course Mth 271
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17:04:08 ppCal1 Section 0.2 EXTRA QUESTION. What is the midpoint between two points What are your points and what is the midpoint? How did you find the midpoint?{}{}What is the midpoint between the points (3, 8) and (7, 12)?
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RESPONSE --> a+b/2 0.2.35 ......(-6.85, 9.35)= 1.25 0.2.38 .......( 5/6, 5/2)= 1.67 3+7/2= 5 7+12/ 2= 9.5 (5, 9.5)
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17:04:34 ** You are given two points. The points each have two coordinates. You have to average the x coordinates to get the x coordinate of the midpoint, then average the y coordinates to get the y coordinate of the midpoint. For example if the points are (3, 8) and (7, 12), the average of the x coordinates is (3 + 7) / 2 = 5 and the average of the y coordinates is (7 + 12) / 2 = 9.5 so the coordinates of the midpoint are (5, 9.5). **
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RESPONSE --> I didnt explain it this well but I understand what I am doing
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17:05:36 0.2.22 (was 0.2.14 solve abs(3x+1) >=4
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RESPONSE --> 3x+1>=4 3x=3 x=1 x>1
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17:06:21 ** abs(a) >= b translates to a >= b OR a <= -b. In this case abs(3x+1) > 4 gives you 3x + 1 >= 4 OR 3x + 1 <= -4, which on solution for x gives x >= 1 OR x < = -5/3. **
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RESPONSE --> Opps! I forgot to do the other part. I didnt traslate both of the possiblities.
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17:07:36 ** the given inequality is equivalent to the two inequalities 3x+1 >= 4 and 3x+1 =< -4. The solution to the first is x >= 1. The solution to the second is x <= -5/3. Thus the solution is x >= 1 OR x <= -5/3. COMMON ERROR: -5/3 > x > 1 INSTRUCTOR COMMENT: It isn't possible for -5/3 to be greater than a quantity and to have that same quantity > 1. Had the inequality read |3x+1|<4 you could have translated it to -4 < 3x+1 <4, but you can't reverse these inequalities without getting the contradiction pointed out here. **
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RESPONSE --> I understand that you need to be very careful when doing these because you do not want to get your signs mixed up
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17:09:04 0.2.24 (was 0.2.16 solve abs(2x+1)<5. What inequality or inequalities did you get from the given inequality, and are these 'and' or 'or' inequalities? Give your solution.
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RESPONSE --> 2x+1<5 ...... -5<2x+1 -3
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17:09:56 ** abs(a) < b means a < b AND -b < -a so from the given inequality abs(2x+1) < 5 you get -5 < 2x+1 AND 2x+1 < 5. These can be combined into the form -5 < 2x+1 < 5 and solved to get your subsequent result. Subtracting 1 from all expressions gives us -6 < 2x < 4, then dividing through by 2 we get -3 < x < 2. **
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RESPONSE --> I left out some of my steps but I got the correct answer
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17:10:55 0.2.5 (was 0.2.23 describe [-2,2 ]
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RESPONSE --> x= --2.....x=2 -2+2/2 =0 so middle 0
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17:11:36 ** The interval [-2, 2] is centered at the midpoint between x=-2 and x=2. You can calculate this midpoint as (-2 + 2) / 2 = 0. It is also clear from a graph of the interval that it is centered at x = 0 The center is at 0. The distance to each endpoint is 2. The interval is | x - center | < distance to endpoints. So the interval here is | x - 0 | < 2, or just | x | < 2. **
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RESPONSE --> I didnt put x<2 I dont know why but I understand the interval
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17:13:37 0.2.10 (was 0.2.28 describe [-7,-1]
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RESPONSE --> -7+1/2 ....-3 .....so 4 and -4
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17:15:36 ** the interval is centered at -4 (midpt between -7 and -1). The distance from the center of the interval to -7 is 3, and the distance from the center of the interval to -1 is 3. This translates to the inequality | x - (-4) | < 3, which simplifies to give us | x + 4 | < 3. **
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RESPONSE --> I dont understand why it is centered at -4 ...I really messed this one up. Yes I do! I have no idea what I am thinking! I know that half way between the two is -4....I just wasnt thinking!
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17:16:51 0.2.12 (was 0.2.30) describe (-infinity, 20) U (24, infinity)
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RESPONSE --> Centered at 22 - infi<2+x> + infi
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17:17:40 ** 22 is at the center of the interval. The endpoints are 2 units from the midpoint, and are not included. Everything that lies more than 2 units from 22 is in one of the intervals, and everything in either of the intervals lies at least 2 units from 22. So the inequality that describes this union of two intervals is | x - 22 | > 2. **
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RESPONSE --> I got the center right but missed the inequality I am not sure how to do these......
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17:19:34 0.2.42 (was 0.2 #36 collies, interval abs( (w-57.5)/7.5 ) < 1
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RESPONSE --> -1= w - 57.5/ 7.5 ...and 1= w-57.5/ 7.5 ....so then 50
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17:19:45 ** The inequality is translated as -1<=(w-57.5)/7.5<=1. Multiplying through by 7.5 we get -7.5<=w-57.5<=7.5 Now add 57.5 to all expressions to get -7.5 + 57.5 <= x <= 7.5 + 57.5 or 50 < x < 65, which tells you that the dogs weigh between 50 and 65 pounds. **
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RESPONSE --> ok
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17:20:26 0.2.40 (was 0.2.38 stocks vary from 33 1/8 by no more than 2. What absolute value inequality or inequalities correspond(s) to this prediction?
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RESPONSE --> 35 1/8
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