On a coordinate plane, triangle D E F has points (negative 8, 8), (10, negative 2), and (negative 8, negative 8). Find the area
2 answers:
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The solution for the given equations x + 3y = 5 and x - 3y = -1 are x=2 and y=1.
Step-by-step explanation:
The given is,
......................................(1)
....................................(2)
Step:1
By elimination method,
Subtracting Equations (1) and (2),
( - )
( ) + (
) = (
)
= 6
= 1
Step:2
Substitute the value of y in equation (1),
+ ( 3 × 1 ) = 5
= 5-3
= 2
Step:3
Check for Solution,
Substitute the values of x and y in Eqn (1),
2 + ( 3 × 1 ) = 5
5 = 5
Result:
The solution for the given equations x + 3y = 5 and x - 3y = -1 are x=2 and y=1, by elimination method.
Answer with Step-by-step explanation:
We are given S be any set which is countable and nonempty.
We have to prove that their exist a surjection g:N
Surjection: It is also called onto function .When cardinality of domain set is greater than or equal to cardinality of range set then the function is onto
Cardinality of natural numbers set =( Aleph naught)
There are two cases
1.S is finite nonempty set
2.S is countably infinite set
1.When S is finite set and nonempty set
Then cardinality of set S is any constant number which is less than the cardinality of set of natura number
Therefore, their exist a surjection from N to S.
2.When S is countably infinite set and cardinality with aleph naught
Then cardinality of set S is equal to cardinality of set of natural .Therefore, their exist a surjection from N to S.
Hence, proved