Answer:

Step by step explanation:









Answer:
Step-by-step explanation:
If you plot the vertex and the point, you see that the point is above the vertex. Therefore, this is a positive parabola with the work form of

We have values for x, y, h, and k. Let's write the equation of the parabola, put it into function notation, then find another x value at which to evaluate it.
and
and
8 = 9a - 1 and
9 = 9a so
a = 1. The equation of the parabola in function notation is

Since the vertex is at (3, -1) it would make sense to evaluate the function at x values close to the vertex. Let's evaluate the function at an x value of 4:
and
and
f(4) = 0. That means that another point on this parabola will be (4, 0).
The normal form of a line is given by the equation x * cos theta + y * sin theta = p where theta is the angle of the normal line from the positive x-axis and p is the length of the normal line. Converting to normal line form, the equation must first be converted into standard form: 2x + 7y = 4. Then dividing the whole equation by sqrt(a^2 + b^2): sqrt(2^2 + 7^2) = sqrt(53). Hence, the equation becomes 2 / sqrt(53) * x + 7 / sqrt(53) * y = 4 / sqrt(53). Therefore, the length of the normal line is 4 / sqrt(53), and the angle is arctan(7/2) = 74.05 degrees.
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Area of trapezoid formula:
A = 1/2(b1 + b2) h
A = 1/2(2.4 + 9)(8.2)
A = 1/2(11.4)(8.2)
A = 46.74 ml^2