Arectangular blue tile has a length of 4.25 inches and a width of 6.75 inches. a similar tile has a length of 12.75 inches. what is the width of the red tile.

The width of the red tile would be inches.

Step-by-step explanation:

Given blue tile has a length of inches, and a width of inches.

Also, length of similar tile is inches.

Let us assume as the width of red tile.

It is given in the question that both tiles are similar.

So, their area will be the same.

Area of blue tile would be

Area of red tile would be

The area of blue tile would be equal to area of red tile.

So, the width of the red tile would be inches.

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}

answer: 1 + 1 = 11

step-by-step explanation: