Pregunta
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Complete the pattern:

Ask by Rojas Joseph. in the United States
Jan 23,2025

Solución de inteligencia artificial de Upstudy

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The pattern uses and for the divisions.
  1. Result:

Solución

To complete the pattern, let’s analyze the given equations step by step.
  1. The first equation is:
    We need to find the value of that will allow us to establish a pattern.
  2. The second equation is:
    To find , we can rearrange this equation:
  3. Let’s calculate using the above equation:
  4. The third equation is:
    We will use the same value we found earlier.
  5. The fourth equation is:
    Rearranging gives us:
Now, let’s calculate the values of from both equations to see if they are consistent.
I’ll perform the calculations for both equations.
Calculate the value by following steps:
  • step0: Calculate:
  • step1: Convert the expressions:
  • step2: Multiply by the reciprocal:
  • step3: Reduce the numbers:
  • step4: Simplify:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Convert the expressions:
  • step2: Multiply by the reciprocal:
  • step3: Reduce the numbers:
  • step4: Multiply the numbers:

    The calculations yield the following results for :
  1. From the second equation:
  2. From the fourth equation:
Now, we can summarize the pattern:
  • The first equation should use .
  • The second equation uses .
  • The third equation should use .
  • The fourth equation uses .
Thus, the completed pattern is:
The values of are and for the respective divisions.

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Bonus Knowledge

To complete the pattern, we can observe how the numbers are structured and the relationship between each division operation.
  1. For , the square must equal 1000. This is because dividing by 1000 gives .
  2. For , to follow the same pattern, we notice is times (which is when divided by 1,000). Therefore, would equal 100.
Continuing down the list, we follow the same pattern:
For , we can reason that the square must be 1000 again (continuing the multiplication/division structure).
For , using .
  1. For
  2. For
  3. For
  4. For
Thus the filled values of the squares:
  • for the first line
  • for the second
  • for the third
  • for the fourth

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