The expressions given in the table can all be simplified. When simplified, three of the expressions in Column A are equivalent to three of the expressions in Column B. Column A
Column B
I.
2x + 13-7x
V.
13 + 7x + 2x
II. 7x-17 + 4x
VI.
17-4x - 7
III. 7x +13 + 2x
VII. 13-7x + 2x
VIII. 4x + 7x - 17
IV. 4x - 7+17
Which pair of expressions is not equivalent?
land VII
ll and VIII
Ill and V
IV and VI

Step-by-step explanation:

after simplifying they look like

I) -5x + 13

II) 11x - 17

III) 9x + 13

IV) 4x + 10

V) 9x + 13

VI) -4x + 10

VII) -5x + 13

VIII) 11x - 17

so, clearly, IV and VI are not the same (equivalent).

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}

1) is right

step-by-step explanation: