Select all the possible input-output pairs for the function
2 answers:
Answer:
A.(-1,-1)
E.(4,64)
Step-by-step explanation:
We are given that
Function
We have to find all possible input-output pairs for the function.
Substitute x=-1
Then, the pair is (-1,-1)
Now, substitute x=-2
Then, pair is (-2,-8)
Now, substitute x=3
Now, substitute x=4
Now, substitute x=1
Then, y=1
Hence, Option A and E are true.
A.(-1,-1)
E.(4,64)
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Answer:
Proved
Step-by-step explanation:
From the given parameters, we have:
i.e. the length of each security numbers
i.e. 2 security numbers
Required
In 513 security numbers, 2 must have matching zeros
To do this, we make use of Pigeonhole principle.
First, we calculate the number of all security numbers not having matching zeros.
Each of the 9 digits can be selected in 2 ways.
2 ways implies that each digit is either 0 or not
So, total selection is:
Apply Pigeonhole principle
The principle states that: suppose there are n items in m containers, where , then there is at least one container that contains more than 1 item.
This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.
Answers:
- Similar = Yes, they are similar
- How: AA similarity
- Similarity statement: triangle HGF ~ triangle HMN
The ~ mark means "similar"
=====================================================
The red angle markings tell us which angles are congruent to one another. We have these two pairs of congruent angles
- angle H = angle H (both triangles unfortunately reuse H) by the single arc marking
- angle G = angle M, by the double arc markings
Because we have two pairs of congruent angles, we use the AA similarity theorem. AA stands for angle angle. We could use three pairs, but two pairs is the minimum needed for similarity statements.
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To figure out what goes in the third answer box, note how the order HGF is given to us. The order is important.
We have H first, G second, F third.
H being first, and it having a single arc, means that whatever has a single arc on the other triangle must be first. That would be H. Unfortunately they reuse angle H which makes things confusing a bit.
G is second in HGF, and G has the double arc marking. Note how M also has this double arc marking. Therefore we have M second in the answer. So far we have HM as part of the third answer.
The only thing left is N. Therefore, we have triangle HMN as the answer for the third box.
Put another way, we have these pairings:
- H (single arc mark) = H (single arc mark)
- G (double arc mark) = M (double arc mark)
- F (no marking) = N (no marking)
This is why the order is important. So we can see how the angles pair up in the order that they do.
This is why triangle HGF is similar to triangle HMN.
We can write that as triangle HGF ~ triangle HMN
The ~ mark means "similar"
We don't have enough information to prove that the triangles are congruent or not. So we cannot say . Your teacher made a typo when using the congruence symbol
Instead, it should be