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

The entry fee for the car was $10.00.

9 answers

The expression \(2.5x + 10\) can be broken down into its parts to interpret the costs:

  • The term \(2.5x\) suggests that \(x\) represents the number of individuals (in this case, Julio and Ashley, so \(x=2\)), and \(2.5\) represents the individual entry fee for each person.
  • The constant \(10\) represents the entry fee for the car.

From this understanding, we can accurately interpret the components of the expression as follows:

  • Each individual entry fee was $2.50 (the \(2.5\) in front of \(x\)).
  • The entry fee for the car was $10 (the constant \(10\)).

Based on your options, the correct interpretation is:

Each individual entry fee was $2.50.

The entry fee for the car was $10.00. (This option also accurately interprets the car fee, but the specific option you are asking for is the individual fee.)

To clarify, the correct interpretation should ideally highlight that the entry fee for the car is $10.

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

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

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.

To evaluate the given equation \(8x - 3y = 2x + 9y\) and the associated statements, we first understand the terminology involved:

  1. Coefficients are the numbers that multiply the variables.
  2. Constants are the standalone numbers in an equation that do not multiply any variables.
  3. Variables are the symbols that represent unknown values (in this case, \(x\) and \(y\)).

In the equation \(8x - 3y = 2x + 9y\):

  • The coefficients are:
    • \(8\) (the coefficient of \(x\) in \(8x\))
    • \(-3\) (the coefficient of \(y\) in \(-3y\))
    • \(2\) (the coefficient of \(x\) in \(2x\))
    • \(9\) (the coefficient of \(y\) in \(9y\))

Now we can analyze the statements provided:

  1. 8, −3, 2, and 9 are coefficients.
  2. 8, negative 3, 2, and 9 are coefficients.
  3. 8, −3, 2, and 9 are constants.
  4. 8, negative 3, 2, and 9 are constants.
  5. There are four variables.
  6. 8 is the only factor of 8x.

The correct statements that describe the coefficients are:

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

Both of these statements are correct interpretations of the coefficients in the given equation.

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 and 3

0.4 and 3

−7
negative 7

0.4
0.4

3
3

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

  • Constants are the numbers that do not change and do not multiply any variable.
  • Variables are the symbols that represent unknown values (in this case, \(x\)).
  • Coefficients are the numbers multiplied by the variables (in this case, \(-7\) is the coefficient of \(x\)).

In this equation:

  • \(0.4\) is a constant.
  • \(3\) is also a constant.
  • \(-7\) is a coefficient, not a constant.

Thus, the constants in the equation are \(0.4\) and \(3\).

The correct answer would be:

0.4 and 3

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

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

x8
Start Fraction x over 8 End Fraction

2
2

3(x+4)2

In the equation \( x^8 = 3(x + 4)^2 \), let's analyze the components to determine which expression represents a product.

  1. 3(x + 4): This represents the product of 3 and \((x + 4)\).
  2. \(x^8\): This is not a product of two distinct factors; it is a single term.
  3. 2: This is just a numeric constant and does not represent a product.
  4. \(3(x + 4)^2\): Here, \( (x + 4)^2 \) is a square of \((x + 4)\), and then multiplied by 3. However, the square itself is a product of \((x + 4)\) with itself, making \( (x + 4)(x + 4) \).

So, the expression that most clearly represents a product within the equation is:

3(x + 4) (or in your format, 3 left parenthesis x plus 4 right parenthesis) as it is a straightforward multiplication of 3 and the expression \((x + 4)\).

The expression 3(x + 4)² also represents a product, but since you may be looking for the simplest product, 3(x + 4) is the most direct.

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

32÷4
32 divided by 4

144÷4
144 divided by 4

96÷4
96 divided by 4

48÷4

To simplify the expression \( 3(42 + 32 \div 4 - 5) \), we need to first focus on simplifying the inside of the parentheses:

  1. Identify the operations inside the parentheses: We have \(42 + 32 \div 4 - 5\).
  2. Following the order of operations (PEMDAS/BODMAS), we first perform the division \(32 \div 4\).

Thus, the quotient that must be found to simplify the expression is:

32 ÷ 4 (or 32 divided by 4).

This calculation should be done before proceeding with the addition and subtraction in the expression.