Let's solve each of the boxes step-by-step:
1. [tex]$\square + (-7.28) = \text{ a positive number}$[/tex]
To make the result a positive number, [tex]$\square$[/tex] must be a number greater than 7.28. Suppose we choose:
[tex]\[
\square = 10
\][/tex]
Checking:
[tex]\[
10 + (-7.28) = 2.72 \quad (\text{which is a positive number})
\][/tex]
2. [tex]$12 + \square = 0$[/tex]
To solve for [tex]$\square$[/tex], we need to isolate the variable:
[tex]\[
\square = -12
\][/tex]
Checking:
[tex]\[
12 + (-12) = 0 \quad (\text{which satisfies the equation})
\][/tex]
3. [tex]$\square - 2 \frac{3}{4} = \text{ a negative number}$[/tex]
To make the result a negative number, [tex]$\square$[/tex] must be less than [tex]$2 \frac{3}{4}$[/tex], which is [tex]$2.75$[/tex]. Suppose we choose:
[tex]\[
\square = -3
\][/tex]
Checking:
[tex]\[
-3 - 2.75 = -5.75 \quad (\text{which is a negative number})
\][/tex]
4. [tex]$\begin{array}{l} -4.8 - \square = \text { a positive number } \end{array}$[/tex]
To make the result a positive number, [tex]$\square$[/tex] must be less than -4.8. Suppose we choose:
[tex]\[
\square = -9.8
\][/tex]
Checking:
[tex]\[
-4.8 - (-9.8) = -4.8 + 9.8 = 5 \quad (\text{which is a positive number})
\][/tex]
5. [tex]$\begin{array}{l} -15 + 15 = \square \end{array}$[/tex]
This is straightforward:
[tex]\[
\square = 0
\][/tex]
Checking:
[tex]\[
-15 + 15 = 0
\][/tex]
So, the filled-in boxes are:
1. [tex]$\boxed{10}$[/tex]
2. [tex]$\boxed{-12}$[/tex]
3. [tex]$\boxed{-3}$[/tex]
4. [tex]$\boxed{-9.8}$[/tex]
5. [tex]$\boxed{0}$[/tex]
