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8090 [49]
3 years ago
14

Evaluate a + 4 when a = 7

Mathematics
1 answer:
aalyn [17]3 years ago
4 0
If a is equal to 7. The answer is 11. 7+4
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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
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra,
nata0808 [166]

Answer:

What is P(A), the probability that the first student is a girl? (3/4)

What is P(A), the probability that the first student is a girl? (3/4)What is P(B), the probability that the second student is a girl? (3/4)

What is P(A), the probability that the first student is a girl? (3/4)What is P(B), the probability that the second student is a girl? (3/4)What is P(A and B), the probability that the first student is a girl and the second student is a girl? (1/2)

The probability that the first student is a girl is (3/4), likewise for the 2nd 3rd and 4th it's still (3/4). The order you pick them doesn't matter.

However, once you're looking at P(A and B) then you're fixing the first position and saying if the first student is a girl what's the probability of the second student being a girl.

3 0
3 years ago
Finding the percent of increase or decrease
madam [21]
What is the question
4 0
3 years ago
a rectangle has an area of 1/6 squar centimeters and a length of 1.5 centimeters what is the width and the perimeter
Alex73 [517]
<span>

(1/6)/ 1.5 = 
(1/6)/(15/10)=
1/6*10/15=10/90=1/9 width</span>
3 0
3 years ago
Answer quick find the coordinates
Mekhanik [1.2K]

Answer:

  (-4, -3), (4, -1), (8, 0), (12, 1)

Step-by-step explanation:

The x- and corresponding y-values are listed in the table. Put each pair in parentheses, <em>x-value first</em>. (That is an <em>ordered pair</em>.)

  (x, y) = (-4, -3) . . . . from the first table entry

  (x, y) = (4, -1) . . . . from the second table entry

  (x, y) = (8, 0) . . . . from the third table entry

  (x, y) = (12, 1) . . . . from the last table entry

3 0
3 years ago
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