ulio and Ashley went to the drive-in theater. They paid an entry fee for the car and individual entry fees for themselves. Their total cost can be modeled by the expression 2.5x+10 . Which of the following answer choices accurately interprets a part of the algebraic expression? (1 point)

Question

ulio and Ashley went to the drive-in theater. They paid an entry fee for the car and individual entry fees for themselves. Their total cost can be modeled by the expression  2.5x+10 . Which of the following answer choices accurately interprets a part of the algebraic expression? (1 point)
Responses

The entry fee for the car was $10.00.
The entry fee for the car was $10.00.

The entry fee for the car was $2.50.
The entry fee for the car was $2.50.

The entry fee for the car was $12.50.
The entry fee for the car was $12.50.

Each individual entry fee was $10.00.

GPT-4o mini · Answer

To interpret the expression $ 2.5x + 10 $: - $ 10 $ represents the total entry fee for the car. - $ 2.5x $ represents the individual entry fees for each person, where $ x $ is the number of people (here it seems x = 2 for Julio and Ashley, so that would be $ 2.5 \times 2 = 5 $). From this, we can determine that: - The entry fee for the car is $10.00. - The individual entry fee for each person is $2.50. Therefore, the accurate interpretation from the given options is: **The entry fee for the car was $10.00.**

Answer

Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)
Responses

There are four variables.
There are four variables.

8 is the only factor of 8x.
8 is the only factor of 8 x .

8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.

8, −3, 2, and 9 are constants.

GPT-4o mini · Answer

To analyze the given equation $ 8x - 3y = 2x + 9y $, let's look at the statements one by one: 1. **There are four variables.** - This is incorrect. The equation contains two variables: $ x $ and $ y $. 2. **8 is the only factor of 8x.** - This is also incorrect. While 8 is a factor of $ 8x $, it is not the only factor; for example, $ 1 \times 8x $ is also a valid factorization. 3. **8, −3, 2, and 9 are coefficients.** - This statement is correct. In the equation, the numbers $ 8 $ and $ 2 $ are coefficients of $ x $, and $ -3 $ and $ 9 $ are coefficients of $ y $. 4. **8, −3, 2, and 9 are constants.** - This is incorrect. Coefficients are defined as the multipliers of variables; constants are standalone numbers without variables. In this case, $ 8, -3, 2, $ and $ 9 $ serve as coefficients. The correct statement is: **8, −3, 2, and 9 are coefficients.**

Answer

An equation can be broken down into expressions, terms, variables, constants, and coefficients. In the equation 0.4−7x=3 , what is/are the constant(s) in the equation?(1 point)
Responses

3
3

0.4
0.4

−7
negative 7

0.4 and 3

GPT-4o mini · Answer

In the equation $ 0.4 - 7x = 3 $: - **Constants** are numbers that do not change and do not have variables attached to them. - In this equation, $ 0.4 $ and $ 3 $ are both constants, while $ -7 $ is a coefficient of the variable $ x $. Therefore, the correct answer is: **0.4 and 3**.

Answer

se the grouping symbols to interpret the following equation: x/8=3(x+4)/2 . Which expression in the equation represents a product?(1 point)
Responses

x/8
Start Fraction x over 8 End Fraction

2
2

3(x+4)
3 left parenthesis x plus 4 right parenthesis

3(x+4)/2

GPT-4o mini · Answer

To determine which expression in the equation $ \frac{x}{8} = \frac{3(x + 4)}{2} $ represents a product, let's analyze each of the response options:

$ \frac{x}{8} $
- This expression represents a fraction, not a product.
$ 2 $
- This is a constant value, not a product.
$ 3(x + 4) $
- This expression represents a product because it shows the constant $ 3 $ multiplied by the expression $ (x + 4) $.
$ \frac{3(x + 4)}{2} $
- While this expression contains a product within it (the $ 3(x + 4) $ part), the entire expression is divided by $ 2 $ and is thus a fraction.

Based on this analysis, the expression that represents a product is:

3(x + 4).

Answer

Consider the expression [3(42+32÷4−5)] . Which quotient must be found to simplify the expression?(1 point) Responses 96÷4 96 divided by 4 48÷4 48 divided by 4 144÷4 144 divided by 4 32÷4

GPT-4o mini · Answer

To simplify the expression $ 3(42 + 32 \div 4 - 5) $, we need to evaluate the part inside the brackets first. Starting with the expression inside the brackets: 1. The first step is to evaluate the division, which is $ 32 \div 4 $. Since this is the only division operation present in the expression inside the brackets before we handle the addition and subtraction, we only need to find **$ 32 \div 4 $** to simplify the expression. Thus, the correct response is: **32 ÷ 4**.

Answer

Consider the expression [3(4^2+32÷4−5)] . Which quotient must be found to simplify the expression?(1 point) Responses 96÷4 96 divided by 4 48÷4 48 divided by 4 144÷4 144 divided by 4 32÷4

GPT-4o mini · Answer

To simplify the expression $ 3(4^2 + 32 \div 4 - 5) $, we will evaluate the expression inside the brackets step by step. 1. **Calculate $ 4^2 $**: $$ 4^2 = 16 $$ 2. **Evaluate $ 32 \div 4 $**: $$ 32 \div 4 = 8 $$ So, now we rewrite the expression as: $$ 3(16 + 8 - 5) $$ Next step is adding and subtracting: $$ 16 + 8 = 24 $$ $$ 24 - 5 = 19 $$ Now, you have: $$ 3(19) $$ However, since the question asks about which quotient must be found to simplify the expression, we see that the division required is $ 32 \div 4 $. Thus, the correct answer is: **32 ÷ 4**.