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insens350 [35]
3 years ago
10

What is the equation of the following line? Be sure to scroll down first to see all answer options.

Mathematics
1 answer:
Virty [35]3 years ago
5 0

Answer:

y=6x

Step-by-step explanation:

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Which is the equation of a hyperbola centered at the origin with x-intercept +\- 3 and asymptote y=2x
Radda [10]

Answer:

{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is  \dfrac{(x - h)^{2}}{a^{2}} - \dfrac{(y - k)^{2}}{b^{2}} = 1

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes arey = k \pm \dfrac{b}{a}(x - h)

1. Calculate h and k. The hyperbola is symmetric about the origin, so  

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3  

3. For 'b': The equation for the asymptote with the positive slope is  

y = k + \dfrac{b}{a}(x - h) = \dfrac{b}{a}x

Thus,  asymptote has the slope of

\begin{array}{rcl}m& =& \dfrac{b}{a}\\\\2& =& \dfrac{b}{3}\\\\b& =& \mathbf{6}\end{array}

4.  The equation of the hyperbola is

\large \boxed{\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}}

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

7 0
3 years ago
How can you tell by looking at the coordinates of the two triangles that Δ A'B'C' is a 180° rotation of Δ ABC? A) The coordinate
MariettaO [177]

under a rotation about the origin of 180°

a point (x, y ) → (- x, - y )

hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC


7 0
3 years ago
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Please solve with explanation 20 points
VashaNatasha [74]

Answer: i don't know but thanks for the points

Step-by-step explanation:

4 0
2 years ago
Charlie has a piece of toast that has cream cheese on one side, and he dropped it once. One time, it landed with the cream chees
Nina [5.8K]
What the heck who puts cream cheese on toast and im pretty sure the answer would be D
8 0
3 years ago
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The rate of change of the volume of a snowball that is melting is proportional to the surface area of the snowball. Suppose the
Alisiya [41]

Answer:

According to the passage, we have the next equation:

\frac{dV}{dt} = \frac{4}{3}\pi*3*r^{2}*\frac{dr}{dt} = K*(4\pi*r^{2} )

where "K" is a proportional constant

Leaving at the end with the next equation:

\frac{dr}{dt} = K

Integrating the equation, we have:

r=K*t+C

where "C" is a constant

Then, we have the 2 conditions for the problem:

1) t=0 → r=10

Replacing in the equation, we have C = 10

2) t=5 → r=8

Replacing in the equation, we have K = -0.4

Finally, the time which the snowball will be completely melted will be when r = 0. So replacing in the equation

0=-0.4*t+10

t = 25 minutes

6 0
3 years ago
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