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Three numbers have absolute values of 2, 4, and 9. The product of all the numbers is positive. a. Find the product. b. Find the different ways to write the signs of the numbers to give a positive product. Tell how many different ways there are in all.

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a) The product of the three absolute values is equal to 72.

b) There are four combinations to obtain a positive number by multiplication:

  1. 2, 4, 9
  2. - 2, - 4, 9
  3. - 2, 4, - 9
  4. 2, - 4, - 9

How to obtain the product of three numbers as a positive number

According to algebra, absolute values (i.e. |x|) are expressions defined by the following formula:

  1. |x| = x, for x ≥ 0.
  2. |x| = - x, for x < 0.

a) In this statement we notice that 2 can be generated both from 2 and - 2, 4 from 4 and - 4 and 9 from 9 and - 9. Then, the product of the three numbers is presented below:

|x₁| · |x₂| · |x₃| = 2 · 4 · 9 = 72

The product of the three absolute values is equal to 72.

b) According to sign laws, there are two forms of obtaining a positive number from three numbers:

  1. Three positive numbers.
  2. Two negative numbers and a positive number.

Based on all these facts, we can conclude the existence of four sign scenarios related to the three absolute numbers:

  1. x₁ = 2, x₂ = 4, x₃ = 9
  2. x₁ = - 2, x₂ = - 4, x₃ = 9
  3. x₁ = - 2, x₂ = 4, x₃ = - 9
  4. x₁ = 2, x₂ = - 4, x₃ = - 9

To learn more on absolute values: https://brainly.com/question/1301718

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