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2 years ago

Find the length of BC.

Mathematics

2 answers:

gavmur [86]2 years ago

8 0

Answer:

B) 8

Step-by-step explanation:

The Segment Addition Postulate basically states that the sum of the segments of a line will equal the length of the entire line.

Thus, AB+BC=AC, and we can substitute:

AB+BC=AC

(4x+8)+(3x-4)=32

4x+8+3x-4=32

7x+4=32

7x=28

x=4

Now that we have x, we can plug it in for segment BC:

BC=3x-4

3(4)-4

12-4

Therefore, choice B is correct

Umnica [9.8K]2 years ago

3 0

Answer:

BC = 8

Step-by-step explanation:

AB + BC = AC

4x + 8 + 3x - 4 = 32

7x + 4 = 32

7x = 32 - 4

7x = 28

x = 28/7

x = 4

BC = 3x - 4 = 3*4 - 4 = 12 - 4 = 8

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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)

Major axis = 10

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

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3.- Determine a

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a = 10/2

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4.- Determine b using the Pythagorean theorem

a² = b² + c²

-Solve for b

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b² = 5² - 3²

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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

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

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