Help please I will give brainliest
2 answers:
You might be interested in
Answer with Step-by-step explanation:
1. We are given that an expression
We have to prove that this expression is always is even for every integer.
There are two cases
1.n is odd integer
2.n is even integer
1.n is an odd positive integer
n square is also odd integer and n is odd .The sum of two odd integers is always even.
When is negative odd integer then n square is positive odd integer and n is negative odd integer.We know that difference of two odd integers is always even integer.Therefore, given expression is always even .
2.When n is even positive integer
Then n square is always positive even integer and n is positive integer .The sum of two even integers is always even.Hence, given expression is always even when n is even positive integer.
When n is negative even integer
n square is always positive even integer and n is even negative integer .The difference of two even integers is always even integer.
Hence, the given expression is always even for every integer.
2.By mathematical induction
Suppose n=1 then n= substituting in the given expression
1+1=2 =Even integer
Hence, it is true for n=1
Suppose it is true for n=k
then is even integer
We shall prove that it is true for n=k+1
=
=
=Even +2(k+1)[/tex] because is even
=Sum is even because sum even numbers is also even
Hence, the given expression is always even for every integer n.
<h3>Answer: 5 cakes</h3>
================================================
Explanation:
Let's start off converting the mixed number 12 & 1/4 to an improper fraction.
Do the same for the other mixed number 2 & 1/3.
-----------------------
From here, we divide the two fractions. I converted them to improper fractions to make the division process easier.
The last step is to convert that result to a mixed number.
Note that 21/4 = 5.25 and 1/4 = 0.25 to help check the answer.
-----------------------
Therefore, she can make 5 cakes. The fractional portion 1/4 is ignored since we're only considering whole cakes rather than partial ones.
Answer: The correct option is C.
Explanation:
A function is called an odd function if,
It means if the points are in the form of (x,y) then (-x,-y) is also in the graph.
Reason for correct option:
In option C, a point (1,2),
It means,
And we have another point (-1,-2).
The other points are (2,3),(-2,-3),(3,-1),(-3,1),(4,0),(-4,0). Therefore the function is an odd function.
Reason for incorrect option:
In option A, a point is (1,3), therefore the value of function at x = -1 should be -3.
But the value of function is 1 at x=-1, therefore it is not an odd function.
In option B, a point is (1,0), therefore the value of function at x = -1 should be 0.
But the value of function is -3 at x=-1, therefore it is not an odd function.
In option D, a point is (1,-1), therefore the value of function at x = -1 should be 1.
But the value of function is -1 at x=-1, therefore it is not an odd function.