Question

Evaluate the expression `3b-ac` when `a\ =\ -2`, `b\ =3`, and `c=0.5`.
Answer
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?
Answer
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
Answer
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.
Answer
simplify 12\left(x+4\right)
Answer
simplify -2\left(2x-5\right)
Answer
simplify \frac{1}{2}\left(6x+10\right)
Answer
simplify 3\left(8-5x\right)\ +\ 2x
Answer
simplify 5x-4\left(2+3x\right)
Answered by GPT 3.5
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.
Answered by GPT 3.5
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
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
To simplify the expression -2(2x - 5), we need to distribute the -2 to each term inside the parentheses. This means multiplying -2 by both 2x and -5:

-2(2x) - 2(-5)

Simplifying further:

-4x + 10

Therefore, the simplified form of -2(2x - 5) is -4x + 10.
Answered by GPT 3.5
To simplify the expression (1/2)(6x + 10), we need to distribute 1/2 to each term inside the parentheses. This means multiplying 1/2 by both 6x and 10:

(1/2)(6x) + (1/2)(10)

Simplifying further:

3x + 5

Therefore, the simplified form of (1/2)(6x + 10) is 3x + 5.
Answered by GPT 3.5
To simplify the expression 3(8 - 5x) + 2x, we need to distribute the 3 to each term inside the parentheses. This means multiplying 3 by both 8 and -5x:

3 * 8 - 3 * 5x + 2x

Simplifying further:

24 - 15x + 2x

Combining like terms:

-13x + 24

Therefore, the simplified form of 3(8 - 5x) + 2x is -13x + 24.
Answered by GPT 3.5
To simplify the expression 5x - 4(2 + 3x), we need to distribute the -4 to each term inside the parentheses. This means multiplying -4 by both 2 and 3x:

5x - 4 * 2 - 4 * 3x

Simplifying further:

5x - 8 - 12x

Combining like terms:

-7x - 8

Therefore, the simplified form of 5x - 4(2 + 3x) is -7x - 8.