So firstly, <u>the factor (4n - 5) cannot be further factored, so we will be focusing on 2n² + 5n + 3.</u>
So for this, we will be factoring by grouping. Firstly, what two terms have a product of 6n² and a sum of 5n? That would be 2n and 3n. Replace 5n with 2n + 3n:
Next, factor 2n² + 2n and 3n + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:
Now we can rewrite this expression as<u> , which is your final answer.</u>
<u><em>Answer:</em></u>
The initial value is 3
It represents the distance between the bird and its nest before any elapsed time which is 3 miles.
<u><em>Step-by-step explanation:</em></u>
The graph is shown in the attached image.
<u>The general form of a straight line is:</u>
y = mx + c
where:
m is the slope and c is the y-intercept.
The y-intercept is also known as the initial value. It is the value of y at x=0.
From the givens, we can note that at x = 0, the y-value is 3. This means that the y-intercept is 3.
Now, in the problem, x represents the time in minutes while y represents the distance of the bird from the nest in miles.
At x = 0, meaning before any time elapsed, the distance of the bird from its nest was 3 miles.
Hope this helps :)
