To translate x^3 to new function we move it 2 to left to x = -2 then down 3 units to y = -3
New graph is (x - -2)^3 - 3
h = -2
You have to sit calmly and quietly and look over this one for a few minutes,
until you see what's going on.
When the top triangle got flopped over to make the bottom one,
the 12-cm side on top made another 12-cm side on the bottom.
Also, the short 6-cm piece made another 6-cm piece hooked onto it,
and when those are put together, they make 12-cm all together.
So now, look at the whole outside triangle that you have, after the two
inside ones are put together. The top slanty side is 12-cm, the bottom
slanty side is 12-cm, and the straight up-and-down side is also 12-cm.
The new big triangle is an equilateral triangle !
What do you know about an equilateral triangle ?
-- All three sides are the same length.
-- All three angles are the same size.
If all three angles are the same size, how big is each one ?
Hint: The three angles of <em>every</em> triangle add up to 180 degrees.
So angle-y must be 1/3 of 180 = 60 degrees.
Answer:
267
Step-by-step explanation:
Let's review "similar" and "congruent." "Congruent" means the same--so two congruent line segments will be the same length; two congruent figures have the same angle measures, same side lengths, same area, etc. "Similar" means that the sides and area are PROPORTIONAL, not the same: you can divide or multiply them all by the same number and get the measures of the other. Note that the angles must still be the same measures.
So, let's look at A, first comparing AB and CD. AB is 4 units long, and CD is 2 units long. 4/2=2, so AB is twice the length of CD. What about BC and DE? BC=6, and DE=3. 6/3=2. Since BOTH AB and BC are twice the length of CD and DE, they are proportional. A is correct!
In B, if side AC has the same slope as side CE, then basically they have the same incline. They are on the same line, and this line has a slope. Since they are both on this line, they both must have the same slope as this line, and therefore the same slope as each other. B is correct.
What about C? Are the triangles congruent? NO, because their side lengths are different (though proportional). C is incorrect. And D? Just looking at the diagram, we can tell that AC is not the same length as DE, so they are NOT congruent (though again, they are proportional). D is incorrect.
Answer: A, B
