \frac{13}{2} \right)^2\implies \left( x-\frac{1}{2} \right)^2+(y-2)^2=\frac{169}{4}

3 0
3 years ago
Read 2 more answers
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