The perimeter formula for a rectangle is 21+ 2w, where l is the length and w is the width
(8x - 1) in
(2x + 4) in

20x+6

Step-by-step explanation:

The perimeter is

P= 2l + 2w

P = 2( 8x-1) + 2(2x+4)

Distribute

   = 16x-2 + 4x+8

Combine like terms

  = 20x+6

Perimeter = 20 x + 6

Step-by-step explanation:

The Perimeter of rectangle = 2l + 2w

Where,

Perimeter of rectangle = 2(8x -1)+ 2(2x + 4)

using Distributive property

Perimeter = 16 x - 2 + 4x + 8

Combine like terms

Perimeter = 16 x + 4x - 2 + 8

Perimeter = 20 x + 6

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}