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# CAHSEE practice: Problems 43-46

Video transcript

Problem 43. Mia found the area of this
shape by dividing it into rectangles as shown. Mia could use the same method to
find the area for which of these shapes? What technique can we use to
figure out the area by dividing it into rectangles? So let's see. What do we have here? Can we divide this
into rectangles? We can divide into a bunch of
triangles, but we can't divide this into a bunch
of rectangles. Or we could have done
it this way as well. There's multiple ways
to think about it. You could have it like this,
and you can draw a bunch of triangles like that. But you can't divide this
into rectangles. This one here, you can't divide
it into rectangles. You could divide it into
triangles and rectangles, but not necessarily just
rectangles. And this here, I really
don't know. It looks like there's some
type of typo in my test. Because obviously I could divide
both of these things right here. The way I'm looking at it,
I see squares here. So obviously I could divide
that into rectangles. But my guess is, if I had to
guess, is that this was a triangle, maybe, before. If it was a triangle, then I
couldn't divide this into rectangles. But maybe this was something
like this. I don't know. I'm only guessing. If it did look like this, then
we could divide it into rectangles the same way that
she did up here, and figure out its area. So assuming that there was
some type of typo in this problem, I'm going to
go with choice D. If choice D was supposed to look
like a figure like that, then you could actually divide
it into a bunch of rectangles. Problem 44. Oh, I see. You know what these
probably were? These were probably to show us
that these are right angles right there. So that that's a right angle,
that's a right angle. And maybe-- well, I don't
know what else they're trying to show us. Who knows? You see what I'm going at. There's clearly some type
of typo on that problem. 44. Simplify. x squared minus 3x plus
1, minus x squared plus 2x plus 7. So let's just write it out. We have x squared
minus 3x plus 1. Then we have to distribute
this minus sign. So minus x squared
minus 2x, right? Minus times plus. Minus 2x. Minus times plus 7 is minus 7. So you have an x squared
minus an x squared. They cancel out. Right? x squared minus
x squared is 0. Then you have minus
3x minus 2x. Is minus 5x. And then you have 1 minus
7, which is minus 6. So you're left with minus 5x
minus 6, which is choice C. Problem 45. What are the coordinates of the
x-intercept of the line 3x plus 4y is equal to 12? They want to know
the x-intercept. Remember, the x-intercept,
if this is a line-- and this is a line. Let me draw the axes. Say the line looks-- I don't
know what it looks like. Say the line looks something
like this. The x-intercept is the value
when y is equal to 0. The x-intercept is going to
be some value x and 0. So let's figure out what
this x-intercept is. So we can even look here. This is definitely not
an x-intercept. This is a y-intercept. This is a y-intercept. In order to be an x-intercept,
in order to be on the x-axis, your y value has to be 0. So the choices are
either B or D. And so if y is 0, let's just
solve the equation. So 3x plus 4 times
0 is equal to 12. Or we get 3x is equal to 12. That's just 0 right there. So x is equal to 4. So the x-intercept
is 4 comma 0. x is 5, y is 0. So this is our choice
right there. 46. Which of the following
statements describes parallel lines? And parallel lines are just
two lines that never intersect, that have the same
slope an they don't sit on top of each other. So those would be two parallel
lines right there. Same y-intercepts but
different slopes. No, I just said, they have to
have the same slope and they never intersect. So they can't have the
same y-intercepts. So it's not that one. Same slope but different
y-intercepts. That looks right. They're parallel, but they're
not on top of each other. Or they have the same slope. Opposite slopes. If they had opposite slopes,
they would intersect. Can't be that. Opposite x-intercepts but
same y-intercepts. No, that's not necessarily
the case. So our answer is B.