SAT Prep: Test 5 Section 9 Part 3

Welcome back.

I'm on problem number 10.

Phillip used 4 pieces of masking
tape, each 6 inches

long, to put up each
of his posters.

So this is per poster.

Good enough.

Phillip had a 300-foot roll of
masking tape when he started.

So he starts at 300 feet.

I can already tell you that
some unit conversion will

happen, because they're talking
about 6 inches here

and they're talking about
300 feet here.

If no tape was wasted, which
of the following represents

the number of feet--and they
underline it-- of masking tape

that was left on the roll after
he put up the n posters?

And they actually tell us that
12 inches are equal to a foot

in case you aren't
from this planet.

So how do we do this?

So he's going to put
up n posters.

So he's going to start
off-- well, how much

tape will he use?

So for each of those n posters,
how much will he use?

He uses 4 pieces
times 6 inches.

But we want to go into feet.

We want to know how many
feet are left.

So let's just convert
immediately to feet.

6 inches is equal to
how many feet?

Well, it's half a foot.

6/12 inches.

So it equals 1/2 foot.

So he does 4 pieces for each
poster, and each of those

pieces is 1/2 foot.

And now we're immediately
in feet length.

So this is how much he uses.

So he will use-- so 4
times 1/2 is just 2.

So he uses 2n feet.

So if he starts with 300, the
amount that he has left is

what he started with
minus what he used.

He used 2n.

So he starts with 300 feet minus
2n feet, so that's the

expression.

That's choice B.

Next problem.

Problem 11.

I'll switch to magenta.

In the x, y coordinate plane,
line m is the reflection of

line l about the x-axis.

If the slope of m-- so m slope--
is equal to minus 4/5,

what is the slope of l?

So you should hopefully be able
to do this on the real

exam without having
to draw it.

Or you could actually just draw
a really quick and dirty

one, and that actually
probably would

do the job for you.

So minus 4/5.

That means for every
5-- and it's a

reflection about the x-axis.

So let's draw a line m.

Now let's just assume that
the origin's here.

They don't tell us that,
but they don't

tell us it's not that.

So that's zero, one, two,
three, four, five.

And this is one, two,
three, four.

Let me do it here.

One, two, three, four.

I just want to draw it
so you understand.

So 4, minus 4, this is 5.

So we know line m.

For every line m, for every
5 it goes to the right,

it goes down 4.

So this could be a legitimate
line m right here.

It could be like this.

Line m could look like that.

So a reflection about the
x-axis, if I were to reflect

it about the x-axis.

This is the x-axis right here,
so I just want to take its

mirror image, or flip
it over the x-axis.

It would look like this.

Oh, I thought I was using
the line tool.

It would look like this.

I'm still not using
the line tool.

Now, I'm using the line tool.

It would look like
that, right?

So what's the slope here?

Well, for every 5 I go to
the right, I move up 4.

So change in y.

Let me make sure this is
line m, this is line l.

Change in y over change in
x for line l is equal to

positive 4/5.

It shouldn't take you
that long to do it.

One thing that you could just
do as well, you could just

draw a quick and dirty one.

It's like, well, if I have
something with a negative

slope-- let's say I have
a negative, really

shallow slope like that.

If I flip it, it's going to have
the same slope, but it's

going to be a positive slope,
but it's still going to be

shallow, so it's going to
be the same magnitude.

You'll flip the sign.

So the answer is B, 4/5.

But I did this just to give
you the intuition.

The next problem.

Or to let you know why you got
it wrong, if you got it wrong.

Anyway.

Problem number 12.

If n is equal to 3p, for what
value of p is n equal to p?

This is kind of crazy.

And at first, I was like,
what are they saying?

And then I read one
of the choices.

Because no matter what,
n is equal to 3p.

There's no circumstance--
well, oh, sorry.

I was incorrect.

There is a circumstance in
which n is equal to 3p.

Well, what's the circumstance?

Well, you might initially say,
well, as long as p is not 0, n

is going to be exactly
3 times p.

But then in our statement, I
just told you the answer.

They both can be 0.

If p is 0, then 3
times 0 is 0.

So there's no real
algebra there.

It's just kind of to realize
that 0 is a choice.

And if you looked at the
choices, you'd immediately see

choice A is 0.

Try it out.

You say, oh, well, if p is
0, then n is also 0.

So then n would equal p.

So next problem.

Problem 13.

That was one of those problems
that in some ways are so easy

that you waste time
on it, making sure

you didn't miss something.

Let's draw what they drew.

So we have a line like that.

I have a line like that.

Then I have a line like that.

And this is line l.

This is y degrees.

This is line m.

This is x degrees, and this
is line n right here.

In the figure above, if z--
oh, they tell us this is z

right here.

In the figure above, if z is
equal to 30, what is the value

of x plus y?

x plus y is what?

Well, what can we figure out?

What do we know about this
angle right here?

It's supplementary
to y, right?

So this is kind of the angle
game, but we're going to have

a little bit more variables
than normal.

It's supplementary to y, so this
is going to be 180 minus

y because y plus this
angle are going to

have to equal 180.

And for the exact same reason,
this angle right here

is 180 minus x.

And what do we know?

We know this angle plus this
angle plus z is equal to 180.

So let's write that down.

This angle, 180 minus y, plus
this angle, plus 180 minus x,

plus z is equal to 180
because they're

all in the same triangle.

So let's try our best
to simplify this.

Well, we could immediately get
rid of one of the 180's on

that side, and that becomes 0.

z is 30, right?

So let's simplify it.

We get minus y minus x, and
then you have 180 plus 30,

plus 210, is equal to 0.

Now let's add x and
y to both sides.

I'm kind of skipping a step.

You could add x to both sides
and then add y to both sides.

But if you add x and y to both
sides, you get 210 is

equal to x plus y.

And that's the answer.

They want to know what
x plus y is.

And that is choice D.

And so the trick here is really
saying, well, they

only give us z.

The only thing I know is that
z is in a triangle with this

angle and this angle.

And let me express those two
angles in terms of x and y,

because they are supplementary
to x and y.

See you in the next video.