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svetoff [14.1K]
3 years ago
9

Simplify

Mathematics
1 answer:
Alexandra [31]3 years ago
3 0

my answer is in the image above

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
OleMash [197]

Answer:

The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

p = -3

The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

Where:

x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

6 0
2 years ago
What is the solution to the system of equations below?
ANEK [815]
A. x = 7, y = 4, z = 3

How?

Just plug in the numbers.

7 + 4 + 3 = 14

11 + 3 = 14

14 = 14

Next.

4 + 3 = 7

Next.

3 = 3

5 0
2 years ago
Which is true of dependent events?
insens350 [35]

Answer:

Might be

Step-by-step explanation:

A.) The probability of all dependent events can be calculated using the OR formula

5 0
3 years ago
each row has a starting cart that it 4 feet long if this row is 43 feet long how many total carts are in it
Margaret [11]

Answer:

43/4 = 10.25 which rounds to the nearest whole number of 10 total carts

5 0
2 years ago
What is the sum of 1/2 + 1/4?<br><br> A. 2/8<br> B. 2/6<br> C. 4/8<br> D. 6/8
Pie

<em>3/4 is the total.</em>

<em></em>

<em></em>

<em>See attached image for explanation.</em>

<em></em>

<em>Please consider marking "Brainliest". </em>

<em></em>

<em>Thanks <3</em>

<em></em>

6 0
2 years ago
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