For the function f(x) = -2(x + 3)^2 -1, identify the vertex, domain, and range. A.) The vertex is (3, -1), the domain is all real numbers, and the range is y ≥ -1. B.) The vertex is (3, -1), the domain is all real numbers, and the range is y ≤ -1. C.) The vertex is (-3, -1), the domain is all real numbers, and the range is y ≤ -1. D.) The vertex is (-3, -1), the domain is all real numbers, and the range is y ≥ -1

Answer:

its 144

Step-by-step explanation:

Answer:

None of the answer choices (a, b, c, d) match this result exactly, but the correct choice closest to this result would be:

a) Y(s) = (s^2 + 4s + 6)/(s^2 + s - 30) - (9s)/(s^2 + 81)

Step-by-step explanation:

To find the Laplace transform of the given differential equation, we'll first take the Laplace transform of each term in the equation. Let's denote Y(s) as the Laplace transform of Y(t).

The differential equation is:

Y''(t) - Y'(t) - 30Y(t) = sin(9t)

Taking the Laplace transform of each term, we get:

L{Y''(t)} - L{Y'(t)} - 30L{Y(t)} = L{sin(9t)}

Using the properties of the Laplace transform, we can find the Laplace transforms of the derivatives as follows:

L{Y''(t)} = s^2Y(s) - sy(0) - y'(0)

L{Y'(t)} = sY(s) - y(0)

So the equation becomes:

s^2Y(s) - sy(0) - y'(0) - sY(s) + y(0) - 30Y(s) = 9/(s^2 + 81)

Now, substitute the initial conditions Y(0) = 6 and Y'(0) = 4:

s^2Y(s) - 6s - 4 - sY(s) + 6 - 30Y(s) = 9/(s^2 + 81)

Now, group like terms:

(s^2 - s - 30)Y(s) - 6s - 4 + 6 = 9/(s^2 + 81)

(s^2 - s - 30)Y(s) - 6s + 2 = 9/(s^2 + 81)

Now, solve for Y(s):

Y(s) = [9/(s^2 + 81) + 6s - 2] / (s^2 - s - 30)

Factoring the denominators:

Y(s) = [9/(s^2 + 81) + 6s - 2] / [(s - 6)(s + 5)]

Now, we have the Laplace transform equation for Y(s):

Y(s) = [9/(s^2 + 81) + 6s - 2] / [(s - 6)(s + 5)]

None of the answer choices (a, b, c, d) match this result exactly, but the correct choice closest to this result would be:

a) Y(s) = (s^2 + 4s + 6)/(s^2 + s - 30) - (9s)/(s^2 + 81)

Step-by-step explanation:

The expression for he earning of Allison and her allowance is as follows :

15x+100y

Part A

Variables are x and y. Coefficients are 15 and 100.

Part (B)

There are two terms in this expression. + is used to separate the terms. 15x and 100y are the terms.

Part (C) As $15 shows her earning from allowances. Hence, 15x shows allowance.

Answer:it’s actually ratio of women to total people in the theater is 0.50

Step-by-step explanation:

A ratio of 1.00 for men to Women indicates that the number of men is equal to the number of women. In other words half of the people in the theater are men and the other half or women. Therefore, the ratio of women to total people must be 1/2 = 0.50