Mai is solving the equation \((x-5)^2=0\). She writes that the solutions are \(x=5\) and \(x=\text- 5\). Han looks at her work and disagrees. He says that only \(x=5\) is a solution. Who do you agree with? Explain your reasoning.

The graph shows a model of the number of square meters, \(A\), of a lake that is covered by algae \(w\) weeks after it was first measured.

In a second lake, the number of square meters, \(B\), covered by algae is modeled by the equation \(B = 975 \boldcdot \left(\frac{2}{5}\right)^w\), where \(w\) is the number of weeks since it was first measured.

Graph of a function on grid, origin O. Horizontal axis, time, weeks, from 0 to 6 by 1's. Vertical axis, area, square meters, from 0 to 300 by 20's. Plotted coordinates as follows: 0 comma 240, 1 comma 120, 2 comma 60, 3 comma 30, 4 comma 15, 5 comma 7 point 5, 6 comma 3 point 75.   

For which algae population model is the area decreasing more rapidly? Explain how you know.

If the equation \((x-4)(x+6)=0\) is true, which is also true according to the zero product property?

1. Solve the equation \(25=4z^2\).
2. Show that your solution or solutions are correct.

To solve the quadratic equation \(3(x-4)^2 = 27\), Andre and Clare wrote the following:

1. Identify the mistake each student made.
2. Solve the equation, and show your reasoning.

Decide if each equation has 0, 1, or 2 solutions, and explain how you know.

1. \(x^2 -144=0\)
2. \(x^2 +144=0\)
3. \(x(x-5)=0\)
4. \((x-8)^2=0\)
5. \((x+3)(x+7)=0\)