SAT Prep: Test 6 Section 7 Part 1

WEBVTT
Kind: captions
Language: en

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I just had dinner so I am well
fed, and I am ready to do more

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SAT problems. So we're on
section seven, on page--

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excuse me, maybe I should
drink some more water--

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section seven of the
sixth test, on page

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733, problem one.

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In a certain game, points are
assigned to every word.

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Each q, x and z in a word-- it
sounds like Scrabble-- is

00:00:24.740 --> 00:00:26.420
worth 5 points.

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And all other letters are
worth 1 point each.

00:00:28.840 --> 00:00:34.320
So q, x and z are 5 points each,
and the other ones are 1

00:00:34.320 --> 00:00:34.840
point each.

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What is the sum of the points

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assigned to the word exquisite?

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Well this is just-- exquisite.

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So let's see, which of
these does it have?

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It has an x, right?

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So that's worth 5 points.

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Does it have any
other of these?

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No-- well, it has a q, right?

00:01:01.200 --> 00:01:03.190
That's worth 5 points.

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It doesn't have a z, right?

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And so how many one-pointers
are there?

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There's 1, 2, 3, 4, 5, 6, 7.

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So 7 one-pointers.

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So that's 7 points, plus 5 plus
5 plus 10 is equal to 17.

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So that's B.

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So that's really just to make
sure that you don't make

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careless mistakes,
that problem.

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Next problem.

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If you've ever played Scrabble,
that problem would

00:01:31.230 --> 00:01:33.010
be a joke for you.

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Problem two.

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If 2x minus 10 is equal to 20,
then x minus 5 is what?

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So the big discovery here is--
you could solve for x, you

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could say 2x is equal to 30, x
is equal to 15, and say 15

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minus 5 equals 10.

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Or you could say, well this is
the same thing as 2 times x

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minus 10 is equal to 20, divide
both sides by 2, x

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minus 10 is equal to 10.

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Oh, sorry, maybe that's why you
shouldn't do it this way.

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2 times x minus 5, x minus
5 is equal to 10.

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So that's the other way you
could have done it, you just

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factor out a 2, you get 2 times
x minus 5 is 20, divide

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both sides by 2, you get
x minus 5 is 10.

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The other way is obviously
to say 2x minus

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10 is equal to 20.

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Add 10 to both sides.

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2x is equal to 30.

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x is equal to 15.

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So then x minus 5 is 15 minus
5, which is equal to 10.

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I don't know which way might
be faster for you.

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This way might-- you have to do
less thinking, and you just

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kind of chug through
it, so you can just

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kind of speed along.

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But this way's a few less steps,
but maybe you might

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make a careless mistake
like what I just did.

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But anyway, let's move on.

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Hopefully, either way you
know how to do it.

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Problem three.

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I'll do it right here.

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If t represents an odd
integer, which of the

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following represents
an even integer?

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So t is an odd integer.

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And we can do this kind of
abstractly, but let's just

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pick a number.

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Let's just say that t is equal
to-- what's an odd integer?

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Well, 3, 3 is an odd integer.

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So let's just say t equals 3--
they didn't say, we could have

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picked t equals 7, who knows.

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So then just go through the
choices and say, well, which

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one of those is going to
be an even integer?

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Choice A is t plus 2.

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Well 3 plus 2 is 5, that is
still odd, so that's not the

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right answer.

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B, 2t minus 1.

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Well that's 6 minus 1,
that's 5, that's odd.

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Choice C is 3t minus 2, that's
9 minus 2, which is still 7,

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so that's still odd.

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Choice D is 3t plus 2,
that's 9 plus 2,

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which is equal to 11.

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And I'm just saying t is 3.

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That's still odd.

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So it's probably
going to be E.

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5t plus 1, and 15 plus 1
is 16, and that's even.

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So that's our answer.

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So sometimes I find it easy
if you just pick a number.

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The other way is if you are
familiar with even and odd

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numbers, you can just say, well,
the only way to go from

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an odd to an even number, is you
either have to multiply by

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an even soon. number, or
add an odd number.

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Those are the only ways you can
go from an odd number to

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an even number.

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So looking at 5t plus 1, you
could say, well when I

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multiply an odd number by an odd
number, I'm going to get

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another odd number, right?

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So this number is odd.

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When I take an odd number
and I add 1 to it,

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I get an even number.

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So you could say 5t plus
1 is definitely going

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to be an even number.

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And it worked with the odd
number that we picked for t.

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Next problem.

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OK, so they drew
a picture here.

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So I will draw a picture
here as best as I can.

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That's one triangle they drew,
this is the other one.

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Looks something like this.

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Like that.

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And then this-- they say
this is A, B, C.

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This is D, E, F.

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These sides are 4, 8, and 9.

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Now what are they saying?

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For the triangles above, the
perimeter of ABC equals the

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perimeter of DEF.

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OK, it equals that.

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If ABC is equilateral, what
is the length of AB?

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OK, so it's equilateral,
right?

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So let's just say that
AB is equal to x.

00:06:03.390 --> 00:06:06.180
Well then, so is BC and AC,
because they told us, this is

00:06:06.180 --> 00:06:07.350
an equilateral triangle.

00:06:07.350 --> 00:06:09.330
All the sides are equal.

00:06:09.330 --> 00:06:11.430
And what is the perimeter
of ABC then?

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It's going to be x plus x plus
x, and that's just 3x.

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And they say that that's the
same thing as the perimeter of

00:06:17.270 --> 00:06:18.620
this triangle.

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What's the perimeter
of this triangle?

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It's 4 plus 8 plus 9.

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So 3x is equal to--what's
12 plus 9-- is 21.

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x is equal to 7, and that is
choice C, and we are done.

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Next problem.

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They have drawn a diagram
here that I will

00:06:42.100 --> 00:06:44.790
now attempt to draw.

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OK.

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And then, let's see they draw
a dividing line, looks like

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it's about 1/4 of the circle.

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And then they have another one
that's like a little less than

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1/4, like that.

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Then they have one that's
like that, roughly.

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Then it goes like that.

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Then it goes like that.

00:07:07.640 --> 00:07:10.240
And then they fill in
the values too.

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So this is K, it's 15%.

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J is 25%.

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O-- let's just call
that other, is O.

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Other is 20%.

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N is 10%.

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M is 15% and L is 15%.

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And these are sales of jeans in
2001, and the letters are

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the brands.

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The circle graph above
represents all the jeans that

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were sold by a retail
store in 2001

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according to their brands.

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If the store sold 900 pairs of
jeans-- so this is the total

00:07:49.480 --> 00:07:53.050
of all of these, is 900
pairs of jeans.

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If the store sold 900 pairs of
jeans other than brands J, K,

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L, M and N, how may did
it sell together?

00:08:01.930 --> 00:08:04.600
OK, so this isn't the total,
this is the other.

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This is essentially this
category, right?

00:08:09.320 --> 00:08:12.220
And other is equal to
20% of the total.

00:08:12.220 --> 00:08:13.370
And that's what they
want to ask us, how

00:08:13.370 --> 00:08:15.030
many did we sell together?

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So 20% of the total times t for
total-- let me just say t

00:08:22.160 --> 00:08:25.200
for total-- is equal to 900.

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And you could also write
this as 1/5.

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Or 0.2.

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1/5 of the total is
equal to 900.

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Multiply both sides by 5.

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That cancels out.

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So you get t is equal to
4,500 pairs of jeans.

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And that is choice E.

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Next problem.

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Oh, I thought this problem might
apply to this pie graph,

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but no, they're talking about
carpets, not jeans.

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So I'll do the next problem
in the next video.

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I'll see you


SAT Prep: Test 6 Section 7 Part 4

WEBVTT
Kind: captions
Language: en

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We are on problem number 14.

00:00:04.360 --> 00:00:06.095
See, what did they draw here?

00:00:06.095 --> 00:00:10.850
That's the y-axis, that's
the x-axis.

00:00:10.850 --> 00:00:13.255
They drew a line that looks
something like this.

00:00:13.255 --> 00:00:18.100
Let's see, negative 3, so it
goes something like this.

00:00:22.580 --> 00:00:23.940
That's close enough.

00:00:23.940 --> 00:00:28.090
And then they're saying that
this is the point negative 3.

00:00:28.090 --> 00:00:29.820
This is the point y
equals negative 1.

00:00:29.820 --> 00:00:31.760
This is of course the y-axis.

00:00:31.760 --> 00:00:33.610
This is the x-axis.

00:00:33.610 --> 00:00:36.790
The figure above shows a graph
of the line of y equals mx

00:00:36.790 --> 00:00:39.000
plus b, where m and
b are constants.

00:00:39.000 --> 00:00:43.160
Which of the following best
represents the graph of y is

00:00:43.160 --> 00:00:48.050
equal to minus 3mx plus b?

00:00:48.050 --> 00:00:53.120
Well, if this yellow line-- this
is y equals mx plus b.

00:00:57.380 --> 00:01:00.230
Well, what is b, first of all?
b is just the y-intercept.

00:01:00.230 --> 00:01:02.770
So the y-intercept is right
here, y equals negative 1.

00:01:02.770 --> 00:01:05.160
So b is negative 1.

00:01:05.160 --> 00:01:06.240
And what's the slope?

00:01:06.240 --> 00:01:12.660
Well, when we run, that's
what-- 1, 2, 3 units.

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Change in x is 3.

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What is the rise?

00:01:17.390 --> 00:01:20.000
The rise, we go down,
so it's negative 1.

00:01:20.000 --> 00:01:21.430
We go down 1.

00:01:21.430 --> 00:01:25.150
So the change in y is
equal to negative 1.

00:01:25.150 --> 00:01:27.500
So the slope is negative 1/3.

00:01:27.500 --> 00:01:29.650
So the equation of this
line is y is equal to

00:01:29.650 --> 00:01:34.740
minus 1/3 x minus 1.

00:01:34.740 --> 00:01:37.560
So if you want to know what
minus 3mx plus b is, what's

00:01:37.560 --> 00:01:41.560
minus 3 times this m?

00:01:41.560 --> 00:01:45.800
What's minus 3 times
minus 1/3?

00:01:45.800 --> 00:01:47.970
Well, the negatives cancel out,
so you just get-- let me

00:01:47.970 --> 00:01:52.000
switch to purple, because that's
that problem-- minus 3

00:01:52.000 --> 00:01:54.070
times-- this is m, right?

00:01:54.070 --> 00:01:55.540
This is m.

00:01:55.540 --> 00:01:59.820
So minus 3 times minus 1/3,
that just equals 1.

00:01:59.820 --> 00:02:04.070
So it equals 1x plus b.

00:02:04.070 --> 00:02:04.570
What's b?

00:02:04.570 --> 00:02:06.760
It's minus 1.

00:02:06.760 --> 00:02:09.729
So the graph we're looking
for is x minus 1.

00:02:09.729 --> 00:02:12.190
And so if we wanted to draw
that, the y-intercept would be

00:02:12.190 --> 00:02:13.700
the same, it would
be right there.

00:02:13.700 --> 00:02:15.330
And then you just have
a slope of 1.

00:02:15.330 --> 00:02:19.830
Slope of 1 looks-- well, that's
as close as I could do

00:02:19.830 --> 00:02:21.670
to drawing it, right--
that's a slope of 1.

00:02:21.670 --> 00:02:27.140
Your change in x should be the
same as your change in y.

00:02:27.140 --> 00:02:30.630
So if you look at all the
choices, first of all, it's

00:02:30.630 --> 00:02:32.410
pretty obvious it's
D, I think.

00:02:32.410 --> 00:02:34.360
And they make it very explicit
that the slope is 1 and the

00:02:34.360 --> 00:02:36.460
y-intercept is negative 1.

00:02:36.460 --> 00:02:38.850
And that's choice D.

00:02:38.850 --> 00:02:40.100
Next problem.

00:02:43.051 --> 00:02:45.750
I get excited when there's
something to draw, because we

00:02:45.750 --> 00:02:47.790
can get through them faster.

00:02:47.790 --> 00:02:50.120
15.

00:02:50.120 --> 00:02:56.120
If the volume of a cube is 8,
what is the shortest distance

00:02:56.120 --> 00:02:59.610
from the center of the cube
to the base of the cube?

00:02:59.610 --> 00:03:01.220
Fascinating.

00:03:01.220 --> 00:03:03.880
So the volume is 8,
so what are the

00:03:03.880 --> 00:03:05.130
dimensions of this cube?

00:03:08.270 --> 00:03:11.890
It's a cube, so all the sides
are the same, right?

00:03:11.890 --> 00:03:15.420
So x times x times x is x to the
third, and that equals 8.

00:03:15.420 --> 00:03:17.810
So the dimensions-- what to
the third power is 8?

00:03:17.810 --> 00:03:19.000
You should know that.

00:03:19.000 --> 00:03:19.930
2, right?

00:03:19.930 --> 00:03:21.720
2 times 2 times 2 is 8.

00:03:21.720 --> 00:03:25.360
So the dimensions of the
cube are 2 by 2 by 2.

00:03:25.360 --> 00:03:28.450
So let's take that cross section
where the center is.

00:03:36.610 --> 00:03:41.490
And if I were to draw it, so
that's just-- so the center of

00:03:41.490 --> 00:03:43.410
the cube is right here.

00:03:43.410 --> 00:03:45.400
And we know the dimensions
of this cross section.

00:03:45.400 --> 00:03:48.020
It's 2, 2, 2, 2.

00:03:48.020 --> 00:03:48.280
Right?

00:03:48.280 --> 00:03:51.290
I just sliced the cube
right there.

00:03:51.290 --> 00:03:52.830
And I just want to make sure
I'm doing this problem.

00:03:52.830 --> 00:03:54.940
From the center of the cube to
the base of the cube-- so the

00:03:54.940 --> 00:04:00.145
base of the cube is going to
be-- if I were to draw the

00:04:00.145 --> 00:04:02.740
cube, this would have been the
base of the cube down here.

00:04:02.740 --> 00:04:06.490
So this is the base
of the cube.

00:04:06.490 --> 00:04:08.820
So they're essentially just
asking us, what's this

00:04:08.820 --> 00:04:11.250
distance right here?

00:04:11.250 --> 00:04:11.870
Well that's easy.

00:04:11.870 --> 00:04:13.300
This is the center, so
it's right in the

00:04:13.300 --> 00:04:14.940
middle, so it's 1. soon.

00:04:14.940 --> 00:04:18.230
It's 1 to the bottom, it's 1 to
the roof of the cube, it's

00:04:18.230 --> 00:04:19.709
1 to each of the sides.

00:04:19.709 --> 00:04:20.910
So it's 1 away.

00:04:20.910 --> 00:04:23.590
So that is answer A.

00:04:27.150 --> 00:04:28.400
Next problem.

00:04:34.060 --> 00:04:37.390
Problem 16.

00:04:37.390 --> 00:04:46.440
If y is equal to 5x cubed over
z, what happens to the value

00:04:46.440 --> 00:04:50.952
of y when both x and
z are doubled?

00:04:53.800 --> 00:04:58.330
So the way I think about it
is, y is equal to 5x cubed

00:04:58.330 --> 00:04:59.670
divided by z.

00:04:59.670 --> 00:05:03.030
Actually do you know what the
very easiest way to do this

00:05:03.030 --> 00:05:04.490
problem is?

00:05:04.490 --> 00:05:06.720
Substitute numbers
for x and z.

00:05:06.720 --> 00:05:10.140
So let's say that x is equal
to 1 and z equals to 1.

00:05:10.140 --> 00:05:12.190
So in this situation,
y is equal to what?

00:05:15.220 --> 00:05:21.790
5 times 1 cubed divided by 1,
well that's just equal to 5.

00:05:21.790 --> 00:05:22.880
Now they're saying,
what happens

00:05:22.880 --> 00:05:24.030
if x and z are doubled?

00:05:24.030 --> 00:05:25.490
So let's take the second
situation.

00:05:25.490 --> 00:05:28.450
x is equal to 2, z
is equal to 2.

00:05:28.450 --> 00:05:35.910
Now, y is equal to 5 times
2 cubed over 2.

00:05:35.910 --> 00:05:38.630
And that is equal to what?

00:05:38.630 --> 00:05:42.920
Well, 2 cubed divided by 2, this
2 cancels with the cubed.

00:05:42.920 --> 00:05:43.760
You get 2 squared.

00:05:43.760 --> 00:05:48.620
So it's just 5 times 2 squared,
which is 5 times 4,

00:05:48.620 --> 00:05:50.100
which is 20.

00:05:50.100 --> 00:05:57.310
So y went from 5 to 20, so y
increased by a factor of 4.

00:05:57.310 --> 00:05:58.810
And that is choice E.

00:05:58.810 --> 00:06:02.280
y is multiplied by 4.

00:06:02.280 --> 00:06:04.860
These questions can be
surprisingly confusing because

00:06:04.860 --> 00:06:06.710
you're like, oh, you have these
variables, do you make x

00:06:06.710 --> 00:06:09.530
into 2x and z into 2z,
and then solve for--

00:06:09.530 --> 00:06:10.430
just try out numbers.

00:06:10.430 --> 00:06:12.700
They're not putting any
restrictions on you, so just

00:06:12.700 --> 00:06:17.260
substitute x and z, 1 and
1, and then double them.

00:06:17.260 --> 00:06:20.490
Next problem.

00:06:20.490 --> 00:06:27.690
The SAT, speed matters more
than maybe rigor.

00:06:27.690 --> 00:06:28.880
All right.

00:06:28.880 --> 00:06:31.840
Problem 17.

00:06:31.840 --> 00:06:38.340
Luke purchased an automobile
for $5,000.

00:06:38.340 --> 00:06:39.680
And the value of the automobile

00:06:39.680 --> 00:06:43.420
decreased by 20% per year.

00:06:43.420 --> 00:06:46.470
The value in dollars of the
automobile n years from the

00:06:46.470 --> 00:06:50.100
date of the purchase is given by
the function v, where v of

00:06:50.100 --> 00:06:59.660
n is equal to 5,000 times 4/5,
which is the same thing as

00:06:59.660 --> 00:07:01.480
0.8, to the nth power.

00:07:01.480 --> 00:07:02.460
Fair enough.

00:07:02.460 --> 00:07:06.350
How many years from the date of
the purchase will the value

00:07:06.350 --> 00:07:09.150
of the automobile be $3,200?

00:07:09.150 --> 00:07:11.400
Well, they're saying the
value is $3,200, so we

00:07:11.400 --> 00:07:12.730
just solve for n.

00:07:12.730 --> 00:07:15.060
v of how many years is
equal to $3,200?

00:07:15.060 --> 00:07:23.200
3,200 is equal to 5,000
times 4/5 to the n.

00:07:23.200 --> 00:07:30.380
Divide both sides by 5,000, you
get 3,200/5,000 is equal

00:07:30.380 --> 00:07:35.860
to 4/5 to the n.

00:07:35.860 --> 00:07:38.690
And then, let's see,
what's 32/5,000?

00:07:38.690 --> 00:07:41.710
You can delete these 0's.

00:07:41.710 --> 00:07:44.760
Let's see, 16/25.

00:07:44.760 --> 00:07:54.540
That equals-- so 16/25 is
equal to 4/5 to the n.

00:07:54.540 --> 00:07:57.120
And we should immediately--
well, hopefully you'd

00:07:57.120 --> 00:08:01.810
recognize is that 16 is 4
squared, and 25 is 5 squared,

00:08:01.810 --> 00:08:09.970
so 16/25 is equal
to 4/5 squared.

00:08:09.970 --> 00:08:10.970
4 squared is 16.

00:08:10.970 --> 00:08:13.310
5 squared is 25.

00:08:13.310 --> 00:08:15.780
So n is equal to 2.

00:08:15.780 --> 00:08:16.930
2 years.

00:08:16.930 --> 00:08:18.210
And that is choice B.

00:08:22.030 --> 00:08:24.260
Let's see if I have time for--
no, we have a couple more

00:08:24.260 --> 00:08:25.300
problems. I'll do
the last three

00:08:25.300 --> 00:08:26.910
problems in the next video.

00:08:26.910 --> 00:08:29.240
I will see you


SAT Prep: Test 6 Section 7 Part 5

WEBVTT
Kind: captions
Language: en

00:00:00.710 --> 00:00:02.660
The home stretch, we're
on problem 18.

00:00:02.660 --> 00:00:06.570
And this diagram actually looks
like something that this

00:00:06.570 --> 00:00:09.410
little tool I'm using is
well-suited to draw.

00:00:09.410 --> 00:00:13.410
Let me try-- I'll draw the one
in the back first, so I can do

00:00:13.410 --> 00:00:16.470
different colors
and everything.

00:00:16.470 --> 00:00:21.370
So I'll do the one in the back
in yellow, and it looks

00:00:21.370 --> 00:00:23.010
something like this.

00:00:23.010 --> 00:00:28.100
Goes like this, then it switches
over like that.

00:00:28.100 --> 00:00:31.790
And then I'll draw the next one,
this orange color, and it

00:00:31.790 --> 00:00:36.200
looks something-- no, I'll do
it in a more drastic color.

00:00:36.200 --> 00:00:37.600
So it does something
like this.

00:00:37.600 --> 00:00:42.330
It goes like this, crosses over,
dips down, then it goes

00:00:42.330 --> 00:00:43.760
over again.

00:00:43.760 --> 00:00:48.660
And then finally, this last
one, and it looks

00:00:48.660 --> 00:00:51.550
something like this.

00:00:51.550 --> 00:00:55.530
Crosses over and it goes
like that, very pretty.

00:00:55.530 --> 00:01:00.990
Now let me switch to
a smaller-- OK.

00:01:00.990 --> 00:01:03.030
Why don't we do white, I
never write in white.

00:01:03.030 --> 00:01:06.910
In the figure above--so they
say this is the start.

00:01:06.910 --> 00:01:08.320
And this is step 1.

00:01:11.645 --> 00:01:14.770
This is step 2.

00:01:14.770 --> 00:01:15.670
OK, what is this?

00:01:15.670 --> 00:01:18.610
In the figure above, three
wires are braided.

00:01:18.610 --> 00:01:22.580
That is, by starting in the
order A, B, C-- OK, so this is

00:01:22.580 --> 00:01:30.890
A, B, C-- and then the order
changes to B-- right, because

00:01:30.890 --> 00:01:33.730
the yellow line is B-- A, C.

00:01:33.730 --> 00:01:37.350
And then we get B, C, A.

00:01:37.350 --> 00:01:37.770
Right?

00:01:37.770 --> 00:01:40.580
There's just the order of the
strings, left to right.

00:01:40.580 --> 00:01:43.380
Or the braids, or the wires.

00:01:43.380 --> 00:01:44.580
OK.

00:01:44.580 --> 00:01:47.040
That is start with the order A,
B, C, the outer left wire

00:01:47.040 --> 00:01:48.670
is brought over wire B, right?

00:01:48.670 --> 00:01:52.380
This is brought over wire B, to
the middle position forming

00:01:52.380 --> 00:01:53.610
the order shown in step 1.

00:01:53.610 --> 00:01:58.350
Than the outer right wire C,
this one, is brought to the

00:01:58.350 --> 00:02:00.750
new middle position shown
in step 2, and so on.

00:02:00.750 --> 00:02:03.850
Alternately bringing each new
left and each new right wire

00:02:03.850 --> 00:02:04.770
to the middle.

00:02:04.770 --> 00:02:09.449
At what numbered step does the
braid first repeat the

00:02:09.449 --> 00:02:13.070
original order A, B, C?

00:02:13.070 --> 00:02:16.910
So what you do is, you first
bring the left over the

00:02:16.910 --> 00:02:18.865
middle, then you bring the right
over the middle, then

00:02:18.865 --> 00:02:20.730
you bring the left over the
middle, then you bring the

00:02:20.730 --> 00:02:22.310
right over the middle.

00:02:22.310 --> 00:02:24.470
So at step 3, what
do we have to do?

00:02:24.470 --> 00:02:27.750
So step 1 we brought the
left over the middle.

00:02:27.750 --> 00:02:29.840
So we went from A, B, C.

00:02:29.840 --> 00:02:32.720
You essentially switch the
left and the middle.

00:02:32.720 --> 00:02:35.330
And then step 2, you switch
the right and the middle.

00:02:35.330 --> 00:02:39.420
So step 3, we switch
B and C again.

00:02:39.420 --> 00:02:41.790
Because we're back on
the left-hand side.

00:02:41.790 --> 00:02:44.930
So you get C, B, A.

00:02:44.930 --> 00:02:46.765
And then step 4, you're
going to switch to

00:02:46.765 --> 00:02:48.690
the right-hand side.

00:02:48.690 --> 00:02:52.170
Step 3 we switched these two.

00:02:52.170 --> 00:02:54.470
Now step 4, we're going
to switch these two.

00:02:54.470 --> 00:02:57.930
So you get C, A, B.

00:02:57.930 --> 00:03:02.020
Then in step 5, we're back
switched on this side.

00:03:02.020 --> 00:03:05.180
So then you get A, C, B.

00:03:05.180 --> 00:03:07.380
And then step 6, you're going
to switch to the right-hand

00:03:07.380 --> 00:03:07.895
side again.

00:03:07.895 --> 00:03:10.610
So you get A, B, C.

00:03:10.610 --> 00:03:12.045
So by step 6, we repeat.

00:03:12.045 --> 00:03:13.890
So that's choice D.

00:03:13.890 --> 00:03:16.030
The hard part here, as far
as I'm concerned, is just

00:03:16.030 --> 00:03:18.070
understanding the problem
and their diagram.

00:03:18.070 --> 00:03:19.460
And then just seeing the pattern
that you're just

00:03:19.460 --> 00:03:20.910
switching the letters.

00:03:20.910 --> 00:03:23.490
First you switch the left
and the middle letter.

00:03:23.490 --> 00:03:24.740
Then you switch the right
and the middle letter.

00:03:24.740 --> 00:03:26.050
Then you switch the left
and the middle letter.

00:03:26.050 --> 00:03:27.610
Then you switch the right
and the middle letter.

00:03:27.610 --> 00:03:29.810
Until you get back to A, B, C.

00:03:29.810 --> 00:03:32.900
Next problem.

00:03:32.900 --> 00:03:34.860
White I don't think is
colorful enough.

00:03:34.860 --> 00:03:36.690
Let me do magenta.

00:03:36.690 --> 00:03:39.450
19.

00:03:39.450 --> 00:03:42.360
In a set of 11 different
numbers-- they're different--

00:03:42.360 --> 00:03:44.920
which of the following
cannot affect the

00:03:44.920 --> 00:03:46.170
value of the median?

00:03:49.370 --> 00:03:54.670
So it's a set of 11 different
numbers, they're different, so

00:03:54.670 --> 00:03:56.210
let's say it's 1 through 11.

00:03:56.210 --> 00:04:02.450
1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11.

00:04:02.450 --> 00:04:05.300
That's 11 different numbers.

00:04:05.300 --> 00:04:06.660
And in this case, what's
the median?

00:04:06.660 --> 00:04:09.010
Well we have 5 on this side, 5--
the median is this, this

00:04:09.010 --> 00:04:10.610
is the middle number, right?

00:04:10.610 --> 00:04:12.000
6 is the middle number.

00:04:12.000 --> 00:04:14.350
Doubling each number-- well,
if you double every number,

00:04:14.350 --> 00:04:17.700
the median's going to become
12, so that's not right.

00:04:17.700 --> 00:04:20.060
Increasing each number by 10--
once again, if you increase

00:04:20.060 --> 00:04:23.280
all of these numbers by 10, this
number's going to be 16,

00:04:23.280 --> 00:04:25.380
so you would've changed
the median.

00:04:25.380 --> 00:04:30.060
Increasing the smallest
number only.

00:04:30.060 --> 00:04:33.690
Well, what if you increase
the smallest number to,

00:04:33.690 --> 00:04:35.430
I don't know, 12?

00:04:35.430 --> 00:04:37.540
So then this 12 would
go all the way on

00:04:37.540 --> 00:04:39.610
the other side, right?

00:04:39.610 --> 00:04:42.840
And then the median would move
to 7 because you would have to

00:04:42.840 --> 00:04:45.480
have 5 below the median and
5 above the median.

00:04:45.480 --> 00:04:46.980
So you can increase that
smallest number.

00:04:46.980 --> 00:04:49.830
But if you increase it by a
large enough amount, it kind

00:04:49.830 --> 00:04:51.930
of goes into the greater than
the median column, and then

00:04:51.930 --> 00:04:54.780
the median would have to
shift to the right.

00:04:54.780 --> 00:04:59.060
Try it out, write out the list
from 2 to 12, and then the

00:04:59.060 --> 00:05:00.480
median becomes 7.

00:05:00.480 --> 00:05:03.080
OK, so we know that choice
B is not right.

00:05:03.080 --> 00:05:06.777
Choice C, increasing-- oh no,
that was choice C-- choice D,

00:05:06.777 --> 00:05:10.640
decreasing the largest number
only-- well, the same

00:05:10.640 --> 00:05:11.390
argument can apply.

00:05:11.390 --> 00:05:15.330
We could take the 11 and
decrease it down to, I don't

00:05:15.330 --> 00:05:17.690
know, decrease it to 0.

00:05:17.690 --> 00:05:20.050
You decrease it to 0, then
that'll-- and you could list

00:05:20.050 --> 00:05:22.450
them all out, 0 through 10--
and then the median number

00:05:22.450 --> 00:05:25.700
will shift to 5, so that
will change it.

00:05:25.700 --> 00:05:29.340
E, increasing the largest
number only.

00:05:29.340 --> 00:05:31.360
I can tell you that's the
answer from deductive

00:05:31.360 --> 00:05:35.210
reasoning, but if we just take
this 11 and we make it one

00:05:35.210 --> 00:05:39.740
billion, does that change the
fact that they're five numbers

00:05:39.740 --> 00:05:41.880
larger than 6 and five
numbers less than 6?

00:05:41.880 --> 00:05:42.990
Ignore the 0.

00:05:42.990 --> 00:05:44.590
Five numbers less than 6?

00:05:44.590 --> 00:05:45.370
No.

00:05:45.370 --> 00:05:47.140
I can make it into a trillion.

00:05:47.140 --> 00:05:50.350
I can change it to any number,
but the fact remains that I

00:05:50.350 --> 00:05:52.475
have the same amount of
numbers larger than 6

00:05:52.475 --> 00:05:54.340
as I do below 6.

00:05:54.340 --> 00:05:59.410
So choice E cannot affect
the value of the median.

00:05:59.410 --> 00:06:01.110
E.

00:06:01.110 --> 00:06:02.360
Next problem.

00:06:06.000 --> 00:06:09.340
OK, something for me to draw.

00:06:09.340 --> 00:06:11.710
Let's see, they have a 1/4
circle, so I'll just draw a

00:06:11.710 --> 00:06:15.500
big circle, and I'll just
focus on a 1/4 of it.

00:06:22.390 --> 00:06:24.810
Close enough.

00:06:24.810 --> 00:06:27.760
That looks like a
1/4 of a circle.

00:06:27.760 --> 00:06:30.690
They say that-- oh, and there's
a rectangle there too,

00:06:30.690 --> 00:06:32.520
fascinating.

00:06:32.520 --> 00:06:35.770
So this rectangle in this 1/4
circle, so this rectangle

00:06:35.770 --> 00:06:37.940
could look like this.

00:06:37.940 --> 00:06:41.640
I know theirs looks taller,
but I think this will do.

00:06:41.640 --> 00:06:43.605
And then I think I'm
almost done.

00:06:43.605 --> 00:06:47.510
I think I'm there,
I think I can.

00:06:47.510 --> 00:06:49.930
And then they shade in some
stuff, so if they shaded it, I

00:06:49.930 --> 00:06:51.920
will shade it.

00:06:51.920 --> 00:06:54.270
A suitably tasteful color.

00:06:57.300 --> 00:07:00.500
OK, so I have shaded what
they have shaded.

00:07:00.500 --> 00:07:02.220
And now, what are they saying?

00:07:02.220 --> 00:07:15.710
They're saying that this
is R, C, T, B, S, A.

00:07:15.710 --> 00:07:20.060
And then they tell us that
is a 90 degree angle.

00:07:20.060 --> 00:07:22.980
And then they tell us that this
distance, from here to

00:07:22.980 --> 00:07:26.390
here, from all the way to the
top-- so it's essentially the

00:07:26.390 --> 00:07:29.700
radius of the circle-- is 6.

00:07:29.700 --> 00:07:31.000
The radius of the circle is 6.

00:07:31.000 --> 00:07:37.410
In the figure above, arc SBT is
1/4 of a circle with center

00:07:37.410 --> 00:07:38.390
R and radius 6.

00:07:38.390 --> 00:07:39.350
Fair enough.

00:07:39.350 --> 00:07:46.130
If the length plus the width
of rectangle ABCR is 8-- so

00:07:46.130 --> 00:07:49.740
the length plus the
width, so ABCR.

00:07:49.740 --> 00:07:52.100
So this is the width,
this is the length.

00:07:52.100 --> 00:07:57.390
So L plus W is equal to 8.

00:07:57.390 --> 00:08:01.220
What is the perimeter of
the shaded region?

00:08:01.220 --> 00:08:02.920
Fascinating.

00:08:02.920 --> 00:08:04.420
Let's do it step by step.

00:08:04.420 --> 00:08:07.140
First we can just figure out
what this part of the

00:08:07.140 --> 00:08:08.310
perimeter is.

00:08:08.310 --> 00:08:11.440
And that's the easiest
part, right?

00:08:11.440 --> 00:08:13.380
Because what's the perimeter
of the whole circle?

00:08:13.380 --> 00:08:15.450
Well, it's the circumference
of the whole circle.

00:08:15.450 --> 00:08:18.170
Circumference is equal
to 2 pi r.

00:08:18.170 --> 00:08:20.210
This is the whole circle
we're talking about.

00:08:20.210 --> 00:08:25.000
So that's equal to 2 pi times
6, so that's equal to 12 pi.

00:08:25.000 --> 00:08:26.950
This is the circumference of
the whole circle, so the

00:08:26.950 --> 00:08:30.880
circumference of this arc, of
this piece, is going to be 1/4

00:08:30.880 --> 00:08:33.610
of that, because it's 1/4
of the whole circle.

00:08:33.610 --> 00:08:37.860
So it's 1/4 of 12 pi,
so that's 3 pi.

00:08:37.860 --> 00:08:40.690
Now, what we need to be able
to figure out is L and W,

00:08:40.690 --> 00:08:43.559
because if we can figure out
L and W, we can figure out

00:08:43.559 --> 00:08:47.600
everything else about
this circle.

00:08:47.600 --> 00:08:49.720
And actually, I'm going to
continue this problem in the

00:08:49.720 --> 00:08:52.430
next video, because I think it
might get a little involved,

00:08:52.430 --> 00:08:53.890
and I don't want you to
get too confused.

00:08:53.890 --> 00:08:55.140
I'll see you in the next video.


SAT Prep: Test 6 Section 7 Part 6

WEBVTT
Kind: captions
Language: en

00:00:00.790 --> 00:00:02.850
All right, this is a fun
problem, so it'll get a video

00:00:02.850 --> 00:00:03.850
on its own.

00:00:03.850 --> 00:00:05.730
I started in the last video,
but I'm going to start over

00:00:05.730 --> 00:00:07.970
just so we get it
all in one take.

00:00:07.970 --> 00:00:13.480
So they say, in the figure
above, arc SBT is 1/4 of a

00:00:13.480 --> 00:00:17.620
circle with center
R and radius 6.

00:00:17.620 --> 00:00:20.590
And they actually tell-- they
draw this distance, which is

00:00:20.590 --> 00:00:22.160
the radius.

00:00:22.160 --> 00:00:24.490
This distance is 6, right?

00:00:24.490 --> 00:00:26.725
So this distance would
also be 6, right?

00:00:32.130 --> 00:00:35.580
If the length plus the width
of rectangle ABCR is 8-- so

00:00:35.580 --> 00:00:37.300
this is ABCR.

00:00:37.300 --> 00:00:39.440
So the length plus
the width is 8.

00:00:39.440 --> 00:00:44.640
So let's call this
L and this is W.

00:00:44.640 --> 00:00:47.660
Actually, this should be-- well,
it doesn't matter, this

00:00:47.660 --> 00:00:49.150
should be height,
but whatever.

00:00:49.150 --> 00:00:51.160
We know that these two
sides are equal to 8.

00:00:51.160 --> 00:00:56.040
So we know that L plus
W is equal to 8.

00:00:56.040 --> 00:00:56.940
Fair enough.

00:00:56.940 --> 00:01:01.750
Then the perimeter of the shaded
region is-- that's this

00:01:01.750 --> 00:01:04.590
perimeter right here, so there's
a lot of pieces to it.

00:01:04.590 --> 00:01:06.490
So let's start with
what I would call

00:01:06.490 --> 00:01:11.080
the low hanging fruit.

00:01:11.080 --> 00:01:14.320
So the low hanging fruit,
in my opinion, is the

00:01:14.320 --> 00:01:16.780
length of this arc.

00:01:16.780 --> 00:01:18.030
Arc SBT.

00:01:20.440 --> 00:01:22.420
What's the length of that?

00:01:22.420 --> 00:01:25.140
Well, it's going to be 1/4 the
circumference of the entire

00:01:25.140 --> 00:01:25.600
circle, right?

00:01:25.600 --> 00:01:28.840
Because this arc represents--
what we drew is 1/4 of the

00:01:28.840 --> 00:01:31.450
circle, so this length is
going to be 1/4 of the

00:01:31.450 --> 00:01:32.600
circumference.

00:01:32.600 --> 00:01:34.270
So the length of the
circumference-- so the

00:01:34.270 --> 00:01:36.690
circumference of, let me see,
the circumference of the

00:01:36.690 --> 00:01:39.510
circle, is what?

00:01:39.510 --> 00:01:42.710
It's 2 pi r.

00:01:42.710 --> 00:01:43.760
r is 6, right?

00:01:43.760 --> 00:01:49.760
So 2 pi times 6, is
equal to 12 pi.

00:01:49.760 --> 00:01:53.920
If the circumference of the
circle is 12 pi, then we could

00:01:53.920 --> 00:02:00.070
call the length of the arc,
right-- let's call this LA--

00:02:00.070 --> 00:02:03.270
the length of the arc
is going to be what?

00:02:03.270 --> 00:02:08.370
It's going to be 1/4
the circumference

00:02:08.370 --> 00:02:10.350
of the whole circle.

00:02:10.350 --> 00:02:14.040
1/4 times 12 pi is
equal to 3 pi.

00:02:17.520 --> 00:02:18.680
Good enough.

00:02:18.680 --> 00:02:21.040
Now what else can we
try to figure out?

00:02:21.040 --> 00:02:25.390
Well, the second lowest hanging
fruit is actually the

00:02:25.390 --> 00:02:26.640
length of this line.

00:02:26.640 --> 00:02:27.820
Which you're probably saying,
well, they give me no

00:02:27.820 --> 00:02:29.920
information, maybe I have to
use the Pythagorean theorem

00:02:29.920 --> 00:02:32.810
with W and L, but it's really
just a visual trick, because

00:02:32.810 --> 00:02:34.770
I'll tell you that you could
actually just look at this

00:02:34.770 --> 00:02:38.000
graph and figure out what the
length from A to C is.

00:02:38.000 --> 00:02:39.510
And I'll give you a hint.

00:02:39.510 --> 00:02:42.860
What is the length
from R to B?

00:02:42.860 --> 00:02:45.780
What is that length?

00:02:45.780 --> 00:02:48.480
Well isn't R to B a radius
of the circle?

00:02:48.480 --> 00:02:48.710
Right?

00:02:48.710 --> 00:02:49.780
It's going from the center
to the edge of

00:02:49.780 --> 00:02:51.070
circle, so it's a radius.

00:02:51.070 --> 00:02:53.560
So RB has length 6.

00:02:53.560 --> 00:02:58.590
And RB is a diagonal of this
rectangle just like AC is, so

00:02:58.590 --> 00:03:01.490
they're symmetric, so this is
also going to be equal to 6.

00:03:01.490 --> 00:03:03.530
And you could look at it a bunch
of different ways, you

00:03:03.530 --> 00:03:06.030
could say that W squared
plus L squared is

00:03:06.030 --> 00:03:07.290
equal to this, AC squared.

00:03:07.290 --> 00:03:10.660
Well, W squared, this is W as
well, right, you could also

00:03:10.660 --> 00:03:12.570
say that W squared plus
L squared is equal

00:03:12.570 --> 00:03:13.790
to this side squared.

00:03:13.790 --> 00:03:15.290
So that's why they're
equal to each other.

00:03:15.290 --> 00:03:21.660
So we know length of AC is
equal to 6, as well.

00:03:21.660 --> 00:03:23.250
Right?

00:03:23.250 --> 00:03:24.120
We figured out that.

00:03:24.120 --> 00:03:26.160
So we have two pieces left.

00:03:26.160 --> 00:03:31.150
We just have that piece,
and that piece.

00:03:31.150 --> 00:03:33.750
What's the length
of this piece?

00:03:33.750 --> 00:03:35.760
Well, this whole
distance is 6.

00:03:35.760 --> 00:03:38.110
We figured that out because
that's a radius.

00:03:38.110 --> 00:03:40.260
And this piece is L, right?

00:03:40.260 --> 00:03:40.830
That's L.

00:03:40.830 --> 00:03:44.150
So that piece is 6 minus L.

00:03:44.150 --> 00:03:45.810
Similarly, what's this piece?

00:03:45.810 --> 00:03:48.440
By the same logic, that's
6 minus W, right?

00:03:48.440 --> 00:03:50.740
This is W, the whole
thing is 6, so this

00:03:50.740 --> 00:03:53.040
leftover is 6 minus W.

00:03:53.040 --> 00:03:59.680
So if we want the perimeter of
this entire shaded region,

00:03:59.680 --> 00:04:05.150
it's this perimeter of this
brown arc, which is 3 pi.

00:04:05.150 --> 00:04:09.010
So let me say, perimeter
is equal to 3 pi.

00:04:09.010 --> 00:04:13.040
Plus the length of AC, plus 6.

00:04:13.040 --> 00:04:17.240
Plus this piece,
plus 6 minus L.

00:04:17.240 --> 00:04:22.200
Plus this piece,
plus 6 minus W.

00:04:22.200 --> 00:04:24.030
And let's simplify that a bit.

00:04:24.030 --> 00:04:28.020
So let's see, that equals 3
pi, and then we have three

00:04:28.020 --> 00:04:32.690
6's, so plus 18, minus
L, minus W.

00:04:32.690 --> 00:04:41.190
And this is the same thing as
3 pi plus 18 minus L plus W.

00:04:41.190 --> 00:04:42.440
Fascinating.

00:04:42.440 --> 00:04:45.470
And really, I kind of just
bumbled my way here.

00:04:45.470 --> 00:04:47.620
You know the problem is
solvable, and that's better

00:04:47.620 --> 00:04:50.430
than most mathematicians have
going for them, and so you

00:04:50.430 --> 00:04:52.660
just kind of have to bumble away
with whatever information

00:04:52.660 --> 00:04:52.940
they give you.

00:04:52.940 --> 00:04:55.820
The real trick here, I think, is
recognizing that AC is the

00:04:55.820 --> 00:04:57.490
same length as RB.

00:04:57.490 --> 00:04:59.380
But once you get to this point,
you have to now employ

00:04:59.380 --> 00:04:59.970
the second trick.

00:04:59.970 --> 00:05:02.270
You have to realize that minus
L minus W, well that looks a

00:05:02.270 --> 00:05:04.850
lot like this L plus
W up here.

00:05:04.850 --> 00:05:08.000
And this is really kind of what
separates the adults from

00:05:08.000 --> 00:05:09.910
the children, I guess.

00:05:09.910 --> 00:05:13.830
So we know that L plus W is 8,
so just substitute here, 8.

00:05:13.830 --> 00:05:19.980
So the perimeter is 3 pi,
plus 18, minus 8.

00:05:19.980 --> 00:05:27.090
That equals 3 pi plus 10,
and that is choice B.

00:05:27.090 --> 00:05:28.960
That was exciting.

00:05:28.960 --> 00:05:30.940
I'll see you in the
next section.


SAT Prep: Test 6 Section 3 Part 5

WEBVTT
Kind: captions
Language: en

00:00:01.210 --> 00:00:04.610
We're on problem 16.

00:00:04.610 --> 00:00:06.960
And they want to know what is
the area of the shaded square?

00:00:06.960 --> 00:00:10.590
Let me shade it because they
call it shaded square.

00:00:10.590 --> 00:00:13.100
So what's that area?

00:00:13.100 --> 00:00:15.030
So how can we do it?

00:00:15.030 --> 00:00:19.180
Well, it's a bit of a trick, but
what you need to realize

00:00:19.180 --> 00:00:26.880
is, you could draw-- Let me draw
some things that might--

00:00:26.880 --> 00:00:28.610
This is actually a really
fun problem.

00:00:28.610 --> 00:00:30.900
Let me draw some interesting
rectangles here.

00:00:34.162 --> 00:00:38.020
Let me draw a rectangle there.

00:00:38.020 --> 00:00:44.640
Let me draw another rectangle
there to there.

00:00:44.640 --> 00:00:48.226
This really is just kind
of a brain teaser.

00:00:48.226 --> 00:00:50.510
Draw another rectangle
from there to there.

00:00:56.680 --> 00:01:06.930
And then let me draw another
rectangle from there to there.

00:01:10.410 --> 00:01:14.720
OK, so let me ask you
a couple of things.

00:01:14.720 --> 00:01:19.980
One: what is the distance of
the base of this rectangle

00:01:19.980 --> 00:01:20.820
right here?

00:01:20.820 --> 00:01:22.090
This distance.

00:01:22.090 --> 00:01:25.540
Well, we know this entire--
whoops, wrong tool-- we know

00:01:25.540 --> 00:01:28.490
this entire distance
is 3, right?

00:01:28.490 --> 00:01:32.310
Because they tell us-- oh,
they don't even tell us.

00:01:32.310 --> 00:01:33.910
They tell us that this
distance is this 1.

00:01:33.910 --> 00:01:36.300
So we know that this
is a cube, right?

00:01:36.300 --> 00:01:38.110
That this distance is 3.

00:01:38.110 --> 00:01:41.180
So this distance is 1.

00:01:41.180 --> 00:01:45.580
And then this distance
down here is 3.

00:01:45.580 --> 00:01:48.445
And they tell us that this is
a shaded square, right?

00:01:48.445 --> 00:01:51.770
So all the sides of this
inner shape are also

00:01:51.770 --> 00:01:53.510
going to be the same.

00:01:53.510 --> 00:01:56.280
So if this is 1, this
is 2, this is also

00:01:56.280 --> 00:01:59.220
going to be 2, right?

00:01:59.220 --> 00:02:02.970
That's going to be 2, that's
going to be 1, that's going to

00:02:02.970 --> 00:02:05.780
be 1, this is going
to be 2, 1.

00:02:05.780 --> 00:02:08.580
I think you get when
I'm saying, right?

00:02:08.580 --> 00:02:11.830
And what is the distances
of the smaller

00:02:11.830 --> 00:02:14.520
square inside of here?

00:02:14.520 --> 00:02:18.940
Well, if this distance is 1,
this distance is 1 from here

00:02:18.940 --> 00:02:22.870
to here, this distance
is also going to be 1

00:02:22.870 --> 00:02:24.640
because 1 plus 1 is 2.

00:02:24.640 --> 00:02:25.660
That's 1.

00:02:25.660 --> 00:02:27.200
Same reason, you can make
the same argument.

00:02:27.200 --> 00:02:30.410
This is 1, this is
1, this is 1.

00:02:30.410 --> 00:02:34.280
So the area of this small square
inside, what's the area

00:02:34.280 --> 00:02:35.740
of that small square?

00:02:35.740 --> 00:02:39.370
What's the area of the magenta
square that I just filled in?

00:02:39.370 --> 00:02:41.270
Well that area is
going to be 1.

00:02:41.270 --> 00:02:41.610
right?

00:02:41.610 --> 00:02:43.240
The magenta square is 1.

00:02:43.240 --> 00:02:49.420
So now all we have to figure
out is the area of these 4

00:02:49.420 --> 00:02:50.630
yellow triangles.

00:02:50.630 --> 00:02:54.360
And what are the areas of each
of those yellow triangles?

00:02:54.360 --> 00:02:58.300
Well, each of those yellow
triangles are-- they have a

00:02:58.300 --> 00:03:02.140
dimension, on the long side,
the dimension is 2.

00:03:02.140 --> 00:03:03.570
Let me find a good color.

00:03:03.570 --> 00:03:06.450
On the long side, the dimension
is 2, right?

00:03:06.450 --> 00:03:10.220
This distance right here is 2.

00:03:10.220 --> 00:03:13.610
And on the short side,
the distance is 1.

00:03:13.610 --> 00:03:16.950
So its area, each yellow
triangle is 2 times 1 times

00:03:16.950 --> 00:03:17.850
1/2, right?

00:03:17.850 --> 00:03:19.890
Because area of a triangle
is area equals

00:03:19.890 --> 00:03:22.160
1/2 base times height.

00:03:22.160 --> 00:03:28.880
So area of each of those
triangles is going to be 1/2

00:03:28.880 --> 00:03:34.950
times 2 times 1, so that
equals 1, right?

00:03:34.950 --> 00:03:37.390
So the area of this triangle
is 1, the area of this

00:03:37.390 --> 00:03:39.006
triangle is 1, the area of this
triangle is 1, the area

00:03:39.006 --> 00:03:40.020
of this triangle is 1.

00:03:40.020 --> 00:03:42.800
And then the area of the square
inside is also 1.

00:03:42.800 --> 00:03:45.540
So it's 1 plus 1 plus
1 plus 1 plus 1.

00:03:45.540 --> 00:03:47.360
The total area is 5.

00:03:47.360 --> 00:03:50.920
Area equals 5, that
was pretty neat.

00:03:50.920 --> 00:03:54.990
And the big thing you need to
realize is that you can split

00:03:54.990 --> 00:03:59.205
up the square on the
inside like this.

00:03:59.205 --> 00:04:03.200
Let me think if there
was another way.

00:04:03.200 --> 00:04:04.440
That's the way that
it occurred to me.

00:04:04.440 --> 00:04:07.130
Maybe there's another way, maybe
I'm over-complicating

00:04:07.130 --> 00:04:07.900
it, I don't know.

00:04:07.900 --> 00:04:10.100
But it looks nice.

00:04:10.100 --> 00:04:12.850
Next problem.

00:04:12.850 --> 00:04:16.899
For all positive integers, j
and k, let j-- I like these

00:04:16.899 --> 00:04:20.680
where they define new math
operations-- j square with an

00:04:20.680 --> 00:04:26.780
r inside of it, k, be defined as
the whole number remainder

00:04:26.780 --> 00:04:29.070
when j is divided by k.

00:04:29.070 --> 00:04:34.320
So this equals remainder
when j is divided by k.

00:04:34.320 --> 00:04:36.680
If you're familiar with the
concept of a modulus, that's

00:04:36.680 --> 00:04:39.890
essentially what this
operation is.

00:04:39.890 --> 00:04:47.760
If 13-- I guess we'll call this
remainder operation-- k

00:04:47.760 --> 00:04:53.010
is equal to 2, what
is the value of k?

00:04:53.010 --> 00:04:55.780
And they tell us in the
beginning that j and k, all of

00:04:55.780 --> 00:04:57.870
these things have to be positive
numbers, right?

00:04:57.870 --> 00:05:01.790
So this is essentially saying
that when I divide 13 by some

00:05:01.790 --> 00:05:12.510
positive number, I get
a remainder of 2.

00:05:12.510 --> 00:05:16.160
Well, what number when I
divide it into 13 is 2?

00:05:16.160 --> 00:05:19.620
I guess another way to think
about it is 13 minus 2 is a

00:05:19.620 --> 00:05:22.040
multiple of this
number, right?

00:05:22.040 --> 00:05:24.050
So you could say, what's
13 minus 2?

00:05:24.050 --> 00:05:25.270
Well it's 11.

00:05:25.270 --> 00:05:30.170
So 11 is a multiple of k, and
actually 11 should be k

00:05:30.170 --> 00:05:36.310
because if 11's a multiple of k,
and 11's not a multiple of

00:05:36.310 --> 00:05:38.090
much, right?

00:05:38.090 --> 00:05:42.320
Eleven's only a multiple of 1
and 11, so k has to be 11.

00:05:42.320 --> 00:05:43.510
And you can test it out.

00:05:43.510 --> 00:05:45.050
I mean, if you get confused,
just try

00:05:45.050 --> 00:05:46.300
out different numbers.

00:05:48.500 --> 00:05:51.460
13 divided by 11 is equal
to one, right?

00:05:51.460 --> 00:05:53.450
Because 11 goes in
13 one time.

00:05:53.450 --> 00:05:57.020
Remainder 2.

00:05:57.020 --> 00:05:57.920
Which satisfies this.

00:05:57.920 --> 00:06:02.830
13 remainder 11 is equal to 2.

00:06:02.830 --> 00:06:04.080
Next problem.

00:06:06.810 --> 00:06:09.270
Problem 18.

00:06:09.270 --> 00:06:11.720
The average of the test
scores of a class of

00:06:11.720 --> 00:06:14.060
p students is 70.

00:06:14.060 --> 00:06:17.190
The average is 70, so what
do we know about that?

00:06:17.190 --> 00:06:21.130
We know that if we were to add
up all of the p students--

00:06:21.130 --> 00:06:23.170
well, actually, let me read the
rest of the problem before

00:06:23.170 --> 00:06:24.670
I do anything.

00:06:24.670 --> 00:06:27.150
And the average of the test
scores of a class of n

00:06:27.150 --> 00:06:29.620
students is 92.

00:06:29.620 --> 00:06:32.150
When the scores of both classes
are combined, the

00:06:32.150 --> 00:06:34.450
average score is 86.

00:06:34.450 --> 00:06:36.750
What is the value of p/n?

00:06:36.750 --> 00:06:43.880
OK, so what is the sum of
the p student scores?

00:06:43.880 --> 00:06:47.720
So their average is 70, so the
sum of all of their scores is

00:06:47.720 --> 00:06:51.810
going to be 70p, right?

00:06:51.810 --> 00:06:53.320
You can take the average
and multiply it by

00:06:53.320 --> 00:06:54.440
the number of students.

00:06:54.440 --> 00:06:58.260
And then you get the sum of all
of their scores, right?

00:06:58.260 --> 00:07:00.300
And if that doesn't make a lot
of sense, think about it.

00:07:00.300 --> 00:07:01.375
What's the definition
of average?

00:07:01.375 --> 00:07:10.920
It's the sum divided by p is
equal to the average, right?

00:07:10.920 --> 00:07:15.520
So if you multiply both sides by
p, you get the sum is equal

00:07:15.520 --> 00:07:18.940
to p times the average.

00:07:18.940 --> 00:07:21.690
In this case, the
average is 70.

00:07:21.690 --> 00:07:24.590
So 70 times p is the sum of
the first class, and then

00:07:24.590 --> 00:07:26.560
what's the sum of the
second class?

00:07:26.560 --> 00:07:30.810
It's going to be 92n for
the same exact reason.

00:07:30.810 --> 00:07:34.430
And now, how many total students
are we averaging?

00:07:34.430 --> 00:07:37.380
Well there are p in this sum and
there are n in this sum,

00:07:37.380 --> 00:07:41.640
so it's p plus n, and they
tell us that this average

00:07:41.640 --> 00:07:43.370
score is 86.

00:07:43.370 --> 00:07:46.410
So we set up our equation
and now let's solve.

00:07:46.410 --> 00:07:53.040
Let's multiply both sides by p
plus n, so you get 70p plus

00:07:53.040 --> 00:08:03.410
92n is equal to 86p plus 86n,
right? p plus n times 86,

00:08:03.410 --> 00:08:05.360
distribute the 86.

00:08:05.360 --> 00:08:06.180
Now what do we want to do?

00:08:06.180 --> 00:08:09.650
We eventually want to figure out
p/n, so let's put the n's

00:08:09.650 --> 00:08:11.020
on the left-hand side.

00:08:11.020 --> 00:08:15.220
So I'm going to subtract 86n
from both sides, so you get

00:08:15.220 --> 00:08:22.710
70p plus-- 92 minus 86 is 6n
is equal to 86p, right?

00:08:22.710 --> 00:08:25.590
I subtracted this from
the other side.

00:08:25.590 --> 00:08:29.690
And then let's subtract 70p from
both sides, so you get 6n

00:08:29.690 --> 00:08:32.360
is equal to 16p, right?

00:08:32.360 --> 00:08:34.140
86 minus 70.

00:08:34.140 --> 00:08:35.965
And then we want to know p/n.

00:08:40.309 --> 00:08:46.620
So we divide both sides by n,
you get 6 is equal to 16p/n

00:08:46.620 --> 00:08:48.920
and now divide both sides
by 16, and you get

00:08:48.920 --> 00:08:53.090
6/16 is equal to p/n.

00:08:53.090 --> 00:08:56.300
And, of course, we
can reduced 6/16.

00:08:56.300 --> 00:09:00.030
6/16 is the same thing as 3/8.

00:09:00.030 --> 00:09:03.040
That is our answer for p/n.

00:09:03.040 --> 00:09:05.170
I'll see you in the
next section.


SAT Prep: Test 6 Section 3 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.760 --> 00:00:04.200
We're now on test number
6 in section 3.

00:00:04.200 --> 00:00:06.140
Let's just get started.

00:00:06.140 --> 00:00:08.250
Problem number 1.

00:00:08.250 --> 00:00:13.560
Which of the following numbers
is between 1/5 and 1/4?

00:00:13.560 --> 00:00:15.170
So when you look at the choices,
you immediately see

00:00:15.170 --> 00:00:17.340
that all of the numbers
are decimals.

00:00:17.340 --> 00:00:19.010
So let's just convert
these to decimals.

00:00:19.010 --> 00:00:20.290
1/5 is what?

00:00:20.290 --> 00:00:22.320
It's 0.2.

00:00:22.320 --> 00:00:25.270
And 1/4 is 0.25.

00:00:25.270 --> 00:00:29.390
So we need a number that's
larger-- so let me call it x--

00:00:29.390 --> 00:00:32.170
than 0.2 and less than 0.25.

00:00:32.170 --> 00:00:35.980
And if you look at the choices,
d is that answer.

00:00:35.980 --> 00:00:38.840
And if you didn't know off
hand that 1/5 is 0.2, you

00:00:38.840 --> 00:00:42.890
could divide 5 into 1.0.

00:00:42.890 --> 00:00:46.850
5 goes into 10 two times.

00:00:46.850 --> 00:00:50.450
2 times 10 is 10, 0, and then,
of course, the decimal you

00:00:50.450 --> 00:00:52.590
bring up, so it's 0.2 times.

00:00:52.590 --> 00:00:54.540
And just do the same
thing with 1/4.

00:00:54.540 --> 00:00:55.970
Next problem.

00:00:55.970 --> 00:00:58.630
Problem 2.

00:00:58.630 --> 00:01:02.150
The following are coordinates
of points in the xy plane.

00:01:02.150 --> 00:01:05.800
Which of these points is
nearest the origin?

00:01:05.800 --> 00:01:08.690
So if we look at all of the
choices-- well, let me

00:01:08.690 --> 00:01:10.110
actually write all
the choices down.

00:01:10.110 --> 00:01:15.020
We have a, a says
0, minus 1/2.

00:01:17.680 --> 00:01:20.160
b is-- I was thinking whether
I should draw these for you,

00:01:20.160 --> 00:01:21.540
but it's good to learn how
to do this without

00:01:21.540 --> 00:01:25.540
drawing-- 0, 1/2.

00:01:25.540 --> 00:01:32.400
c is 1/2, minus 1/2.

00:01:32.400 --> 00:01:38.550
d is 1/2, 1/2.

00:01:38.550 --> 00:01:45.530
And e is minus 1, minus 1.

00:01:45.530 --> 00:01:50.110
So if we look at all the
choices, we didn't move at all

00:01:50.110 --> 00:01:51.520
along the x-axis here, right?

00:01:51.520 --> 00:01:52.560
Because we're still
at x equals 0.

00:01:52.560 --> 00:01:54.740
We want to figure out how
far it is away from 0.

00:01:54.740 --> 00:01:57.130
So we didn't move at all from
the x-axis and we went one

00:01:57.130 --> 00:02:00.510
below the y-axis here,
to minus one.

00:02:00.510 --> 00:02:03.070
Clearly b is closer than
a because b is

00:02:03.070 --> 00:02:05.220
only 1/2 away, right?

00:02:05.220 --> 00:02:08.320
Once again, we didn't move on
the x-axis, and we only moved

00:02:08.320 --> 00:02:10.470
1/2 away on the y-axis.

00:02:10.470 --> 00:02:11.680
So a is not our choice.

00:02:11.680 --> 00:02:13.350
So far, b is our
best contender.

00:02:13.350 --> 00:02:17.790
It's only 1/2 away
from the origin.

00:02:17.790 --> 00:02:22.720
c is 1/2 away in the x direction
and 1/2 away in the

00:02:22.720 --> 00:02:25.720
y direction, and if you do
the math, if you use the

00:02:25.720 --> 00:02:27.365
Pythagorean theorem, you'll see
that, of course, is going

00:02:27.365 --> 00:02:29.080
to be further than 1/2.

00:02:29.080 --> 00:02:31.270
And let me just draw a little
bit of a graphic for you just

00:02:31.270 --> 00:02:34.240
so you get the intuition.

00:02:34.240 --> 00:02:35.550
How I can do that without
drawing it.

00:02:35.550 --> 00:02:36.800
So this point is 0, 1/2.

00:02:42.630 --> 00:02:44.200
So that point is here.

00:02:44.200 --> 00:02:48.450
That's our best contender
right now, 0, 1/2.

00:02:48.450 --> 00:02:52.480
The point 1/2, negative
1/2 is here.

00:02:52.480 --> 00:02:56.570
See, this is 1/2
minus 1/2 here.

00:03:01.160 --> 00:03:03.450
So its distance from
the origin is

00:03:03.450 --> 00:03:06.450
this line right here.

00:03:06.450 --> 00:03:08.980
And that difference is
definitely going to be longer

00:03:08.980 --> 00:03:09.730
than this distance.

00:03:09.730 --> 00:03:11.170
How do I know?

00:03:11.170 --> 00:03:13.890
Because this distance is the
same thing as this distance,

00:03:13.890 --> 00:03:17.800
it's the same thing as 1/2 to
the negative side, right?

00:03:17.800 --> 00:03:19.570
And if you do the Pythagorean
theorem, we

00:03:19.570 --> 00:03:20.340
could figure it out.

00:03:20.340 --> 00:03:24.420
This distance is 1/2
half as well.

00:03:24.420 --> 00:03:28.700
This is going to be the square
root of 1/2 squared plus 1/2

00:03:28.700 --> 00:03:31.950
squared, so 1/4 plus
1/4, which is 1/2.

00:03:31.950 --> 00:03:35.020
So it's the square root of
1/2, which is 1 over the

00:03:35.020 --> 00:03:37.190
square root of 2.

00:03:37.190 --> 00:03:39.550
Which is the same thing as two
square roots of 2 over 2.

00:03:39.550 --> 00:03:42.750
Any way you look at it, it is
a bigger number than 1/2.

00:03:42.750 --> 00:03:46.120
When you take a square root of
a fraction, you're going to

00:03:46.120 --> 00:03:47.680
get something bigger than
the fraction, right?

00:03:47.680 --> 00:03:49.250
So this is essentially the
square root of 1/2.

00:03:49.250 --> 00:03:51.810
So it's going to be
bigger than 1/2.

00:03:51.810 --> 00:03:53.930
So we know that this
isn't the choice.

00:03:53.930 --> 00:03:57.005
And d is the same distance as c,
d is up here, it's just in

00:03:57.005 --> 00:03:59.740
the positive quadrant, right?

00:03:59.740 --> 00:04:02.190
This distance is 1/2 and then
this distance is 1/2.

00:04:02.190 --> 00:04:07.320
So d, for the same reasons,
is further then b.

00:04:07.320 --> 00:04:09.910
And e is the furthest
of them all, right?

00:04:09.910 --> 00:04:12.890
It's one away in two directions,
so it's out here

00:04:12.890 --> 00:04:14.520
someplace relative to
this origin, so

00:04:14.520 --> 00:04:15.330
that's not the choice.

00:04:15.330 --> 00:04:18.190
So b is definitely the closest,
and it's only 1/2

00:04:18.190 --> 00:04:20.610
units away from the origin.

00:04:20.610 --> 00:04:21.860
Next problem.

00:04:25.040 --> 00:04:28.120
I will change colors
for variety.

00:04:28.120 --> 00:04:29.370
Problem 3.

00:04:31.730 --> 00:04:33.330
OK, they drew a lot here.

00:04:33.330 --> 00:04:36.090
Let me see if I can draw the
same thing they did.

00:04:36.090 --> 00:04:37.746
So they have a horizontal
line.

00:04:40.920 --> 00:04:43.380
I want to draw just like
the way they did it.

00:04:43.380 --> 00:04:51.730
And so then there's
1, 2, 3, 4, 5.

00:04:51.730 --> 00:04:53.660
I'm telling you, drawing
it is the hardest part.

00:04:56.180 --> 00:05:04.110
And they have something
like this, like that,

00:05:04.110 --> 00:05:09.310
and then like that.

00:05:09.310 --> 00:05:12.410
And then the next two don't go
all the way through, they go

00:05:12.410 --> 00:05:14.090
kind of halfway.

00:05:14.090 --> 00:05:15.050
That one goes like that.

00:05:15.050 --> 00:05:17.100
And that one.

00:05:17.100 --> 00:05:19.090
That's my best shot.

00:05:19.090 --> 00:05:25.670
And they say that this is x
degrees, x degrees, x degrees,

00:05:25.670 --> 00:05:28.980
x degrees, x degrees, x
degrees, x degrees.

00:05:28.980 --> 00:05:32.940
And they say that this big one
right here is y degrees.

00:05:32.940 --> 00:05:37.180
In the figure above, what
is the value of y?

00:05:37.180 --> 00:05:40.880
Well, the first thing I would
do is figure out what the

00:05:40.880 --> 00:05:42.080
value of x is.

00:05:42.080 --> 00:05:43.840
And how do I do that?

00:05:43.840 --> 00:05:46.470
Well, you could make a whole
circle or whatever, but you

00:05:46.470 --> 00:05:52.010
could say look, all of these
x's here, how many is that?

00:05:52.010 --> 00:05:55.470
1, 2, 3, 4, 5, x's right?

00:05:55.470 --> 00:05:58.660
These five x's are collectively
supplementary to

00:05:58.660 --> 00:05:59.350
each other, right?

00:05:59.350 --> 00:06:01.590
They're going to add
up to 180 degrees.

00:06:01.590 --> 00:06:07.240
So we know that 5x is equal
to 180 degrees.

00:06:07.240 --> 00:06:12.230
And that x is equal to-- how
many times does 5 go into 180?

00:06:12.230 --> 00:06:17.740
5 goes into 150 30 times, and
so there's another 30, so

00:06:17.740 --> 00:06:20.210
it'll go into it 36 times.

00:06:20.210 --> 00:06:22.680
So x equal to 36 degrees,
you just divide

00:06:22.680 --> 00:06:24.470
180 by 5 to get that.

00:06:24.470 --> 00:06:27.780
So how do we figure out y?

00:06:27.780 --> 00:06:30.820
Well, the easy way to do this
is say well, if you go into

00:06:30.820 --> 00:06:38.180
the other side of the circle,
that's also going to be equal

00:06:38.180 --> 00:06:40.470
to 180 degrees, right?

00:06:40.470 --> 00:06:41.910
So we have two x's here.

00:06:45.510 --> 00:06:48.160
And then we have y, right?

00:06:48.160 --> 00:06:54.090
So you could say y plus
2x is equal to 180.

00:06:54.090 --> 00:06:55.290
I know what x is.

00:06:55.290 --> 00:06:59.990
x is 36 degrees, so y
plus 2 times 36 is

00:06:59.990 --> 00:07:03.170
72 is equal to 180.

00:07:03.170 --> 00:07:12.340
y is equal to 180 minus 72,
which is 108 degrees.

00:07:12.340 --> 00:07:15.360
Now, if you wanted to do this
really, really, really fast,

00:07:15.360 --> 00:07:17.080
what you could have said
is well, you know what?

00:07:17.080 --> 00:07:19.440
If I kept drawing these
x's all the way

00:07:19.440 --> 00:07:21.730
around the circle, right?

00:07:21.730 --> 00:07:27.420
So let's say that I had
lines like this.

00:07:27.420 --> 00:07:30.820
Say this line actually just
continues on like this.

00:07:30.820 --> 00:07:35.310
And let's say that this line
continued on like this.

00:07:35.310 --> 00:07:38.790
And we know that this is kind
of a visualization exercise,

00:07:38.790 --> 00:07:42.290
but you'd have known that this
is x, this is x, this is x.

00:07:42.290 --> 00:07:43.620
And then how many x's
total are there?

00:07:43.620 --> 00:07:46.790
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

00:07:46.790 --> 00:07:49.020
There would have been
10 x's, right?

00:07:49.020 --> 00:07:51.630
And we're going all the way
around the circle, so 10x

00:07:51.630 --> 00:07:54.090
would equal 360.

00:07:54.090 --> 00:07:55.760
x is equal to 36.

00:07:55.760 --> 00:07:58.380
And then a really easy thing,
you could've said well y is 3

00:07:58.380 --> 00:08:00.150
of these x's, right?

00:08:00.150 --> 00:08:01.870
1, 2, 3.

00:08:01.870 --> 00:08:04.190
y is three of those x's,
so three times

00:08:04.190 --> 00:08:06.650
36 is equal to 108.

00:08:06.650 --> 00:08:07.740
Either way would've been fine.

00:08:07.740 --> 00:08:09.970
I think the way we did it the
first time, well, it didn't

00:08:09.970 --> 00:08:11.880
take too long, but if you
can do it faster,

00:08:11.880 --> 00:08:13.832
that all the better.

00:08:13.832 --> 00:08:16.490
Because at some point,
the SAT really just

00:08:16.490 --> 00:08:18.770
becomes a speed exam.

00:08:18.770 --> 00:08:20.020
Problem number 4.

00:08:22.800 --> 00:08:34.130
If 6,565 is equal to 65 times
x plus 1, then x equals?

00:08:34.130 --> 00:08:36.280
So the real trick here is being
able to divide fast.

00:08:36.280 --> 00:08:42.710
Divide both sides by 65, you
get 65 goes into 6,565 goes

00:08:42.710 --> 00:08:48.200
into 65 one time, 1 time 65, 0,
0, 6, goes into it 0 times.

00:08:48.200 --> 00:08:51.410
Get a 0, 65, goes into
65 one time.

00:08:51.410 --> 00:08:54.560
So you divide both sides
by 65, you get 101 is

00:08:54.560 --> 00:08:56.920
equal to x plus 1.

00:08:56.920 --> 00:09:00.180
Subtract 1 from both sides,
you get 100 is equal to x.

00:09:00.180 --> 00:09:01.960
This is just kind of
a speed problem.

00:09:01.960 --> 00:09:04.500
Maybe they want to make you
have a careless mistake.

00:09:04.500 --> 00:09:05.920
The answer is c.

00:09:05.920 --> 00:09:07.880
I'll see you in the
next video.


SAT Prep: Test 6 Section 3 Part 3

WEBVTT
Kind: captions
Language: en

00:00:01.470 --> 00:00:02.930
Welcome back.

00:00:02.930 --> 00:00:05.020
I don't like to rush too
much on these videos.

00:00:05.020 --> 00:00:07.060
I just wanted to continue
the next one.

00:00:07.060 --> 00:00:09.170
So what we did, I just wrote out
everything they tell us in

00:00:09.170 --> 00:00:10.040
the problem.

00:00:10.040 --> 00:00:12.780
We figured out x is equal to
y, so they must both be

00:00:12.780 --> 00:00:14.520
45-degree angles.

00:00:14.520 --> 00:00:17.910
And since y is opposite of this
angle, it must be 45.

00:00:17.910 --> 00:00:20.690
And since this angle, this
angle, and this angle are the

00:00:20.690 --> 00:00:23.450
same triangle and this one's
45 and this one's 90, this

00:00:23.450 --> 00:00:25.410
must also equal 45.

00:00:25.410 --> 00:00:28.070
And what I said is we need to
figure out this green line.

00:00:28.070 --> 00:00:30.280
And I made the claim, and I
think you'll believe me, that

00:00:30.280 --> 00:00:31.930
this green line is the
same length of the

00:00:31.930 --> 00:00:33.410
line that I just drew.

00:00:33.410 --> 00:00:36.400
This peach line, right?

00:00:36.400 --> 00:00:39.610
And also, what else do we know
about this larger triangle?

00:00:39.610 --> 00:00:41.505
Well, its hypotenuse is here.

00:00:41.505 --> 00:00:45.480
Its hypotenuse is this magenta
line right there.

00:00:45.480 --> 00:00:47.920
And let me redraw it here.

00:00:47.920 --> 00:00:49.390
So its hypotenuse is
this magenta line.

00:00:49.390 --> 00:00:51.120
What's the length of
the magenta line?

00:00:51.120 --> 00:00:52.550
It's 4 plus 8.

00:00:52.550 --> 00:00:54.480
They gave us that information.

00:00:54.480 --> 00:00:56.510
So it's 12.

00:00:56.510 --> 00:01:01.360
And we want to figure
out this peach line.

00:01:01.360 --> 00:01:04.720
I'm just re-drawing it so that
you know that we're clear of

00:01:04.720 --> 00:01:08.360
all of the mess, right?

00:01:08.360 --> 00:01:10.400
I'm saying this green line is
the same as this peach line,

00:01:10.400 --> 00:01:12.620
and I just re-drew this
peach line here.

00:01:12.620 --> 00:01:15.010
What do we also know about
this triangle?

00:01:15.010 --> 00:01:18.870
Well, if this angle up here is
45, what's this angle here?

00:01:18.870 --> 00:01:20.410
That's also going
to be 45, right?

00:01:20.410 --> 00:01:24.590
Because these two lines are
perpendicular, so this is 45.

00:01:24.590 --> 00:01:26.870
And we also know that this angle
x is this angle here, so

00:01:26.870 --> 00:01:27.850
that's also 45.

00:01:27.850 --> 00:01:30.020
Or you can figure it
out any other way.

00:01:30.020 --> 00:01:31.440
So there we go.

00:01:31.440 --> 00:01:33.770
We have a 45-45-90 triangle.

00:01:33.770 --> 00:01:34.710
We know its hypotenuse.

00:01:34.710 --> 00:01:37.650
Can we figure out the sides?

00:01:37.650 --> 00:01:39.500
Well we know the sides are
going to be equal, right?

00:01:39.500 --> 00:01:40.860
Because the base angles
are equal.

00:01:40.860 --> 00:01:43.175
We also know that in
a 45-45-90 triangle

00:01:43.175 --> 00:01:44.610
the sides are equal.

00:01:44.610 --> 00:01:47.270
In fact, you can even look at
the beginning of the book,

00:01:47.270 --> 00:01:50.130
they even define a 45-45-90
triangle.

00:01:50.130 --> 00:01:53.540
But we'll work it out just so
you see it worked out without

00:01:53.540 --> 00:01:55.690
having to memorize.

00:01:55.690 --> 00:01:59.310
So x squared-- this is just
Pythagorean theorem-- plus x

00:01:59.310 --> 00:02:00.380
squared is equal to
the hypotenuse

00:02:00.380 --> 00:02:03.500
squared is equal to 144.

00:02:03.500 --> 00:02:07.290
2x squared is equal to 144.

00:02:07.290 --> 00:02:11.410
x squared is equal to 72.

00:02:11.410 --> 00:02:14.140
x is equal to the square
root of 72.

00:02:14.140 --> 00:02:16.530
So what's the square
root of 72?

00:02:16.530 --> 00:02:19.780
The square root of 72 is the
square root of 36 times 2,

00:02:19.780 --> 00:02:23.440
which is the same thing as the
square root of 36 times the

00:02:23.440 --> 00:02:25.320
square root of 2.

00:02:25.320 --> 00:02:27.090
And what does that
turn out to be?

00:02:27.090 --> 00:02:30.050
Well, the square root
of 36 is 6, right?

00:02:30.050 --> 00:02:36.290
So our answer is 6 square
roots of 2.

00:02:36.290 --> 00:02:40.900
So that is choice b.

00:02:40.900 --> 00:02:42.150
Next problem.

00:02:49.410 --> 00:02:50.660
Problem 8.

00:02:53.100 --> 00:02:55.410
The price of ground
coffee bean is d

00:02:55.410 --> 00:02:57.980
dollars for 8 ounces.

00:02:57.980 --> 00:03:04.710
So d dollars for 8 ounces.

00:03:04.710 --> 00:03:10.810
And each ounce makes c cups
of brewed coffee.

00:03:10.810 --> 00:03:18.130
So one ounce makes c cups
of brewed coffee.

00:03:18.130 --> 00:03:30.920
In terms of c and d, what is the
dollar cost of the ground

00:03:30.920 --> 00:03:34.190
coffee beans required
to make one cup?

00:03:34.190 --> 00:03:36.320
We just want to make one
cup and we say how much

00:03:36.320 --> 00:03:38.950
does that cost us?

00:03:38.950 --> 00:03:40.110
OK.

00:03:40.110 --> 00:03:45.470
So let's see how many cups we
can make with d dollars, OK?

00:03:45.470 --> 00:03:47.790
So d dollars, we would
get 8 ounces.

00:03:47.790 --> 00:03:53.190
So d dollars, we get 8 ounces.

00:03:53.190 --> 00:03:57.320
And then each ounce, you
get c cups, right?

00:03:57.320 --> 00:04:00.540
One ounce turns into c cups,
so 8 ounces will

00:04:00.540 --> 00:04:02.020
turn into 8c cups.

00:04:06.220 --> 00:04:08.550
But we only want
one cup, right?

00:04:08.550 --> 00:04:16.279
So we're saying d dollars
is equal to 8c cups.

00:04:16.279 --> 00:04:19.060
But we only want one cup, so
let's divide both sides of

00:04:19.060 --> 00:04:20.310
this by 8c.

00:04:24.070 --> 00:04:25.870
So what are we left with?

00:04:25.870 --> 00:04:32.890
We're left with d over 8c
dollars is equal to one cup.

00:04:32.890 --> 00:04:37.010
And that is choice a.

00:04:37.010 --> 00:04:39.270
Not too bad, huh?

00:04:39.270 --> 00:04:40.520
Next problem.

00:04:44.350 --> 00:04:45.655
Problem number 9.

00:04:48.930 --> 00:04:57.250
If 10/a is equal to b/12,
what is the value of ab?

00:04:57.250 --> 00:05:00.220
So this is just straight
cross-multiplication.

00:05:00.220 --> 00:05:05.160
a times b is equal to 10 times
12, so ab is equal to 10 times

00:05:05.160 --> 00:05:07.290
12, which equals 120.

00:05:07.290 --> 00:05:08.120
We are done.

00:05:08.120 --> 00:05:09.670
120 is our answer.

00:05:09.670 --> 00:05:11.440
If you haven't learned to
cross-multiply, it's just a

00:05:11.440 --> 00:05:14.880
quick way-- when you see two
fractions equal each other,

00:05:14.880 --> 00:05:17.520
you can take the numerator of
the left times the denominator

00:05:17.520 --> 00:05:18.570
of the right.

00:05:18.570 --> 00:05:20.710
And that equals the denominator
of the left times

00:05:20.710 --> 00:05:21.880
the numerator of the right.

00:05:21.880 --> 00:05:22.820
And how do we know that?

00:05:22.820 --> 00:05:27.110
Well, we could do
it step by step.

00:05:27.110 --> 00:05:30.680
You can multiply both
sides times a.

00:05:30.680 --> 00:05:32.350
That cancels out and you're
left with 10 is

00:05:32.350 --> 00:05:35.060
equal to ab over 12.

00:05:35.060 --> 00:05:37.950
And then you multiply both sides
times 12, you get 120 is

00:05:37.950 --> 00:05:39.630
equal to ab.

00:05:39.630 --> 00:05:42.350
That just skips one
step right there.

00:05:42.350 --> 00:05:43.600
Next problem.

00:05:47.660 --> 00:05:51.180
Problem 10.

00:05:51.180 --> 00:05:52.360
They give us a little
sequence here.

00:05:52.360 --> 00:05:58.990
150, 30, 6, and then
it keeps going.

00:05:58.990 --> 00:06:01.730
In the sequence above, each term
after the first term is

00:06:01.730 --> 00:06:03.780
1/5 of the preceding term.

00:06:03.780 --> 00:06:06.310
What is the fifth term
of the sequence?

00:06:06.310 --> 00:06:08.550
So 1/5 of the preceding term.

00:06:08.550 --> 00:06:11.260
So the next term is going
to be 1/5 of this.

00:06:11.260 --> 00:06:15.260
So that's what, that's
6/5, right?

00:06:15.260 --> 00:06:17.040
I just multiplied
1/5 times that.

00:06:17.040 --> 00:06:20.100
So the next term is going to be
1/5 times this, so that's

00:06:20.100 --> 00:06:21.900
6/25, right?

00:06:21.900 --> 00:06:28.400
1/5 times 6/5 is
equal to 6/25.

00:06:28.400 --> 00:06:33.080
So that is the fifth term.

00:06:33.080 --> 00:06:35.220
And you could write it as a
fraction or you could write it

00:06:35.220 --> 00:06:37.020
as a decimal, I think
you'd get 0.24 if

00:06:37.020 --> 00:06:39.370
you do it as a decimal.

00:06:39.370 --> 00:06:41.660
Next problem.

00:06:41.660 --> 00:06:43.600
I'm suspicious, that
seemed too easy.

00:06:43.600 --> 00:06:51.930
Problem 11.

00:06:51.930 --> 00:06:55.520
Five points-- a, b, c, d, and
e-- lie on a line, not

00:06:55.520 --> 00:06:57.540
necessarily in that order.

00:06:57.540 --> 00:07:03.170
ab has length 24.

00:07:03.170 --> 00:07:05.120
Point c is the midpoint of ab.

00:07:05.120 --> 00:07:07.590
So let's draw this and
let's see if we can

00:07:07.590 --> 00:07:09.590
avoid messing up.

00:07:09.590 --> 00:07:11.450
OK.

00:07:11.450 --> 00:07:14.810
So let me draw a and b.

00:07:14.810 --> 00:07:22.770
So a, b.

00:07:22.770 --> 00:07:24.876
This is how I'd do it if
I was taking it, taking

00:07:24.876 --> 00:07:27.230
the test. ab is 24.

00:07:27.230 --> 00:07:29.380
Point c is the midpoint of ab.

00:07:29.380 --> 00:07:31.620
So point c is right here.

00:07:31.620 --> 00:07:32.810
And it's the midpoint.

00:07:32.810 --> 00:07:37.140
So this is 12, and this is 12.

00:07:37.140 --> 00:07:39.040
So far so good?

00:07:39.040 --> 00:07:41.650
And point d is the
midpoint of ac.

00:07:44.820 --> 00:07:48.540
So this distance is 6, and this
distance is 6, right?

00:07:48.540 --> 00:07:49.330
It's getting smaller.

00:07:49.330 --> 00:07:50.910
I should have drawn this bigger,
but I think you get

00:07:50.910 --> 00:07:51.710
what I'm saying.

00:07:51.710 --> 00:07:55.380
This is point d here
in yellow.

00:07:55.380 --> 00:08:02.530
If the distance between d and
e-- so this is d-- and the

00:08:02.530 --> 00:08:07.950
distance between d and e is 5,
what is one possible distance

00:08:07.950 --> 00:08:09.000
between a and e?

00:08:09.000 --> 00:08:11.895
So they're essentially saying
where could e be?

00:08:14.400 --> 00:08:17.520
So let me blow things
up a little bit.

00:08:17.520 --> 00:08:19.160
Let me redraw this.

00:08:21.890 --> 00:08:25.180
And let me focus on a and c
because that's the part that

00:08:25.180 --> 00:08:27.980
got all scrunched up.

00:08:27.980 --> 00:08:38.840
So if this is a, this is c, and
they tell us that d is the

00:08:38.840 --> 00:08:40.090
midpoint of these two.

00:08:42.919 --> 00:08:47.970
And we figured out that a to c
was 12 and a to d is 6, right?

00:08:47.970 --> 00:08:51.040
This distance is 6, which is
the same as this distance,

00:08:51.040 --> 00:08:52.870
that's also 6.

00:08:52.870 --> 00:08:55.270
And then they tell us at the
end, if the distance between d

00:08:55.270 --> 00:08:57.930
and e is 5, what is one
possible distance

00:08:57.930 --> 00:08:59.240
between a and e?

00:08:59.240 --> 00:09:01.920
So we know that e is on
this line as well.

00:09:01.920 --> 00:09:04.880
So there's two places
where e could be.

00:09:04.880 --> 00:09:08.950
e could be 5 in this direction,
it could be here.

00:09:08.950 --> 00:09:15.650
e could be there or e could be 5
in this direction where this

00:09:15.650 --> 00:09:19.540
is 5 and this is 5.

00:09:19.540 --> 00:09:24.390
So if e is here, what is the
distance from a to e?

00:09:24.390 --> 00:09:25.810
Well, this distance from
a to e is just

00:09:25.810 --> 00:09:27.240
going to be 1, right?

00:09:27.240 --> 00:09:31.160
You go one to e and then 5 to
d, and that adds up to 6.

00:09:31.160 --> 00:09:37.260
So one possible distance
for ae is 1.

00:09:37.260 --> 00:09:41.880
The other one is you go 6 to
d and then you go 5 to e.

00:09:41.880 --> 00:09:44.510
So the other possibility
is 11.

00:09:44.510 --> 00:09:46.680
And so, oh, this isn't
multiple choice.

00:09:46.680 --> 00:09:49.070
You could fill out either
one of those choices.

00:09:49.070 --> 00:09:50.830
See you in the next video.


SAT Prep: Test 6 Section 3 Part 2

WEBVTT
Kind: captions
Language: en

00:00:01.530 --> 00:00:01.920
All right.

00:00:01.920 --> 00:00:04.930
We're on problem number five.

00:00:04.930 --> 00:00:08.052
OK, problem number five.

00:00:08.052 --> 00:00:17.170
If m to the x times m to
the 7th is equal to 28.

00:00:17.170 --> 00:00:20.800
They also tell us that m to the
5th, and then that whole

00:00:20.800 --> 00:00:26.700
thing to the y power, is
equal to m to the 15th.

00:00:26.700 --> 00:00:30.236
What is the value of x plus y?

00:00:30.236 --> 00:00:31.872
x plus y equals what?

00:00:31.872 --> 00:00:34.710
So this is really just a test
of whether you know your

00:00:34.710 --> 00:00:36.100
exponent rules.

00:00:36.100 --> 00:00:39.680
So what is m to the x
times m to the 7th?

00:00:39.680 --> 00:00:42.670
So your temptation might have
been to say 7x, but no.

00:00:42.670 --> 00:00:45.970
Remember, when you multiply two
numbers of the same base,

00:00:45.970 --> 00:00:48.620
and the base is m, you
add the exponents.

00:00:48.620 --> 00:00:51.020
So it's m to the x plus 7.

00:00:51.020 --> 00:00:53.280
And they actually wanted to
tempt you to do 7x because

00:00:53.280 --> 00:00:55.940
they actually use the number 28
here, which is a multiple

00:00:55.940 --> 00:00:58.540
of 7, so they were tempting
you to do 7x.

00:00:58.540 --> 00:01:01.820
But we know that you add the
exponents when you multiply m

00:01:01.820 --> 00:01:03.860
to the x times m to the 7th.

00:01:03.860 --> 00:01:09.060
And so we have m to the x times
m to the 7th-- oh sorry,

00:01:09.060 --> 00:01:10.105
I wrote it down wrong.

00:01:10.105 --> 00:01:12.080
It equals m to the 28.

00:01:12.080 --> 00:01:13.990
Sorry, well you knew that.

00:01:13.990 --> 00:01:16.935
Anyway, m to the x times m to
the 7th is equal to m to the x

00:01:16.935 --> 00:01:21.280
plus 7, and that equals
m to the 28.

00:01:21.280 --> 00:01:25.660
So the exponents have to equal
each other, so x plus 7 is

00:01:25.660 --> 00:01:27.860
equal to 28.

00:01:27.860 --> 00:01:31.060
x is equal to 21.

00:01:31.060 --> 00:01:32.340
Now let's go here.

00:01:32.340 --> 00:01:34.950
Here we have m to the 5th,
and then we're raising

00:01:34.950 --> 00:01:37.080
that to the yth power.

00:01:37.080 --> 00:01:40.240
So here we actually would
multiply the exponents, if you

00:01:40.240 --> 00:01:41.800
remember your exponent rules.

00:01:41.800 --> 00:01:48.160
So you have m to the 5y is
equal to m to the 15th.

00:01:48.160 --> 00:01:50.610
So 5y must equal 15.

00:01:50.610 --> 00:01:56.710
5y is equal to 15,
y is equal to 3.

00:01:56.710 --> 00:01:57.820
So what's x plus y?

00:01:57.820 --> 00:02:02.280
It's 21 plus 3, which
equals 24.

00:02:02.280 --> 00:02:05.670
And that is choice d.

00:02:05.670 --> 00:02:06.920
Next problem.

00:02:10.430 --> 00:02:13.070
Looks like there's going
to be some drawing

00:02:13.070 --> 00:02:14.676
for Sal in this problem.

00:02:14.676 --> 00:02:20.160
I'll try my best. Oh, I thought
I was using-- undo.

00:02:20.160 --> 00:02:21.250
Edit undo.

00:02:21.250 --> 00:02:22.770
I thought I was using
the line tool.

00:02:22.770 --> 00:02:24.510
OK.

00:02:24.510 --> 00:02:26.880
That's my y-axis, draw
a straight line.

00:02:26.880 --> 00:02:28.570
I drew a straight line.

00:02:28.570 --> 00:02:32.270
That's my x-axis.

00:02:32.270 --> 00:02:33.540
And then what do
they have here?

00:02:33.540 --> 00:02:44.730
They have 19-- let's see,
1985, '86, '87,

00:02:44.730 --> 00:02:51.300
'88, '89, then '90.

00:02:51.300 --> 00:02:57.240
Let's see, 1985 is, maybe,
looks about 148,000.

00:02:57.240 --> 00:03:03.450
So if this is 150,000,
1985 is here.

00:03:03.450 --> 00:03:05.710
Let me just draw it all out.

00:03:05.710 --> 00:03:11.540
1985, then 1986 is up
here at 160,000.

00:03:11.540 --> 00:03:13.096
This is 140,000.

00:03:13.096 --> 00:03:13.436
soon.

00:03:13.436 --> 00:03:17.370
So 1986 is up here at 160,000.

00:03:17.370 --> 00:03:24.280
1987 is a little bit less, 1987
looks like about 150,000,

00:03:24.280 --> 00:03:27.340
I don't know, eyeballing
it at 156,000.

00:03:27.340 --> 00:03:33.870
1987 is here.

00:03:33.870 --> 00:03:44.270
1988 looks like a little
bit above 140,000.

00:03:44.270 --> 00:03:48.410
1989 is between 130,000
and 120,000.

00:03:48.410 --> 00:03:50.950
All the work here is drawing
what you hopefully already

00:03:50.950 --> 00:03:52.430
have in your book.

00:03:52.430 --> 00:03:54.080
So where was I?

00:03:54.080 --> 00:03:56.390
Oh sorry, this is 1988.

00:03:56.390 --> 00:04:00.120
1988 was a little bit
better than 140,000.

00:04:00.120 --> 00:04:00.710
Ignore that one.

00:04:00.710 --> 00:04:09.620
1989 looks like about 126,000.

00:04:09.620 --> 00:04:13.310
Then 1990 is, I don't know,
112,000 or something.

00:04:13.310 --> 00:04:18.184
1990 is out here.

00:04:18.184 --> 00:04:23.350
And then if I were to connect
the dots, look

00:04:23.350 --> 00:04:24.600
something like that.

00:04:30.230 --> 00:04:31.540
And then let's read
the question.

00:04:31.540 --> 00:04:33.890
According to the graph above,
which of the following is

00:04:33.890 --> 00:04:37.280
closest to the decrease per year
in the number of homes

00:04:37.280 --> 00:04:41.610
sold between 1987 and 1990.

00:04:41.610 --> 00:04:44.890
So we're talking about from
1987, so it's from

00:04:44.890 --> 00:04:47.410
this year, to 1990.

00:04:47.410 --> 00:04:50.220
So how much did we decrease
in the first year, right?

00:04:50.220 --> 00:04:52.070
The first year we decreased
by this much.

00:04:52.070 --> 00:04:54.600
And I'm going to look in the
book because I don't know how

00:04:54.600 --> 00:04:56.700
well I drew this graph.

00:04:56.700 --> 00:05:04.910
But in 1987, it looks like
we're about 156,000.

00:05:04.910 --> 00:05:11.950
And then as we go to 1988, it
looks like about 142,000 just

00:05:11.950 --> 00:05:13.620
eyeballing it, right?

00:05:18.130 --> 00:05:20.180
So this distance right
here is what?

00:05:20.180 --> 00:05:23.710
It'd be 156,000 minus 142,000.

00:05:23.710 --> 00:05:27.010
About minus 14,000, right?

00:05:27.010 --> 00:05:29.966
That's how much we changed
over this one year.

00:05:29.966 --> 00:05:32.860
And if I look at the choices,
there already is choice c,

00:05:32.860 --> 00:05:34.920
which is 14,000, but let
me just do one more

00:05:34.920 --> 00:05:36.460
just to make sure.

00:05:36.460 --> 00:05:39.180
So if we want to figure out from
1988 to 1989, so we said

00:05:39.180 --> 00:05:44.080
1988 is at 142,000,
where is 1989?

00:05:44.080 --> 00:05:59.310
Looks like 128,000, I
would say 128,000.

00:05:59.310 --> 00:06:04.270
And so 142,000 minus 128,000,
that's also 14,000.

00:06:04.270 --> 00:06:08.060
And if we do the last one,
that's 128,000, and then this

00:06:08.060 --> 00:06:13.110
looks something about
114,000 right here.

00:06:13.110 --> 00:06:15.660
So this is also 14,000.

00:06:15.660 --> 00:06:19.450
So the answer is c, 14,000.

00:06:19.450 --> 00:06:21.520
Next problem.

00:06:21.520 --> 00:06:22.770
Problem 7.

00:06:25.293 --> 00:06:30.450
you Here we have this diagram
that shows up actually a lot

00:06:30.450 --> 00:06:31.675
when you're taking the SAT.

00:06:31.675 --> 00:06:34.510
I'll show you why.

00:06:34.510 --> 00:06:37.110
This is a very common
thing you'll see.

00:06:39.950 --> 00:06:43.335
A line like that.

00:06:43.335 --> 00:06:46.790
A line like that.

00:06:46.790 --> 00:06:48.986
And then they connect it here.

00:06:48.986 --> 00:06:50.465
Now let's read the problem.

00:06:53.140 --> 00:06:55.560
I already have suspicion what
they're going to ask.

00:06:55.560 --> 00:07:04.080
So this is a, b, c, d, and e.

00:07:04.080 --> 00:07:06.390
They tell us this is
perpendicular.

00:07:06.390 --> 00:07:07.910
This is perpendicular.

00:07:07.910 --> 00:07:09.090
This is x.

00:07:09.090 --> 00:07:11.020
This is y.

00:07:11.020 --> 00:07:18.190
In the figure above, ae and cd
are each particular to ce.

00:07:18.190 --> 00:07:19.450
Fair enough.

00:07:19.450 --> 00:07:26.920
If x is equal to y, the length
of ab is 4, and the length of

00:07:26.920 --> 00:07:31.460
bd is 8, what is the
length of ce?

00:07:31.460 --> 00:07:34.250
So we're trying to figure out--
let me draw ce, let's

00:07:34.250 --> 00:07:36.860
have our gold in a different
color-- we're trying to figure

00:07:36.860 --> 00:07:39.950
out this line right there.

00:07:39.950 --> 00:07:42.700
And one thing I didn't write,
they told us x is equal to y,

00:07:42.700 --> 00:07:44.700
so immediately that should
hit a trigger.

00:07:44.700 --> 00:07:48.510
x is equal to y and this is a
90-degree angle, so we know

00:07:48.510 --> 00:07:56.490
that x plus y plus 90 is equal
to 180, or that x plus y is

00:07:56.490 --> 00:07:57.300
equal to 90.

00:07:57.300 --> 00:08:00.960
And if they're equal to each
other, x must equal y, which

00:08:00.960 --> 00:08:03.310
equals 45 degrees, right?

00:08:03.310 --> 00:08:08.510
So this is 45, this is 45, and
if y is 45, what is this angle

00:08:08.510 --> 00:08:09.240
going to be?

00:08:09.240 --> 00:08:14.280
Well it's opposite to y, so this
will also be 45 degrees.

00:08:14.280 --> 00:08:18.760
And this is a right angle too,
so 45 plus 90 plus this angle

00:08:18.760 --> 00:08:21.800
has to equal 180, so what's
this angle going to be?

00:08:21.800 --> 00:08:24.270
Well, that's also going
to be 45 degrees.

00:08:24.270 --> 00:08:26.420
This also has to be a
45-45-90 triangle.

00:08:26.420 --> 00:08:29.010
If you ever see a triangle where
one of the angles is 90

00:08:29.010 --> 00:08:31.650
and the other is 45, the other
one has to be 45 because they

00:08:31.650 --> 00:08:33.530
add up to 180.

00:08:33.530 --> 00:08:37.199
And what we want to figure
out is this length here.

00:08:37.199 --> 00:08:39.330
So I'm going to show you a
little trick, and this trick--

00:08:39.330 --> 00:08:41.190
well, it doesn't always work,
it's not really a trick, it's

00:08:41.190 --> 00:08:44.800
just a visualization exercise,
really-- we say, we want to

00:08:44.800 --> 00:08:46.750
figure out this length.

00:08:46.750 --> 00:08:48.690
Well that length, I'm going to
say-- I'm going to make the

00:08:48.690 --> 00:08:51.250
claim, and I think you'll
believe this claim is the same

00:08:51.250 --> 00:08:53.130
is this length, I'm essentially
creating a

00:08:53.130 --> 00:08:57.920
rectangle-- is the same
as that length, right?

00:08:57.920 --> 00:08:59.750
So if we figure out this length,
we solve the problem,

00:08:59.750 --> 00:09:02.760
this light brown length.

00:09:02.760 --> 00:09:06.170
And we also know-- let
me draw the bottom--

00:09:06.170 --> 00:09:07.610
do we know the length?

00:09:07.610 --> 00:09:10.460
Actually, we don't even have
to know this bottom line.

00:09:10.460 --> 00:09:12.180
We don't know the length
of that bottom line.

00:09:12.180 --> 00:09:14.410
We need to figure
out this length.

00:09:14.410 --> 00:09:17.690
We know since this line is
parallel to this line.

00:09:17.690 --> 00:09:20.820
We know this is a
90-degree angle.

00:09:20.820 --> 00:09:23.740
Well, do we know
the hypotenuse?

00:09:23.740 --> 00:09:24.280
Sure.

00:09:24.280 --> 00:09:27.120
The hypotenuse is 4 plus 8,
it's this big red line.

00:09:27.120 --> 00:09:29.880
And let me draw the hypotenuse
in a different color.

00:09:29.880 --> 00:09:34.090
The hypotenuse, right here,
that's the hypotenuse.

00:09:34.090 --> 00:09:35.790
Actually, I'm running out of
time, so I'm going to continue

00:09:35.790 --> 00:09:37.490
this in the next video.

00:09:37.490 --> 00:09:38.740
See