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Black_prince [1.1K]
3 years ago
5

If m∠5 =53° and m∠7 =125° , find the measures of each numbered angle.Then explain how u found each angle,citing definitions and

conjectures that support your steps.

Mathematics
1 answer:
bija089 [108]3 years ago
4 0
#5 = 53° #7 = 125° #6 = 55° #2 = 72° #3 = 55° #1 = 53° #4 = 127°

triangle = 180°
alternating interior angles are the same (#6 & #3 and #5 and #1)
#3 and #7 should equal 180°
#1 and #4 should also equal 180°
#6 and #7 should equal 180°
#4 and #5 should equal 180°
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The equation y=\frac{-x^2-6x+31}{8} represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }, we find that the distance between (x, y) is

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On the parabola, these distances are equal so, we solve for y:

\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}

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