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3 years ago

What is the distance between (-5, -6)(−5,−6)and (-3, -8)(−3,−8)?

1 answer:

8 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-3-(-5)]^2+[-8-(-6)]^2}\implies d = \sqrt{(-3+5)^2+(-8+6)^2} \\\\\\ d = \sqrt{2^2+(-2)^2}\implies d = \sqrt{4+4}\implies d = \sqrt{8}\implies d\approx 2.83$

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3 years ago

1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

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The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

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###

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$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

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