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

Answer 1

To interpret the expression \(2.5x + 10\), we can break it down as follows:

• \(2.5x\) likely represents the total cost associated with the individual entry fees for both Julio and Ashley. If \(x\) is the number of people (in this case, 2), then \(2.5 \times 2 = 5\) which indicates that the individual entry fee for each person is $2.50.

• The \(10\) in the expression likely represents a fixed cost or entry fee for the car.

Given these interpretations, we conclude the following:

• Each individual entry fee was $2.50.
• The entry fee for the car was $10.00.

The correct interpretation based on the choices provided is:

The entry fee for the car was $10.00.

Answer 2

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)

Answer 3

In the equation \( 0.4 - 7x = 3 \):

• Constants are values that do not change. They are the fixed numbers in the equation.
• In this case, the constants are 0.4 and 3.

Therefore, the constants in the equation are 0.4 and 3.

Answer 4

Use the grouping symbols to interpret the following equation: x8=3(x+4)2 . Which expression in the equation represents a product?(1 point)

Answer 5

In the equation \( x^8 = 3(x + 4)^2 \):

To find which expression represents a product, we can analyze the components on both sides of the equation.

1. On the left side, \( x^8 \) is not expressed as a product of two factors, but rather a single term raised to an exponent.

2. On the right side, \( 3(x + 4)^2 \) indicates a product. Specifically, it consists of:

   • The coefficient \( 3 \)
   • The expression \( (x + 4)^2 \), which represents the square of the binomial \( x + 4 \).

To clarify the product, we can expand \( 3(x + 4)^2 \):

• The term \( (x + 4)^2 \) can be thought of as \( (x + 4) \times (x + 4) \).
• Therefore, the entire expression \( 3(x + 4)^2 \) represents the product \( 3 \times (x + 4) \times (x + 4) \).

Thus, the expression that represents a product in the equation is 3(x + 4)^2.