List the members of these sets. a.{x | x is a real number such that x2 = 1} b.{x | x is a positive integer less than 12} c.{x | x is the square of an integer and x < 100} d.{x | x is an integer such that x2 = 2}

The sets are:

We need to find all the values of x that meet the given restrictions for each set.

a) Here we know that x is a real number and we must have:

x^2  = 1

Solving for x:

x = ±√1 = ±1

Then this set is:

{-1, 1}

b) Here x is a positive integer smaller than 12, this is just:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

c) In this case x is a square number, and it must be smaller than 100, so let's find all the square values smaller than 100.

Then this set is:

{1, 4, 9, 16, 25, 36, 49, 64, 81}

d) Here x must be an integer, such that x^2 = 2

Solving the equation we get:

x = ±√2

But √2 is an irrational number, so there is no integer number that meets this restriction, this means that we have an empty set, this is written as:

{∅}.

If you want to learn more about sets, you can read:

link

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

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: