1. Commutative property of multiplication This is because it represents a*b=b*a
2. Associative property of multiplication. Multiplication problems end with the same product no matter the order of factors.
3. Correct
4. Correct
5. Associative property of addition. Even though the grouping symbols are different, it is equivalent because you are adding all the terms together.
6. Correct
The last one should also be associative property since it applies every time you combine like terms.
Just a reminder: Distributive property is only when you multiply in the form of a(b+c)=ab+ac
Answer:
cost of producing the 501st item = $9.92
Step-by-step explanation:
The function representing the cost is given by;
C(x) = 10000 + 90x - 0.08x²
To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.
Thus;
C(500) = 10000 + 90(500) - 0.08(500)²
C(500) = 10000 + 45000 - 20000
C(500) = $35000
Similarly;
C(501) = 10000 + 90(501) - 0.08(501)²
C(501) = 10000 + 45090 - 20080.08
C(501) = $35009.92
cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92
In a 45 - 45 - 90 right triangle, the hypotenuse is √2 · legs = hypotenuse, so legs=
and to rationalize the denominator all we have to do is multiply the numerator and denominator by √2. 
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