Julio 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

Responses

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

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

Each individual entry fee was $10.00.
Each individual entry fee was $10.00.

The entry fee for the car was $10.00.

Answer 1

To interpret the expression \(2.5x + 10\):

• \(2.5x\) represents the total individual entry fees for Julio and Ashley (where \(x\) is the entry fee per person, and since there are two people, it is \(2.5\) times the individual fee for each).
• The constant \(10\) represents the entry fee for the car.

1. Understanding the components:
   • Since \(x\) represents the individual entry fee, if we let \(x = 2.5\), then the total individual entry cost for both would be \(2.5 \times 2 = 5.0\).
   • Thus, \(10\) (the entry fee for the car) does not correspond to \(2.5\) but is a flat amount for the car.

Analyzing the choices:

• "The entry fee for the car was $12.50." (Incorrect)
• "The entry fee for the car was $2.50." (Incorrect)
• "Each individual entry fee was $10.00." (Incorrect)
• "The entry fee for the car was $10.00." (Correct)

Therefore, the correct interpretation from the choices provided is:

The entry fee for the car was $10.00.

Answer 2

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

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

8, −3, 2, and 9 are constants.

Answer 3

To analyze the equation \(8x - 3y = 2x + 9y\) and the statements provided:

1. Understanding variables and coefficients:

   • In the equation, \(x\) and \(y\) are the variables.
   • 8, -3, 2, and 9 are not variables, they are numerical coefficients of the respective variables in the equation.

2. Analyzing the choices:

   • "There are four variables." (Incorrect)
     There are only two variables: \(x\) and \(y\).
   • "8, −3, 2, and 9 are coefficients." (Correct)
     They are the coefficients corresponding to \(x\) and \(y\) in the equation.
   • "8 is the only factor of 8x." (Incorrect)
     While 8 is a coefficient (factor), the term \(x\) itself is also significant, and it's not accurate to say it’s the only factor.
   • "8, −3, 2, and 9 are constants." (Incorrect)
     These numbers are coefficients, but not constants in this context (the constant term would be a term without a variable).

Thus, the correct statement is:

8, −3, 2, and 9 are coefficients.

Answer 4

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

0.4
0.4

−7
negative 7

3
3

0.4 and 3

Answer 5

In the equation \(0.4 - 7x = 3\), we can break down the components as follows:

• Constants: These are the fixed values that do not change and do not contain any variables. In this equation, the constants are \(0.4\) and \(3\).
• Variables: The variable in this equation is \(x\).
• Coefficients: The coefficient is the number multiplying the variable, which in this case is \(-7\) (the coefficient of \(x\)).

Now, identifying the constants:

1. 0.4 is a constant.
2. 3 is also a constant.
3. −7 is not a constant; it is a coefficient.

Therefore, the correct answer regarding the constant(s) in the equation is:

0.4 and 3.

Answer 6

Use 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

3(x+4)2
Start Fraction 3 left parenthesis x plus 4 right parenthesis over 2 End Fraction

2
2

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

x8

Answer 7

To interpret the equation \(\frac{x}{8} = \frac{3(x+4)}{2}\) and identify which expression represents a product, let's analyze the options given:

1. \(\frac{3(x+4)}{2}\): This represents the division of \(3(x+4)\) by \(2\), and \(3(x+4)\) is indeed a product because it involves multiplying 3 by the quantity \(x + 4\).

2. 2: This is a constant, not a product.

3. \(3(x+4)\): This expression represents a product, as it is the multiplication of 3 and the expression \((x+4)\).

4. \(\frac{x}{8}\): This is also a division and does not represent a product.

Now, the expressions that represent a product in the entire equation are \(3(x+4)\) and \(3(x+4)/2\) (but the latter was broken down).

Since you are looking for a single expression that represents a product, the correct response would be:

3(x + 4).

Answer 8

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

144÷4
144 divided by 4

32÷4
32 divided by 4

48÷4

Answer 9

To simplify the expression \(3(4^2 + 32 \div 4 - 5)\), we need to evaluate the terms inside the parentheses step by step.

1. Calculate \(4^2\) first: \[ 4^2 = 16 \]

2. Then calculate \(32 \div 4\): \[ 32 \div 4 = 8 \]

3. Now, substitute these values back into the expression: \[ 3(16 + 8 - 5) \]

4. Now, we simplify the expression inside the parentheses: \[ 16 + 8 - 5 = 19 \]

So the full expression simplifies to: \[ 3 \times 19 \]

The only quotient that must be found to simplify the expression is \(32 \div 4\). Thus, the correct answer is:

32 ÷ 4.