By decomposing the figure in simpler shapes, we will see that the total area is:
a = 180 cm²
<h3>
How to find the area of the composite figure?</h3>
Remember that the area of a rectangle of width W and length L is:
A = L*W
And the area of a triangle with base B and height H is:
A = B*H/2.
Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.
So the area of that part is:
A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²
Now, the bottom triangle has a base of 12 cm, and a height of:
15cm - 6cm = 9cm
Then its area is:
A' = 12cm*9cm/2 = 54cm²
This means that the total area of the figure is:
total area = 54cm² + 54cm² = 108cm²
If you want to learn more about area:
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The roots of the given polynomials exist
, and
.
<h3>What is the formula of the quadratic equation?</h3>
For a quadratic equation of the form
the solutions are

Therefore by using the formula we have

Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get

simplifying the equation, we get



Therefore, the roots of the given polynomials are
, and
.
To learn more about quadratic equations refer to:
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You can solve this in two ways.
1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.
2. Analytical. Calculate the derivative of the function f(x)

Solve the equation:

will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:

You get the same answer: x=-2, y=-9
So the answer is
<span>B. (-2, -9)</span>
I believe the correct answer to your question would be choice B. The trail is no more than 6 miles long.