What does side LN equal?

MN = x(x + 1)/(x + 3)

Step-by-step explanation:

We are given;

MN/LN = PN/QN

From the diagram;

Let MN = y

LN = x + 1 + y

PN = x

QN = x + 3 + x = 2x + 3

Thus;

y/(x + y + 1) = x/(2x + 3)

Rearranging gives;

y(2x + 3) = x(x + y + 1)

2xy + 3y = x² + xy + x

x² + x = xy + 3y

x(x + 1) = y(x + 3)

y = x(x + 1)/(x + 3)

Thus; MN = x(x + 1)/(x + 3)

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

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}