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3 years ago

Samantha conjectures that for x < -1, it is true that x5 - 2 > x. Is her conjecture correct? Why or why not?

Mathematics

1 answer:

Ronch [10]3 years ago

4 0

Answer:

The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

x^5 -2 ?? x

(-2)^5 -2 ?? (-2)

-32 -2 ?? -2

-34 < -2 . . . . . . not greater than

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Drag and drop each expression into the box to correctly classify it as having a positive or negative product

AfilCa [17]

Following expressions will have negative product

$(\frac{1}{2})(-\frac{1}{2})\ and\ (-\frac{1}{2})(\frac{1}{2})$

Following expressions will have positive product

$(-\frac{1}{2})(-\frac{1}{2})\ and\ (\frac{1}{2})(\frac{1}{2})$

Further explanation:

We will see at each expression one by one

First expression is:

$(-\frac{1}{2})(\frac{1}{2})$

In the given expression one term is positive and one term is negative. The product of negative and positive terms is negative.

Second Expression is:

$(-\frac{1}{2})(-\frac{1}{2})$

Both terms are negative and the product of two negative terms is positive.

Third Expression is:

$(\frac{1}{2})(-\frac{1}{2})$

The expression has one positive and one negative term so the product will be negative

Fourth Expression is:

$(\frac{1}{2})(\frac{1}{2})$

Both terms are positive so the product will also be positive

Keywords: Product, Expressions

Learn more about expressions at:

#LearnwithBrainly

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Answer:

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