The equation given in the question is
5x^2 - 5x - 100 = 5x^2 - 25x + 20x - 100
= 5x(x - 5) + 20(x - 5)
= (5x + 20)(x - 5)
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the third option or option "C". I hope that this is the answer that you were looking for and the answer has actually come to your desired help.
Answers:
- Distributive Property
- Inverse Property
- Identity Property
- Associative Property
- Commutative Property
- Multiplication Property of Zero
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Explanations:
- The distributive property is a*(b+c) = a*b+a*c. We multiply the outer term 'a' by each term inside (b and c), then add up the results. In this specific case, we are multiplying the outer 2 by x and 3. So that's why 2(x+3) = 2x+2*3 = 2x+6. The concept of factoring takes this process in reverse, so we go from 2x+6 to 2(x+3).
- The inverse property, specifically the additive inverse property, is where we can add any number to its negative counterpart to always get 0. The expression 2+(-2) is the same as 2-2. We can think of it like "we're on the 2nd floor and we go down 2 floors to end up on floor 0". In general, the additive inverse property is x+(-x) = 0, which is the same as -x+x = 0.
- We can multiply any number by 1, to get the same number. So that's why 1*x = 1x = x. Similarly, x*1 = x as well. This is the multiplicative identity property, often shortened to "identity property".
- The parenthesis shifted around, so this means we'll use the associative property. In general, that is a+(b+c) = (a+b)+c.
- We can multiply two numbers in any order. The general format is a*b = b*a. This is the commutative property of multiplication. The version for addition is a+b = b+a.
- Multiplying 0 by any number leads to 0. So we could have the most complicated expression thought possible, but if we multiply it by 0, then the whole thing goes to 0. At the end of this complicated expression is where the 0 is buried. This idea is useful when it comes to the zero product property where if A*B = 0, then either A = 0 or B = 0 or both are the case.
Answer:
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Step-by-step explanation:
1. 3.14 x 4.5 x 12.5 + 3.14 x 4.5^2 = 240.21 = 240 cm^2
2. 14x(14x(sqrt(22^2+14^2)) = 561.1PI cm^2