What is the length of segment FG?
2 answers:
Answer:
D. 10.49
Step-by-step explanation:
(see attached for reference)
Here we have two right triangles formed by dividing a larger right triangle by the Altitude (height) of the larger right triangle.
In this special case, all 3 triangles (2 small and 1 large) are SIMILAR and hence we can use the ratios of similar triangles to solve this.
In our case, ΔGFE is similar to ΔGHF
hence FG/GE = GH/FG
We are given that GE = 10 and GH = 11, hence
FG/10 = 11/FG
FG² = (10)(11)
FG² = 110
FG = ±√110
FG= 10.49
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<span>A function, f, is continuous at x = 4 if
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Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
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