Each side of a square classroom is 8 meters long. The school wants to replace the carpet in the classroom with new carpet that c
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Answer: g(f(0)) = 2 and (f ° g)(2) = -3.
Step-by-step explanation: We are given the following two functions in the form of ordered pairs :
f = {(-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)}
g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)} .
We are to find g(f(0)) and (f ° g)(2).
We know that, for any two functions p(x) and q(x), the composition of functions is defined as
From the given information, we note that
f(0) = 0, g(0) = 2, g(2) = 2 and f(2) = -3.
So, we get
Thus, g(f(0)) = 2 and (f ° g)(2) = -3.
<h3>Answer: 112.5 square units</h3>
Work Shown:
A = area of the triangle
A = base*height/2
A = 9*7/2 = 63/2 = 31.5 ... see note1 below
B = area of rectangle
B = base*height
B = 9*3 = 27
C = area of parallelogram
C = base*height .... see note2 below
C = 9*6 = 54
If you're confused where I got the 6 from, check out the attached image below.
D = total area of the composite figure
D = A+B+C
D = 31.5 + 27 + 54
D = 112.5
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note1: The vertical component of the triangle is 9 units because this is part of the rectangle. The rectangle has opposite sides that are the same length. The parallelogram's vertical sides are 9 units long as shown by the single tickmark.
note2: a rectangle is essentially a special case of a parallelogram. In other words, a rectangle is a parallelogram with 4 right angles. So this is why the formula "area = base*height" shows up identical for both rectangles and parallelograms. Keep in mind that the height is always perpendicular to the base. You will not use the segments marked with double tickmarks.