Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?triangles WXZ and XYZ that share side XZ with right angle XZW, WZ equals 12, XZ equals 6, and YZ equals 3Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate. 6 over 12 equals 3 over 6 6 over 3 equals 6 over 12 6 over 6 equals 3 over 12 12 over 6 equals 3 over 6

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}

you just switch the numbers basically so it would be 3/17