SAT Prep: Test 3 Section 4 Part 4

Welcome back.

I almost ran out of time in that
last video, so let's just

start from the beginning for
problem number fourteen.

So I drew the figure, and they
told us that this line is

perpendicular to that line,
and they drew it here.

And that this is perpendicular
to that, and

they drew it there.

They told us this was 125
degrees, this is x.

And then the one piece of
information they tell us, is

that LN, this line,
is equal to LM.

And I marked it here.

What we said at the end of the
last video was, well if these

two sides are equal, we also
know from geometry class, that

the base angles are also
going to be equal.

And then let's see what we can
do with that, whether we can

figure out x.

Well the first step we can do,
is we can say, well if this is

125 degrees, what is this
angle right here?

Well they're going to have to
add up to 180, because they're

supplementary.

So this is going to be,
what's 180 minus 125?

Well what's 80 minus 25?

It's 55 degrees.

So if that's 55, then this
is also going to be 55.

And then if these are both 55,
what is this angle up here?

Well they're all in a triangle,
so they have

to add up to 180.

So 55 plus 55 is 110, so this
one has to be 70 degrees.

Or 180 minus 110.

You have to add up
to 180 degrees.

So this is 70 degrees
right here.

And now can we figure out
what this angle is here?

This is what I call
the angle game.

You just have to keep figuring
out of angles.

Well if this is 70 degrees, this
angle plus this angle,

they're going to be
complementary.

They're going to come out to
90, because this is 90.

So all we have left is
90 degrees here.

So if these two have to
add up to 90 degrees,

then this is 20 degrees.

That says 20.

I know I wrote it really
small, you

probably can't read it.

We know that this whole thing is
a right angle because this

is a right angle.

So if this is 90, we know that
this whole thing is 90.

So this is 20.

And now finally, I think
we're ready for x.

Because x plus 90 plus 20 has
to be equal to 180 because

it's in the same triangle.

So x plus 90 plus 20
is equal to 180.

x plus 110 is equal to 180.

x is equal to 70 degrees.

And we are done.

Next problem.

Problem number fifteen.

A measuring cup contains 1/5
a cup of orange juice.

It is then filled to the 1 cup
mark that is a mixture

containing equal amounts of
orange, grapefruit and

pineapple juices.

What fraction of the final
mixture is orange juice?

This is interesting.

You have 1/5 already orange
juice, and then the next 4/5

is going to be equal parts--
because we're going to fill to

the 1 cup mark.

It's going to be equal parts
orange, grapefruit-- I'll just

write grape-- and pineapple.

So the next 4/5 is going to be
split amongst these three, and

it's equally.

So how much more orange juice
are we putting in?

We took 4/5, and 1/3 of
this 4/5 is going

to be orange juice.

So the amount of orange juice
we're putting in now is 1/3

times the 4/5.

So we're putting in
4/15 orange juice.

And we already had
1/5 orange juice.

So 1/5 plus 4/15.

That equals 3/15 plus 4/15,
which equals 7/15.

That is the final mixture
of orange juice.

And doesn't that make
sense intuitively?

That makes sense because there's
20% orange juice, and

then we're adding maybe a little
bit less than a 1/4.

So we'll have a little bit less
than 1/2 in the glass.

All right.

Next problem.

I don't know, my cousin's
answer seems a little

suspicious.

She had marked up this book.

All right.

Problem number sixteen.

If a plus 2b is equal
to 125% of 4b.

So that equals 125%.

If you want to write 125%
as a decimal, which I

like to do, it's 1.25.

125% of 4b, what is the
value of a over b?

So we want to figure
out a over b.

Let's just solve this thing.

So a plus 2b is equal to,
what's 1.25 times 4?

If you have $1.25 and
you have that 4

times, it's $5.00, right?

4 times 1 and then 4 times
a quarter, that's another

dollar, so that's 5b.

And then subtract 2b
from both sides.

You get a is equal to 3b.

Divide both sides by b,
and you get a over

b is equal to 3.

And you are done the problem.

Problem number seventeen.

They have a number line.

This number line, let me see
how much I have to draw of

this number line, to minimize
my drawing.

They say 0 is here, 1 is here.

How many hash marks are there?

1, 2, 3, 4, 5, 6,
7, 8 hash marks.

Oh it says there.

On the number line above, there
are 9 equal intervals

between 0 and 1.

What is the value of x?

So there's 1, 2, 3,
4, 5, 6, 7, 8, 9.

I have 9 equal intervals, and
then x is right-- I'm just

going to make sure I
draw it correctly.

We have 2 marks, and
then we have x.

And actually we have the
square root of x.

So they're 9 equal
intervals, right?

So we could just do this is 1/9,
this is 2/9, this is 3/9,

4/9, this is 8/9, this is 9/9.

This is 8/9, this is 7/9, this
is 6/9, this is 5/9, because 9

equal intervals.

So we know that the square root
of x is equal to 6/9.

Square both sides.

What's 6/9?

That's the same thing as 2/3.

So you square both sides.

You get x is equal to 4/9.

2 squared, 3 squared.

We are done.

Next problem.

Problem eighteen.

In the xy-coordinate plane, the
distance between point B--

so B is the point 10 comma 18.

The distance between the point
B and the point A-- A is

point x comma 3.

So the distance is 17 between
these points.

What is one possible
value of x?

So this is the distance formula,
and the distance

formula is really just the
Pythagorean theorem.

What we do is we say, well the
distance squared is equal to

the change in x squared, plus
the change in y squared.

And this is really just the
Pythagorean theorem.

If you haven't learned that yet,
actually I don't think

I've done a distance formula
video, that's on my to-do

list. But I'll do that.

It's just the Pythagorean
theorem.

The distance squared, so 17
squared, is equal to-- what's

the change in x?

So let's just call that 10 minus
x squared plus-- and

then we know that change
in y-- so 18 minus 3.

So it's 15 squared.

I know 15 squared is 225.

This is going to be equal
to x squared minus 20x.

It could be plus 100.

What's 17 squared?

17 times 17?

7 times 7 is 49.

1 times 7 is 7, plus 4 is 11.

0 plus 17.

It is 289.

And so then we can subtract
289 from both sides.

So you get 0 is equal to x
squared minus 20x plus-- add

these two together--
325 minus 289.

I only have 10 seconds
left, so I'll do

it in the next video.