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Chapter 0: Problem 77

State the name of the property illustrated. $$6+(2+7)=(6+2)+7$$

Short Answer

Expert verified
The property illustrated is the Associative Property.

Step by step solution

01

Observe the equation

First, look closely at the equation \(6+(2+7)=(6+2)+7\). We see that the numbers being added remain the same on both sides, but the placement of the parenthesis, which dictates the order of operations, is different.
02

Identify the property

Recall different mathematical properties, such as the commutative property, associative property, and distributive property. It becomes clear that the equation is demonstrating the associative property of addition.
03

Definition of the property

The associative property of addition states that the way numbers are grouped does not change their sum. In other words, if you are adding three or more numbers, it doesn't matter how you group them, you will always get the same answer. This means that for any numbers a, b, and c: \(a+(b+c) = (a+b)+c\).

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Most popular questions from this chapter

Find the intersection of the sets. $$\\{s, e, t\\} \cap\\{t, e, s\\}$$

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-5,-0 . \overline{3}, 0, \sqrt{2}, \sqrt{4}\\}$$

Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \% .\) Now the sale price is reduced by another \(30 \%\). If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?

$$\text { Factor completely.}$$ $$(x-y)^{4}-4(x-y)^{2}$$

$$\text { Factor completely.}$$ $$6 x^{4}+35 x^{2}-6$$
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