Below is the augmented matrix using the standard form of a quadratic equation that can help you write the quadratic equation going through the 3 points: \large \text{(-1,11) } \large \text{(1,5)} and \large \text{(2,11)} Hint: standard form \large ax^2+bx+c=y

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}

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

the answer is option a you would get more money.it would be $250.

step-by-step explanation:

for option b 200/2=100=50% 100/2=50=25% 50/5=10=5% it would be $220