For this case we must factor the following expression:
We rewrite the middle term as a sum of two terms whose product is
And whose sum is
These numbers are:
-5 and -3
So:
We factor the maximum common denominator of each group:
We take common factor
Answer:
Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)
Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is
.
Plugging 15 and 35 in x, we can find the values of the function, i.e.
and
.
Then, the average change is
Use point slope form to answer this
Y = x - 10
EG and FH are diagonals of the rhombus and the bisect each other at the centre to for a righ angle triangle with the side of the rhombus as the hypothenus.
By pythagoras theorem,
