Now consider the product of a nonzero rational number and an irrational number. Again, assume x = , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to , where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown. Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?

Irrational number

Step-by-step explanation:

It's given,

y = (By simplifying the product of rational number 'x' and an irrational number 'y')

Where m and n are the integers and is a rational number.

(Since x = is a rational number)

Therefore, will be a rational number.

y = ⇒ Irrational number = Rational number

which is a contradictory statement.

Therefore, multiplication of rational and irrational number will be irrational.

answer: i don't understand. what are the options

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: