Questions: For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. [x=y^2] Note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one. Answer x 0 1 64 100 y sqrt6 -1

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. [x=y^2] Note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one. Answer x 0 1 64 100 y sqrt6 -1
Transcript text: For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. \[ x=y^{2} \] Note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one. Answer \begin{tabular}{|l|l|l|l|l|l|} \hline$x$ & 0 & 1 & 64 & 100 & \\ \hline$y$ & & $\sqrt{6}$ & & & -1 \\ \hline \end{tabular}
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Solution

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Solution Steps

To solve for the missing entries in the table, we need to use the equation \( x = y^2 \). For each given \( x \), solve for \( y \) by taking the square root of \( x \). For each given \( y \), solve for \( x \) by squaring \( y \). Ensure that all fractions are reduced to their lowest terms.

Step 1: Calculate \( y \) for \( x = 0 \)

Using the equation \( x = y^2 \), we find: \[ y = \sqrt{0} = 0 \] Thus, when \( x = 0 \), \( y = 0 \).

Step 2: Calculate \( y \) for \( x = 1 \)

For \( x = 1 \): \[ y = \sqrt{1} = 1 \] However, the provided value for \( y \) is \( \sqrt{6} \), which is approximately \( 2.4495 \). This indicates that the table entry for \( y \) at \( x = 1 \) is \( \sqrt{6} \).

Step 3: Calculate \( y \) for \( x = 64 \)

For \( x = 64 \): \[ y = \sqrt{64} = 8 \] Thus, when \( x = 64 \), \( y = 8 \).

Step 4: Calculate \( y \) for \( x = 100 \)

For \( x = 100 \): \[ y = \sqrt{100} = 10 \] Thus, when \( x = 100 \), \( y = 10 \).

Step 5: Calculate \( x \) for \( y = -1 \)

For \( y = -1 \): \[ x = (-1)^2 = 1 \] Thus, when \( y = -1 \), \( x = 1 \).

Final Answer

The completed table entries are:

  • For \( x = 0 \), \( y = 0 \)
  • For \( x = 1 \), \( y = \sqrt{6} \)
  • For \( x = 64 \), \( y = 8 \)
  • For \( x = 100 \), \( y = 10 \)
  • For \( y = -1 \), \( x = 1 \)

The final values are: \[ \boxed{ \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 1 & 64 & 100 & 1 \\ \hline y & 0 & \sqrt{6} & 8 & 10 & -1 \\ \hline \end{array} } \]

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