The sum of three numbers is 19 two times the first number is increased by six times the second number plus the third number is 12 why in the number is the Sims requirements below can best be used to determine the three numbers

Step-by-step explanation: x+    y+z=19   ...(1)

2x+6y+z=12   ...(2)

3x+8y+z=-14    ...(3)

(2)-(1) gives

x+5y =-7   ...(4)

(3)-(1)  gives

2x+7y= -33   ...(5)

multiply (4) by 2

2x+10y=-14   ...(6)

(6)-(5) gives

3y=19

y=19/3

x+95/3=-7

x=7+95/3=(21+95)/3=116/3

from (1)

116/3+19/3+z=19

(116+19)/3+z=19

135/3+z=19

45+z=19

z=19-45=-26

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}

step-by-step explanation: