<h3>
Answer: 28</h3>
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Explanation:
Method 1
Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.
There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.
Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.
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Method 2
There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.
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Method 3
Use the nCr combination formula with n = 8 and r = 2
There are 28 combinations possible. Order doesn't matter (eg: match-up AB is the same as match-up BA).
Notice how the (8*7)/2 expression is part of the steps shown above in the nCr formula.
Answer:
5
Step-by-step explanation:
A 30-60-90 triangle's sides equal as follows:
Hypotanuse= x (a number)
Long side= x/2( also can be calculated as x* 1/2) * 
Short side = x/2 or x * 1/2
Remark
The quick answer is C does not represent a function. It has two y values for x = 2. These two points are (2,1) and (2,3). That eliminates C. No x can have 2 y values and be called a function. A function can have many x vales for a single y and still be a function.
A has all different x values, so it could be classed as a function. There are no values where x has more than 1 y value.
B also has all different x values. It too is a function.
Answer
A and B are both functions. C is not.
D <<<<< Answer
Answer:
x=76 degrees
Step-by-step explanation:
< dij + < jih = 180 straight line
< dij + 107 = 180
subtract 107 from each side
< dij = 73
<jdi + < dij + <idj = 180 triangle
31 + 73 + < idj = 180
combine like terms
104+ < idj = 180
subtract 104 from each side
< idj = 76
<idj = < ajf vertical angles
76 < ajf
<ajf = x
x=76 degrees
Only two triangles:
The 90* angle is stable, so you can change only the position of the 50* and 40* angles.
1 triangle: 40* is right to the 90*
2 triangle: 40* is left to the 90*
Hope this helped you!
