Math Problem Statement

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

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

Solution

The equation given in the image is:

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

You want to find values of xx and yy where both are positive and the value must be 5 for each pair.

Let's start by solving for xx based on your condition that y=5y = 5. To do that:

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

Square both sides to remove the square root:

25=x+225 = x + 2

Now solve for xx:

x=252=23x = 25 - 2 = 23

So, when y=5y = 5, x=23x = 23.

Thus, the values are x=23x = 23 and y=5y = 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 yy to something other than 5?
  3. Can you graph this equation to see how yy depends on xx?
  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 xx must be greater than or equal to 2-2 for the function to be valid.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Root Functions

Formulas

y = √(x + 2)

Theorems

Properties of Square Root

Suitable Grade Level

Grades 8-10