Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to
the slope of CE?
A) 6 − 3
−3 − 1
= 3 − (−3)
−1 − 3
B) 6 − 3
−3 − (−1)
= 3 − 3
−1 − 3
C) 6 − 3
−3 − (−1)
= 3 − (−3)
−1 − 3
D) −3 − (−1)
6 − 3
= 3 − (−3)
−1 − 3
A) 6 − 3
−3 − 1
= 3 − (−3)
−1 − 3
B) 6 − 3
−3 − (−1)
= 3 − 3
−1 − 3
C) 6 − 3
−3 − (−1)
= 3 − (−3)
−1 − 3
D) −3 − (−1)
6 − 3
= 3 − (−3)
−1 − 3
1 answer:
Answer:
Option C is the correct option.
Step-by-step explanation:
Considering the triangle ABC, the slope of the line CA is given by
Again, considering the triangle CDE, the slope of the line EC is given by
Since CA and EC represents the same straight line so, we can write
Therefore, option C is the correct option. (Answer)
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Let’s look at the permutations of the letters “ABC.” We can write the letters in any of the following ways:
ABC
ACB
BAC
BCA
CBA
CAB
Since there are 3 choices for the first spot, two for the next and 1 for the last we end up with (3)(2)(1) = 6 permutations. Using the symbolism of permutations we have:
. Note that the first 3 should also be small and low like the second one but I couldn’t get that to look right.
Now let’s see how this changes if the letters are AAB. Since the two As are identical, we end up with fewer permutations.
AAB
ABA
BAA
To make the point a bit better let’s think of one A are regular and one as bold A.
ABA and ABA look different now because we used bold for one of the As but if we don’t do this we see that these are actual the same. If they represented a word they would be the same exact word.
So in this case the formula would be
. We use 2! In the denominator because there are 2 repeating letters. If there were three we would use 3!
Hopefully, this is enough to let you see that the answer is A. The number of permutations is limited by the number of items that are identical.
ABC
ACB
BAC
BCA
CBA
CAB
Since there are 3 choices for the first spot, two for the next and 1 for the last we end up with (3)(2)(1) = 6 permutations. Using the symbolism of permutations we have:
Now let’s see how this changes if the letters are AAB. Since the two As are identical, we end up with fewer permutations.
AAB
ABA
BAA
To make the point a bit better let’s think of one A are regular and one as bold A.
ABA and ABA look different now because we used bold for one of the As but if we don’t do this we see that these are actual the same. If they represented a word they would be the same exact word.
So in this case the formula would be
Hopefully, this is enough to let you see that the answer is A. The number of permutations is limited by the number of items that are identical.
Alright, lets get started.
The foreign exchange rate between the japanese yen and the euro is 190:1 given.
It means 1 euro = 190 yen
We are asked to find how many yen will be equal to 10 euros.
Means we need to multiply given euros with 190 because 1 euro = 190 yen
Hence 10 euros yen
10 euros = 1900 yen : Answer
Hope it will help :)