?(1 point)
Responses
a number line that goes 0 to 20, and a dot is on 2.
a number line that goes 0 to 20, and a dot is on 4
a number line that goes 0 to 20, and a dot is on 8
a number line that goes 0 to 20, and a dot is on 10
11 answers
To solve the equation \( \frac{1}{2}x - 2 = 3 \), we will isolate \( x \).
Add 2 to both sides: \[ \frac{1}{2}x = 3 + 2 \] \[ \frac{1}{2}x = 5 \]
Multiply both sides by 2 to solve for \( x \): \[ x = 5 \times 2 \] \[ x = 10 \]
Therefore, the solution to the equation is \( x = 10 \).
The graph that best represents this solution on a number line would be the one with a dot on 10.
So, the correct response is: a number line that goes 0 to 20, and a dot is on 10.
To find the number in the equation "The sum of 8 and a number divided by 3 equals 6," we can set up the equation as follows:
Let \( x \) be the number.
The equation can be expressed as: \[ \frac{8 + x}{3} = 6 \]
Now, we will solve for \( x \).
Multiply both sides by 3 to eliminate the fraction: \[ 8 + x = 6 \times 3 \] \[ 8 + x = 18 \]
Subtract 8 from both sides: \[ x = 18 - 8 \] \[ x = 10 \]
So, the number is \( 10 \), which does not appear to be in the provided responses. Please double-check the problem or the answer choices. If there is anything else you would like to clarify or if there are additional details, let me know!
Given the provided answer choices:
Since none of the choices correspond to the calculated solution of \( x = 10\), I will choose the closest option, which is 6.
If you need further clarification or additional help, please let me know!
To analyze the equation \(20h + 40 = 480\):
Let's break down the equation:
From this, we can see that Stacey received a bonus of $40 and $20 for each hour she worked, and in total, she earned $480.
Therefore, the best representation from the choices provided is:
Stacey was paid $40 last week. She was paid a $20 bonus and $480 for each hour she worked.
However, this choice seems somewhat confusing with regard to the numbers given (it implies an amount per hour). The correct version considering the total earned would be:
Stacey was paid $480 last week. She was paid a $20 bonus and $40 for each hour she worked.
If one of the options doesn't quite match up, the latter would be the accurate interpretation of the equation.
In conclusion:
Stacey was paid $480 last week. She was paid a $20 bonus and $40 for each hour she worked.
To analyze the equation \(2000 - 200x = 1000\):
The equation can be interpreted as follows: Jenny starts with $2000 and spends $200 each day. After spending for \(x\) days, she has $1000 remaining.
Now, let's rewrite that in context of a situation:
"Jenny went on vacation. She started with $2000 and spent $200 each day. Solve for x to find the number of days Jenny has been on vacation if she has $1000 left to spend."
This exact scenario matches the first response option.
Thus, the best representation of the situation described by the equation \(2000 - 200x = 1000\) is:
Jenny went on vacation. She started with $2000 and spent $200 each day. Solve for x to find the number of days Jenny has been on vacation if she has $1000 left to spend.
To find out how much each additional hour of parking costs, we can set up the problem based on the information given.
Now, we can calculate how much she spent on the additional hours.
Calculate additional hours: \[ \text{Additional hours} = 6 \text{ hours} - 2 \text{ hours} = 4 \text{ hours} \]
Calculate the cost for additional hours: \[ \text{Total cost for additional hours} = \text{Total cost} - \text{Base rate} \] \[ \text{Total cost for additional hours} = 31 - 3 = 28 \]
Calculate the cost per additional hour: \[ \text{Cost per additional hour} = \frac{\text{Total cost for additional hours}}{\text{Additional hours}} = \frac{28}{4} = 7 \]
Thus, each additional hour of parking costs $7.00.
The correct response is: $7.00.
