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Answer:
- c
- b
- a
Step-by-step explanation:
This is as much about English comprehension as it is about math. When you read an English sentence, you need to figure out what each of the pronouns, phrases, and modifiers is referring to. When the sentence refers to math operations, you need to determine what each math operation is being applied to. In most cases, a math operation involves two operands, so the trick is to figure out what those are.
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1. "Two-thirds of the sum ..." will look like 2/3( + ). "The sum of a number and 5" will look like (x+5). So, the words are describing ...
2/3(x +5) . . . . matches C
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2. "Seven decreased by ..." will look like 7 -( ). "The quotient of a number and 3" will look like (n/3). So, the words are describing ...
7 -n/3 . . . . matches B
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3. Consider the order of operations. When you evaluate 2x²+9, the last operation you perform is addition. That is, the result is a sum. One of the elements of that sum is 9 (the second one). The other element of that sum is the product 2x². The elements of that product are 2 and the square of x. So, one way to describe this expression is ...
the sum of the product of 2 and the square of a number, and 9.
The order of operations requires that squares be evaluated before multiplication and division, so it is not unreasonable (if slightly more ambiguous) to write this as ...
the sum of 2 times a number squared and 9 . . . . choice A
