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All right.

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We are on problem number ten.

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This says the absolute value of
10 minus k is equal to 3.

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And that we know that the
absolute value of k minus 5 is

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equal to 8.

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And they say, what is the value
of k that satisfies both

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equations above?

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Well let's do the first one.

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The absolute value of 10
minus k is equal to 3.

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That tells us that 10 minus k
is equal to 3, or 10 minus k

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is equal to minus 3.

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If 10 minus k is 3, just based
on the first equation alone, I

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get k is equal to 7.

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10 minus 7 is equal to 3.

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And here, k is equal to 13.

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So just on this first
constraint, we have k is equal

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to 7 or 13.

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So now let's do the second
constraint, and

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I'll do it in yellow.

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So k minus 5 is 8.

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That absolute value is equal to
8, so it's either k minus 5

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is equal to 8, or k minus
5 is equal to minus 8.

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If k minus 5 is 8,
then k is 13.

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If k minus 5 is equal to minus
8, then that means k is equal

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to minus 3.

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In order for k to satisfy both
of this equations, I've just

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kind of solved it.

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What k satisfies both
of these equations?

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Well 7 only satisfies the first
one, and negative 3 only

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satisfies the second one.

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But 13, k equals 13,
satisfies both.

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So that is your answer.

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13.

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Next problem.

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Problem number eleven.

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I've gotta do some drawing.

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I think I'm going to go
for a walk after this.

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I need to work off
that turkey.

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I have a line here,
that's line M.

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I have line L, something
like that.

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And then I have this
perpendicular line,

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up here like that.

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And then what do they tell us?

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They tell us that this
is perpendicular.

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Let me switch colors.

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They tell us that this
is 65 degrees.

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They tell us that this, right
here, is x degrees.

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Oh, and there's another
line there, I

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haven't even drawn it.

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There's another line, that I
haven't drawn, that is this.

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Switching back to the green.

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This is 20 degrees,
and so this is x.

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x is just this thing right here,
not this whole thing.

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This is 20 degrees.

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What is the value of x
in the figure above?

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So we just gotta do what I like
to affectionately call

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the angle game.

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And the angle game, I just try
to figure out as many angles

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as I can figure out.

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So what is the measure
of this angle?

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Well this angle and this angle
are complementary.

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They add up to 90 degrees.

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We know this is 90, so this
whole thing is 90.

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So if this and this add up
to 90, what is this?

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25 plus 65 is 90, correct?

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Yes.

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You can tell addition
is my weak point.

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So this is 25 degrees,
this is 20 degrees.

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Can we figure out x?

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Well, sure.

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We know that all of these 3
angles combined have to add up

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to 180 now.

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Because they're all kind of
collectively supplementry.

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You go around, you go halfway
around the circle.

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So we know that x plus 20
plus 25 is equal 180.

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x plus 45 is equal to 180.

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So x is equal to, this is where
I always mess up, so x

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is equal to 135.

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So that's our answer.

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Next problem.

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So number twelve.

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That last problem was one that
my cousin had marked up pretty

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incorrectly, so I had to take
some pause just to make sure I

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didn't mark it up incorrectly.

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OK.

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Problem number twelve.

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The median of a set of 9
consecutive integers is 42.

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What is the greatest
of these integers?

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So the median of 9 consecutive
integers is 42.

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So 42 is the middle number,
and there's

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9 consecutive numbers.

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How many numbers are going
to be greater than 42?

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Median means middle.

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So that means there are
4 greater and 4 less.

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Because there's a total
of 9 numbers.

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4 less, 42, and then
4 greater.

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And they're consecutive numbers,
so what are going to

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be the 4 numbers greater
that it?

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Well 43, 44, 45, 46.

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The question asks us, what is
the greatest of the numbers?

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Well sure, it's going
to be 46.

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And you could have written out
all the numbers, but you know

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42 is the middle, there are 4
greater and 4 less, just do 4.

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It saves you a little time.

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Problem number thirteen.

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Let the function f be
defined by f of x is

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equal to x plus 1.

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If 2f of p is equal to 20.

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So 2 times f of p
is equal to 20.

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What is the value of f of 3p?

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This looks fun.

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So 2 times f of p is equal
to 20, what is f of 3p?

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So let's evaluate
2 times f of p.

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2 times f of p, well that
equals 2 times p plus 1.

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We know that equals 20.

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And so you know that 2p plus 2,
I just distributed the 2,

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is equal to 20.

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2p is equal to 18,
p is equal to 9.

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We just solve for p.

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They're just trying to confuse
you with notation.

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There's nothing really
that fancy here.

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It's a very simple equation
to solve.

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And once you know p equals 9,
then we say f of 3p, that's

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the same thing, because
p equals 9, f of 27.

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And now this becomes just a
simple function evaluation.

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f of 27 is equal to 27 plus 1.

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27 plus 1 is just 28.

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That's it.

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Next problem.

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Problem number fourteen.

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I'll do in green.

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Problem number fourteen.

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I have to do some drawing now.

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I'll do it big because
it looks complicated.

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Big line there.

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I have another line here that's
almost horizontal.

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And then this looks like it's
perpendicular, it is.

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And then we'll go
like that there.

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And add another perpendicular
line like that.

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That's a nice looking drawing.

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So then this is J, K, L, N, M.

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They tell us that this is 90
degrees, it's perpendicular.

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This is x degrees.

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They also tell us that
this is 125 degrees.

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They also tell us that this
is perpendicular.

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In the figure above, KN is
perpendicular to JL.

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We knew that because
they drew it.

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And LM is perpendicular to JL.

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We knew that because they
drew that there.

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If the lengths of LN and LM
are equal, these are equal

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lengths, what is
the value of x?

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Well if we know that these 2
sides are equal, what do we

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also know about its
base angles?

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This angle is going to have
to be equal to this angle.

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So if that angle is equal to
that angle, let's figure out

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what that is.

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If this purple angle here
is 125, what is this?

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Well they're supplementary,
so they add up to 180.

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So this is 125.

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I just realized I only
have 35 seconds

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left to do this problem.

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Actually, I will continue it in
the next video, because I

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only have 20 seconds
now to do this.

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So I'll see you in
the next video.