Which best describes the system of equations? y = 4x + 3 y = 2x − 4 a) consistent b) inconsistent c) consistent and dependent d) consistent and independent

D) Consistent and Independent

Step-by-step explanation:

The system of equations,

and

is consistent and independent if

The system is consistent and dependent if

The system is inconsistent if

Now, in the given system

4x - y + 3 = 0 and

2x - y - 4 = 0

So,

Hence, the given system is consistent and independent.

answer:   14

step-by-step explanation:          

pu you stank bo u ugly bo lol

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}