Answer:
- See the graphs attached and the explanation below
Explanation:
The most simple sine function, considered the parent function, is:

That function has:
- Midline, also known as rest or equilibrium position: y = 0
- Minimum: - 1
- Maximum: 1
- Amplitude: the distance between a minimum or a maximum and the midline = 1
- period: the interval of repetition of the function = 2π
The more general sine function is:

That function has:
- Midline: y = D (it is a vertical shift from the parent function)
- Minimum: - A + D
- Maximum: A + D
- Amplitude: A
- period: 2π/B
- phase shift: C (it is a horizontal shift of the from the parent function)
Now, you have to draw the sine function with the given key features:
- Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
- midline y = - 1 ⇒ D = - 1
Substitute the know values and use the y-intercept to find C:

Substitute (0, -1)

Hence, the function to graph is:

To draw that function use this:
- Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
- Minima: 3(-1) - 1 = - 3 - 1 = -4
- y-intercept: (0, - 1)
- x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
- first point of the midline: (0, -1) it is the same y-intercept
With that you can understand the graphs attached.
The answer is roughly 21.4 copies per minute
an estimate
Answer:
Step-by-step explanation:
You can't ever let this go negative. At least not at the grade you are in.
It can be 0.
So the domain must start at x = 7
sqrt(5*7 - 35) = sqrt(0) = 0
x can have any value (including 7) between 7 and infinity. If you choose a number less than 7 (like 6) the square root will go negative and that's not to be done.
So the interval is
7 ≤ x < ∞
Answer:
I think it's the top left one
Step-by-step explanation:
We can factor 120 into
2 * 2 * 2 * 3 * 5
I think there are nine different possibilities
1) 8 * 3 * 5
2) 4 * 2 * 15
3) 4 * 6 * 5
4) 4 * 10 * 3
5) 2 * 2 * 30
6) 2 * 3 * 20
7) 2 * 5 * 12
8) 2 * 6 * 10
9) 2 * 15 * 4