Mitchell plays a trading card game. He has the starter pack of cards and adds to his collection by purchasing a booster pack each week that contains the same number of cards. On the graph, points are plotted and a line is drawn through the points to show the linear relationship between the total number of cards in Mitchell's collection and the number of weeks he has been collecting. Mitchell's Trading Card Collection 225 210 195 Total Number of Cards 180 165 150 135 120 105 90 75 60 45 30 15 0 0 2 8 5 6 7 Number of Weeks a What is the initial value of the function represented by the graph? b. What is the rate of change of the function represented by the graph? = 60​

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}

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)