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Answer 1

#F+D= 160#

There were F wins for the Flying Turtles against teams other than Dolphins. There were 95 victories in total for the Flying Turtles. If they didn't win a single match against the Dolphins then #F =95# but if they did win a match against them it must be less than that. Therefore the following can be deduced:

#F leq 95#

Similarly, #D leq 84# This gives us the upper bound #F+D leq 179#

#x + y = 19# where #19# is the total number of matches played between the Flying Turtles and the Dolphins and #x# is the number of victories of the Flying Turtles against the Dolphins and #y# is the number of victories of the Dolphins against the Flying turtles. This makes sense because if one of them wins, the other must lose. So, the sum of all victories must equal the number of matches played, assuming there are no ties. However, please note that this method only works under the assumption that there are no ties, or that a tie is treated as a half victory.

This gives us the following expressions:

#F = 95-x# since you subtract #x# victories against the Dolphins to get the victories against teams other than the Dolphins. (total number of victories minus victories against the Dolphins)

Same goes for D. #D = 84-y#

If we add these two numbers together we get the expression #F+D =95-x + 84-y=# #179 - (x+y)#

Since #x + y = 19#

#F+D=179 - 19=160#

As this is less than our upper bound it is a reasonable answer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.