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Is the product of a negative and a positive integer always negative?
Yes.
Is the product of any two integers an integer?
Yes, the product of 2 integers are always an integers. ex. -2*3=-6
What can you say about the sum of an even integer and an even integer use inductive reasoning to form a conjecture then use deductive reasoning to show that the conjecture is true?
Conjecture: the sum of two even integers is always an even integer.Suppose M and N are two even integers.M is even and so it is divisible by 2 without remainder. That is to say, there is some integer X, such that M = 2X.Similarly, N = 2Y for some Y.Then M + N = 2X + 2Y=2*(X + Y) due to the distributive property of multiplication over addition of integers.And, by the closure of the set of integers under addition, X+Y is an integer.Therefore, M + N is equal to 2 times an integer and therefore it is an even integer.
Is the product of two perfect squares sometimes a perfect square?
yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.
What does an integer plus another integer equal?
an integer plus and integer will always be an integer. We say integers are closed under addition.
What does a good speaker always include?
~apex Inductive reasoning
Inductive reasoning is empirical in nature which means that it is based on observations and?
Inductive reasoning use theories and assumptions to validate observations. It involves reasoning from a specific case or cases to derive a general rule. The result of inductive reasoning are not always certain because it uses conclusion from observations to make generalizations. Inductive reasoning is helpful for extrapolation, prediction, and part to whole arguments.
When you multiply an integer less than 1 and an integer less than -1 what is the product?
2
What is the product of a negative integer and a positive integer?
always a negative
What is the product of a positive integer and a negative integer is always?
Negative
What is the product of a positive integer and negative integer?
always a negative
Is the product of a negative integer and a positive integer always positive?
No
What is the product of a negative integer and a negative integer?
A negative integer multiplied by a negative integer is always a positive integer product. -x * -y = xy
Is the sum of integers always an integer?
Yes, by definition, the sum of two integers is always an integer. Likewise, the product and difference of two integers is always an integer.
When is the product of a negative integer and positive integer greater than both of its factors?
Always.
When is the product of a negative integer and a positive integer less than both of its factors?
Always
Is the product of a negative and a positive integer always negative?
Yes.
