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son4ous [18]
3 years ago
6

Help please asap will mark brainliest !

Mathematics
1 answer:
Ber [7]3 years ago
8 0

Answer:

b = 29

Step-by-step explanation:

C x D = A x B

15(11x - 91) = 7(2x + 10)

165x - 1365 = 14x + 70

add 1365 to both sides of the equation:

165x = 14x + 1435

subtract 14x from both sides:

151x = 1435

divide both sides by 151:

x = 9.5

b = 2(9.5) + 10 = 29

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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
Please view the attachment.
quester [9]
-1 * (-4) = 4; 3 * (-4) = -12; 6 * (-4) = -24; -3 * (-4) = 12
7 0
3 years ago
Susan needs to simplify the expression shown below.
mash [69]

Answer:

The answer to 75 - ( 8 + 45 ÷ 3 ) × 2= 29

3 0
2 years ago
62% of trees were saved from a fire. If this represents 1420 trees, how many trees were originally in the forest?Round to the ne
tresset_1 [31]

Answer:

2290 trees

Step-by-step explanation:

Given data

Let the total number of trees be x

62% of the total trees x is 1420 trees

mathematically

62/100x= 1420

0.62x= 1420

divide both sides by 0.62

x= 1420/0.62

x= 2290.32

To the nearest whole tree= 2290 trees

5 0
2 years ago
24 ÷ v x k when v=2 and k=4
Leya [2.2K]

Answer:

48

Step-by-step explanation:

24 ÷ v x k

24 ÷ 2 x 4    

(Since it's multiplication and division, you just go from left to right in order)

12 x 4

48

5 0
2 years ago
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