Paul and his neighbors decided to build a fence along his farm. after three hours, they have 15 meters of fencing complete. they decide to take a 2-hour break for lunch and then resume building the fence. after four more hours, they have a fence that is a total of 55 meters long. never been good with graphs, the y-axis goes by 5's and goes all the way up to 55 starting from 5. the y-axis is the length of the fence in meters, and the x-axis goes to 10 by ones which is the number of hours

Let the  be the time in hours, and  meters of fencing completed. 

We know that After three hours, they have 15 meters of fencing complete, our graph will go from the point (0,0) to the point (3,15). We also know that they decide to take a 2-hour break for lunch and then resume building the fence, so our graph will go from the point (3,15) to the the point (5,15). Finally, After four more hours, they have a fence that is a total of 55 meters long, so the final part of our graph will go from the point (5,15) to the point (9,55)

We can conclude that the graph of t vs y is:

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}

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40