Evaluate the expression `3b-ac` when `a\ =\ -2`, `b\ =3`, and `c=0.5`.
To evaluate the expression `3b - ac` when `a = -2`, `b = 3`, and `c = 0.5`, we substitute the given values into the expression:
`3b - ac = 3(3) - (-2)(0.5)`
Simplifying:
`3b - ac = 9 - (-1)`
Continuing to simplify:
`3b - ac = 9 + 1`
Finally:
`3b - ac = 10`
Therefore, the value of the expression `3b - ac` when `a = -2`, `b = 3`, and `c = 0.5` is 10.
A state park charges an entrance fee plus $15 for each night of camping. The table shows this relationship. Which algebraic expression describes the total cost for camping `n` nights?
The table is not provided, so we cannot determine the specific relationship between the number of nights and the total cost. However, based on the information given, we can determine the algebraic expression that describes the total cost for camping `n` nights.
Let `x` represent the entrance fee and `y` represent the cost per night of camping. The total cost for camping `n` nights can be expressed as:
Total cost = (entrance fee) + (cost per night of camping) * (number of nights)
So, an algebraic expression that describes the total cost for camping `n` nights would be:
Total cost = x + y * n
A state park charges an entrance fee plus $15 for each night of camping. The table shows this relationship. Which algebraic expression describes the total cost for camping `n` nights?
15n + 20
20n + 15
15n - 20
35n
Based on the information given, the algebraic expression that describes the total cost for camping n nights is 15n + 20.
In this expression, 15n represents the cost for the number of nights (n) spent camping at $15 per night, and the additional $20 represents the entrance fee.
While on vacation, you rent a scooter. You pay $7.50 for each hour you use it. It costs $3 to rent a helmet. Write an algebraic expression that describes the total cost in terms of hours, x, that you rent the scooter.
To write an algebraic expression that describes the total cost in terms of hours, x, that you rent the scooter, we can follow these steps:
1. Determine the cost per hour: The cost per hour of using the scooter is $7.50.
2. Determine the cost of renting a helmet: The cost of renting a helmet is $3.
3. Multiply the cost per hour by the number of hours: To find the cost of renting the scooter for x hours, we multiply the cost per hour ($7.50) by the number of hours (x), which gives us 7.50x.
4. Add the cost of renting a helmet: To find the total cost, we add the cost of renting a helmet ($3) to the cost of renting the scooter for x hours (7.50x).
Therefore, the algebraic expression that describes the total cost in terms of hours, x, that you rent the scooter is: 7.50x + 3.
simplify 12\left(x+4\right)
To simplify the expression 12(x + 4), we distribute the 12 to each term inside the parentheses. This means multiplying 12 by both x and 4:
12(x) + 12(4)
Simplifying further:
12x + 48
Therefore, the simplified form of 12(x + 4) is 12x + 48.