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.