Add 5 gal 2qt + 4gal 3qt
1 answer:
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Answer:
see below
Step-by-step explanation:
Put -1 where x is in each expression and evaluate it.
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You will find that the expression is zero when the numerator is zero. And you will find the numerator is zero when it has a factor that is equivalent to ...
(x +1)
Substituting x=-1 into this factor makes it be ...
(-1 +1) = 0
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Evaluating the first expression, we have ...
This first expression is one you want to "check."
You can see that the reason the expression is zero is that x+1 has a sum of zero. You can look for that same sum in the other expressions. (The tricky one is the one with the factor (x -(-1)). You know, of course, that -(-1) = +1.)
Answers:
- a) 2048
- b) 2047
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Explanation:
If a set has n elements inside it, then it has 2^n different subsets.
Consider a set like {a,b,c}. It has n = 3 elements.
It has 2^n = 2^3 = 8 subsets
Those 8 subsets are...
- {a,b,c} ..... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } .... the empty set
As you can see, each subset consists of items that are selected from the original set {a,b,c}. We can't have any repeat letters.
In that list, items 2 through 4 represent subsets with exactly two things inside it. Items 5 through 7 are known as singletons as they only have one item inside each set. The empty set can be written with the symbol or you could have a pair of braces with nothing inside them. The empty set is a subset of any set.
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Note how I included {a,b,c} as a subset. Any set is a subset of itself.
A proper subset will ignore the original set and only look at smaller subsets. If we say B is a proper subset of A, then set B will have fewer items compared to set A. Without the "proper" in there, it's possible that A = B.
So all we've done really is kick out one set which drops 2^n to (2^n)-1 when counting the number of proper subsets. I'm using parenthesis to indicate the "-1" is not part of the exponent. If you wrote this on your paper, then you would likely write
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For this problem, n = 11
This means there are 2^n = 2^11 = 2048 subsets and (2^n)-1 = 2048-1 = 2047 proper subsets.
Answer:
Step-by-step explanation:
by properties of parallel lines
because they form a straight angle