Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

let a be a rational number and b be an irrational number.
assume that a + b = x and that x is rational.
then b = x – a = x + (–a).
x + (–a) is rational because
however, it was stated that b is an irrational number. this is a contradiction.
therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.
in conclusion, the sum of a rational number and an irrational number is irrational.

which of the following best completes the proof?
it is the sum of two rational numbers.
it is the sum of two irrational numbers.
it represents a non-terminating, non-repeating decimal.
its terms cannot be combined.

Does anyone know how to solve and graph this: 4 + | a + 2 | < 7the only part i don't get is the "4 +"

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Two trains leave stations 546 miles apart at the same time and travel toward each other. one train travels at 95 miles per hour while the other travels at 115 miles per hour l. how long will it take for the two trains to meet