1. Which of the following sets are rings with respect to the usual operations of addition and multiplication? If the set is a ring, is it also a field? 7 Z 7Z Z 18 Z18 Q ( √ 2 ) = { a + b √ 2 : a , b ∈ Q } Q(2)={a+b2:a, b∈Q} Q ( √ 2 , √ 3 ) = { a + b √ 2 + c √ 3 + d √ 6 : a , b , c , d ∈ Q }

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:

what are you trying find out?

step-by-step explanation:

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.

did you get the answer?