Calculate the answers

|-3-|-7-7||

Does |n+m| = |n|+|m| for all integers na and m? If so, give some examples. If not, give a counterexample.

The Weathertalk Analysis Problem. Read the following story about the TV weatherperson and identify as many places as possible that the weatherperson could use addition or subtraction of integers to answer her questions.

Write and solve the number sentences she could use.

Ms. Cloudcover, the TV weatherperson, noted that Sunday’s temperature was 12, much warmer than the -7 on Friday and the -2 on Saturday. She remembered that Thursday’s temperature was 0 and checked to see how far Saturday’s temperature had fallen from Thursday’s temperature. She made a
note to report the average temperature for the 3-day weekend
and the temperature change from Friday to Saturday and from
Saturday to Sunday. Then she began work on a report about
how the high temperatures for each day of the past week had been over or under the normal high temperature for that day.
She wrote,
Sun: -8
Mon: -5
Tues: -2
Wed: 6
Thurs: 3
Fri: -4
Sat: 9
She wondered whether the net effect of the week was more or less than normal. Before she left for the day, she noted that today’s low temperature was and figured the difference between it and the record low of for today’s date.

|-3-|-7-7||

= |-3-(14)|
= |-3-14|
= |-17|
= 17

|n+m| = |n|+|m|
is only true if both m and n ≥ 0
all you need to show is ONE counterexample and the statement would not be true
e.g.
|9-5) = |9| + |-5|
4 = 9+5
4 = 14 ---> false !

Please do not expect tutors to just do your homework for you.
I will leave the last one for you to finish

To calculate the given expression |-3-|-7-7||, follow these steps:

1. Start by evaluating the expression inside the innermost absolute value symbols: |7-7|. Since 7-7 equals 0, the expression simplifies to |-3-|0||.

2. Now evaluate the expression inside the outermost absolute value symbols: |-3|. Since -3 is negative, the expression becomes |-(-3)|.

3. To remove the negative sign inside the absolute value, change the sign of the number: |-(-3)| becomes |3|.

4. Finally, evaluate the absolute value of 3. Since 3 is positive, the expression becomes 3.

Therefore, the answer is 3.

Regarding the second question about whether |n+m| = |n|+|m| for all integers n and m, this statement is not always true. It depends on the values of n and m. To find a counterexample, we need to find values of n and m for which the equation does not hold.

Counterexample:
Let n = -2 and m = 3.

|n+m| = |-2 + 3| = |1| = 1

|n| + |m| = |-2| + |3| = 2 + 3 = 5

Therefore, in this case, |n+m| does not equal |n|+|m|, providing a counterexample.

Moving on to the third question about the Weathertalk Analysis Problem, here are the places where the weatherperson could use addition or subtraction of integers:

1. To find the temperature change from Friday to Saturday: Subtract the temperature on Friday (-7) from the temperature on Saturday (-2) to find the difference: -2 - (-7) = 5.

2. To find the temperature change from Saturday to Sunday: Subtract the temperature on Saturday (9) from the temperature on Sunday (-8) to find the difference: -8 - 9 = -17.

3. To calculate the average temperature for the 3-day weekend: Add the temperatures of Friday (-7), Saturday (-2), and Sunday (-8) and divide by 3: (-7) + (-2) + (-8) / 3 = -17 / 3.

4. To find the difference between Saturday's temperature (9) and Thursday's temperature (0): Subtract the temperature on Thursday (0) from the temperature on Saturday (9) to find the difference: 9 - 0 = 9.

5. To find the difference between today's low temperature and the record low temperature for today's date: Subtract the record low temperature from the current low temperature.

These are some examples of number sentences the weatherperson could use and how to solve them based on the given information.