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asambeis [7]
3 years ago
6

What is the measure of X? angles are not necessarily drawn to scale

Mathematics
1 answer:
Schach [20]3 years ago
5 0

Answer:

xº=71º

Step-by-step explanation:

Take the triangle BDH

Once the sum of interior angles of a triangle is 180º:

40º+31º+yº=180º

71º+yº=180º

yº=109º

Once yº and xº are supplementary angles (add up to 180º):

yº+xº=180º

109º+xº=180º

xº=71º

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A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.
Anna71 [15]

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

\sqrt{(x-5)^2+(y-(-3))^2}is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

Equating the two equations given, we have

\sqrt{(x-5)^2+(y-(-3))^2} = |y-1|

square both sides to get

(x-5)²+(y+3)²=(y-1)²

expand the y components

(x-5)² + y²+6y+9 = y²-2y+1

subtract y²+6y+9 from both sides

(x-5)² = -8y - 8

expand the x components

x²-10x+25 = -8y - 8

add 8 to both sides to isolate the -8y

x²-10x+33 = -8y

divide both sides by -8 to isolate y

(x²-10x+33)/(-8) = y

6 0
3 years ago
Find the measures of the interior angles of the triangle.
miv72 [106K]

Answer:

X = 45

Step-by-step explanation:

8 0
3 years ago
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Someone please help me with this question! How can I prove it?
Alex73 [517]

Answer:

TS=QV

Step-by-step explanation:

To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.

In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.

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2 years ago
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Which of the
kondor19780726 [428]

The pic is attached.

7 0
3 years ago
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Did I do this right?
Rasek [7]

Answer:

Yea u did......

Step-by-step explanation:

you did right because all the steps are right

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