All right.

We are on problem number ten.

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

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

equal to 8.

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

equations above?

Well let's do the first one.

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

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

is equal to minus 3.

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

get k is equal to 7.

10 minus 7 is equal to 3.

And here, k is equal to 13.

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

to 7 or 13.

So now let's do the second
constraint, and

I'll do it in yellow.

So k minus 5 is 8.

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

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

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

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

to minus 3.

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

kind of solved it.

What k satisfies both
of these equations?

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

satisfies the second one.

But 13, k equals 13,
satisfies both.

So that is your answer.

13.

Next problem.

Problem number eleven.

I've gotta do some drawing.

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

I need to work off
that turkey.

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

I have line L, something
like that.

And then I have this
perpendicular line,

up here like that.

And then what do they tell us?

They tell us that this
is perpendicular.

Let me switch colors.

They tell us that this
is 65 degrees.

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

Oh, and there's another
line there, I

haven't even drawn it.

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

Switching back to the green.

This is 20 degrees,
and so this is x.

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

This is 20 degrees.

What is the value of x
in the figure above?

So we just gotta do what I like
to affectionately call

the angle game.

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

as I can figure out.

So what is the measure
of this angle?

Well this angle and this angle
are complementary.

They add up to 90 degrees.

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

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

25 plus 65 is 90, correct?

Yes.

You can tell addition
is my weak point.

So this is 25 degrees,
this is 20 degrees.

Can we figure out x?

Well, sure.

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

to 180 now.

Because they're all kind of
collectively supplementry.

You go around, you go halfway
around the circle.

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

x plus 45 is equal to 180.

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

is equal to 135.

So that's our answer.

Next problem.

So number twelve.

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

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

didn't mark it up incorrectly.

OK.

Problem number twelve.

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

What is the greatest
of these integers?

So the median of 9 consecutive
integers is 42.

So 42 is the middle number,
and there's

9 consecutive numbers.

How many numbers are going
to be greater than 42?

Median means middle.

So that means there are
4 greater and 4 less.

Because there's a total
of 9 numbers.

4 less, 42, and then
4 greater.

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

be the 4 numbers greater
that it?

Well 43, 44, 45, 46.

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

Well sure, it's going
to be 46.

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

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

It saves you a little time.

Problem number thirteen.

Let the function f be
defined by f of x is

equal to x plus 1.

If 2f of p is equal to 20.

So 2 times f of p
is equal to 20.

What is the value of f of 3p?

This looks fun.

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

So let's evaluate
2 times f of p.

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

We know that equals 20.

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

is equal to 20.

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

We just solve for p.

They're just trying to confuse
you with notation.

There's nothing really
that fancy here.

It's a very simple equation
to solve.

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

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

And now this becomes just a
simple function evaluation.

f of 27 is equal to 27 plus 1.

27 plus 1 is just 28.

That's it.

Next problem.

Problem number fourteen.

I'll do in green.

Problem number fourteen.

I have to do some drawing now.

I'll do it big because
it looks complicated.

Big line there.

I have another line here that's
almost horizontal.

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

And then we'll go
like that there.

And add another perpendicular
line like that.

That's a nice looking drawing.

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

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

This is x degrees.

They also tell us that
this is 125 degrees.

They also tell us that this
is perpendicular.

In the figure above, KN is
perpendicular to JL.

We knew that because
they drew it.

And LM is perpendicular to JL.

We knew that because they
drew that there.

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

lengths, what is
the value of x?

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

also know about its
base angles?

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

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

what that is.

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

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

So this is 125.

I just realized I only
have 35 seconds

left to do this problem.

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

only have 20 seconds
now to do this.

So I'll see you in
the next video.