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.