PLEASE HELP

Indira created four graphs, each containing a system of equations. She drew only a part of the line for each equation. By inspection, which graph contains a system with infinitely many solutions?

THIRD OPTION.

Step-by-step explanation:

For this case it is important to know that  by definition, there are three possible cases for the solution of a System of equations. These are shown below:

 1. If the lines intersect each other, then the System of equations has ONE SOLUTION.

2. If the lines are parallel, then the System of equations has NO SOLUTION.

3. If the two equations are the same line, then the System of equations has INFINITELY MANY SOLUTIONS.

Observe the graphs attached in the exercise.

You can notice in the third graph that the "line a" and the "line b" are exactly the same line.

Therefore, based on the explained before, you can conclude that the third graph given in the exercise contains a System of equations with Infinitely many solutions.

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}

312312

step-by-step explanation: