Answer:
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Step-by-step explanation:
Answer:
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A good place to start is to set
to y. That would mean we are looking for
to be an integer. Clearly,
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
is a radical, it only outputs values from
, which means y is on the closed interval:
.
With that, we don't really have to consider y anymore, since we know the interval that
is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval
, which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.
1/5 equals 12 so 12 times 5 is 60 so
a=36
b=24
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Sample Response:
<em>The linear equations have the same slope, so the rate of change for each is the same. As long as the rate of change is the same, the lines will stay the same distance apart and not intersect.</em>
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