15. rodney is performing a science experiment. the table shows the temperature of two liquids he is using. graph the integers that represent the temperatures on a number line. which beaker’s liquid is closer to 0°c? explain.
(table: beaker a -4°c, beaker b 2°c)
(number line: -5 -4 -3 -2 -1 0 1 2 3)

16. sydney owes her mother $5 and her brother owes her mother $7. graph the integers that represent the amount they owe their mother as a negative integer on a number line. how much more will her brother have to repay their mother than sydney? explain.
(number line: -8 -7 -6 -5 -4 -3 -2 -1 0)

17. mp use math tools explain how to find the distance between 1 and −3 on a number line.

18. at midnight, the outside temperature was 0°f.
a. by 6:00 a.m., the temperature had dropped 4°f, and then the temperature raised 10°f by noon. what is the temperature at noon?
b. what represents zero in this situation? explain.

19. create describe a real-world situation that can be represented by a negative integer. then write the integer.

20. mp justify conclusions craig has $28 in his checking account. he wants to make a withdrawal of $30. will his checking account balance be represented by a positive or negative integer after the withdrawal? justify your conclusion.

Question

15. rodney is performing a science experiment. the table shows the temperature of two liquids he is using. graph the integers that represent the temperatures on a number line. which beaker’s liquid is closer to 0°c? explain.
(table: beaker a -4°c, beaker b 2°c)
(number line: -5 -4 -3 -2 -1 0 1 2 3)

16. sydney owes her mother $5 and her brother owes her mother $7. graph the integers that represent the amount they owe their mother as a negative integer on a number line. how much more will her brother have to repay their mother than sydney? explain.
(number line: -8 -7 -6 -5 -4 -3 -2 -1 0)

17. mp use math tools explain how to find the distance between 1 and −3 on a number line.

18. at midnight, the outside temperature was 0°f.
   a. by 6:00 a.m., the temperature had dropped 4°f, and then the temperature raised 10°f by noon. what is the temperature at noon?
   b. what represents zero in this situation? explain.

19. create describe a real-world situation that can be represented by a negative integer. then write the integer.

20. mp justify conclusions craig has $28 in his checking account. he wants to make a withdrawal of $30. will his checking account balance be represented by a positive or negative integer after the withdrawal? justify your conclusion.

Accepted Answer

### Question 15
# Explanation:
## Step1: Find absolute values
The temperature of Beaker A is $-4^\circ C$, its absolute value is $|-4| = 4$. The temperature of Beaker B is $2^\circ C$, its absolute value is $|2| = 2$.
## Step2: Compare absolute values
Since $2 < 4$, the distance of $2$ from $0$ is less than the distance of $-4$ from $0$.
# Answer: Beaker B's liquid is closer to $0^\circ C$ because the absolute value of $2$ (which is $2$) is less than the absolute value of $-4$ (which is $4$), meaning $2^\circ C$ is closer to $0^\circ C$ than $-4^\circ C$.

### Question 16
# Explanation:
## Step1: Represent owed amounts as integers
Sydney owes $\$5$, so we represent it as $-5$. Her brother owes $\$7$, so we represent it as $-7$.
## Step2: Calculate the difference
To find how much more her brother has to repay, we calculate $|-7| - |-5| = 7 - 5 = 2$.
# Answer: Her brother will have to repay $\$2$ more. Because the amount Sydney owes is represented by $-5$ (distance from $0$ is $5$) and her brother's is $-7$ (distance from $0$ is $7$), and $7 - 5 = 2$.

### Question 17
# Explanation:
## Step1: Recall distance formula on number line
The distance between two numbers $a$ and $b$ on a number line is $|a - b|$ (or $|b - a|$).
## Step2: Apply the formula
For $a = 1$ and $b = -3$, the distance is $|1 - (-3)| = |1 + 3| = |4| = 4$. Alternatively, we can count the units between $1$ and $-3$ on the number line: from $-3$ to $0$ is $3$ units, and from $0$ to $1$ is $1$ unit, so total $3 + 1 = 4$ units.
# Answer: To find the distance between $1$ and $-3$ on a number line, we can use the formula for the distance between two points $a$ and $b$, which is $|a - b|$. Substituting $a = 1$ and $b = -3$, we get $|1 - (-3)| = |4| = 4$. Or, we can count the units: from $-3$ to $0$ is $3$ units, and from $0$ to $1$ is $1$ unit, so the total distance is $3 + 1 = 4$.

### Question 18a
# Explanation:
## Step1: Start with initial temperature
The initial temperature at midnight is $0^\circ F$.
## Step2: Calculate temperature at 6:00 A.M.
It dropped $4^\circ F$, so the temperature at 6:00 A.M. is $0 - 4 = -4^\circ F$.
## Step3: Calculate temperature at noon
Then it raised $10^\circ F$, so the temperature at noon is $-4 + 10 = 6^\circ F$.
# Answer: The temperature at noon is $6^\circ F$.

### Question 18b
# Explanation:
In this situation, the temperature at midnight is $0^\circ F$. So the zero represents the outside temperature at midnight. It is the reference point from which we measure the changes (drop or rise) in temperature.
# Answer: The zero in this situation represents the outside temperature at midnight ($0^\circ F$). It is the initial temperature from which we track the changes (drop and rise) in temperature over time.

### Question 19
# Explanation:
A real - world situation: A person owes $\$10$ to a friend. In terms of integers, we can represent the amount of money the person has (considering the debt) as $-10$ because the debt is a negative financial situation (owing money means having a negative balance relative to the amount owed).
# Answer: Situation: John owes his friend $\$10$. The integer representing this situation is $-10$ (because owing money can be represented as a negative integer, where the negative sign indicates a debt or a deficit).

### Question 20
# Explanation:
## Step1: Calculate the balance after withdrawal
Craig has $\$28$ in his account. He withdraws $\$30$. The balance after withdrawal is $28-30=-2$.
## Step2: Determine the sign of the balance
Since $-2$ is a negative integer, his checking account balance will be represented by a negative integer. This is because the amount he withdraws ($\$30$) is more than the amount he has in his account ($\$28$), so he will have a negative balance (he owes the bank $\$2$ in this context).
# Answer: His checking account balance will be represented by a negative integer. Craig has $\$28$ and withdraws $\$30$. Calculating the balance: $28 - 30=-2$, which is a negative integer. Since the withdrawal amount is greater than the account balance, the resulting balance is negative.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 15

Step1: Find absolute values

Step2: Compare absolute values

Step1: Represent owed amounts as integers

Step2: Calculate the difference

Step1: Recall distance formula on number line

Step2: Apply the formula

Answer:

Question 16