find each value. draw a model, if needed.
15 -11 + 9 =
16 56 + (-52) =
17 -7 + (-12) =
18 6 + (-4) =
19 -96 + 15 =
20 a submarine was situation 800 feet below sea level. if it ascends 250 feet, what is its new position?
21 on the first play, the football team lost 6 yards. on the second play the team lost 5 yards. what was their total change in yards?

Question

Accepted Answer

### Problem 15: $-11 + 9$
# Explanation:
## Step 1: Analyze signs and values
We have a negative number $-11$ and a positive number $9$. When adding a negative and a positive, we subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. The absolute value of $-11$ is $11$, and the absolute value of $9$ is $9$. Since $11>9$, the result will be negative.
## Step 2: Perform the subtraction
Subtract the smaller absolute value from the larger one: $11 - 9 = 2$. Then apply the sign of the number with the larger absolute value (negative), so $-11 + 9=- (11 - 9)=-2$.
# Answer: $-2$

### Problem 16: $56+(-52)$
# Explanation:
## Step 1: Simplify the expression
Adding a negative number is the same as subtracting its positive counterpart. So $56+(-52)=56 - 52$.
## Step 2: Perform the subtraction
$56-52 = 4$.
# Answer: $4$

### Problem 17: $-7+(-12)$
# Explanation:
## Step 1: Analyze the signs
Both numbers are negative. When adding two negative numbers, we add their absolute values and keep the negative sign.
## Step 2: Add the absolute values
The absolute value of $-7$ is $7$, and the absolute value of $-12$ is $12$. Adding these absolute values: $7 + 12=19$. Then apply the negative sign, so $-7+(-12)=-(7 + 12)=-19$.
# Answer: $-19$

### Problem 18: $6+(-4)$
# Explanation:
## Step 1: Simplify the expression
Adding a negative number is the same as subtracting its positive counterpart. So $6+(-4)=6 - 4$.
## Step 2: Perform the subtraction
$6 - 4=2$.
# Answer: $2$

### Problem 19: $-96 + 15$
# Explanation:
## Step 1: Analyze signs and values
We have a negative number $-96$ and a positive number $15$. The absolute value of $-96$ is $96$, and the absolute value of $15$ is $15$. Since $96>15$, the result will be negative.
## Step 2: Perform the subtraction
Subtract the smaller absolute value from the larger one: $96 - 15 = 81$. Then apply the negative sign, so $-96+15=-(96 - 15)=-81$.
# Answer: $-81$

### Problem 20: Submarine Position
# Explanation:
## Step 1: Define the initial position
The submarine is $800$ feet below sea level. We can represent this as $-800$ feet (using negative to indicate below sea level).
## Step 2: Define the change in position
It ascends $250$ feet. Ascending means moving up, so this is a positive change. We add this change to the initial position: $-800+250$.
## Step 3: Perform the addition
We have a negative number $-800$ and a positive number $250$. The absolute value of $-800$ is $800$, and the absolute value of $250$ is $250$. Since $800>250$, the result will be negative. Subtract the smaller absolute value from the larger one: $800 - 250 = 550$. Then apply the negative sign, so $-800 + 250=- (800 - 250)=-550$. So the new position is $550$ feet below sea level.
# Answer: $550$ feet below sea level (or $-550$ feet relative to sea level)

### Problem 21: Football Team's Yard Change
# Explanation:
## Step 1: Define the changes
Losing yards means a negative change. On the first play, they lost $6$ yards, so that's $-6$ yards. On the second play, they lost $5$ yards, so that's $-5$ yards.
## Step 2: Find the total change
To find the total change, we add these two changes: $-6+(-5)$.
## Step 3: Add the negative numbers
When adding two negative numbers, we add their absolute values and keep the negative sign. The absolute value of $-6$ is $6$, and the absolute value of $-5$ is $5$. Adding these: $6 + 5 = 11$. Then apply the negative sign, so $-6+(-5)=-11$. So the total change is a loss of $11$ yards.
# Answer: A loss of $11$ yards (or $-11$ yards)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 15: \(-11 + 9\)

Step 1: Analyze signs and values

Step 2: Perform the subtraction

Step 1: Simplify the expression

Step 2: Perform the subtraction

Step 1: Analyze the signs

Step 2: Add the absolute values

Answer:

Problem 16: \(56+(-52)\)