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

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

Answer 1

To interpret the expression \(2.5x + 10\), we can break it down into its components:

• The term \(10\) represents a fixed cost, which in this context is likely the entry fee for the car.
• The term \(2.5x\) represents the variable cost, where \(x\) is the number of individual tickets (in this case, the number of people, which is 2 — Julio and Ashley) and \(2.5\) is the cost per individual entry.

Based on this interpretation, it can be concluded that the entry fee for the car is $10.00.

So, the correct answer 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

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

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.

Answer 3

To analyze the given equation \(8x - 3y = 2x + 9y\), let’s identify the components:

1. Constants: In an equation, constants are the fixed numbers that do not change. In this case, the numbers \(2\), \(8\), \(-3\), and \(9\) are all fixed values. Thus, they can be referred to as constants.

2. Variables: The variables in the equation are \(x\) and \(y\). There are only two variables here, not four.

3. Factors and Coefficients: The coefficients are the numbers that multiply the variables. In this equation, the coefficient of \(x\) in \(8x\) is \(8\) and in \(2x\) is \(2\). The coefficient of \(y\) in \(-3y\) is \(-3\) and in \(9y\) is \(9\).

Considering these points, the correct statement among the options provided is:

8, −3, 2, and 9 are constants.

This statement accurately identifies those numbers as constants.

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

3
3

0.4
0.4

0.4 and 3

0.4 and 3

−7

Answer 5

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

• Constants are the fixed numerical values that do not change. In this equation:

  • \(0.4\) is a constant.
  • \(3\) is also a constant.

• Variables: The variable in this equation is \(x\).

• Coefficients: The coefficient of the variable \(x\) is \(-7\).

Given the above analysis, the constants in the equation are \(0.4\) and \(3\).

Therefore, the correct response is:

0.4 and 3.

Answer 6

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

x8
Start Fraction x over 8 End Fraction

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

2
2

3(x+4)

Answer 7

To determine which expression in the equation \( x^8 = 3(x + 4)^2 \) represents a product, let's break down each option:

1. \( x^8 \): This is an exponent, not a product.

2. \( 3(x + 4)^2 \): This expression contains the multiplication of \(3\) and \((x + 4)^2\), which is indeed a product.

3. \( 2 \): This is just a number, not a product.

4. \( 3(x + 4) \): While this is also a product (specifically, the multiplication of \(3\) and \((x + 4)\)), the more complete expression for this context is \(3(x + 4)^2\).

The expression that clearly represents a product in the equation is \( 3(x + 4)^2 \).

Thus, the correct response is:

3(x+4)².

Answer 8

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

48÷4
48 divided by 4

32÷4
32 divided by 4

96÷4
96 divided by 4

144÷4

Answer 9

To simplify the expression \(3(42 + 32 \div 4 - 5)\), we need to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's focus specifically on the component we need to simplify first, particularly the division:

1. Inside the parentheses:
   • The expression is \(42 + 32 \div 4 - 5\).
   • According to the order of operations, we perform the division \(32 \div 4\) first.

From this breakdown, the quotient that must be found to simplify the expression is:

32 ÷ 4 (or 32 divided by 4).

So, the correct response is:

32 ÷ 4.