[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.11,0:00:02.48,Default,,0000,0000,0000,,All right.
Dialogue: 0,0:00:02.48,0:00:06.39,Default,,0000,0000,0000,,We are on problem number ten.
Dialogue: 0,0:00:06.39,0:00:12.46,Default,,0000,0000,0000,,This says the absolute value of\N10 minus k is equal to 3.
Dialogue: 0,0:00:12.46,0:00:17.11,Default,,0000,0000,0000,,And that we know that the\Nabsolute value of k minus 5 is
Dialogue: 0,0:00:17.11,0:00:18.33,Default,,0000,0000,0000,,equal to 8.
Dialogue: 0,0:00:18.33,0:00:20.87,Default,,0000,0000,0000,,And they say, what is the value\Nof k that satisfies both
Dialogue: 0,0:00:20.87,0:00:22.57,Default,,0000,0000,0000,,equations above?
Dialogue: 0,0:00:22.57,0:00:23.68,Default,,0000,0000,0000,,Well let's do the first one.
Dialogue: 0,0:00:23.68,0:00:25.85,Default,,0000,0000,0000,,The absolute value of 10\Nminus k is equal to 3.
Dialogue: 0,0:00:25.85,0:00:32.75,Default,,0000,0000,0000,,That tells us that 10 minus k\Nis equal to 3, or 10 minus k
Dialogue: 0,0:00:32.75,0:00:34.41,Default,,0000,0000,0000,,is equal to minus 3.
Dialogue: 0,0:00:37.47,0:00:41.71,Default,,0000,0000,0000,,If 10 minus k is 3, just based\Non the first equation alone, I
Dialogue: 0,0:00:41.71,0:00:42.94,Default,,0000,0000,0000,,get k is equal to 7.
Dialogue: 0,0:00:42.94,0:00:44.62,Default,,0000,0000,0000,,10 minus 7 is equal to 3.
Dialogue: 0,0:00:44.62,0:00:47.43,Default,,0000,0000,0000,,And here, k is equal to 13.
Dialogue: 0,0:00:47.43,0:00:50.62,Default,,0000,0000,0000,,So just on this first\Nconstraint, we have k is equal
Dialogue: 0,0:00:50.62,0:00:52.40,Default,,0000,0000,0000,,to 7 or 13.
Dialogue: 0,0:00:52.40,0:00:54.11,Default,,0000,0000,0000,,So now let's do the second\Nconstraint, and
Dialogue: 0,0:00:54.11,0:00:55.77,Default,,0000,0000,0000,,I'll do it in yellow.
Dialogue: 0,0:00:55.77,0:00:57.18,Default,,0000,0000,0000,,So k minus 5 is 8.
Dialogue: 0,0:01:00.19,0:01:03.47,Default,,0000,0000,0000,,That absolute value is equal to\N8, so it's either k minus 5
Dialogue: 0,0:01:03.47,0:01:09.48,Default,,0000,0000,0000,,is equal to 8, or k minus\N5 is equal to minus 8.
Dialogue: 0,0:01:09.48,0:01:12.77,Default,,0000,0000,0000,,If k minus 5 is 8,\Nthen k is 13.
Dialogue: 0,0:01:12.77,0:01:16.63,Default,,0000,0000,0000,,If k minus 5 is equal to minus\N8, then that means k is equal
Dialogue: 0,0:01:16.63,0:01:18.24,Default,,0000,0000,0000,,to minus 3.
Dialogue: 0,0:01:18.24,0:01:25.11,Default,,0000,0000,0000,,In order for k to satisfy both\Nof this equations, I've just
Dialogue: 0,0:01:25.11,0:01:26.57,Default,,0000,0000,0000,,kind of solved it.
Dialogue: 0,0:01:26.57,0:01:28.65,Default,,0000,0000,0000,,What k satisfies both\Nof these equations?
Dialogue: 0,0:01:28.65,0:01:31.58,Default,,0000,0000,0000,,Well 7 only satisfies the first\None, and negative 3 only
Dialogue: 0,0:01:31.58,0:01:32.48,Default,,0000,0000,0000,,satisfies the second one.
Dialogue: 0,0:01:32.48,0:01:35.87,Default,,0000,0000,0000,,But 13, k equals 13,\Nsatisfies both.
Dialogue: 0,0:01:35.87,0:01:38.20,Default,,0000,0000,0000,,So that is your answer.
Dialogue: 0,0:01:38.20,0:01:40.06,Default,,0000,0000,0000,,13.
Dialogue: 0,0:01:40.06,0:01:41.31,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:01:43.31,0:01:44.81,Default,,0000,0000,0000,,Problem number eleven.
Dialogue: 0,0:01:44.81,0:01:46.06,Default,,0000,0000,0000,,I've gotta do some drawing.
Dialogue: 0,0:01:51.06,0:01:52.53,Default,,0000,0000,0000,,I think I'm going to go\Nfor a walk after this.
Dialogue: 0,0:01:52.53,0:01:56.01,Default,,0000,0000,0000,,I need to work off\Nthat turkey.
Dialogue: 0,0:01:56.01,0:02:02.85,Default,,0000,0000,0000,,I have a line here,\Nthat's line M.
Dialogue: 0,0:02:02.85,0:02:08.12,Default,,0000,0000,0000,,I have line L, something\Nlike that.
Dialogue: 0,0:02:08.12,0:02:11.48,Default,,0000,0000,0000,,And then I have this\Nperpendicular line,
Dialogue: 0,0:02:11.48,0:02:14.22,Default,,0000,0000,0000,,up here like that.
Dialogue: 0,0:02:14.22,0:02:15.33,Default,,0000,0000,0000,,And then what do they tell us?
Dialogue: 0,0:02:15.33,0:02:16.58,Default,,0000,0000,0000,,They tell us that this\Nis perpendicular.
Dialogue: 0,0:02:19.52,0:02:20.43,Default,,0000,0000,0000,,Let me switch colors.
Dialogue: 0,0:02:20.43,0:02:24.94,Default,,0000,0000,0000,,They tell us that this\Nis 65 degrees.
Dialogue: 0,0:02:24.94,0:02:31.56,Default,,0000,0000,0000,,They tell us that this, right\Nhere, is x degrees.
Dialogue: 0,0:02:31.56,0:02:33.17,Default,,0000,0000,0000,,Oh, and there's another\Nline there, I
Dialogue: 0,0:02:33.17,0:02:34.69,Default,,0000,0000,0000,,haven't even drawn it.
Dialogue: 0,0:02:34.69,0:02:40.05,Default,,0000,0000,0000,,There's another line, that I\Nhaven't drawn, that is this.
Dialogue: 0,0:02:40.05,0:02:41.64,Default,,0000,0000,0000,,Switching back to the green.
Dialogue: 0,0:02:46.05,0:02:51.63,Default,,0000,0000,0000,,This is 20 degrees,\Nand so this is x.
Dialogue: 0,0:02:51.63,0:02:55.39,Default,,0000,0000,0000,,x is just this thing right here,\Nnot this whole thing.
Dialogue: 0,0:02:55.39,0:02:58.90,Default,,0000,0000,0000,,This is 20 degrees.
Dialogue: 0,0:02:58.90,0:03:03.37,Default,,0000,0000,0000,,What is the value of x\Nin the figure above?
Dialogue: 0,0:03:03.37,0:03:07.32,Default,,0000,0000,0000,,So we just gotta do what I like\Nto affectionately call
Dialogue: 0,0:03:07.32,0:03:10.63,Default,,0000,0000,0000,,the angle game.
Dialogue: 0,0:03:10.63,0:03:12.61,Default,,0000,0000,0000,,And the angle game, I just try\Nto figure out as many angles
Dialogue: 0,0:03:12.61,0:03:13.53,Default,,0000,0000,0000,,as I can figure out.
Dialogue: 0,0:03:13.53,0:03:16.36,Default,,0000,0000,0000,,So what is the measure\Nof this angle?
Dialogue: 0,0:03:16.36,0:03:18.88,Default,,0000,0000,0000,,Well this angle and this angle\Nare complementary.
Dialogue: 0,0:03:18.88,0:03:20.42,Default,,0000,0000,0000,,They add up to 90 degrees.
Dialogue: 0,0:03:20.42,0:03:23.81,Default,,0000,0000,0000,,We know this is 90, so this\Nwhole thing is 90.
Dialogue: 0,0:03:23.81,0:03:37.13,Default,,0000,0000,0000,,So if this and this add up\Nto 90, what is this?
Dialogue: 0,0:03:37.13,0:03:39.21,Default,,0000,0000,0000,,25 plus 65 is 90, correct?
Dialogue: 0,0:03:39.21,0:03:40.10,Default,,0000,0000,0000,,Yes.
Dialogue: 0,0:03:40.10,0:03:42.74,Default,,0000,0000,0000,,You can tell addition\Nis my weak point.
Dialogue: 0,0:03:42.74,0:03:45.87,Default,,0000,0000,0000,,So this is 25 degrees,\Nthis is 20 degrees.
Dialogue: 0,0:03:45.87,0:03:46.98,Default,,0000,0000,0000,,Can we figure out x?
Dialogue: 0,0:03:46.98,0:03:48.02,Default,,0000,0000,0000,,Well, sure.
Dialogue: 0,0:03:48.02,0:03:51.09,Default,,0000,0000,0000,,We know that all of these 3\Nangles combined have to add up
Dialogue: 0,0:03:51.09,0:03:52.71,Default,,0000,0000,0000,,to 180 now.
Dialogue: 0,0:03:52.71,0:03:55.63,Default,,0000,0000,0000,,Because they're all kind of\Ncollectively supplementry.
Dialogue: 0,0:03:55.63,0:03:57.52,Default,,0000,0000,0000,,You go around, you go halfway\Naround the circle.
Dialogue: 0,0:03:57.52,0:04:04.61,Default,,0000,0000,0000,,So we know that x plus 20\Nplus 25 is equal 180.
Dialogue: 0,0:04:04.61,0:04:08.16,Default,,0000,0000,0000,,x plus 45 is equal to 180.
Dialogue: 0,0:04:08.16,0:04:13.76,Default,,0000,0000,0000,,So x is equal to, this is where\NI always mess up, so x
Dialogue: 0,0:04:13.76,0:04:16.14,Default,,0000,0000,0000,,is equal to 135.
Dialogue: 0,0:04:16.14,0:04:18.74,Default,,0000,0000,0000,,So that's our answer.
Dialogue: 0,0:04:18.74,0:04:19.99,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:04:33.46,0:04:36.45,Default,,0000,0000,0000,,So number twelve.
Dialogue: 0,0:04:36.45,0:04:39.25,Default,,0000,0000,0000,,That last problem was one that\Nmy cousin had marked up pretty
Dialogue: 0,0:04:39.25,0:04:42.72,Default,,0000,0000,0000,,incorrectly, so I had to take\Nsome pause just to make sure I
Dialogue: 0,0:04:42.72,0:04:44.25,Default,,0000,0000,0000,,didn't mark it up incorrectly.
Dialogue: 0,0:04:44.25,0:04:44.55,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:04:44.55,0:04:45.40,Default,,0000,0000,0000,,Problem number twelve.
Dialogue: 0,0:04:45.40,0:04:53.32,Default,,0000,0000,0000,,The median of a set of 9\Nconsecutive integers is 42.
Dialogue: 0,0:04:53.32,0:04:56.50,Default,,0000,0000,0000,,What is the greatest\Nof these integers?
Dialogue: 0,0:04:56.50,0:05:01.23,Default,,0000,0000,0000,,So the median of 9 consecutive\Nintegers is 42.
Dialogue: 0,0:05:01.23,0:05:07.16,Default,,0000,0000,0000,,So 42 is the middle number,\Nand there's
Dialogue: 0,0:05:07.16,0:05:08.90,Default,,0000,0000,0000,,9 consecutive numbers.
Dialogue: 0,0:05:12.29,0:05:14.56,Default,,0000,0000,0000,,How many numbers are going\Nto be greater than 42?
Dialogue: 0,0:05:14.56,0:05:16.10,Default,,0000,0000,0000,,Median means middle.
Dialogue: 0,0:05:16.10,0:05:28.87,Default,,0000,0000,0000,,So that means there are\N4 greater and 4 less.
Dialogue: 0,0:05:28.87,0:05:29.90,Default,,0000,0000,0000,,Because there's a total\Nof 9 numbers.
Dialogue: 0,0:05:29.90,0:05:33.07,Default,,0000,0000,0000,,4 less, 42, and then\N4 greater.
Dialogue: 0,0:05:33.07,0:05:34.57,Default,,0000,0000,0000,,And they're consecutive numbers,\Nso what are going to
Dialogue: 0,0:05:34.57,0:05:36.17,Default,,0000,0000,0000,,be the 4 numbers greater\Nthat it?
Dialogue: 0,0:05:36.17,0:05:40.37,Default,,0000,0000,0000,,Well 43, 44, 45, 46.
Dialogue: 0,0:05:40.37,0:05:43.95,Default,,0000,0000,0000,,The question asks us, what is\Nthe greatest of the numbers?
Dialogue: 0,0:05:43.95,0:05:47.01,Default,,0000,0000,0000,,Well sure, it's going\Nto be 46.
Dialogue: 0,0:05:47.01,0:05:48.66,Default,,0000,0000,0000,,And you could have written out\Nall the numbers, but you know
Dialogue: 0,0:05:48.66,0:05:52.19,Default,,0000,0000,0000,,42 is the middle, there are 4\Ngreater and 4 less, just do 4.
Dialogue: 0,0:05:52.19,0:05:53.90,Default,,0000,0000,0000,,It saves you a little time.
Dialogue: 0,0:05:53.90,0:05:55.72,Default,,0000,0000,0000,,Problem number thirteen.
Dialogue: 0,0:06:01.56,0:06:07.01,Default,,0000,0000,0000,,Let the function f be\Ndefined by f of x is
Dialogue: 0,0:06:07.01,0:06:12.26,Default,,0000,0000,0000,,equal to x plus 1.
Dialogue: 0,0:06:12.26,0:06:14.61,Default,,0000,0000,0000,,If 2f of p is equal to 20.
Dialogue: 0,0:06:14.61,0:06:20.66,Default,,0000,0000,0000,,So 2 times f of p\Nis equal to 20.
Dialogue: 0,0:06:20.66,0:06:23.84,Default,,0000,0000,0000,,What is the value of f of 3p?
Dialogue: 0,0:06:23.84,0:06:25.37,Default,,0000,0000,0000,,This looks fun.
Dialogue: 0,0:06:25.37,0:06:30.20,Default,,0000,0000,0000,,So 2 times f of p is equal\Nto 20, what is f of 3p?
Dialogue: 0,0:06:30.20,0:06:33.99,Default,,0000,0000,0000,,So let's evaluate\N2 times f of p.
Dialogue: 0,0:06:33.99,0:06:44.52,Default,,0000,0000,0000,,2 times f of p, well that\Nequals 2 times p plus 1.
Dialogue: 0,0:06:44.52,0:06:46.76,Default,,0000,0000,0000,,We know that equals 20.
Dialogue: 0,0:06:46.76,0:06:51.00,Default,,0000,0000,0000,,And so you know that 2p plus 2,\NI just distributed the 2,
Dialogue: 0,0:06:51.00,0:06:53.30,Default,,0000,0000,0000,,is equal to 20.
Dialogue: 0,0:06:53.30,0:06:58.79,Default,,0000,0000,0000,,2p is equal to 18,\Np is equal to 9.
Dialogue: 0,0:06:58.79,0:07:01.08,Default,,0000,0000,0000,,We just solve for p.
Dialogue: 0,0:07:01.08,0:07:02.88,Default,,0000,0000,0000,,They're just trying to confuse\Nyou with notation.
Dialogue: 0,0:07:02.88,0:07:04.33,Default,,0000,0000,0000,,There's nothing really\Nthat fancy here.
Dialogue: 0,0:07:04.33,0:07:06.44,Default,,0000,0000,0000,,It's a very simple equation\Nto solve.
Dialogue: 0,0:07:06.44,0:07:09.86,Default,,0000,0000,0000,,And once you know p equals 9,\Nthen we say f of 3p, that's
Dialogue: 0,0:07:09.86,0:07:13.41,Default,,0000,0000,0000,,the same thing, because\Np equals 9, f of 27.
Dialogue: 0,0:07:13.41,0:07:15.61,Default,,0000,0000,0000,,And now this becomes just a\Nsimple function evaluation.
Dialogue: 0,0:07:15.61,0:07:21.15,Default,,0000,0000,0000,,f of 27 is equal to 27 plus 1.
Dialogue: 0,0:07:21.15,0:07:24.35,Default,,0000,0000,0000,,27 plus 1 is just 28.
Dialogue: 0,0:07:24.35,0:07:25.58,Default,,0000,0000,0000,,That's it.
Dialogue: 0,0:07:25.58,0:07:26.41,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:07:26.41,0:07:27.83,Default,,0000,0000,0000,,Problem number fourteen.
Dialogue: 0,0:07:32.03,0:07:33.28,Default,,0000,0000,0000,,I'll do in green.
Dialogue: 0,0:07:35.50,0:07:36.87,Default,,0000,0000,0000,,Problem number fourteen.
Dialogue: 0,0:07:36.87,0:07:39.47,Default,,0000,0000,0000,,I have to do some drawing now.
Dialogue: 0,0:07:39.47,0:07:42.95,Default,,0000,0000,0000,,I'll do it big because\Nit looks complicated.
Dialogue: 0,0:07:42.95,0:07:45.10,Default,,0000,0000,0000,,Big line there.
Dialogue: 0,0:07:45.10,0:07:49.76,Default,,0000,0000,0000,,I have another line here that's\Nalmost horizontal.
Dialogue: 0,0:07:49.76,0:07:55.01,Default,,0000,0000,0000,,And then this looks like it's\Nperpendicular, it is.
Dialogue: 0,0:07:57.97,0:08:02.94,Default,,0000,0000,0000,,And then we'll go\Nlike that there.
Dialogue: 0,0:08:02.94,0:08:05.07,Default,,0000,0000,0000,,And add another perpendicular\Nline like that.
Dialogue: 0,0:08:08.69,0:08:11.13,Default,,0000,0000,0000,,That's a nice looking drawing.
Dialogue: 0,0:08:11.13,0:08:23.60,Default,,0000,0000,0000,,So then this is J, K, L, N, M.
Dialogue: 0,0:08:26.31,0:08:29.30,Default,,0000,0000,0000,,They tell us that this is 90\Ndegrees, it's perpendicular.
Dialogue: 0,0:08:29.30,0:08:32.17,Default,,0000,0000,0000,,This is x degrees.
Dialogue: 0,0:08:32.17,0:08:37.50,Default,,0000,0000,0000,,They also tell us that\Nthis is 125 degrees.
Dialogue: 0,0:08:37.50,0:08:41.05,Default,,0000,0000,0000,,They also tell us that this\Nis perpendicular.
Dialogue: 0,0:08:41.05,0:08:46.95,Default,,0000,0000,0000,,In the figure above, KN is\Nperpendicular to JL.
Dialogue: 0,0:08:46.95,0:08:48.04,Default,,0000,0000,0000,,We knew that because\Nthey drew it.
Dialogue: 0,0:08:48.04,0:08:52.23,Default,,0000,0000,0000,,And LM is perpendicular to JL.
Dialogue: 0,0:08:52.23,0:08:54.15,Default,,0000,0000,0000,,We knew that because they\Ndrew that there.
Dialogue: 0,0:08:54.15,0:09:07.42,Default,,0000,0000,0000,,If the lengths of LN and LM\Nare equal, these are equal
Dialogue: 0,0:09:07.42,0:09:10.91,Default,,0000,0000,0000,,lengths, what is\Nthe value of x?
Dialogue: 0,0:09:10.91,0:09:13.37,Default,,0000,0000,0000,,Well if we know that these 2\Nsides are equal, what do we
Dialogue: 0,0:09:13.37,0:09:16.51,Default,,0000,0000,0000,,also know about its\Nbase angles?
Dialogue: 0,0:09:16.51,0:09:20.21,Default,,0000,0000,0000,,This angle is going to have\Nto be equal to this angle.
Dialogue: 0,0:09:23.32,0:09:25.20,Default,,0000,0000,0000,,So if that angle is equal to\Nthat angle, let's figure out
Dialogue: 0,0:09:25.20,0:09:26.11,Default,,0000,0000,0000,,what that is.
Dialogue: 0,0:09:26.11,0:09:29.83,Default,,0000,0000,0000,,If this purple angle here\Nis 125, what is this?
Dialogue: 0,0:09:29.83,0:09:33.54,Default,,0000,0000,0000,,Well they're supplementary,\Nso they add up to 180.
Dialogue: 0,0:09:33.54,0:09:35.23,Default,,0000,0000,0000,,So this is 125.
Dialogue: 0,0:09:35.23,0:09:37.06,Default,,0000,0000,0000,,I just realized I only\Nhave 35 seconds
Dialogue: 0,0:09:37.06,0:09:39.01,Default,,0000,0000,0000,,left to do this problem.
Dialogue: 0,0:09:39.01,0:09:41.02,Default,,0000,0000,0000,,Actually, I will continue it in\Nthe next video, because I
Dialogue: 0,0:09:41.02,0:09:42.62,Default,,0000,0000,0000,,only have 20 seconds\Nnow to do this.
Dialogue: 0,0:09:42.62,0:09:43.87,Default,,0000,0000,0000,,So I'll see you in\Nthe next video.