Mary thinks the triangle is equilateral. how would you support or dispute her conjecture?
1 answer:
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<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.
These tables have infinitely many values, but the simplest ones would be:
a) x|y
3|5
6|10
9|15
b) x|y
2|1
4|2
6|3
Your graph for c would look like the attached picture
a) x|y
3|5
6|10
9|15
b) x|y
2|1
4|2
6|3
Your graph for c would look like the attached picture