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Fill in the value their must be 5 for each x and y and it can’t be negative 

The equation given in the image is:

\[
y = \sqrt{x + 2}
\]

You want to find values of \( x \) and \( y \) where both are positive and the value must be 5 for each pair.

Let's start by solving for \( x \) based on your condition that \( y = 5 \). To do that:

\[
y = 5 = \sqrt{x + 2}
\]

Square both sides to remove the square root:

\[
25 = x + 2
\]

Now solve for \( x \):

\[
x = 25 - 2 = 23
\]

So, when \( y = 5 \), \( x = 23 \). 

Thus, the values are \( x = 23 \) and \( y = 5 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you verify the solution by substituting the values back into the equation?
2. What happens if you change the value of \( y \) to something other than 5?
3. Can you graph this equation to see how \( y \) depends on \( x \)?
4. How would the solution change if the equation had a negative square root?
5. What is the domain of this function given that square roots must be non-negative?

**Tip:** Remember, the square root function always outputs a non-negative value, so \( x \) must be greater than or equal to \(-2\) for the function to be valid.

Fill in the value their must be 5 for each x and y and it can’t be negative

Learn how to solve the square root equation y = √(x + 2), finding values for x and y where both are positive and equal to 5. Suitable for students in Grades 8-10, this problem explores key algebraic concepts related to square root functions.

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