To determine the temperature on Tuesday, let's perform a step-by-step calculation:
1. The temperature on Monday is given as [tex]\(-4^{\circ} C\)[/tex].
2. The change in temperature from Monday to Tuesday is given as [tex]\(-13^{\circ} C\)[/tex]. This means that Tuesday is [tex]\(13^{\circ} C\)[/tex] colder than Monday.
To find the temperature on Tuesday, we start from the temperature on Monday and subtract the temperature change:
[tex]\[
\text{Temperature on Tuesday} = \text{Temperature on Monday} + \text{Temperature Change}
\][/tex]
Substituting the given values:
[tex]\[
\text{Temperature on Tuesday} = (-4^{\circ} C) + (-13^{\circ} C)
\][/tex]
Performing the addition of these two negative numbers:
[tex]\[
-4 + (-13) = -4 - 13 = -17
\][/tex]
Therefore, the temperature on Tuesday is:
[tex]\[
-17^{\circ} C
\][/tex]
Hence, the correct answer is [tex]\(-17^{\circ} C\)[/tex].
