The length of a rectangle is five times its width. the perimeter of the rectangle is at most 96 cm. which inequality models the relationship between the width and the perimeter of the rectangle? a. 2w+2⋅(5w)≤96 b. 2w+2⋅(5w)> 96 c. 2w+2⋅(5w)≥96 d. 2w+2⋅(5w)< 96

The relation between the length and the width is  l=5w ---(1) Perimeter is at most 96 means  2l + 2w ≤96 (2)  Substitute (1) in (2)  » 2(5w) + 2w≤96  Or  2w + 2.(5w)≤96  The correct answer is A

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}