Solve the equation. 6n + n + n - 3 = 4 + 3n + n + 1

2 answers:

7 0

1. Combine like terms.
$8n - 3 = 5 + 4n \\ (8n - 3) + 3 = (5 + 4n) + 3 \\ (8n) - 4n = (8 + 4n) - 4n \\ 4n = 8$
Now divide both sides by 4 to get:
$n = 2$

Alborosie3 years ago

4 0

So first add the common terms
13n
And then add 3,4and 1 equals 8
And then divide 8 by 13 and u get 0.615

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

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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:

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