Organize from least to greatest

y=31x/15 < y=27x/13 < y=15x/7 < y=13x/6 < y=11x/5 < y=21x/9 (=7x/3) < y=19x/8

Step-by-step explanation:

since all equations base on a linear, simple expression of x, we can simply compare the fractions.

in general, the bigger the number at the bottom, the smaller the individual fraction. that is our first indicator.

we then notice that many fractions represent the value of 2 plus one fraction.

31/15 = 2 1/15

27/13 = 2 1/13

15/7 = 2 1/7

13/6 = 2 1/6

11/5 = 2 1/5

the only exceptions are 21/9 and 19/8

but 21/9 is actually 7/3 = 2 1/3

and fits therefore into the list above.

that leaves 19/8 = 2 3/8.

the list above can be sorted based on the single fraction at the end (remember, the bigger the number at the bottom, the smaller the value). so, from least to greatest :

2 1/15 (31/15)

2 1/13 (27/13)

2 1/7 (15/7)

2 1/6 (13/6)

2 1/5 (11/5)

2 1/3 (7/3 = 21/9)

where did now 2 3/8 fit in ?

well, 3/8 is almost 1/2 (so, relatively big), and we start our comparison with the biggest number in the list so far :

1/3 (from 2 1/3).

what is bigger - 1/3 or 3/8 ?

let's find the smallest number that can be divided by 3 and by 8. that would be 24. so now we bring both fractions to the same base of 24.

1/3 = 8/24

3/8 = 9/24

=> 3/8 > 1/3

and therefore, 19/8 is the largest value and at the end of the list.

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.

slope =   (y2 -y1) ÷ (x2 -x1)

slope = (0 -0) / (-5, -7)

slope = 0 / -12 = 0

the slope of the line is zero.   it is perfectly horizontal.

step-by-step explanation: