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makvit [3.9K]
4 years ago
10

Find the value of X​

Mathematics
1 answer:
Aloiza [94]4 years ago
7 0

Answer:

57

Step-by-step explanation:

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Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?​
Alex Ar [27]

Answer:

\frac{x^2}{12}-\frac{y^2}{4}=1

Step-by-step explanation:

Since our foci are located on the x-axis, then our major axis is going to be the horizontal transverse axis of the hyperbola:

<u>Formula for hyperbola with horizontal transverse axis centered at origin</u>

  • <u />\frac{x^2}{a^2}-\frac{y^2}{b^2}=1
  • Directrices -> x=\pm\frac{a^2}{c}
  • Foci -> (\pm c,0) where a^2+b^2=c^2
  • a>b

Since we are given our directrices of x=\pm3 and foci of (\pm4,0), then we can set up the directrices equation to solve for a^2:

x=\pm\frac{a^2}{c}\\ \\\pm3=\pm\frac{a^2}{4}\\ \\12=a^2

Now we can determine b^2 to complete our equation for the hyperbola:

a^2+b^2=c^2\\\\12+b^2=4^2\\\\12+b^2=16\\\\b^2=4

Therefore, our equation for our hyperbola is \frac{x^2}{12}-\frac{y^2}{4}=1

5 0
2 years ago
A triangle has the side lengths of 12, 34, 45. Is it a right triangle?
deff fn [24]

Answer:

no

Step-by-step explanation:

a^2+b^2=c^2?

12^2+34^2=45^2?

1300≠2025

5 0
3 years ago
Find the area of the triangle formed by the vertex and x-intercepts of parabola y=-x^2-3x+10
Sonbull [250]

Answer:

42.875

Step-by-step explanation:

First you find the x-intercepts and the vertex of the equation.

(-5, 0), (-2, 0), (-3/2, 49/4)

You use those coordinates to find the sides of the triangle and then you use the lengths to find the semiperimeter.

Lastly, you use Heron's formula to compute the area.

3 0
3 years ago
I have 5 questions
LenKa [72]

Answer:number one is b I just answered it don't listen to the person who just randomly answered

Cuz I got it wrong I'm so mad

Step-by-step explanation:

5 0
3 years ago
What is 1/9 (2m - 16) = 1/3 (2m +4)
Serjik [45]

Answer:

-7

Step-by-step explanation:

Hope it helped!

3 0
3 years ago
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