Part a: factor 2x2y2 + 6xy2 + 18x2y2. show your work. part b: factor x2 + 10x + 25. show your work. part c: factor x2 − 36. show your work.

A.

B.

C.

Step-by-step explanation:

Part A. The expression consists of three terms: The first and the last terms are like terms, we can add them:

Now,

So,

Part B. The expression is a square of so

Part C. Use the difference of squares formula:

Part A: 0< x <2

Part B: 2< x <4 and x > 10

Part C: 4 < x < 10

Part D: 0 ft

Step-by-step explanation:

The ordered pairs are (0, 60), (2, 75), (4, 75), (6, 40), (8, 20), (10, 0), (12, 0), (14, 0), where the first number represents the x-axis, the time, and the second the y-axis, the height.

The domain is the set formed by the x values. A  set formed by the y values is the function image.

When x increases and y also increases, the function is crescent, and the height of the balloon is increasing, it happens at the interval 0< x < 2, after 2 seconds, the height remains constant (75 ft) until 4 seconds. After 10 seconds the height remains constant too (0 ft), so the height remains constant at the domain intervals 2 < x < 4 and x > 10.

In the interval 4< x <10, the higher is decreasing (from 75 to 0). After 10 seconds the water balloon has reached the ground (0 ft) so it possible had burst, so, at 16 seconds the higher will remains 0 ft.