Answer:
Step-by-step explanation:triangle P: 12, 24, and 30
triangle Q: 9, 40, and 41
triangle R: 5, 18, and 21
Which triangle is a right triangle? Explain your reasoning.
We need to cancel out the discontinuity in x = 4
In order to do that, factorize the numerator:
5x⁴ - 20x³ = 5x³(x-4)
This way, your function will be:
f(x) = <span>5x³(x-4) / (x-4)
and the two parentheses cancel out, leaving
</span>f(x) = <span>5x³
</span>
which at x = 4 gives:
f(4) = <span>5·4³</span> = 5 · 64 = 320
Therefore K = 320.
The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)
Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1
We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
.. 0 = a*(1 -2)^2 +1
.. 0 = a*1 +1
.. -1 = a
Now we know the equation is
.. y = -(x -2)^2 +1
_____
If we like, we can expand it to
.. y = -(x^2 -4x +4) +1
.. y = -x^2 +4x -3
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An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
.. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a
.. -1 = a
Then the equation of the graph can be written as
.. y = -(x -1)(x -3)
In expanded form, this is
.. y = -(x^2 -4x +3)
.. y = -x^2 +4x -3 . . . . . . same as above
There is no real solution to this problem
two exterior angles for those angles would be 140 and 85
