Carlos has a nail in his car tire. The tire is not flat, but he's on his way to get it fixed. He's driving at a constant speed,
1 answer:
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Answer:
∠A = 70°
Step-by-step explanation:
I'm... guessing this is what you mean? It would've been helpful if you'd provided pictures.
Since all parallelograms consist of two pairs of vertically opposite angles, ∠A and ∠C are equivalent.
Which means that 2x + 50 = 3x + 40.
In which you solve the equation.
2x + 50 = 3x + 40
-2x -2x
50 = x + 40
-40 -40
x = 10
Now, to find ∠A, substitute x into the equation:
∠A = 2x + 50
x = 10
∠A = 20 + 50
∠A = 70
Hence, ∠A = 70°
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.