Let a be a rational number and b be an irrational number. a + b = c, assume c is rational

a + b - a = c - a, subtract a from both sides

b = c - a, which means that b is rational. But this contradicts the initial assumption.
The above proof shows that the sum of an irrational and rational number is always . Explain.

The classrooms are trying to raise $1,200.00 for charity. mrs. leblanc's class has raised 50%. mr. patel's class has raised $235.14 ms. warner's class has raised 1/3 as much as mrs. leblanc's class. how much more money is needed to reach the goal of $1,200.00?

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

The cost for an uberi is $2.50 plus $2.00 mile. if the total for the uber ride was $32.50, how many miles did the customer travel?