Find the area of the following shape. You must show all work to receive credit

Mathematics

2 answers:

kirza4 [7]3 years ago

3 0

Answer:

42 square units

Step-by-step explanation:

Draw segments - 5 to A, A to the point of intersection of Band C and from from the point of intersection of B, C upto 2. It will form a square with each side 8 units and four triangles.

Subtracting the area of 4 four triangles from the area of the square will give you the area of the required shape.

Area of the shape

$= {8}^{2} - \frac{1}{2} \times 3 \times 6 - \frac{1}{2} \times 5 \times 2 - \frac{1}{2} \times 2 \times 3\\ - \frac{1}{2} \times 2 \times 5 \\ \\ = 64 - 3 \times 3 - 5 \times 1 - 1\times 3 - 1 \times 5 \\ \\ = 64 - 9 - 5 - 3 - 5 \\ \\ = 64 - 22 \\ = 42 \: {units}^{2}$

frutty [35]3 years ago

3 0

Answer:

42 units squared

Step-by-step explanation:

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nikklg [1K]

<h3>Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>

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Explanation:

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

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Side notes:

Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
Choice 2 is not true. Point B is not on the parabola.
Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.