SAT Prep: Test 3 Section 8 Part 1

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Language: en

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Welcome back.

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We're now starting section
eight on page 547.

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OK.

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And I think we're in the third
test. So problem number one,

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if e is a set of even numbers--
even integers,

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sorry-- e is a set of even
integers, p is a set of

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positive integers, and f is a
set of integers less than 5,

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which of the following
integers will be

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in all three sets?

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So we're looking for something
that meets all the

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constraints.

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So it has to be even, it has to
be positive, and it has to

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be less than 5.

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OK, so choice A is 6.

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6 is not less than 5.

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Choice B is 4.

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4 is even, 4 is positive,
4 is less than 5.

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So the answer is B.

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And the other choices don't
work because, C, 1 is odd.

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D, 0 is not positive.

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And the last choice,
E, negative 2.

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Well, that's not positive
either.

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Problem number two.

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So our answer was B.

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Choice B was 4.

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Problem number two.

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If 8 plus the square root
of k is equal to 15,

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then what does k equal?

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Well, subtract 8 from both
sides, and you get square root

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of k is equal to 7.

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Square both sides,
k is equal to 49.

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Next problem.

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Problem number three.

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Let's see If I can
clear image.

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Problem number three.

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In a poll, 35 people
were in favor of

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building a new library.

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So 35, yes, they want it.

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14, against it.

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14 said no.

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And 1 person doesn't know.

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1 person just has no opinion.

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What fraction of those polled
were in favor of building a

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new library.

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So the people that were
in favor were 35.

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And the fraction of the total
people polled-- so the total

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people polled was 35 plus
14 plus 1, right?

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And what is this?

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That's 50.

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So that's equal to 35 over 50.

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And 35 over 50, if we divide
the top and bottom

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by 7, you get 7/10.

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So the answer is A.

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7/10 were in favor
of the library.

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Problem number four.

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We've got a kind of crazy
looking figure here.

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You have a line that goes
something like this, and it

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goes like that and then it
goes like this and looks

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something like that.

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Close enough.

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And what's going on here?

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So they tell us that
this angle is 70.

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That's 70.

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This is 30.

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They say that this is
t and this is u.

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You probably can't read
that but you see

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it in your own book.

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In the figure above, what is
the value of t plus u?

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This is the angle game again.

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Let's see what angles
we can figure out.

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So, this is 70, this is 30.

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So this angle right here
plus 70, plus 30 has

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to equal 180, right?

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This angle plus 70, plus 30.

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70 plus 30 is 100.

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So this is 80 degrees
right here.

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If this is 80 degrees,
this is the

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opposite angle to 80 degrees.

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So that's going to also
be 80 degrees.

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We learned that in
geometry class.

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And so if this is 80 degrees--
first of all, what do all of

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these angles combined equal? t
plus u, plus 80 are all on the

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same triangle.

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So they have to add up to 180.

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So we know that t plus u has
to be 100 degrees, and

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that's choice C.

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Next problem.

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[? Invert. ?]

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OK, problem number five.

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Oh, there's a big graph.

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According to the graph above,
between which two consecutive

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years was the greatest change
in the price of coffee?

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Oh, I think I'm going to
have to draw this.

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Just so that you see what
I see, hopefully.

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OK, and then let me just
write the years.

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So this is, it goes
'81 through '86.

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So '81, '82, '83,
'84, '85, '86.

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Let's see, in 1981-- so let's
see, we have $3.00, $3.75, we

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have $4.00, $4.25,
$4.50, $4.75.

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In 1981 it cost $3.75.

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It's going to take me a little
time to draw this whole thing.

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In 1982 it was at $3.50.

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Oops, that's $3.50 down
here, not $3.00.

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Let me write that,
that's $3.50.

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Back to what I was doing.

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In 1983 it went to $4.25.

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In 1984 it went all
the way to $4.75.

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In 1985 it was at $3.75 again.

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That looks something
like that.

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And then 1986 goes to $4.50.

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1986, $4.50.

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OK, and what are
they asking us?

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According to the graph above,
between which two consecutive

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years was the greatest change
in the price of coffee?

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Well, let's figure that out.

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So here, the change is $0.25.

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Here, the change, going from
this year to this year, is--

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let's see, $0.25,
$0.50, $0.75.

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That's a good contender
right there.

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$0.75.

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Going from here to here we
only had a $0.50 change.

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Then we went from
$4.75 to $3.50.

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So this is a pretty big
change, actually.

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This looks like our winner.

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That's from $4.75 to
actually $3.75, so

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this is a $1.00 change.

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And then we went from $3.75 to
$4.50, so we had a $0.75

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change again.

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So the biggest change happened
from 1984 to 1985, choice D.

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All that work for a fairly
straightforward problem.

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Next problem.

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Problem number six.

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More drawing for me.

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OK.

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let's see, more drawing.

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Got to be focused,
Sal, focused.

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This is negative 1, this
is negative 2, this

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is 1, this is 2.

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1 and 2.

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And what does this
graph look like?

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Let's see, we go from here to
here, it looks like, and then

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we stay flat here, and then we
go like this, and then we go

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flat again.

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And what are they asking?

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The graph of y equals g of x.

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So this is y is equal
to g of x.

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Shown above.

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If g of k is equal to 1, which
of the following is a possible

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value of k?

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So g of k is equal to 1.

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So when does this
graph equal 1?

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Well, this graph equals 1--
add a different color-- it

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equals 1 here-- oh,
it equals 1 here.

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It equals 1 this entire
period, right?

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All of these values are where
g of x is equal to 1.

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So what could be the
values of k?

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Well, the values of k could
be anywhere between

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negative 1 and 0.

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All of those could be values
of k, anywhere from here.

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Because at all of these values,
g of k is equal to 1.

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So let's see.

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They have choices.

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Minus 1.5 is here.

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No, that's over there.

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Minus 0.5 is right here.

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And g of minus 0.5 is right
here, so that's 1. g of minus

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0.5 is equal to 1.

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So that looks pretty good.

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So that is our answer.

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Choice B.

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Let's see if I can squeeze
in problem number seven.

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I think that would be the most
videos I've ever done-- most

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problems in 10 minutes.

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If a, b and c are different
positive integers, and 2 to

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the a, times 2 to the b, times
2 to the c, is equal to 64,

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then they want to know, what is
2 to the a, plus 2 to the

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b, plus 2 to the c?

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Fascinating.

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Well, what do we know about
exponent rules?

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2 to the a, times 2 to the b,
times 2 to the c, that's 2 to

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the a, plus b, plus c, right?

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2 to the what power is 64?

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2 to the sixth power, right?

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2 to the sixth power is 64.

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Actually, I'm going to
run out of time.

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So I'm going to do this
in the next video.

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I only have 15 seconds left.

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See you soon.


SAT Prep: Test 3 Section 8 Part 2

WEBVTT
Kind: captions
Language: en

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Welcome back.

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I shouldn't try to squeeze in
videos because then I rush,

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and then you won't learn, and
everything breaks down.

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So problem number 7, a, b, and
c are different positive

00:00:11.030 --> 00:00:17.460
integers, and 2 to the a times 2
to the b times 2 to the c is

00:00:17.460 --> 00:00:20.770
equal to 64.

00:00:20.770 --> 00:00:24.900
They want to know what is 2
to the a plus 2 to the b

00:00:24.900 --> 00:00:28.380
plus 2 to the c?

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Well, here two things
we can use.

00:00:30.740 --> 00:00:34.120
We can use our exponent rules
where if we have the same base

00:00:34.120 --> 00:00:37.080
and we multiply it we can
just add the exponents.

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So this is equal to 2 to
the a plus b plus c.

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Then, can we write 64
as a power of 2?

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Sure.

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Let's see, 2 to the
third is equal to

00:00:50.730 --> 00:00:53.270
8 and 64 is 8 squared.

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So if we square both sides of
that, that's 2 to the sixth.

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You might already know that,
2 to the sixth is 64.

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You could think of it as
2 to the fifth is 32.

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2 to the sixth is
64, of course.

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So a plus b plus c
has to equal 6.

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What do they tell us?

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a, b and c are different
positive integers.

00:01:20.690 --> 00:01:21.750
So what are a, b and c?

00:01:21.750 --> 00:01:25.040
Well let's see, they could
be 1, 2 and 3, right?

00:01:25.040 --> 00:01:29.430
Because 1 plus 2 plus
3 is equal to 6.

00:01:29.430 --> 00:01:31.610
So there we have it. a, b,
and c are 1, 2 and 3.

00:01:31.610 --> 00:01:34.370
So 2 to the a plus 2 to the b
plus 2 to the c is the same

00:01:34.370 --> 00:01:40.590
thing as 2 to the 1, plus
2 squared, plus 2 cubed.

00:01:40.590 --> 00:01:44.540
That's equal to 2
plus 4 plus 8.

00:01:44.540 --> 00:01:47.800
6 plus 8 is equal to 14.

00:01:47.800 --> 00:01:50.500
That is choice A.

00:01:50.500 --> 00:01:56.730
Next problem, I'll switch
colors for variety.

00:01:56.730 --> 00:02:03.810
Problem number 8, in the xy
plane, the center of a circle

00:02:03.810 --> 00:02:06.820
has the coordinates
3 comma minus 7.

00:02:06.820 --> 00:02:08.750
Let's see if I have
to draw this.

00:02:08.750 --> 00:02:13.990
If one endpoint of a diameter of
the circle is minus 2 comma

00:02:13.990 --> 00:02:21.090
7-- so this is an endpoint of
the diameter, this is center--

00:02:21.090 --> 00:02:23.740
what are the coordinates
of the other

00:02:23.740 --> 00:02:26.670
endpoint of this diameter?

00:02:26.670 --> 00:02:30.080
Well sure, maybe I'll draw it
for you, just so you get a

00:02:30.080 --> 00:02:32.260
sense of all this action
that's going on.

00:02:38.440 --> 00:02:40.600
So the center is 3
comma negative 7.

00:02:40.600 --> 00:02:43.680
So this is 3-- let me
do it in a different

00:02:43.680 --> 00:02:48.470
color-- 3, minus 7.

00:02:48.470 --> 00:02:50.700
So this is the center.

00:02:50.700 --> 00:02:52.755
This one diameter is
at negative 2, 7.

00:03:10.550 --> 00:03:12.640
Actually, I drew this too big.

00:03:12.640 --> 00:03:13.780
So this is one endpoint.

00:03:13.780 --> 00:03:16.820
So actually the circle
is going to be huge.

00:03:16.820 --> 00:03:19.100
Actually let me redraw this
because it's going to be a

00:03:19.100 --> 00:03:19.990
huge circle.

00:03:19.990 --> 00:03:22.655
I didn't do this
appropriately.

00:03:25.900 --> 00:03:30.510
This is the coordinate axes--
I'll draw it big like this.

00:03:30.510 --> 00:03:36.540
So the center-- and I'll do it
in a different color-- the

00:03:36.540 --> 00:03:45.240
center is at 3, then minus 7.

00:03:45.240 --> 00:03:46.300
Right?

00:03:46.300 --> 00:03:50.280
And then one endpoint
is at minus 2.

00:03:50.280 --> 00:03:50.660
Oh no.

00:03:50.660 --> 00:03:51.610
You know what?

00:03:51.610 --> 00:03:52.500
I misread the problem.

00:03:52.500 --> 00:03:55.790
The other endpoint is
at minus 2, minus 7.

00:03:55.790 --> 00:04:01.810
So the other endpoint is
here, minus 2, minus 7.

00:04:01.810 --> 00:04:02.770
So it's here.

00:04:02.770 --> 00:04:04.570
So I could use this graph.

00:04:04.570 --> 00:04:06.840
So the other endpoint
is minus 2, minus 7.

00:04:06.840 --> 00:04:08.445
It shows you how important
it is to read

00:04:08.445 --> 00:04:09.990
these problems properly.

00:04:09.990 --> 00:04:12.840
So if you drew the circle,
the circle actually looks

00:04:12.840 --> 00:04:14.090
something like this.

00:04:18.950 --> 00:04:20.899
The important thing to realize--
and you actually

00:04:20.899 --> 00:04:24.750
didn't even have to draw the
circle-- is that this

00:04:24.750 --> 00:04:27.420
diameter, it. this is
the diameter that

00:04:27.420 --> 00:04:28.760
they're talking about.

00:04:28.760 --> 00:04:32.310
I know I'm drawing it kind of
funny, but this is the point

00:04:32.310 --> 00:04:33.670
right here, 3, minus 7.

00:04:33.670 --> 00:04:35.240
This is minus 2, minus 7.

00:04:35.240 --> 00:04:39.320
So to go from this point to this
point we didn't change

00:04:39.320 --> 00:04:41.330
our y-coordinates.

00:04:41.330 --> 00:04:43.430
We just changed x.

00:04:43.430 --> 00:04:43.970
What did we do?

00:04:43.970 --> 00:04:45.710
We went how far back?

00:04:45.710 --> 00:04:48.990
We went from x equals 3
to x equals minus 2.

00:04:48.990 --> 00:04:51.300
So we went 5 back, right?

00:04:51.300 --> 00:04:53.600
So the other endpoint of the
diameter-- we just have to go

00:04:53.600 --> 00:04:55.840
5 in this direction.

00:04:55.840 --> 00:04:58.950
So if we started x equals
3, we're going to end up

00:04:58.950 --> 00:05:00.840
with x equals 8.

00:05:00.840 --> 00:05:04.440
Then the y is going to stay the
same because we're moving

00:05:04.440 --> 00:05:04.780
horizontally.

00:05:04.780 --> 00:05:07.190
So it's 8, negative 7.

00:05:07.190 --> 00:05:09.520
That is choice E.

00:05:09.520 --> 00:05:12.440
Sorry for misreading it at
first, but that shows it can

00:05:12.440 --> 00:05:13.460
happen to the best of us.

00:05:13.460 --> 00:05:14.280
No, just kidding.

00:05:14.280 --> 00:05:15.720
I'm not even the best of us.

00:05:15.720 --> 00:05:16.970
All right, next problem.

00:05:20.790 --> 00:05:30.110
9, a regulation for riding a
certain amusement park ride

00:05:30.110 --> 00:05:34.110
requires that a child be between
30 inches and 50

00:05:34.110 --> 00:05:35.440
inches tall.

00:05:35.440 --> 00:05:40.280
So between 30, so height has to
be greater than 30 and less

00:05:40.280 --> 00:05:41.920
than 50 inches tall.

00:05:41.920 --> 00:05:42.930
Fair enough.

00:05:42.930 --> 00:05:46.590
Which of the following
inequalities can be used to

00:05:46.590 --> 00:05:50.680
determine whether or not a
child's height satisfies the

00:05:50.680 --> 00:05:52.830
regulation for this ride?

00:05:52.830 --> 00:05:56.600
OK, so they are essentially just
rewriting this equation

00:05:56.600 --> 00:06:00.870
and saying it as
absolute value.

00:06:00.870 --> 00:06:02.670
A number line could probably
be useful here.

00:06:02.670 --> 00:06:07.400
So if I say-- that's my
number line-- this is

00:06:07.400 --> 00:06:11.130
30 and this is 50.

00:06:11.130 --> 00:06:13.770
We know, just from this
inequality, that my height can

00:06:13.770 --> 00:06:15.620
be anywhere around here.

00:06:15.620 --> 00:06:19.440
Whenever I see these absolute
value problems, they're really

00:06:19.440 --> 00:06:22.740
picking kind of a median, or the
middle point, between the

00:06:22.740 --> 00:06:25.760
two, and they're using the
absolute value to say, well my

00:06:25.760 --> 00:06:29.120
distance away from that middle
point can't be more than a

00:06:29.120 --> 00:06:30.210
certain amount.

00:06:30.210 --> 00:06:32.550
So what you can do is you can
pick the middle point.

00:06:32.550 --> 00:06:35.410
If you want to convert this
into an absolute value

00:06:35.410 --> 00:06:38.010
equation, you pick
the middle point.

00:06:38.010 --> 00:06:39.030
So what's the middle point?

00:06:39.030 --> 00:06:41.390
30 plus 50 is 80.

00:06:41.390 --> 00:06:42.780
The middle point is 40, right?

00:06:42.780 --> 00:06:44.430
I should have been able to do it
in my head because it's 10

00:06:44.430 --> 00:06:46.110
away from each other.

00:06:46.110 --> 00:06:48.090
So we can say-- instead of
saying that the height has to

00:06:48.090 --> 00:06:50.580
be greater than 30 or the height
has to be less than

00:06:50.580 --> 00:06:55.750
50-- we could say that the
difference between the height

00:06:55.750 --> 00:07:02.270
and 40, and it's absolute
value-- we don't care if the

00:07:02.270 --> 00:07:05.620
height is less than 40 or
greater than 40-- but that

00:07:05.620 --> 00:07:08.790
absolute distance between
the height and 40 can't

00:07:08.790 --> 00:07:09.605
be more than what?

00:07:09.605 --> 00:07:12.620
Well, we can't go more than 10
to the positive and we can't

00:07:12.620 --> 00:07:14.640
go more than 10 to
the negative.

00:07:14.640 --> 00:07:17.860
So the absolute value has
to be less than 10.

00:07:17.860 --> 00:07:18.415
That's how you should
[? convert ?]

00:07:18.415 --> 00:07:18.600
this.

00:07:18.600 --> 00:07:21.190
If you wanted to convert this
to absolute value, how they

00:07:21.190 --> 00:07:24.810
tend to do it on the SAT, pick
the average point and then

00:07:24.810 --> 00:07:29.150
figure out how far can you
vary from the average?

00:07:29.150 --> 00:07:31.820
The average point was 40, and
you can vary at most 10.

00:07:31.820 --> 00:07:36.850
So the difference between
the height and 40 has to

00:07:36.850 --> 00:07:37.630
be less than 10.

00:07:37.630 --> 00:07:40.860
This could also have been
written as 40 minus h

00:07:40.860 --> 00:07:42.220
is less than 10.

00:07:42.220 --> 00:07:44.490
But the choice is h minus
40 is less than 10, and

00:07:44.490 --> 00:07:48.200
that is choice D.

00:07:48.200 --> 00:07:57.850
Problem 10, a right, circular
cylinder with radius 5 and

00:07:57.850 --> 00:07:59.600
height 4 has volume V.

00:07:59.600 --> 00:08:03.330
In terms of V-- oh
look at that.

00:08:03.330 --> 00:08:04.560
OK.

00:08:04.560 --> 00:08:10.530
So a right, circular cylinder,
so it looks like this.

00:08:10.530 --> 00:08:12.210
That's the base.

00:08:12.210 --> 00:08:16.350
That's the top of
the cylinder.

00:08:16.350 --> 00:08:22.000
Then you have a line like that
and you have a line like that.

00:08:22.000 --> 00:08:23.640
What are they telling us?

00:08:23.640 --> 00:08:26.280
They're telling us
it's radius 5.

00:08:26.280 --> 00:08:34.620
So this distance is 5,
radius 5, height 4.

00:08:34.620 --> 00:08:35.870
The volume is V.

00:08:39.340 --> 00:08:42.150
OK, so the volume is V.

00:08:42.150 --> 00:08:43.250
So what does V equal?

00:08:43.250 --> 00:08:45.850
So V is equal to-- you just
have to figure out

00:08:45.850 --> 00:08:46.986
the area of the space.

00:08:46.986 --> 00:08:48.820
Actually I have a minute left.

00:08:48.820 --> 00:08:51.060
So I'm going to do problem
number 10 in the next video so

00:08:51.060 --> 00:08:52.770
as to not rush


SAT Prep: Test 3 Section 8 Part 4

WEBVTT
Kind: captions
Language: en

00:00:02.210 --> 00:00:02.820
Welcome back.

00:00:02.820 --> 00:00:04.950
We're on problem number 15.

00:00:04.950 --> 00:00:07.155
And I've tried it as best
as I can to draw it.

00:00:07.155 --> 00:00:10.210
And they're pretty much saying--
well, I'll read it--

00:00:10.210 --> 00:00:12.740
Doug's biology experiment
involving timing 12

00:00:12.740 --> 00:00:13.700
hamsters in a maze.

00:00:13.700 --> 00:00:16.079
Each hamster received at
least one practice

00:00:16.079 --> 00:00:17.170
before being timed.

00:00:17.170 --> 00:00:20.390
The scatter plot above shows the
time each hamster took to

00:00:20.390 --> 00:00:22.960
complete the maze and the
corresponding number of

00:00:22.960 --> 00:00:25.450
practices that each
hamster received.

00:00:25.450 --> 00:00:28.360
Based on the data, which of the
following functions best

00:00:28.360 --> 00:00:32.310
models the relationship between
t, the number of

00:00:32.310 --> 00:00:42.230
seconds to complete the maze--
this is the t-axis-- and p,

00:00:42.230 --> 00:00:43.460
the number of practices?

00:00:43.460 --> 00:00:45.090
This is p, the number
of practices.

00:00:45.090 --> 00:00:50.480
So we want to find t
as a function of p.

00:00:50.480 --> 00:00:51.720
So t is a function of p.

00:00:51.720 --> 00:00:55.310
So, one, it looks like the
hamsters didn't learn much

00:00:55.310 --> 00:00:56.310
when they got practice.

00:00:56.310 --> 00:00:59.190
No matter how much practice
they got, the hamsters, it

00:00:59.190 --> 00:01:03.160
looks like they roughly took
about the same amount of time.

00:01:03.160 --> 00:01:07.560
We could try to draw a line
here that fits this curve.

00:01:07.560 --> 00:01:11.020
Maybe it would look something
like this.

00:01:11.020 --> 00:01:13.690
I don't know, something
like that.

00:01:13.690 --> 00:01:16.290
I mean, it's not going to be--
you could try to be cute and

00:01:16.290 --> 00:01:18.160
try to draw something maybe with
a little bit of a slope

00:01:18.160 --> 00:01:20.170
or anything, but I mean, really,
this looks like a flat

00:01:20.170 --> 00:01:21.720
line when you look at it.

00:01:21.720 --> 00:01:23.400
So what would be the equation
of that line?

00:01:23.400 --> 00:01:24.450
Well, the equation of
that line would be

00:01:24.450 --> 00:01:27.680
like 45 or 44 or something.

00:01:27.680 --> 00:01:30.360
So if you said t of p is equal
to-- and actually, they have a

00:01:30.360 --> 00:01:36.180
choice that looks just like
that-- t of p is equal to 44.

00:01:36.180 --> 00:01:39.470
No matter how many practices
the mice got, regardless of

00:01:39.470 --> 00:01:43.130
how many, they on average
take roughly 44 seconds.

00:01:43.130 --> 00:01:47.590
So practice doesn't really help
mice much, as opposed to

00:01:47.590 --> 00:01:49.110
students preparing
for the SAT.

00:01:49.110 --> 00:01:50.820
And all of the other ones
don't make any sense.

00:01:50.820 --> 00:01:52.320
I mean, t of p equals p.

00:01:52.320 --> 00:01:54.490
That would be something
like this.

00:01:54.490 --> 00:01:57.720
Choice A is something like
that, that has no sense.

00:01:57.720 --> 00:02:00.340
No, sorry, choice
A is our answer.

00:02:00.340 --> 00:02:03.350
Choice B looks something
like that.

00:02:03.350 --> 00:02:06.000
Choice C, 44p.

00:02:06.000 --> 00:02:07.220
That will be even
a super steep.

00:02:07.220 --> 00:02:08.690
That makes no sense.

00:02:08.690 --> 00:02:13.660
P/44, that's going to be like
a really shallow graph.

00:02:13.660 --> 00:02:15.780
And then you could
have p plus 44.

00:02:15.780 --> 00:02:18.260
That would start here and then
have a slope of 1, so it would

00:02:18.260 --> 00:02:18.800
look like that.

00:02:18.800 --> 00:02:20.720
So none of the other ones
are even close.

00:02:20.720 --> 00:02:22.150
So it's definitely choice A.

00:02:22.150 --> 00:02:26.060
t of p is equal to 44.

00:02:26.060 --> 00:02:27.310
Last problem.

00:02:29.310 --> 00:02:32.090
And I'll do a new color.

00:02:32.090 --> 00:02:36.230
Problem 16.

00:02:36.230 --> 00:02:41.440
And they drew this thing,
so I have a big square.

00:02:41.440 --> 00:02:52.170
And then we have a
square like that.

00:02:52.170 --> 00:02:54.270
Actually, I should just
use the line tool,

00:02:54.270 --> 00:02:55.470
that would be better.

00:02:55.470 --> 00:02:58.421
A square like that.

00:02:58.421 --> 00:02:59.840
A square like that.

00:03:02.690 --> 00:03:09.161
And then I have a square
like that, roughly.

00:03:09.161 --> 00:03:11.390
It's not perfectly drawn because
these three squares

00:03:11.390 --> 00:03:13.770
look the same, and they tell
us they're the same.

00:03:13.770 --> 00:03:16.132
They tell us that this is W.

00:03:16.132 --> 00:03:17.940
And this is L.

00:03:17.940 --> 00:03:21.940
W, W, W.

00:03:21.940 --> 00:03:24.030
L, L.

00:03:24.030 --> 00:03:27.300
The pattern shown above is
composed of rectangles.

00:03:27.300 --> 00:03:30.510
This pattern is used repeatedly
to completely cover

00:03:30.510 --> 00:03:34.960
a rectangular region 12 units
long and 11 units wide.

00:03:34.960 --> 00:03:47.290
So they're covering a region
that's 12L long and 10L wide.

00:03:47.290 --> 00:03:50.710
So this is like a thumbnail
of the floor.

00:03:50.710 --> 00:03:56.640
How many rectangles of dimension
L by W are needed?

00:04:02.570 --> 00:04:03.290
OK.

00:04:03.290 --> 00:04:05.790
Well, when they say how many
rectangles of dimension L by

00:04:05.790 --> 00:04:07.910
W, that's just each of
these rectangles

00:04:07.910 --> 00:04:08.890
that they drew here.

00:04:08.890 --> 00:04:09.200
Right?

00:04:09.200 --> 00:04:12.650
Because all of these have
dimensions L by W, L by W, L

00:04:12.650 --> 00:04:15.610
by W, L by W, L by W, right?

00:04:15.610 --> 00:04:18.350
So if we could figure out just
how many of these-- this

00:04:18.350 --> 00:04:22.460
pattern has 1, 2, 3, 4, 5
of those on it, right?

00:04:22.460 --> 00:04:26.050
So if we could just figure out
how many of this pattern would

00:04:26.050 --> 00:04:31.330
fit onto this, then
we're done.

00:04:31.330 --> 00:04:34.180
So how can we figure that out?

00:04:34.180 --> 00:04:40.340
So do we know a relationship
between L and W?

00:04:40.340 --> 00:04:41.560
Well, sure.

00:04:41.560 --> 00:04:45.040
We see here that two L's are the
same thing as three W's.

00:04:45.040 --> 00:04:53.900
We know that 2L is equal
to three W's.

00:04:53.900 --> 00:04:56.950
And since all our dimensions
are given in L, let's solve

00:04:56.950 --> 00:04:58.520
for W and substitute.

00:04:58.520 --> 00:05:03.570
So let's say that W is equal
to-- just divide both sides by

00:05:03.570 --> 00:05:08.950
3-- W is equal to 2/3 L.

00:05:08.950 --> 00:05:11.850
All I said is 2L is the
same thing as 3W and I

00:05:11.850 --> 00:05:12.770
divided it by 3.

00:05:12.770 --> 00:05:16.550
So W is equal to 2/3 L.

00:05:16.550 --> 00:05:21.350
So can we represent the height
and the width of this

00:05:21.350 --> 00:05:24.190
rectangle now in terms
of only L's?

00:05:24.190 --> 00:05:24.540
Well, sure.

00:05:24.540 --> 00:05:26.150
What's the height?

00:05:26.150 --> 00:05:29.140
What's the length of
this rectangle?

00:05:29.140 --> 00:05:31.470
Well, the length is definitely
just 2L, right?

00:05:31.470 --> 00:05:32.420
L plus L.

00:05:32.420 --> 00:05:33.530
That's the length.

00:05:33.530 --> 00:05:35.880
And what's the width?

00:05:35.880 --> 00:05:37.690
Well, W is what?

00:05:37.690 --> 00:05:45.320
It's 2/3 L plus L, so what's the
width of this rectangle?

00:05:45.320 --> 00:05:49.310
What's 2/3 of something plus
1 whole of that something?

00:05:49.310 --> 00:05:51.030
Or 2/3 plus 3/3?

00:05:51.030 --> 00:05:56.480
So the width is 5/3 L.

00:05:56.480 --> 00:06:04.920
So each of these rectangles
is 5/3 L by 2L.

00:06:04.920 --> 00:06:06.460
So how many of these rectangles
are we going to

00:06:06.460 --> 00:06:10.030
have to put onto this floor?

00:06:10.030 --> 00:06:11.040
How many total?

00:06:11.040 --> 00:06:16.500
Well, going in this dimension
they have a length of 2L.

00:06:16.500 --> 00:06:21.220
So if we have to-- if they're
2L each, then we're going to

00:06:21.220 --> 00:06:22.620
need six of them, right?

00:06:22.620 --> 00:06:24.900
We're going to need 6
in this direction.

00:06:24.900 --> 00:06:27.330
Because we're going to go a
total distance of 12L, and

00:06:27.330 --> 00:06:28.570
they're 2L each.

00:06:28.570 --> 00:06:30.380
So they're going to be
6 in that direction.

00:06:30.380 --> 00:06:33.500
And how many are we going to
need in this direction?

00:06:33.500 --> 00:06:36.570
Well, we have to go a total
distance of 10L.

00:06:36.570 --> 00:06:39.810
And the width of each
of them is 5/3 L.

00:06:42.320 --> 00:06:44.500
So what's 10 divided by 5/3?

00:06:44.500 --> 00:06:46.360
So the L's cancel out.

00:06:46.360 --> 00:06:50.752
So 10 divided by 5/3 is the same
thing as 10 times 3/5.

00:06:50.752 --> 00:06:53.200
And that just equals 6.

00:06:53.200 --> 00:06:56.130
So we're going to need
6 rectangles in this

00:06:56.130 --> 00:06:57.470
direction as well.

00:06:57.470 --> 00:06:59.650
So how many total rectangles
are we going to need?

00:06:59.650 --> 00:07:05.090
Well, 6 times 6 is equal
to 36 total rectangles.

00:07:05.090 --> 00:07:07.120
And then, how many of these
smaller rectangles

00:07:07.120 --> 00:07:08.030
are in each of these?

00:07:08.030 --> 00:07:10.030
We'll need 36 of this pattern.

00:07:10.030 --> 00:07:10.830
And then how many of the

00:07:10.830 --> 00:07:11.890
rectangles are in that pattern?

00:07:11.890 --> 00:07:12.430
Well, we counted.

00:07:12.430 --> 00:07:13.690
There's 5.

00:07:13.690 --> 00:07:17.180
So we're going to need 5 times
36 total of these smaller

00:07:17.180 --> 00:07:19.090
rectangles.

00:07:19.090 --> 00:07:21.820
So 5 times 36 is what?

00:07:21.820 --> 00:07:23.260
150 plus 30?

00:07:23.260 --> 00:07:25.470
It's 180.

00:07:25.470 --> 00:07:28.070
We will need 180 of these
smaller rectangles.

00:07:28.070 --> 00:07:30.140
So that is choice E.

00:07:30.140 --> 00:07:34.680
And we are done with
this test three.

00:07:34.680 --> 00:07:37.520
I'll see you in test four.


SAT Prep: Test 3 Section 4 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:01.350
Welcome back.

00:00:01.350 --> 00:00:04.940
We are now on section four of
our third test, and so we're

00:00:04.940 --> 00:00:06.480
on page 530.

00:00:06.480 --> 00:00:08.890
And let's start with
problem number one.

00:00:11.620 --> 00:00:19.340
If s plus t is equal to 3,
what is the value of s

00:00:19.340 --> 00:00:23.400
plus t minus 6?

00:00:23.400 --> 00:00:26.480
Well, we know that s plus t is
equal to 3, so they're just

00:00:26.480 --> 00:00:28.250
asking us what is 3 minus 6.

00:00:28.250 --> 00:00:31.600
Well 3 minus 6 is minus 3.

00:00:31.600 --> 00:00:32.850
And that is choice A.

00:00:35.340 --> 00:00:36.590
Number two.

00:00:39.430 --> 00:00:43.130
They have a box on the cube.

00:00:43.130 --> 00:00:44.800
Let me see if I can
draw this box.

00:00:44.800 --> 00:00:53.370
So it looks like, and then the
back side's like this, and

00:00:53.370 --> 00:01:00.650
then let me draw a little
dotted-- And then the sides

00:01:00.650 --> 00:01:13.160
are A-- let me do that in a
different color-- A, B, C, D,

00:01:13.160 --> 00:01:17.240
E, P, and Q.

00:01:17.240 --> 00:01:20.800
And they say, on the cube in the
figure above, each of the

00:01:20.800 --> 00:01:24.270
following points is the same
distance from P as

00:01:24.270 --> 00:01:26.030
it is from Q except?

00:01:26.030 --> 00:01:27.580
And these are all the choices.

00:01:27.580 --> 00:01:31.520
A, B, C, D, and E.

00:01:31.520 --> 00:01:34.950
So we want to look for a point
that isn't the same distance

00:01:34.950 --> 00:01:37.370
from P as it is from Q.

00:01:37.370 --> 00:01:41.610
A is one edge from P and one
edge from Q, so it's not A.

00:01:41.610 --> 00:01:48.050
B is two edges from P no
matter how you go.

00:01:48.050 --> 00:01:50.800
And it is also two edges from
Q no matter how you go, so

00:01:50.800 --> 00:01:52.490
it's not B.

00:01:52.490 --> 00:02:01.720
C is one edge from Q, but to get
to P you gotta go at least

00:02:01.720 --> 00:02:02.950
three edges.

00:02:02.950 --> 00:02:04.890
1, 2, 3, to go to C.

00:02:04.890 --> 00:02:05.640
So it's going to be C.

00:02:05.640 --> 00:02:08.590
C is much closer to Q than
it is to P, so it is

00:02:08.590 --> 00:02:10.050
not the same distance.

00:02:10.050 --> 00:02:11.170
So our choice is C.

00:02:11.170 --> 00:02:12.210
C is C.

00:02:12.210 --> 00:02:13.160
All right.

00:02:13.160 --> 00:02:14.410
Problem number three.

00:02:18.020 --> 00:02:20.200
And I'll switch to a
less tacky color.

00:02:20.200 --> 00:02:22.910
Problem number three.

00:02:22.910 --> 00:02:25.860
Oh boy, there's all sorts
of stuff to draw.

00:02:25.860 --> 00:02:26.950
Maybe I won't draw it.

00:02:26.950 --> 00:02:28.050
Let's see if I can get
by without drawing.

00:02:28.050 --> 00:02:30.930
The bar graph above shows where
fraud is committed on

00:02:30.930 --> 00:02:31.470
the internet.

00:02:31.470 --> 00:02:34.690
Which of the following circle
graphs most accurately

00:02:34.690 --> 00:02:37.340
displays the same graph?

00:02:37.340 --> 00:02:37.830
Well I'll try it.

00:02:37.830 --> 00:02:41.260
So they say websites.

00:02:41.260 --> 00:02:46.060
Websites is this huge number.

00:02:46.060 --> 00:02:51.050
Websites, that's 78%.

00:02:51.050 --> 00:02:55.460
Let me say that that is
this purple color.

00:02:55.460 --> 00:02:57.640
Actually I should do this
with the rectangle too.

00:02:57.640 --> 00:03:00.970
The websites is a purple color,
and then let's say that

00:03:00.970 --> 00:03:11.580
email is, well I'll do it
this color, at 18%.

00:03:11.580 --> 00:03:20.760
And then they tell us that news
groups is 2%, so it's a

00:03:20.760 --> 00:03:24.200
really small percentage, 2%.

00:03:24.200 --> 00:03:30.450
And then finally, they tell
us that other is also 2%.

00:03:35.070 --> 00:03:37.840
And then you want to see a pie
graph that's the same thing.

00:03:37.840 --> 00:03:42.080
So if this is the pie graph.

00:03:42.080 --> 00:03:44.360
So 78% is going to
be this purple,

00:03:44.360 --> 00:03:46.200
it's going to be websites.

00:03:46.200 --> 00:03:48.670
So that's a little bit
more than 3/4, right?

00:03:48.670 --> 00:03:51.420
78% is 3% more than 3/4.

00:03:51.420 --> 00:03:52.460
3/4 would look like this.

00:03:52.460 --> 00:03:55.400
A little bit more than
3/4 is going to look

00:03:55.400 --> 00:03:57.130
something like this.

00:03:57.130 --> 00:03:57.610
Oh, oops.

00:03:57.610 --> 00:04:01.750
I'm still using the line tool.

00:04:01.750 --> 00:04:06.920
But a little bit more than
3/4 is going to look

00:04:06.920 --> 00:04:08.170
something like this.

00:04:14.770 --> 00:04:18.390
And then I can actually
even fill it.

00:04:18.390 --> 00:04:20.430
That's going to be a little
bit more than 3/4.

00:04:20.430 --> 00:04:26.380
And then the blue stuff, 18%,
that's going to look

00:04:26.380 --> 00:04:29.260
something like 18%.

00:04:29.260 --> 00:04:35.000
That's a little less than 25%,
so it's going to be like that.

00:04:35.000 --> 00:04:36.550
So we could fill that too.

00:04:45.040 --> 00:04:47.150
The other pieces are going to
be these thin slivers like

00:04:47.150 --> 00:04:49.100
this, 2% and 2%.

00:04:54.360 --> 00:04:57.290
This is really just translating
that into this.

00:04:57.290 --> 00:04:58.860
And they're actually going
to be even thinner than

00:04:58.860 --> 00:04:59.970
the way I drew it.

00:04:59.970 --> 00:05:04.020
And out of all the choices, the
one that has this purple

00:05:04.020 --> 00:05:07.560
region, websites, the dark
region on the graph.

00:05:07.560 --> 00:05:12.920
The only one that has that,
where it's more than 3/4, are

00:05:12.920 --> 00:05:15.120
choices C and D, right?

00:05:15.120 --> 00:05:20.000
That's the only one where it
has more than 75% is shaded

00:05:20.000 --> 00:05:20.930
the websites' color.

00:05:20.930 --> 00:05:22.640
It's either going
to be C or D.

00:05:22.640 --> 00:05:25.700
And then when you look at the
difference between C and D,

00:05:25.700 --> 00:05:28.830
choice C has nothing
for other in there.

00:05:28.830 --> 00:05:31.880
Choice C just has news
groups, no other.

00:05:31.880 --> 00:05:35.370
So it has to be D, because
news groups and other are

00:05:35.370 --> 00:05:36.120
actually same size.

00:05:36.120 --> 00:05:37.610
So they should be the
same proportions.

00:05:37.610 --> 00:05:40.640
So the choice is D.

00:05:40.640 --> 00:05:41.890
Next problem.

00:05:45.910 --> 00:05:47.980
Problem number four.

00:05:47.980 --> 00:05:51.380
The numerator of a certain
fraction is 5 less than the

00:05:51.380 --> 00:05:53.440
denominator.

00:05:53.440 --> 00:05:55.850
So let's say that the
denominator is x.

00:05:55.850 --> 00:06:00.000
The numerator is 5 less than
the denominator, so the

00:06:00.000 --> 00:06:01.950
numerator is x minus 5.

00:06:01.950 --> 00:06:04.230
The numerator is 5 less
than the denominator.

00:06:04.230 --> 00:06:07.880
And they say the fraction
is equal to 3/4.

00:06:07.880 --> 00:06:10.160
What is the denominator
of this fraction?

00:06:10.160 --> 00:06:12.010
So we just solve for x.

00:06:12.010 --> 00:06:13.580
So let's cross multiply.

00:06:13.580 --> 00:06:18.310
x times 3, so 3x, is equal
4 times x minus 5.

00:06:22.580 --> 00:06:29.220
So 3x is equal to 4x minus 20.

00:06:29.220 --> 00:06:30.940
And you can subtract.

00:06:30.940 --> 00:06:35.280
So you get 20 is equal to,
subtract 3x from both sides,

00:06:35.280 --> 00:06:38.240
is equal to x, and that's
the denominator.

00:06:38.240 --> 00:06:41.830
So that is choice D.

00:06:41.830 --> 00:06:44.200
The next problem has a bunch
of drawing for me to do.

00:06:44.200 --> 00:06:47.090
Let's see if I can finish
it in time.

00:06:47.090 --> 00:06:49.900
So we have the two axes.

00:06:49.900 --> 00:06:51.295
Let me draw the two axes.

00:06:51.295 --> 00:06:56.060
This is a big problem,
so I'll draw it big.

00:06:56.060 --> 00:07:04.990
I've got the two axes, and then
it goes from k to 6k.

00:07:07.640 --> 00:07:15.570
k, 2k, 3k, 4k, 5k, 6k.

00:07:15.570 --> 00:07:19.442
6k, 5k, 4k, 3k, you
get the point.

00:07:19.442 --> 00:07:21.230
And then it goes from 1 to 6.

00:07:21.230 --> 00:07:28.890
1, 2, 3, 4, 5, 6.

00:07:28.890 --> 00:07:32.680
And then the triangle looks like
it goes from-- if I were

00:07:32.680 --> 00:07:36.284
to draw a line-- it goes
from 2k to 6k, and

00:07:36.284 --> 00:07:37.840
then from 2 to 6.

00:07:40.640 --> 00:07:44.258
They actually draw the line
like this, 2k it is.

00:07:44.258 --> 00:07:45.900
This is a triangle.

00:07:45.900 --> 00:07:48.590
I don't know if I'll have time
to do it in this video, but

00:07:48.590 --> 00:07:50.280
everything should work out.

00:07:50.280 --> 00:08:02.050
The triangle goes from 2k to 5k,
good thing I caught that,

00:08:02.050 --> 00:08:03.300
and it's at 0.2.

00:08:05.445 --> 00:08:06.695
That's its base.

00:08:09.260 --> 00:08:11.620
And then it goes up to
6, where it kind

00:08:11.620 --> 00:08:12.475
of is in the middle.

00:08:12.475 --> 00:08:13.795
It goes up to here.

00:08:18.170 --> 00:08:19.940
This is what the triangle
looks like.

00:08:19.940 --> 00:08:22.920
I have redrawn the problem.

00:08:22.920 --> 00:08:28.150
And this is B, A, C.

00:08:28.150 --> 00:08:31.370
And they say, in the figure
above, the scale on the x-axis

00:08:31.370 --> 00:08:34.270
is different from the
scale on the y-axis.

00:08:34.270 --> 00:08:41.566
If the area of triangle ABC is
18, what is the value of k?

00:08:41.566 --> 00:08:43.270
The area is 18.

00:08:43.270 --> 00:08:48.990
So area is equal to 1/2 base
times height for a triangle.

00:08:48.990 --> 00:08:50.930
We know that the area is 18.

00:08:50.930 --> 00:08:53.810
So 18 is equal to 1/2.

00:08:53.810 --> 00:08:55.230
What's the base?

00:08:55.230 --> 00:08:59.710
Well we went from 2k to 5k.

00:08:59.710 --> 00:09:01.030
So we went 3k.

00:09:01.030 --> 00:09:02.880
We went 1, 2, 3.

00:09:02.880 --> 00:09:03.700
We went 3k.

00:09:03.700 --> 00:09:06.430
So the base is 3k.

00:09:06.430 --> 00:09:07.810
And what's the height?

00:09:07.810 --> 00:09:09.260
Well from 2 to 6.

00:09:09.260 --> 00:09:12.540
So the height is 4, and we
just saw solve for k.

00:09:12.540 --> 00:09:20.330
So 18 is equal to 1/2 times 4 is
2 times 3k is equal to 6k.

00:09:20.330 --> 00:09:22.880
k is equal to 3.

00:09:22.880 --> 00:09:25.040
And that is choice E.

00:09:25.040 --> 00:09:26.200
And we are done.

00:09:26.200 --> 00:09:28.700
You just have to know area is
equal to 1/2 base times

00:09:28.700 --> 00:09:31.750
height, and then just put in the
base, which is 3k, and the

00:09:31.750 --> 00:09:33.840
height, and solve for k.

00:09:33.840 --> 00:09:35.890
I'll see you in the
next video.


SAT Prep: Test 3 Section 4 Part 2

WEBVTT
Kind: captions
Language: en

00:00:01.470 --> 00:00:04.840
Problem number six.

00:00:04.840 --> 00:00:05.530
That's too skinny.

00:00:05.530 --> 00:00:07.140
I want to use this tool.

00:00:07.140 --> 00:00:08.620
Problem number six.

00:00:08.620 --> 00:00:12.210
I had to restart my computer,
so everything got reset.

00:00:12.210 --> 00:00:17.730
If m and k are positive, it's
fairly complicated.

00:00:17.730 --> 00:00:27.820
And they that 10m squared k to
the negative 1 is equal to

00:00:27.820 --> 00:00:40.580
100m, what is m to the negative
1 in terms of k?

00:00:40.580 --> 00:00:44.340
Let's see if we can simplify
that thing I wrote at the top.

00:00:44.340 --> 00:00:48.730
k to the negative one
is equal to 100m.

00:00:48.730 --> 00:00:54.830
Well let's divide both sides
by 10, you get m squared.

00:00:54.830 --> 00:00:57.110
k to the negative one-- that's
the same thing as m squared

00:00:57.110 --> 00:01:00.360
over k-- is equal to, and we
divide the other side by ten,

00:01:00.360 --> 00:01:02.070
is equal to 10m.

00:01:02.070 --> 00:01:05.360
Let's divide both sides by m,
and they're positive, so we

00:01:05.360 --> 00:01:06.130
can do that.

00:01:06.130 --> 00:01:06.870
So it's not 0.

00:01:06.870 --> 00:01:12.070
So you get m over k is equal
to 10, because m squared

00:01:12.070 --> 00:01:19.550
divided by m is just 10.

00:01:19.550 --> 00:01:24.050
m is equal to 10k.

00:01:24.050 --> 00:01:26.720
But they don't want us to figure
out what m is in terms

00:01:26.720 --> 00:01:28.490
of k, they want to know
m to negative one.

00:01:28.490 --> 00:01:31.010
Well m to the negative 1 is just
1 over m, so if we just

00:01:31.010 --> 00:01:34.450
invert both sides of this, we
know that 1 over m is equal to

00:01:34.450 --> 00:01:37.320
1 over 10k.

00:01:37.320 --> 00:01:38.880
That's the same thing,
of course, as m to

00:01:38.880 --> 00:01:40.450
the negative 1.

00:01:40.450 --> 00:01:44.630
And 1 over 10k, that's
choice D.

00:01:44.630 --> 00:01:46.090
Problem number seven.

00:01:48.970 --> 00:01:52.080
We are on problem number
seven, that

00:01:52.080 --> 00:01:53.570
I will do in mauve.

00:01:53.570 --> 00:01:57.040
Edna and Nancy leave the house
for a common friend at the

00:01:57.040 --> 00:01:59.800
same time, and walk
for 4 hours.

00:01:59.800 --> 00:02:02.700
4 hours is how far they walk.

00:02:02.700 --> 00:02:06.450
Edna walks due east at
the average rate of 4

00:02:06.450 --> 00:02:07.740
kilometers per hour.

00:02:20.810 --> 00:02:23.632
Nancy walks due north
at an average of 3

00:02:23.632 --> 00:02:25.496
kilometers per hour.

00:02:37.330 --> 00:02:39.190
I'm doing this a little bit
messy, but you get the point.

00:02:39.190 --> 00:02:43.710
Nancy's going north, Edna's
going east. What is the

00:02:43.710 --> 00:02:48.070
straight-line distance between
them in kilometers at the end

00:02:48.070 --> 00:02:50.860
of 4 hours?

00:02:50.860 --> 00:02:53.390
So this is Pythagorean
theorem.

00:02:53.390 --> 00:02:58.630
At the end of 4 hours, how far
has Edna traveled east?

00:02:58.630 --> 00:03:00.870
They're starting at the same
point, oh I don't like that.

00:03:04.750 --> 00:03:08.180
How far has Edna gone east?

00:03:08.180 --> 00:03:10.480
Well, she's going to be
going 4 kilometers per

00:03:10.480 --> 00:03:17.290
hour times 4 hours.

00:03:17.290 --> 00:03:21.160
And that equals 16 kilometers.

00:03:21.160 --> 00:03:24.690
That's how far Edna went
east. Now how far

00:03:24.690 --> 00:03:28.740
did Nancy go north?

00:03:28.740 --> 00:03:32.720
Well she went at, oh my god
I was using the line tool.

00:03:35.720 --> 00:03:36.970
Undo.

00:03:42.230 --> 00:03:46.530
So same thing, she went north
at 3 kilometers per

00:03:46.530 --> 00:03:50.890
hour times 4 hours.

00:03:50.890 --> 00:03:54.540
So she traveled 12 kilometers.

00:03:54.540 --> 00:03:57.870
This is a Pythagorean
theorem problem.

00:03:57.870 --> 00:04:01.190
After 4 hours, Nancy's
there, Edna's there.

00:04:01.190 --> 00:04:03.200
And you just need to figure out
the straight-line distance

00:04:03.200 --> 00:04:05.000
between them.

00:04:05.000 --> 00:04:06.250
We just have to figure
out this.

00:04:08.960 --> 00:04:14.330
And actually, a trick to this,
let's say that we want to

00:04:14.330 --> 00:04:17.620
solve for x, you could say that
x squared is equal to 12

00:04:17.620 --> 00:04:21.899
squared plus 16 squared.

00:04:21.899 --> 00:04:23.570
And you could figure it out.

00:04:23.570 --> 00:04:29.140
Or you can make the further
realization that this is

00:04:29.140 --> 00:04:31.590
essentially a 3,
4, 5 triangle.

00:04:31.590 --> 00:04:35.580
You could say that this is 4
times 4, this is 3 times 4, so

00:04:35.580 --> 00:04:39.100
this side is going
to be 5 times 4.

00:04:39.100 --> 00:04:42.050
If you remember your 3, 4, 5
triangle, Pythagorean theorem.

00:04:42.050 --> 00:04:43.610
If you don't, just do this.

00:04:43.610 --> 00:04:49.640
You get x squared is equal
to 144 plus 256.

00:04:49.640 --> 00:04:53.500
So x squared is equal to
400, and then you get

00:04:53.500 --> 00:04:54.270
x is equal to 20.

00:04:54.270 --> 00:04:56.330
So you could do it either way,
this would have been a little

00:04:56.330 --> 00:04:57.510
bit less math.

00:04:57.510 --> 00:05:02.510
So x is equal to 20,
so it is choice E.

00:05:07.790 --> 00:05:11.000
East, the other one
walks north.

00:05:11.000 --> 00:05:12.250
This is choice E.

00:05:16.050 --> 00:05:17.600
Problem number eight.

00:05:17.600 --> 00:05:20.790
I'm using an old workbook that
was used by my cousin when she

00:05:20.790 --> 00:05:22.200
was in seventh grade.

00:05:22.200 --> 00:05:25.370
She's now in tenth grade, and
she's marked up some of these

00:05:25.370 --> 00:05:27.760
problems. So I have a little
bit trouble reading.

00:05:27.760 --> 00:05:29.870
And she was only in seventh
grade, but some of the

00:05:29.870 --> 00:05:32.130
problems are circled incorrect
so that's what's making me

00:05:32.130 --> 00:05:34.360
second guess myself every
now and then.

00:05:34.360 --> 00:05:36.930
But anyway, back to the
problems. She now doesn't get

00:05:36.930 --> 00:05:40.040
any problems incorrect,
back to the problem.

00:05:43.100 --> 00:05:44.950
She's actually the reason why I
started doing this, because

00:05:44.950 --> 00:05:48.510
I worked with her, and
she saw improvement.

00:05:48.510 --> 00:05:50.020
And then I worked with her
brother, and they saw

00:05:50.020 --> 00:05:50.130
improvement.

00:05:50.130 --> 00:05:52.700
And then I said, well let me
just make a bunch of videos,

00:05:52.700 --> 00:05:55.626
so a bunch of people can
see some improvement.

00:05:55.626 --> 00:05:57.830
So let's see what they
have drawn here for

00:05:57.830 --> 00:05:59.200
problem number eight.

00:05:59.200 --> 00:06:00.450
So let me draw the x-axis.

00:06:03.040 --> 00:06:06.030
Let me draw the y-axis.

00:06:06.030 --> 00:06:08.800
And then they drew a parabola.

00:06:08.800 --> 00:06:11.090
The figure above shows the graph
of a quadratic function

00:06:11.090 --> 00:06:13.235
that has a minimum
at point 1, 1.

00:06:13.235 --> 00:06:17.655
At the point 1 comma 1, it
has its minimum point.

00:06:17.655 --> 00:06:19.485
Let me do that in a
different color.

00:06:19.485 --> 00:06:22.130
That's the minimum
point there.

00:06:22.130 --> 00:06:26.430
If f of b is equal to f of 3,
which of the following could

00:06:26.430 --> 00:06:29.660
be the value of b?

00:06:29.660 --> 00:06:32.690
So on the graph they drew,
if you go to 3.

00:06:32.690 --> 00:06:37.350
1, 2, 3, and if you
just follow up.

00:06:37.350 --> 00:06:41.910
You go to 1, 2, 3, 4,
5, so you go up 5.

00:06:44.510 --> 00:06:52.630
1, 2, 3, 4, 5, there's
a point here.

00:06:52.630 --> 00:06:54.910
And at least this side of the
parabola, or the quadratic,

00:06:54.910 --> 00:06:58.460
goes something like this.

00:06:58.460 --> 00:07:00.300
I'm trying to draw as carefully
as possible.

00:07:00.300 --> 00:07:01.850
And the other side
is symmetric.

00:07:01.850 --> 00:07:03.380
It'll do the same thing.

00:07:08.560 --> 00:07:13.760
And they say f of b is
equal to f of 3.

00:07:13.760 --> 00:07:16.690
So f of 3 is here, and if you
want to get the exact number

00:07:16.690 --> 00:07:18.630
it's f of 3 is equal to 5.

00:07:18.630 --> 00:07:20.440
But that actually doesn't
even matter.

00:07:20.440 --> 00:07:24.300
Because this is 1, this
is the point 1, 1.

00:07:24.300 --> 00:07:27.460
This is the point, this
is x is equal to 3.

00:07:27.460 --> 00:07:30.290
And the big realization is, well
this is a quadratic, this

00:07:30.290 --> 00:07:32.610
is a parabola, this is
it's minimum point.

00:07:32.610 --> 00:07:36.450
So it's going to be symmetric
around this point.

00:07:36.450 --> 00:07:44.160
So if it reaches 5 here, so it
took 2 units to reach 5 going

00:07:44.160 --> 00:07:46.690
to the right, going in the
positive x direction.

00:07:46.690 --> 00:07:51.230
So similarly, it's going to take
2 units to reach 5 going

00:07:51.230 --> 00:07:54.180
in the negative x direction.

00:07:54.180 --> 00:07:56.450
So what's 2 units less than 1?

00:07:56.450 --> 00:07:58.750
So 1, 2, you'd get
to negative 1.

00:07:58.750 --> 00:08:01.230
So at b could be equal
to negative 1.

00:08:01.230 --> 00:08:04.450
Actually b would be equal
to negative 1.

00:08:04.450 --> 00:08:06.800
So the correct answer is C.

00:08:06.800 --> 00:08:10.356
The choice is b is equal
to negative 1.

00:08:10.356 --> 00:08:12.960
Let's see if I can squeeze
in problem number nine.

00:08:17.650 --> 00:08:18.900
Problem number nine.

00:08:21.150 --> 00:08:25.400
A family of 5 is planning
a 4-day camping trip.

00:08:25.400 --> 00:08:30.260
So 5 people times 4 days.

00:08:30.260 --> 00:08:34.330
Each person will need 1
bottle of water for

00:08:34.330 --> 00:08:36.120
each day of the trip.

00:08:36.120 --> 00:08:39.549
So times 1 bottle per
day, per person.

00:08:39.549 --> 00:08:43.640
If water is sold only in
3-bottle packages, how many

00:08:43.640 --> 00:08:46.490
packages must the family
buy for the trip?

00:08:46.490 --> 00:08:48.670
Well how much water
do they need?

00:08:48.670 --> 00:08:51.540
There's 5 people, 4 days, and
they each need a bottle of

00:08:51.540 --> 00:08:52.460
water a day.

00:08:52.460 --> 00:08:57.220
So they need 20 bottles.

00:08:57.220 --> 00:09:01.090
And it only comes in packages
of 3, or multiples of 3.

00:09:01.090 --> 00:09:03.275
If they bought 6 packages it
would be 18 bottles, that's

00:09:03.275 --> 00:09:03.780
not enough.

00:09:03.780 --> 00:09:05.330
So they have to get
7 packages.

00:09:05.330 --> 00:09:09.570
7 packages times 3 is equal to
21 bottles, so they have to

00:09:09.570 --> 00:09:11.180
buy 7 packages.

00:09:11.180 --> 00:09:12.670
Not too bad.

00:09:12.670 --> 00:09:13.340
All right.

00:09:13.340 --> 00:09:15.180
I'll do the next problem
in the next video.

00:09:15.180 --> 00:09:16.790
I'll see you soon.


SAT Prep: Test 3 Section 4 Part 3

WEBVTT
Kind: captions
Language: en

00:00:02.110 --> 00:00:02.480
All right.

00:00:02.480 --> 00:00:06.390
We are on problem number ten.

00:00:06.390 --> 00:00:12.460
This says the absolute value of
10 minus k is equal to 3.

00:00:12.460 --> 00:00:17.114
And that we know that the
absolute value of k minus 5 is

00:00:17.114 --> 00:00:18.330
equal to 8.

00:00:18.330 --> 00:00:20.870
And they say, what is the value
of k that satisfies both

00:00:20.870 --> 00:00:22.570
equations above?

00:00:22.570 --> 00:00:23.680
Well let's do the first one.

00:00:23.680 --> 00:00:25.850
The absolute value of 10
minus k is equal to 3.

00:00:25.850 --> 00:00:32.750
That tells us that 10 minus k
is equal to 3, or 10 minus k

00:00:32.750 --> 00:00:34.410
is equal to minus 3.

00:00:37.470 --> 00:00:41.710
If 10 minus k is 3, just based
on the first equation alone, I

00:00:41.710 --> 00:00:42.940
get k is equal to 7.

00:00:42.940 --> 00:00:44.620
10 minus 7 is equal to 3.

00:00:44.620 --> 00:00:47.430
And here, k is equal to 13.

00:00:47.430 --> 00:00:50.620
So just on this first
constraint, we have k is equal

00:00:50.620 --> 00:00:52.400
to 7 or 13.

00:00:52.400 --> 00:00:54.113
So now let's do the second
constraint, and

00:00:54.113 --> 00:00:55.770
I'll do it in yellow.

00:00:55.770 --> 00:00:57.175
So k minus 5 is 8.

00:01:00.190 --> 00:01:03.470
That absolute value is equal to
8, so it's either k minus 5

00:01:03.470 --> 00:01:09.480
is equal to 8, or k minus
5 is equal to minus 8.

00:01:09.480 --> 00:01:12.770
If k minus 5 is 8,
then k is 13.

00:01:12.770 --> 00:01:16.630
If k minus 5 is equal to minus
8, then that means k is equal

00:01:16.630 --> 00:01:18.240
to minus 3.

00:01:18.240 --> 00:01:25.110
In order for k to satisfy both
of this equations, I've just

00:01:25.110 --> 00:01:26.570
kind of solved it.

00:01:26.570 --> 00:01:28.650
What k satisfies both
of these equations?

00:01:28.650 --> 00:01:31.580
Well 7 only satisfies the first
one, and negative 3 only

00:01:31.580 --> 00:01:32.480
satisfies the second one.

00:01:32.480 --> 00:01:35.870
But 13, k equals 13,
satisfies both.

00:01:35.870 --> 00:01:38.200
So that is your answer.

00:01:38.200 --> 00:01:40.060
13.

00:01:40.060 --> 00:01:41.310
Next problem.

00:01:43.310 --> 00:01:44.810
Problem number eleven.

00:01:44.810 --> 00:01:46.060
I've gotta do some drawing.

00:01:51.060 --> 00:01:52.530
I think I'm going to go
for a walk after this.

00:01:52.530 --> 00:01:56.010
I need to work off
that turkey.

00:01:56.010 --> 00:02:02.850
I have a line here,
that's line M.

00:02:02.850 --> 00:02:08.119
I have line L, something
like that.

00:02:08.119 --> 00:02:11.480
And then I have this
perpendicular line,

00:02:11.480 --> 00:02:14.220
up here like that.

00:02:14.220 --> 00:02:15.330
And then what do they tell us?

00:02:15.330 --> 00:02:16.580
They tell us that this
is perpendicular.

00:02:19.520 --> 00:02:20.430
Let me switch colors.

00:02:20.430 --> 00:02:24.940
They tell us that this
is 65 degrees.

00:02:24.940 --> 00:02:31.560
They tell us that this, right
here, is x degrees.

00:02:31.560 --> 00:02:33.170
Oh, and there's another
line there, I

00:02:33.170 --> 00:02:34.690
haven't even drawn it.

00:02:34.690 --> 00:02:40.050
There's another line, that I
haven't drawn, that is this.

00:02:40.050 --> 00:02:41.645
Switching back to the green.

00:02:46.050 --> 00:02:51.630
This is 20 degrees,
and so this is x.

00:02:51.630 --> 00:02:55.390
x is just this thing right here,
not this whole thing.

00:02:55.390 --> 00:02:58.900
This is 20 degrees.

00:02:58.900 --> 00:03:03.370
What is the value of x
in the figure above?

00:03:03.370 --> 00:03:07.320
So we just gotta do what I like
to affectionately call

00:03:07.320 --> 00:03:10.630
the angle game.

00:03:10.630 --> 00:03:12.610
And the angle game, I just try
to figure out as many angles

00:03:12.610 --> 00:03:13.530
as I can figure out.

00:03:13.530 --> 00:03:16.360
So what is the measure
of this angle?

00:03:16.360 --> 00:03:18.880
Well this angle and this angle
are complementary.

00:03:18.880 --> 00:03:20.420
They add up to 90 degrees.

00:03:20.420 --> 00:03:23.810
We know this is 90, so this
whole thing is 90.

00:03:23.810 --> 00:03:37.130
So if this and this add up
to 90, what is this?

00:03:37.130 --> 00:03:39.210
25 plus 65 is 90, correct?

00:03:39.210 --> 00:03:40.100
Yes.

00:03:40.100 --> 00:03:42.740
You can tell addition
is my weak point.

00:03:42.740 --> 00:03:45.870
So this is 25 degrees,
this is 20 degrees.

00:03:45.870 --> 00:03:46.980
Can we figure out x?

00:03:46.980 --> 00:03:48.020
Well, sure.

00:03:48.020 --> 00:03:51.090
We know that all of these 3
angles combined have to add up

00:03:51.090 --> 00:03:52.710
to 180 now.

00:03:52.710 --> 00:03:55.630
Because they're all kind of
collectively supplementry.

00:03:55.630 --> 00:03:57.520
You go around, you go halfway
around the circle.

00:03:57.520 --> 00:04:04.611
So we know that x plus 20
plus 25 is equal 180.

00:04:04.611 --> 00:04:08.160
x plus 45 is equal to 180.

00:04:08.160 --> 00:04:13.762
So x is equal to, this is where
I always mess up, so x

00:04:13.762 --> 00:04:16.140
is equal to 135.

00:04:16.140 --> 00:04:18.740
So that's our answer.

00:04:18.740 --> 00:04:19.990
Next problem.

00:04:33.460 --> 00:04:36.450
So number twelve.

00:04:36.450 --> 00:04:39.250
That last problem was one that
my cousin had marked up pretty

00:04:39.250 --> 00:04:42.720
incorrectly, so I had to take
some pause just to make sure I

00:04:42.720 --> 00:04:44.250
didn't mark it up incorrectly.

00:04:44.250 --> 00:04:44.550
OK.

00:04:44.550 --> 00:04:45.400
Problem number twelve.

00:04:45.400 --> 00:04:53.320
The median of a set of 9
consecutive integers is 42.

00:04:53.320 --> 00:04:56.500
What is the greatest
of these integers?

00:04:56.500 --> 00:05:01.230
So the median of 9 consecutive
integers is 42.

00:05:01.230 --> 00:05:07.160
So 42 is the middle number,
and there's

00:05:07.160 --> 00:05:08.900
9 consecutive numbers.

00:05:12.290 --> 00:05:14.560
How many numbers are going
to be greater than 42?

00:05:14.560 --> 00:05:16.100
Median means middle.

00:05:16.100 --> 00:05:28.870
So that means there are
4 greater and 4 less.

00:05:28.870 --> 00:05:29.900
Because there's a total
of 9 numbers.

00:05:29.900 --> 00:05:33.070
4 less, 42, and then
4 greater.

00:05:33.070 --> 00:05:34.572
And they're consecutive numbers,
so what are going to

00:05:34.572 --> 00:05:36.170
be the 4 numbers greater
that it?

00:05:36.170 --> 00:05:40.370
Well 43, 44, 45, 46.

00:05:40.370 --> 00:05:43.950
The question asks us, what is
the greatest of the numbers?

00:05:43.950 --> 00:05:47.010
Well sure, it's going
to be 46.

00:05:47.010 --> 00:05:48.660
And you could have written out
all the numbers, but you know

00:05:48.660 --> 00:05:52.190
42 is the middle, there are 4
greater and 4 less, just do 4.

00:05:52.190 --> 00:05:53.900
It saves you a little time.

00:05:53.900 --> 00:05:55.715
Problem number thirteen.

00:06:01.560 --> 00:06:07.010
Let the function f be
defined by f of x is

00:06:07.010 --> 00:06:12.260
equal to x plus 1.

00:06:12.260 --> 00:06:14.610
If 2f of p is equal to 20.

00:06:14.610 --> 00:06:20.660
So 2 times f of p
is equal to 20.

00:06:20.660 --> 00:06:23.840
What is the value of f of 3p?

00:06:23.840 --> 00:06:25.370
This looks fun.

00:06:25.370 --> 00:06:30.200
So 2 times f of p is equal
to 20, what is f of 3p?

00:06:30.200 --> 00:06:33.990
So let's evaluate
2 times f of p.

00:06:33.990 --> 00:06:44.520
2 times f of p, well that
equals 2 times p plus 1.

00:06:44.520 --> 00:06:46.760
We know that equals 20.

00:06:46.760 --> 00:06:51.000
And so you know that 2p plus 2,
I just distributed the 2,

00:06:51.000 --> 00:06:53.300
is equal to 20.

00:06:53.300 --> 00:06:58.790
2p is equal to 18,
p is equal to 9.

00:06:58.790 --> 00:07:01.080
We just solve for p.

00:07:01.080 --> 00:07:02.880
They're just trying to confuse
you with notation.

00:07:02.880 --> 00:07:04.330
There's nothing really
that fancy here.

00:07:04.330 --> 00:07:06.440
It's a very simple equation
to solve.

00:07:06.440 --> 00:07:09.860
And once you know p equals 9,
then we say f of 3p, that's

00:07:09.860 --> 00:07:13.410
the same thing, because
p equals 9, f of 27.

00:07:13.410 --> 00:07:15.610
And now this becomes just a
simple function evaluation.

00:07:15.610 --> 00:07:21.150
f of 27 is equal to 27 plus 1.

00:07:21.150 --> 00:07:24.350
27 plus 1 is just 28.

00:07:24.350 --> 00:07:25.580
That's it.

00:07:25.580 --> 00:07:26.410
Next problem.

00:07:26.410 --> 00:07:27.830
Problem number fourteen.

00:07:32.030 --> 00:07:33.280
I'll do in green.

00:07:35.500 --> 00:07:36.870
Problem number fourteen.

00:07:36.870 --> 00:07:39.470
I have to do some drawing now.

00:07:39.470 --> 00:07:42.950
I'll do it big because
it looks complicated.

00:07:42.950 --> 00:07:45.100
Big line there.

00:07:45.100 --> 00:07:49.760
I have another line here that's
almost horizontal.

00:07:49.760 --> 00:07:55.010
And then this looks like it's
perpendicular, it is.

00:07:57.970 --> 00:08:02.940
And then we'll go
like that there.

00:08:02.940 --> 00:08:05.070
And add another perpendicular
line like that.

00:08:08.690 --> 00:08:11.130
That's a nice looking drawing.

00:08:11.130 --> 00:08:23.595
So then this is J, K, L, N, M.

00:08:26.310 --> 00:08:29.300
They tell us that this is 90
degrees, it's perpendicular.

00:08:29.300 --> 00:08:32.170
This is x degrees.

00:08:32.170 --> 00:08:37.500
They also tell us that
this is 125 degrees.

00:08:37.500 --> 00:08:41.049
They also tell us that this
is perpendicular.

00:08:41.049 --> 00:08:46.950
In the figure above, KN is
perpendicular to JL.

00:08:46.950 --> 00:08:48.040
We knew that because
they drew it.

00:08:48.040 --> 00:08:52.230
And LM is perpendicular to JL.

00:08:52.230 --> 00:08:54.150
We knew that because they
drew that there.

00:08:54.150 --> 00:09:07.420
If the lengths of LN and LM
are equal, these are equal

00:09:07.420 --> 00:09:10.910
lengths, what is
the value of x?

00:09:10.910 --> 00:09:13.370
Well if we know that these 2
sides are equal, what do we

00:09:13.370 --> 00:09:16.510
also know about its
base angles?

00:09:16.510 --> 00:09:20.210
This angle is going to have
to be equal to this angle.

00:09:23.320 --> 00:09:25.200
So if that angle is equal to
that angle, let's figure out

00:09:25.200 --> 00:09:26.110
what that is.

00:09:26.110 --> 00:09:29.830
If this purple angle here
is 125, what is this?

00:09:29.830 --> 00:09:33.540
Well they're supplementary,
so they add up to 180.

00:09:33.540 --> 00:09:35.230
So this is 125.

00:09:35.230 --> 00:09:37.060
I just realized I only
have 35 seconds

00:09:37.060 --> 00:09:39.010
left to do this problem.

00:09:39.010 --> 00:09:41.020
Actually, I will continue it in
the next video, because I

00:09:41.020 --> 00:09:42.620
only have 20 seconds
now to do this.

00:09:42.620 --> 00:09:43.870
So I'll see you in
the next video.


SAT Prep: Test 3 Section 4 Part 4

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:01.140
Welcome back.

00:00:01.140 --> 00:00:04.220
I almost ran out of time in that
last video, so let's just

00:00:04.220 --> 00:00:06.410
start from the beginning for
problem number fourteen.

00:00:06.410 --> 00:00:09.660
So I drew the figure, and they
told us that this line is

00:00:09.660 --> 00:00:11.790
perpendicular to that line,
and they drew it here.

00:00:11.790 --> 00:00:13.340
And that this is perpendicular
to that, and

00:00:13.340 --> 00:00:14.420
they drew it there.

00:00:14.420 --> 00:00:16.980
They told us this was 125
degrees, this is x.

00:00:16.980 --> 00:00:18.870
And then the one piece of
information they tell us, is

00:00:18.870 --> 00:00:21.390
that LN, this line,
is equal to LM.

00:00:21.390 --> 00:00:22.870
And I marked it here.

00:00:22.870 --> 00:00:24.950
What we said at the end of the
last video was, well if these

00:00:24.950 --> 00:00:27.965
two sides are equal, we also
know from geometry class, that

00:00:27.965 --> 00:00:29.900
the base angles are also
going to be equal.

00:00:29.900 --> 00:00:32.130
And then let's see what we can
do with that, whether we can

00:00:32.130 --> 00:00:34.310
figure out x.

00:00:34.310 --> 00:00:37.480
Well the first step we can do,
is we can say, well if this is

00:00:37.480 --> 00:00:41.960
125 degrees, what is this
angle right here?

00:00:41.960 --> 00:00:43.960
Well they're going to have to
add up to 180, because they're

00:00:43.960 --> 00:00:45.050
supplementary.

00:00:45.050 --> 00:00:48.230
So this is going to be,
what's 180 minus 125?

00:00:48.230 --> 00:00:50.480
Well what's 80 minus 25?

00:00:50.480 --> 00:00:58.960
It's 55 degrees.

00:00:58.960 --> 00:01:04.450
So if that's 55, then this
is also going to be 55.

00:01:04.450 --> 00:01:09.790
And then if these are both 55,
what is this angle up here?

00:01:09.790 --> 00:01:11.790
Well they're all in a triangle,
so they have

00:01:11.790 --> 00:01:13.380
to add up to 180.

00:01:13.380 --> 00:01:20.870
So 55 plus 55 is 110, so this
one has to be 70 degrees.

00:01:20.870 --> 00:01:22.790
Or 180 minus 110.

00:01:22.790 --> 00:01:24.710
You have to add up
to 180 degrees.

00:01:24.710 --> 00:01:26.820
So this is 70 degrees
right here.

00:01:26.820 --> 00:01:32.590
And now can we figure out
what this angle is here?

00:01:32.590 --> 00:01:33.980
This is what I call
the angle game.

00:01:33.980 --> 00:01:36.920
You just have to keep figuring
out of angles.

00:01:36.920 --> 00:01:42.190
Well if this is 70 degrees, this
angle plus this angle,

00:01:42.190 --> 00:01:43.490
they're going to be
complementary.

00:01:43.490 --> 00:01:46.420
They're going to come out to
90, because this is 90.

00:01:46.420 --> 00:01:49.320
So all we have left is
90 degrees here.

00:01:49.320 --> 00:01:52.460
So if these two have to
add up to 90 degrees,

00:01:52.460 --> 00:01:55.110
then this is 20 degrees.

00:01:55.110 --> 00:01:55.690
That says 20.

00:01:55.690 --> 00:01:56.720
I know I wrote it really
small, you

00:01:56.720 --> 00:01:58.880
probably can't read it.

00:01:58.880 --> 00:02:02.440
We know that this whole thing is
a right angle because this

00:02:02.440 --> 00:02:03.090
is a right angle.

00:02:03.090 --> 00:02:05.330
So if this is 90, we know that
this whole thing is 90.

00:02:05.330 --> 00:02:06.870
So this is 20.

00:02:06.870 --> 00:02:08.872
And now finally, I think
we're ready for x.

00:02:08.872 --> 00:02:12.020
Because x plus 90 plus 20 has
to be equal to 180 because

00:02:12.020 --> 00:02:13.780
it's in the same triangle.

00:02:13.780 --> 00:02:19.740
So x plus 90 plus 20
is equal to 180.

00:02:19.740 --> 00:02:23.660
x plus 110 is equal to 180.

00:02:23.660 --> 00:02:26.180
x is equal to 70 degrees.

00:02:26.180 --> 00:02:27.820
And we are done.

00:02:27.820 --> 00:02:29.070
Next problem.

00:02:33.410 --> 00:02:36.230
Problem number fifteen.

00:02:36.230 --> 00:02:40.935
A measuring cup contains 1/5
a cup of orange juice.

00:02:47.870 --> 00:02:51.800
It is then filled to the 1 cup
mark that is a mixture

00:02:51.800 --> 00:02:54.930
containing equal amounts of
orange, grapefruit and

00:02:54.930 --> 00:02:56.680
pineapple juices.

00:02:56.680 --> 00:03:00.850
What fraction of the final
mixture is orange juice?

00:03:00.850 --> 00:03:03.230
This is interesting.

00:03:03.230 --> 00:03:08.610
You have 1/5 already orange
juice, and then the next 4/5

00:03:08.610 --> 00:03:12.230
is going to be equal parts--
because we're going to fill to

00:03:12.230 --> 00:03:12.940
the 1 cup mark.

00:03:12.940 --> 00:03:21.090
It's going to be equal parts
orange, grapefruit-- I'll just

00:03:21.090 --> 00:03:22.875
write grape-- and pineapple.

00:03:27.500 --> 00:03:32.410
So the next 4/5 is going to be
split amongst these three, and

00:03:32.410 --> 00:03:34.040
it's equally.

00:03:34.040 --> 00:03:37.510
So how much more orange juice
are we putting in?

00:03:37.510 --> 00:03:40.705
We took 4/5, and 1/3 of
this 4/5 is going

00:03:40.705 --> 00:03:41.620
to be orange juice.

00:03:41.620 --> 00:03:46.360
So the amount of orange juice
we're putting in now is 1/3

00:03:46.360 --> 00:03:48.960
times the 4/5.

00:03:48.960 --> 00:03:52.380
So we're putting in
4/15 orange juice.

00:03:52.380 --> 00:03:54.460
And we already had
1/5 orange juice.

00:03:54.460 --> 00:03:59.230
So 1/5 plus 4/15.

00:03:59.230 --> 00:04:07.460
That equals 3/15 plus 4/15,
which equals 7/15.

00:04:07.460 --> 00:04:13.470
That is the final mixture
of orange juice.

00:04:13.470 --> 00:04:15.840
And doesn't that make
sense intuitively?

00:04:15.840 --> 00:04:18.970
That makes sense because there's
20% orange juice, and

00:04:18.970 --> 00:04:24.050
then we're adding maybe a little
bit less than a 1/4.

00:04:24.050 --> 00:04:28.120
So we'll have a little bit less
than 1/2 in the glass.

00:04:28.120 --> 00:04:28.540
All right.

00:04:28.540 --> 00:04:29.330
Next problem.

00:04:29.330 --> 00:04:32.440
I don't know, my cousin's
answer seems a little

00:04:32.440 --> 00:04:34.882
suspicious.

00:04:34.882 --> 00:04:37.880
She had marked up this book.

00:04:37.880 --> 00:04:38.070
All right.

00:04:38.070 --> 00:04:39.320
Problem number sixteen.

00:04:42.360 --> 00:04:53.470
If a plus 2b is equal
to 125% of 4b.

00:04:53.470 --> 00:04:56.110
So that equals 125%.

00:04:56.110 --> 00:04:58.340
If you want to write 125%
as a decimal, which I

00:04:58.340 --> 00:05:00.840
like to do, it's 1.25.

00:05:00.840 --> 00:05:06.970
125% of 4b, what is the
value of a over b?

00:05:06.970 --> 00:05:09.640
So we want to figure
out a over b.

00:05:09.640 --> 00:05:11.820
Let's just solve this thing.

00:05:11.820 --> 00:05:16.730
So a plus 2b is equal to,
what's 1.25 times 4?

00:05:16.730 --> 00:05:18.820
If you have $1.25 and
you have that 4

00:05:18.820 --> 00:05:21.030
times, it's $5.00, right?

00:05:21.030 --> 00:05:23.356
4 times 1 and then 4 times
a quarter, that's another

00:05:23.356 --> 00:05:25.390
dollar, so that's 5b.

00:05:25.390 --> 00:05:28.170
And then subtract 2b
from both sides.

00:05:28.170 --> 00:05:32.220
You get a is equal to 3b.

00:05:32.220 --> 00:05:36.450
Divide both sides by b,
and you get a over

00:05:36.450 --> 00:05:38.660
b is equal to 3.

00:05:38.660 --> 00:05:40.590
And you are done the problem.

00:05:40.590 --> 00:05:41.840
Problem number seventeen.

00:05:48.100 --> 00:05:49.350
They have a number line.

00:05:51.550 --> 00:05:53.670
This number line, let me see
how much I have to draw of

00:05:53.670 --> 00:05:56.370
this number line, to minimize
my drawing.

00:05:56.370 --> 00:06:01.970
They say 0 is here, 1 is here.

00:06:01.970 --> 00:06:03.060
How many hash marks are there?

00:06:03.060 --> 00:06:08.940
1, 2, 3, 4, 5, 6,
7, 8 hash marks.

00:06:08.940 --> 00:06:09.460
Oh it says there.

00:06:09.460 --> 00:06:11.900
On the number line above, there
are 9 equal intervals

00:06:11.900 --> 00:06:12.890
between 0 and 1.

00:06:12.890 --> 00:06:16.260
What is the value of x?

00:06:16.260 --> 00:06:25.750
So there's 1, 2, 3,
4, 5, 6, 7, 8, 9.

00:06:25.750 --> 00:06:30.900
I have 9 equal intervals, and
then x is right-- I'm just

00:06:30.900 --> 00:06:31.990
going to make sure I
draw it correctly.

00:06:31.990 --> 00:06:34.410
We have 2 marks, and
then we have x.

00:06:34.410 --> 00:06:38.530
And actually we have the
square root of x.

00:06:38.530 --> 00:06:40.590
So they're 9 equal
intervals, right?

00:06:40.590 --> 00:06:46.260
So we could just do this is 1/9,
this is 2/9, this is 3/9,

00:06:46.260 --> 00:06:50.780
4/9, this is 8/9, this is 9/9.

00:06:50.780 --> 00:06:57.700
This is 8/9, this is 7/9, this
is 6/9, this is 5/9, because 9

00:06:57.700 --> 00:06:58.670
equal intervals.

00:06:58.670 --> 00:07:02.550
So we know that the square root
of x is equal to 6/9.

00:07:02.550 --> 00:07:04.650
Square both sides.

00:07:04.650 --> 00:07:05.310
What's 6/9?

00:07:05.310 --> 00:07:08.640
That's the same thing as 2/3.

00:07:08.640 --> 00:07:09.860
So you square both sides.

00:07:09.860 --> 00:07:14.450
You get x is equal to 4/9.

00:07:14.450 --> 00:07:16.550
2 squared, 3 squared.

00:07:16.550 --> 00:07:18.520
We are done.

00:07:18.520 --> 00:07:19.770
Next problem.

00:07:25.990 --> 00:07:27.240
Problem eighteen.

00:07:29.700 --> 00:07:34.200
In the xy-coordinate plane, the
distance between point B--

00:07:34.200 --> 00:07:38.050
so B is the point 10 comma 18.

00:07:38.050 --> 00:07:41.880
The distance between the point
B and the point A-- A is

00:07:41.880 --> 00:07:45.080
point x comma 3.

00:07:45.080 --> 00:07:47.800
So the distance is 17 between
these points.

00:07:47.800 --> 00:07:50.840
What is one possible
value of x?

00:07:50.840 --> 00:07:54.220
So this is the distance formula,
and the distance

00:07:54.220 --> 00:07:56.900
formula is really just the
Pythagorean theorem.

00:07:56.900 --> 00:08:03.390
What we do is we say, well the
distance squared is equal to

00:08:03.390 --> 00:08:09.800
the change in x squared, plus
the change in y squared.

00:08:09.800 --> 00:08:12.080
And this is really just the
Pythagorean theorem.

00:08:12.080 --> 00:08:14.230
If you haven't learned that yet,
actually I don't think

00:08:14.230 --> 00:08:16.040
I've done a distance formula
video, that's on my to-do

00:08:16.040 --> 00:08:16.960
list. But I'll do that.

00:08:16.960 --> 00:08:18.210
It's just the Pythagorean
theorem.

00:08:18.210 --> 00:08:22.560
The distance squared, so 17
squared, is equal to-- what's

00:08:22.560 --> 00:08:24.070
the change in x?

00:08:24.070 --> 00:08:35.640
So let's just call that 10 minus
x squared plus-- and

00:08:35.640 --> 00:08:39.530
then we know that change
in y-- so 18 minus 3.

00:08:39.530 --> 00:08:44.330
So it's 15 squared.

00:08:44.330 --> 00:08:48.410
I know 15 squared is 225.

00:08:48.410 --> 00:09:02.590
This is going to be equal
to x squared minus 20x.

00:09:02.590 --> 00:09:08.480
It could be plus 100.

00:09:08.480 --> 00:09:09.530
What's 17 squared?

00:09:09.530 --> 00:09:12.460
17 times 17?

00:09:12.460 --> 00:09:15.120
7 times 7 is 49.

00:09:15.120 --> 00:09:19.900
1 times 7 is 7, plus 4 is 11.

00:09:19.900 --> 00:09:22.000
0 plus 17.

00:09:22.000 --> 00:09:27.580
It is 289.

00:09:27.580 --> 00:09:32.190
And so then we can subtract
289 from both sides.

00:09:32.190 --> 00:09:37.340
So you get 0 is equal to x
squared minus 20x plus-- add

00:09:37.340 --> 00:09:42.790
these two together--
325 minus 289.

00:09:42.790 --> 00:09:44.280
I only have 10 seconds
left, so I'll do

00:09:44.280 --> 00:09:46.110
it in the next video.


SAT Prep: Test 3 Section 4 Part 5

WEBVTT
Kind: captions
Language: en

00:00:00.850 --> 00:00:03.150
I'm back, and I just
have to finish up

00:00:03.150 --> 00:00:04.505
problem number eighteen.

00:00:04.505 --> 00:00:06.275
I just want to make
sure I did this.

00:00:06.275 --> 00:00:12.910
10 minus x squared, this will
be x squared minus 20x, plus

00:00:12.910 --> 00:00:14.790
100, plus 225.

00:00:14.790 --> 00:00:17.180
This is where I always
mess up.

00:00:17.180 --> 00:00:21.930
Let's see, what's
325 minus 289?

00:00:21.930 --> 00:00:26.650
It's 25 plus 11, so it's 36.

00:00:26.650 --> 00:00:30.400
So we're left with 0 is
equal to x squared

00:00:30.400 --> 00:00:35.240
minus 20x plus 36.

00:00:35.240 --> 00:00:38.390
And now we just have to factor
this right here.

00:00:38.390 --> 00:00:39.640
I'll do it up here.

00:00:44.090 --> 00:00:47.400
So what two numbers, when you
multiply them, is equal to 36,

00:00:47.400 --> 00:00:51.770
and when you add or subtract
them, you get minus 20?

00:00:51.770 --> 00:00:53.020
What do you get, let's see.

00:00:57.990 --> 00:00:59.180
18 and 2.

00:00:59.180 --> 00:01:00.775
18 times 2 is 36.

00:01:00.775 --> 00:01:03.420
And if you make them both
negative when they add, they

00:01:03.420 --> 00:01:05.440
go to negative 20.

00:01:05.440 --> 00:01:12.620
That's x minus 18,
and x minus 2.

00:01:12.620 --> 00:01:17.000
I just factored this as x
minus 18 and x minus 2.

00:01:17.000 --> 00:01:21.750
And you can review my
presentation on factoring

00:01:21.750 --> 00:01:23.820
quadratics if you forgot
how to do this.

00:01:23.820 --> 00:01:26.970
But I just said, well
18 times 2 is 36.

00:01:26.970 --> 00:01:28.860
And they have to be negative,
because when they add together

00:01:28.860 --> 00:01:30.196
you get minus 20.

00:01:30.196 --> 00:01:35.930
So x could be equal to 18,
or x could be equal to 2.

00:01:35.930 --> 00:01:39.380
And those are the possible
choices.

00:01:39.380 --> 00:01:39.840
And that's it.

00:01:39.840 --> 00:01:41.930
This was a short video,
just a leftover from

00:01:41.930 --> 00:01:43.440
problem number eighteen.

00:01:43.440 --> 00:01:45.450
I'll see you in the next


SAT Prep: Test 3 Section 2 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:05.806
We are on number six, which
I will do in this color.

00:00:09.740 --> 00:00:15.110
If y is the midpoint of
x, z, which of the

00:00:15.110 --> 00:00:16.190
following must be true?

00:00:16.190 --> 00:00:26.130
So if I had a line, x, z, y is
the midpoint of this, right?

00:00:26.130 --> 00:00:29.290
So this length is equal to this
length, because equal

00:00:29.290 --> 00:00:30.650
distance between the two.

00:00:30.650 --> 00:00:36.770
So the choices they give us,
choice one, they say yz is

00:00:36.770 --> 00:00:39.150
equal to 1/2xz.

00:00:42.500 --> 00:00:49.370
Let's see, yz is this length,
and xz is this whole length.

00:00:49.370 --> 00:00:52.630
And yeah, sure, yz is going to
be 1/2 of the whole length,

00:00:52.630 --> 00:00:54.870
because it's the midpoint.

00:00:54.870 --> 00:00:58.330
Because this is the same
distance as this distance, so

00:00:58.330 --> 00:01:00.870
this distance will be
1/2 of the whole.

00:01:00.870 --> 00:01:02.920
So this is right.

00:01:02.920 --> 00:01:12.870
Two: 1/2xz is equal to 2xy.

00:01:12.870 --> 00:01:15.170
So now they're saying
1/2 of this entire

00:01:15.170 --> 00:01:20.625
distance is equal to xy.

00:01:20.625 --> 00:01:23.080
It's not equal to 2xy.

00:01:23.080 --> 00:01:24.330
This is wrong.

00:01:24.330 --> 00:01:26.380
This would have been right
if there wasn't a 2 here.

00:01:26.380 --> 00:01:27.920
If we got rid of this,
then it's right.

00:01:27.920 --> 00:01:29.400
Then it's something
similar to this.

00:01:29.400 --> 00:01:31.410
Then it would be saying
that this is 1/2

00:01:31.410 --> 00:01:31.930
of the whole thing.

00:01:31.930 --> 00:01:35.110
But when you put that 2 here,
it makes it wrong.

00:01:35.110 --> 00:01:37.630
xz is actually equal to 2xy,
so that's not right.

00:01:37.630 --> 00:01:39.490
So this is not right.

00:01:39.490 --> 00:01:48.910
And choice three says,
2xy is equal to xz.

00:01:48.910 --> 00:01:51.060
And this looks right, because
that's saying this

00:01:51.060 --> 00:01:54.560
distance times 2.

00:01:54.560 --> 00:01:56.580
So the times 2 will give us the
whole distance, and the

00:01:56.580 --> 00:01:58.160
whole distance is xz.

00:01:58.160 --> 00:02:00.210
The whole distance is xz,
so this is right.

00:02:00.210 --> 00:02:05.340
So choices one and three are
correct, and that is choice E.

00:02:05.340 --> 00:02:08.120
Next problem, number seven.

00:02:15.230 --> 00:02:30.030
If 2r is equal to 5s, and 5s
is equal to 6t, what does r

00:02:30.030 --> 00:02:31.650
equal in terms of t?

00:02:31.650 --> 00:02:33.160
And these are easy, because you
don't really have to solve

00:02:33.160 --> 00:02:34.390
for anything.

00:02:34.390 --> 00:02:38.490
2r is equal to 5s, 5s is
equal to 6t, so 2r is

00:02:38.490 --> 00:02:40.352
equal to 6t, right?

00:02:40.352 --> 00:02:43.770
So 2r is equal to 6t.

00:02:43.770 --> 00:02:46.380
2r is equal to something that's
equal to 6t, so 2r is

00:02:46.380 --> 00:02:47.262
equal to 6t.

00:02:47.262 --> 00:02:49.090
And they want to know
r in terms of t.

00:02:49.090 --> 00:02:56.000
So r is equal to-- divide both
sides by 2-- r is equal to 3t,

00:02:56.000 --> 00:02:57.250
which is choice C.

00:02:59.830 --> 00:03:01.080
Problem eight.

00:03:03.610 --> 00:03:06.120
A total of k passengers
went on a bus trip.

00:03:09.360 --> 00:03:13.080
Each of the n buses that were
used to transport the

00:03:13.080 --> 00:03:15.640
passengers could seat a maximum
of x passengers.

00:03:15.640 --> 00:03:20.875
So n buses, x capacity.

00:03:24.950 --> 00:03:33.930
If 1 bus had 3 empty seats-- so
1 had 3 empty seats-- and

00:03:33.930 --> 00:03:37.230
the remaining buses were filled,
which of the following

00:03:37.230 --> 00:03:43.460
represents the relationship
among n, x, and k?

00:03:43.460 --> 00:03:45.690
Well, let's think about
what happens.

00:03:45.690 --> 00:03:53.080
Essentially, we used all of
our capacity except for 3

00:03:53.080 --> 00:03:54.300
seats, right?

00:03:54.300 --> 00:03:57.840
So we could say-- I don't know
how they want to write it, but

00:03:57.840 --> 00:03:59.530
I'll just say what I'll
write-- so the total

00:03:59.530 --> 00:04:05.215
passengers traveled-- that's
what they said is k-- is going

00:04:05.215 --> 00:04:07.160
to be equal to our
total capacity.

00:04:07.160 --> 00:04:13.790
Our total capacity is n buses
times x people per bus.

00:04:13.790 --> 00:04:16.410
But then we know that there
are 3 empty seats.

00:04:16.410 --> 00:04:19.250
We would be done if there
were no empty seats.

00:04:19.250 --> 00:04:21.000
Then we would have just said,
well, we had n buses.

00:04:21.000 --> 00:04:25.320
Each of them held its entire
capacity, so we

00:04:25.320 --> 00:04:28.080
took n times x people.

00:04:28.080 --> 00:04:30.550
We know that there are 3 empty
seats out of all the buses.

00:04:30.550 --> 00:04:32.200
There's 1 bus with
3 empty seats.

00:04:32.200 --> 00:04:36.150
So we know that there's 3 less
people than the full capacity.

00:04:36.150 --> 00:04:39.070
So that's our answer,
k equals nx minus 3.

00:04:39.070 --> 00:04:42.631
And that is choice A.

00:04:42.631 --> 00:04:45.330
It wasn't too bad, huh?

00:04:45.330 --> 00:04:46.300
Problem number nine.

00:04:46.300 --> 00:04:48.130
Looks like Sal's going to
have to do some drawing.

00:04:53.095 --> 00:04:54.780
I haven't used red
in a long time.

00:04:54.780 --> 00:04:57.265
Probably because it's tacky,
but I'll use red.

00:04:57.265 --> 00:05:01.240
So I have this line here.

00:05:01.240 --> 00:05:03.710
I have another line that,
at least from the

00:05:03.710 --> 00:05:04.750
drawing, looks parallel.

00:05:04.750 --> 00:05:06.035
I don't know if it is.

00:05:06.035 --> 00:05:10.446
I know that we can assume that
we have this line that looks

00:05:10.446 --> 00:05:13.220
like it goes in like that.

00:05:13.220 --> 00:05:14.160
Almost done.

00:05:14.160 --> 00:05:18.490
And then I have a line that
looks something like this.

00:05:18.490 --> 00:05:27.480
And then the labels are, this
is 80 degrees, and they tell

00:05:27.480 --> 00:05:36.880
us that this, right here,
is 50 degrees,

00:05:36.880 --> 00:05:40.470
and this is x degrees.

00:05:40.470 --> 00:05:40.850
That's all they tell us.

00:05:40.850 --> 00:05:45.292
And this is line l, this
line m, this is line k.

00:05:45.292 --> 00:05:48.510
And they say the figure above
line l is parallel to line m.

00:05:48.510 --> 00:05:53.010
Well, OK, so we know-- and they
look parallel too-- What

00:05:53.010 --> 00:05:56.810
is the value of x?

00:05:56.810 --> 00:06:00.250
This is the angle game, if
you've seen the geometry

00:06:00.250 --> 00:06:02.410
videos that I've done.

00:06:02.410 --> 00:06:04.370
Well, first of all, we can just
figure out corresponding

00:06:04.370 --> 00:06:08.590
angles, or we'll do our
best to figure out

00:06:08.590 --> 00:06:09.465
corresponding angles.

00:06:09.465 --> 00:06:10.475
So let me ask you a question.

00:06:10.475 --> 00:06:16.640
If this angle is 80 degrees,
what is-- and when I do these

00:06:16.640 --> 00:06:18.950
problems, I literally just try
to figure out all the angles

00:06:18.950 --> 00:06:21.760
in a direction that will
eventually get me to x-- so

00:06:21.760 --> 00:06:22.900
what angles can I figure out?

00:06:22.900 --> 00:06:26.700
Well, if this is 80,
what angle is this?

00:06:26.700 --> 00:06:30.070
Well, these 2 angles are
supplementary, right?

00:06:30.070 --> 00:06:31.385
So they add up to 180.

00:06:31.385 --> 00:06:36.740
So this is 80, this is going
to be 100 degrees.

00:06:36.740 --> 00:06:43.410
Now, if this angle right here
is 100 degrees, well, then

00:06:43.410 --> 00:06:46.760
what is-- well, let's just
keep doing this--

00:06:46.760 --> 00:06:48.010
what is this angle?

00:06:51.100 --> 00:06:54.000
Well, they're alternate interior
angles, right?

00:06:54.000 --> 00:06:57.430
And if you remember from your
parallel lines in geometry

00:06:57.430 --> 00:06:59.890
class, or if you remember from
the videos on alternate

00:06:59.890 --> 00:07:02.560
interior angles, or on the angle
game I've done, we know

00:07:02.560 --> 00:07:06.190
that this angle is equal
to this angle.

00:07:06.190 --> 00:07:09.930
So this angle is also
100 degrees.

00:07:09.930 --> 00:07:11.920
And we know that because this
line right here is a

00:07:11.920 --> 00:07:14.720
transversal, and these two
lines are parallel.

00:07:14.720 --> 00:07:16.670
That's how we can make
that assumption.

00:07:16.670 --> 00:07:20.800
Now, if this is 100, this angle
is 50, what's going to

00:07:20.800 --> 00:07:24.080
be this angle right here?

00:07:24.080 --> 00:07:28.380
Well, once again, we know that
these 3 angles together form

00:07:28.380 --> 00:07:29.990
180, right?

00:07:29.990 --> 00:07:32.340
All 3 combined are
supplementary.

00:07:32.340 --> 00:07:36.140
So if 100, 150-- so these are
150, so this one has to be 30

00:07:36.140 --> 00:07:39.040
degrees, because it all
adds up to 180.

00:07:39.040 --> 00:07:40.400
I think we're almost there.

00:07:40.400 --> 00:07:43.840
If this angle is 30 degrees,
what is x?

00:07:43.840 --> 00:07:45.920
What is this angle?

00:07:45.920 --> 00:07:50.610
Well, this angle and x are also
supplementary, so they

00:07:50.610 --> 00:07:54.240
have to add up to 180 degrees.

00:07:54.240 --> 00:07:57.740
So if this is 30,
then x is 150.

00:07:57.740 --> 00:08:00.965
These are supplementary
along this line.

00:08:00.965 --> 00:08:04.980
And so x is 150 degrees,
and that is choice A.

00:08:07.600 --> 00:08:17.020
Next problem, problem 10.

00:08:17.020 --> 00:08:26.510
They tell us 3x squared is less
than 3x, and the whole

00:08:26.510 --> 00:08:28.590
thing squared.

00:08:28.590 --> 00:08:32.679
For what value of x is the
above statement false?

00:08:32.679 --> 00:08:43.250
OK, so the choices are A is
minus 3, B is 0, C is 1/3, D

00:08:43.250 --> 00:08:49.950
is 1, and then E is none of
the above, essentially.

00:08:49.950 --> 00:08:52.070
OK, so let's see, is it
false for this one?

00:08:52.070 --> 00:08:58.430
Minus 3 squared, so it's 3 times
9 is less than-- what's

00:08:58.430 --> 00:09:04.260
3 times minus 3?-- minus 9
squared is less than 81.

00:09:04.260 --> 00:09:05.950
So 27 is less than 81.

00:09:05.950 --> 00:09:07.410
That's true.

00:09:07.410 --> 00:09:12.950
For 0, 3 times 0 squared
is 0, is less than 0

00:09:12.950 --> 00:09:14.820
squared, which is 0.

00:09:14.820 --> 00:09:15.610
Well, that's not true.

00:09:15.610 --> 00:09:16.910
0 is less than 0?

00:09:16.910 --> 00:09:18.040
Not true.

00:09:18.040 --> 00:09:22.596
So this is our choice,
choice B.

00:09:22.596 --> 00:09:25.580
Well, I only have 30 seconds
left, so I'll do number 11 in

00:09:25.580 --> 00:09:26.710
the next video.

00:09:26.710 --> 00:09:28.370
I'll see you soon.