Match the reasons with the statements in the proof to prove ab || dc , given that ad is parallel to bc and ad = cb .
given:
ad || bc
ad = cb
prove:
ab || dc
1. ad || bc, ad = cb (a. if lines are parallel, then alternate interior angles are equal.)
2. ac = ac (b. if alternate interior angles are congruent, then lines are parallel.)
3. 2 = 3 (c. cpcte)
4. acd = cab (d. reflexive property of equality)
5. 1 = 4 (e. sas)
6. ab || dc (f. given)

Given: and AD=CB

To Prove:

1. , AD=CB

Reason: Given

2. AC = AC

Reason: Reflexive Property of Equality

3.

Reason: If Lines are parallel, then Alternate Interior Angles are Equal).

4.

Reason: SAS

5.

Reason: CPCTE

6.

Reason: If Alternate Interior Angles are Congruent, then Lines are Parallel.

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}

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.