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3 years ago

8

Which expression is equivalent to (

3" alt="(x^{2} )^3" align="absmiddle" class="latex-formula">
$x^{8}$

$x^{6}$

$x^{5}$

1 answer:

son4ous [18]3 years ago

8 0

X^6 because you have to multiply the exponents

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Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$

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Answer:

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Step-by-step explanation:

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2x - 5= 5x + 7 linear equations

Bezzdna [24]

Answer:

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Step-by-step explanation:

2x - 5= 5x + 7

Subtract 2x from each side

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Subtract 7 from each side

-5-7 = 3x+7-7

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Divide by 3

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