Try to prove the hypothesis from part b that the sum of a rational and an irrational number is an irrational number. let’s say is x an irrational number and y is a rational number. the rational number y can be written as y=a/b , where a and b are integers and b does not equal 0. leave the irrational number x as x since it can’t be written as the ratio of two integers. prove the hypothesis using a proof by contradiction. in other words, try to show that x+y equals a rational number instead of an irrational number. let the sum equal m/n , where m and n are integers and n does not equal 0. plug in the values to get this equation: x+a/b=m/n now, solve the equation for x .

The next step of your proof is to subtract (a/b) from both sides.

Then you get, x = (m/n) - (a/b)

Since rationals are closed over addition, (m/n) + (-a/b) is a rational number.

Therefore, x (an irrational number) = a rational number                            This is a false statement which is a contradiction. So, the assumption was incorrect.

Thus, the sum of a rational and irrational number is an irrational number. QED

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

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