Identify the translation rule on a coordinate plane that verifies that square a(-4, 3), b(-4, 8), c(-9, 3), d(-9, 8) and square a'(-3, 2), b'(-3, 7), c'(-8, 2), d'(-8, 7) are congruent.

 The translation rule that verifies that square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent is

(x, y)  ⇒ (x+1, y-1).

Step-by-step explanation:  We are given to identify the translation rule on a coordinate plane that verifies that

square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent.

We see that the co-ordinates of the vertices of square ABCD and A'B'C'D' are related as follows :

A(-4, 3)  ⇒  A'(-4+1, 3-1) = A'(-3, 2),

B(-4, 8)  ⇒  B'(-4+1, 8-1) = B'(-3, 7),

C(-9, 3)  ⇒  C'(-9+1, 3-1) = C'(-8, 2),

D(-9, 8)  ⇒  D'(-9+1, 8-1) = C'(-8, 7).

Therefore, the required translation rule is given by

(x, y)  ⇒ (x+1, y-1).

Thus, the translation rule that verifies that square A(-4, 3), B(-4, 8), C(-9, 3), D(-9, 8) and square A'(-3, 2), B'(-3, 7), C'(-8, 2), D'(-8, 7) are congruent is

(x, y)  ⇒ (x+1, y-1).

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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}