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name:math is life ©core____directions: find each sum or difference.1) $-9 + 14 =$ __ positive or negative2) $7-(-6) =$ __ positive or negative3) $-3 -8 =$ __ positive or negative4) $3 -8 + -2 =$ __ positive or negative5) $-4 -(-14) =$ __ positive or negative6) $7 -9 + 4 =$ __ positive or negativedirections: solve each word problem. you must show work to solve. you will receive a no hw if you do not show work.7) a treasure chest sits 1,256 feet below sea level. a captain looking for the treasure is in a house 769 feet above sea level. what is the vertical distance between the treasure chest and the house?show your work.a. $-496$ feetb. 496 feetc. 1,256 feetd. 2,025 feetpositive or negative8) thomas works as an underwater photographer. he starts at a depth of 20 feet, ascends 9 feet, descends 12 feet, and then descends 15 feet more. write and simplify an expression to find his final depth. expression:__answer:__9) anna is collecting samples in a cavern and starts 40 feet underground. she ascends 11 feet, descends 13 feet, descends 5 feet, and ascends 18 feet. write and simplify an expression to find her final location. expression:__answer:__10) marley gets on an elevator at the $30^{th}$ floor of a building. she goes up 6 floors to pick up a package then goes down 14 floors for a meeting. write and simplify an expression to show what floor marley is on now. expression:__answer:____

Explanation:

Step1: Evaluate signed numbers

$-9 + 14 = 5$

Step2: Evaluate signed numbers

$7 - (-6) = 7 + 6 = 13$

Step3: Evaluate signed numbers

$-3 - 8 = -11$

Step4: Evaluate signed numbers

$3 - 8 + (-2) = 3 - 8 - 2 = -7$

Step5: Evaluate signed numbers

$-4 - (-14) = -4 + 14 = 10$

Step6: Evaluate signed numbers

$7 - 9 + 4 = 2$

Step7: Define distance values

Let sea level = 0. Treasure chest: $-1256$ ft, house: $769$ ft. Distance = $|769 - (-1256)|$

Step8: Calculate vertical distance

$|769 + 1256| = |2025| = 2025$

Step9: Write depth expression

Start depth: $-20$ ft. Ascend = $+9$, descend = $-12$, $-15$. Expression: $-20 + 9 - 12 - 15$

Step10: Simplify depth expression

$-20 + 9 - 12 - 15 = -38$

Step11: Write location expression

Start: $-40$ ft. Ascend = $+11$, $+18$; descend = $-13$, $-5$. Expression: $-40 + 11 - 13 - 5 + 18$

Step12: Simplify location expression

$-40 + 11 - 13 - 5 + 18 = -29$

Step13: Write floor expression

Start: $30$. Up = $+6$, down = $-14$. Expression: $30 + 6 - 14$

Step14: Simplify floor expression

$30 + 6 - 14 = 22$

Answer:

1. $5$ (Positive)
2. $13$ (Positive)
3. $-11$ (Negative)
4. $-7$ (Negative)
5. $10$ (Positive)
6. $2$ (Positive)
7. D. 2,025 feet (Positive)
8. Expression: $-20 + 9 - 12 - 15$; Answer: $-38$ feet
9. Expression: $-40 + 11 - 13 - 5 + 18$; Answer: $-29$ feet
10. Expression: $30 + 6 - 14$; Answer: $22$nd floor