An algebra tile configuration. 3 tiles are in the Factor 1 spot: one is labeled + x and 2 are labeled negative. 4 tiles are in the Factor 2 spot: one is labeled + x and 3 are labeled negative. 12 tiles are in the Product spot: 1 is labeled + x squared, 5 are labeled negative x, and 6 are labeled negative. Did Cherise use algebra tiles to correctly represent the product of (x – 2)(x – 3)? No, she did not multiply the x-tiles by the negative integer tiles correctly. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly. No, she did not add the terms together correctly. Yes, the product is x2 – 5x – 6.

No, she did not multiply the negative integer tiles by the other negative integer tiles correctly.

Step-by-step explanation:

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}

if x = 1, then the answer is 3.5