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Mathematics

1 answer:

tester [92]4 years ago

8 0

Answer:

x=50 ∠BCX=65

Step-by-step explanation:

The angles is a triangle add up to 180 so

70+45+∠BCX=180 so

115+∠BCX=180 (subtract 115 from both sides)

∠BCX=65

A line adds up to 180

so 2x+15+65=180

so 2x+80=180 (subtract 80 from both sides)

2x=100 (divide by 2)

x=50

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Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5).

mash [69]

If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal: $\frac{(x-h) ^{2} }{ a^{2} } - \frac{(y-k) ^{2} }{ b^{2} } =1$ . a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem. $( 2)^{2} + b^{2} =( 3)^{2}$ and $b= \sqrt{5}$ . Now we have everything we need to rewrite the equation: $\frac{(x-4) ^{2} }{4} - \frac{(y-5) ^{2} }{5} =1$