You can solve a system using substitution, elimination, or graphing method.
If you solve using substitution or elimination, the variable will cancel out on both sides and you will be left with a number equal to a number. If "number = number" is a TRUE statement, then the solution is ALL Real Numbers. <em>If it is a FALSE statement, then you will have NO solutions.</em>
If you solve using the graphing method and the lines are exactly the same, then the solution is Infinite solutions (aka ALL Real Numbers). <em>If the lines are parallel, then you will have NO solution.</em>
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Answer:
It depends, see answer below
Step-by-step explanation:
By arithmetic, we refer to the elementary operations between numbers. You can build the integer, rational, real and complex number systems from the natural numbers, so it is enough to obtain arithmetic for natural numbers.
In the axiomatic formulation of natural numbers, you assume that there exists a non empty set N such that multiplication and addition are defined in N with the commutative, associative, distributive and modulus properties. If you take this approach, you need all of the above: Numbers exist, Multiplication, Addition.
A different approach is the following: assume the Peano axioms: The set of natural numbers exists, and it obeys an inductive structure (without going in further details, every natural number has a unique sucessor, and mathematical induction is valid). You can define addition and multiplication inductively, so in this case you only need to assume that numbers exist.
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Answer:
511
Step-by-step explanation:
Each tube can be included in the mix, or not. There are 2^9 = 512 possible subsets of a set of 9 objects, including the complete set and the empty set. The empty set will not make a color, so there are ...
2^9 - 1 = 511 distinct color groupings that can be made
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The assumption in the above answer is that no tube color can be made by any combination of other tube colors.* We also assume that the choice of tubes is what makes a "color grouping", and that the colors within that grouping made by using different ratios of paint quantities are not counted separately.
Answer:
Step-by-step explanation:
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