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Using the equation `C=5+12x,`which of the following statements could be a correct interpretation of the coefficient of a term?

Answer:

julia earns $5 every hour for her pet-sitting job.

julia earns $12 every hour for her pet sitting job

the total amount julia earns.

the initial amount of money julia has in her pocket

5 answers

In the equation \( C = 5 + 12x \), the coefficient of the term associated with \( x \) is \( 12 \), and the constant term is \( 5 \).

Here's a breakdown of the options:

  1. Julia earns $5 every hour for her pet-sitting job. - This is incorrect because the $5 is a constant amount, not a rate per hour.

  2. Julia earns $12 every hour for her pet-sitting job. - This is correct. The coefficient \( 12 \) represents the hourly earnings gained from pet-sitting, where \( x \) could represent the number of hours worked.

  3. The total amount Julia earns. - This is not specific enough to be correct without context; the equation gives her total earnings based on hours worked and an initial amount.

  4. The initial amount of money Julia has in her pocket. - This is correct. The $5 represents an initial amount (or starting income) that she has.

Given the interpretations above, the correct interpretation of the coefficient of \( x \) (which is \( 12 \)) is:

Julia earns $12 every hour for her pet-sitting job.

Which of the following statements about the equation `3x-1=7+x` is correct?
answers:
there are two constants in the equation

x does not have a coefficient

there are two terms in the equation

A coeffcient is negitive

Let's analyze the equation \( 3x - 1 = 7 + x \) and the statements given:

  1. There are two constants in the equation. - This is correct as there are two constant values: \(-1\) on the left side and \(7\) on the right side.

  2. x does not have a coefficient. - This is incorrect. The variable \( x \) does have a coefficient, which is \( 1 \) (implied) on the right side and \( 3 \) on the left side.

  3. There are two terms in the equation. - This is incorrect. The equation consists of multiple terms: \( 3x \) and \(-1\) on the left, and \(7\) and \(x\) on the right side. In total, there are four terms.

  4. A coefficient is negative. - This is incorrect in the context of this specific equation. The coefficients of \( x \) are positive \( 3 \) and \( 1 \) (implied).

Therefore, the correct statement about the equation \( 3x - 1 = 7 + x \) is:

There are two constants in the equation.

Derrick and Maria 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 `4.5x+15`.  Which of the following answer choices accurately interprets a part of the algebraic expression?

answers:

the entry fee for the car was $4.50

each individual entry fee was $15.00

each individual entry fee was $4.50

the entry fee for the car was $19.50

Let's analyze the expression \( 4.5x + 15 \) to interpret its components:

  • \( 4.5x \): This part of the expression represents the total individual entry fees for Derrick and Maria. Here, \( 4.5 \) is the coefficient, which indicates the individual entry fee per person, and \( x \) represents the number of people (which would be 2 in this case, as it includes Derrick and Maria).

  • \( 15 \): This part of the expression presumably represents the fixed entry fee for the car.

Now, let's evaluate each of the answer choices:

  1. The entry fee for the car was $4.50 - This is incorrect. The total car entry fee is represented by the \( 15 \) in the expression.

  2. Each individual entry fee was $15.00 - This is incorrect. The coefficient \( 4.5 \) indicates that each individual entry fee is $4.50.

  3. Each individual entry fee was $4.50 - This is correct. The coefficient \( 4.5 \) represents the entry fee per person.

  4. The entry fee for the car was $19.50 - This is incorrect. The car entry fee is represented as \( 15 \).

Therefore, the accurate interpretation from the provided options is:

Each individual entry fee was $4.50.