Given:
The given equation is:

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.
To find:
The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.
Solution:
We have,

The height of the ball is at least 36 feet above the ground. It means
.



Splitting the middle term, we get



The critical points are:


These two points divide the number line in 3 intervals
.
Intervals Check point
Result
0
False
4
True
8
False
The inequality is true for (2,6) and the sign of inequality is
. So, the ball is above 36 feet between 2 to 6 seconds.

Therefore, the required inequality is
and the ball is 36 feet above for 4 seconds.
D. 41x + 11y
You add the like terms so the 23 and 18 to equal 41
Answer:
What is the change for each consecutive input?
✔ 1
What is the change for each consecutive output?
✔ 0.35
What is the rate of change for the relationship?
✔ 0.35
Step-by-step explanation:
The change for each input is 1 beacause the inputs are 10,11,12,13
The change for each consecutive output is 0.35 beacuse we need to subtract 4.1 from 3.75
The rate of change for the relationship is also 0.35
a² + 10a + 16
Find two numbers whose product equals 16 and sum equals 10:
<u>Product = 16</u> <u>Sum = 10</u>
1 * 16 1 + 16 = 17 <em>doesn't work</em>
2 * 8 2 + 8 = 10 THIS WORKS!
4 * 4 4 + 4 = 8 <em>doesn't work</em>
Since 2 & 8 satisfy our requirements, those are the values that go into the parentheses.
Answer: (a + 2)(a + 8)
Note: when there is a coefficient for a², a different method is used to find the factors.