To solve this problem, we need to understand how the submarine's position changes over time. We start with the submarine's initial depth, which is -1260 feet. The submarine descends 5 feet per minute for 12 minutes. We will analyze each available expression to find the one that correctly represents the new position of the submarine.
1. First Expression: [tex]\(-5 \times 12 + 1260\)[/tex]
- This first expression calculates [tex]\(-5 \times 12\)[/tex], which is the descent of the submarine (since it's descending 5 feet per minute for 12 minutes).
- So, the value is: [tex]\(-5 \times 12 = -60\)[/tex].
- Then it adds this descent to the starting depth: [tex]\(-60 + 1260 = 1200\)[/tex].
So, this expression gives the new position of the submarine, which is 1200 feet above sea level.
2. Second Expression: [tex]\(-1260 + (-5) \times 12\)[/tex]
- Here, we start with the initial depth of [tex]\(-1260\)[/tex] feet.
- The descent is calculated as [tex]\((-5) \times 12\)[/tex], which equals [tex]\(-60\)[/tex].
- Adding this descent to the initial depth: [tex]\(-1260 + -60 = -1320\)[/tex].
This expression ends up placing the submarine at -1320 feet below sea level.
3. Third Expression: [tex]\(-1260 + (5) \times 12\)[/tex]
- Starting again at [tex]\(-1260\)[/tex] feet.
- The multiplication is now [tex]\( (5) \times 12 = 60 \)[/tex].
- Adding this value to the initial depth: [tex]\(-1260 + 60\)[/tex] results in [tex]\(-1200\)[/tex].
This expression describes the submarine at -1200 feet below sea level.
4. Fourth Expression: [tex]\(1260 - (-5) \times 12\)[/tex]
- This starts with [tex]\(1260\)[/tex], the opposite of the initial depth.
- The descent is calculated as [tex]\((-5) \times 12\)[/tex], which equals [tex]\(-60\)[/tex].
- Then subtracting this: [tex]\(1260 - (-60)\)[/tex] results in [tex]\(1260 + 60\)[/tex], which equals [tex]\(1320\)[/tex].
This expression incorrectly gives the new position as 1320 feet above sea level.
Based on the step-by-step analysis, let's match these against our results:
- The correct expressions for the new position (based on given descent rate and time) are:
- [tex]\(-5 \times 12 + 1260\)[/tex] gives 1200 feet
- [tex]\(-1260 + (-5) \times 12\)[/tex] gives -1320 feet
- [tex]\(-1260 + (5) \times 12\)[/tex] gives -1200 feet
- [tex]\(1260 - (-5) \times 12\)[/tex] gives 1320 feet
So, after closely examining the question and the step-by-step solutions:
The correct expression that represents the submarine's new position is:
[tex]\[
-1,260 + (-5)(12)
\][/tex]
This expression results in the submarine being 1320 feet below sea level.
