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Rom4ik [11]
3 years ago
6

Identify the similar triangles them find the x

Mathematics
1 answer:
Alex Ar [27]3 years ago
4 0

Answer:

ADB and ABC are similar

x = 8

Step-by-step explanation:

hypotenuse in ADB = \sqrt{4^2 + 2^2 } = \sqrt{20}

since two triangles are similar,

\frac{2+x}{\sqrt{20} } = \frac{\sqrt{20}}{2}

solving for x, x=8

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Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *
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Answer:

The answer to your question is   \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1          

Step-by-step explanation:

Data

Foci  (-2, 2)  (4, 2)

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Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

                  2c = 6

                    c = 6/2

                    c = 3

3.- Determine a

                  2a = 10

                    a = 10/2

                    a = 5

4.- Determine b using the Pythagorean theorem

                   a² = b² + c²

-Solve for b

                   b² = a² - c²

                   b² = 5² - 3²

                   b² = 25 - 9

                   b² = 16

                   b = 4

5.- Find the center (1, 2)  From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

                      \frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1

                       \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1                

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X to the 14th power over y to the 18th power is ur answer
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