The lengths of two sides of a triangle are 14 inches and 4 inches which of following is the dimensions is the third side of the triangle? 10 in 11 in 8 in 9 in

The sum of any 2 sides of a triangle must be bigger than the length of the third side.

Given 2 sides we can make 3 inequality's to solve:

Let X = the length of the third side.

#1) 14 + 4 > x

18 > x

#2) 14 + X > 4

x > 4-14 = -10 ( This doesn't work because we can't have a side length that is a negative number)

#3) 4 + X > 14

x >14-4 = 10

So using #1 and #3 X has to be greater than 10 and less than 18

The length of the third side is 11.

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}

50- 250 is correct i did that one too

step-by-step explanation: