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Using the equation C=18+4x

, which of the following statements could be a correct interpretation of the coefficient of a term?

Statement #1: Tatiana spent $4.00 per book at the public library.

Statement #2: Tatiana spent $18.00 per book at the public library.

5 answers

The equation \( C = 18 + 4x \) can be interpreted in the context of a situation involving costs. In this equation:

  • \( C \) represents the total cost.
  • \( x \) represents the number of books checked out.
  • The term \( 4x \) indicates that for each book checked out, an additional $4 is added to the total cost.
  • The constant term \( 18 \) represents a fixed cost that is incurred regardless of the number of books checked out.

Now, let's analyze the two statements in relation to the equation:

Statement #1: "Tatiana spent $4.00 per book at the public library."

  • This interpretation refers to the coefficient \( 4 \) associated with the variable \( x \). Since \( 4x \) signifies that Tatiana spends $4 for each book, this statement is accurate.

Statement #2: "Tatiana spent $18.00 per book at the public library."

  • This interpretation misrepresents the constant \( 18 \). The $18 represents a fixed cost rather than a cost per book; therefore, this statement is inaccurate.

Based on this analysis, Statement #1 could be a correct interpretation of the coefficient of the term, while Statement #2 is not.

Consider the expression [15+(−5)]+6/2
. What is the result of the first simplification that would need to take place, according to the order of operations?(1 point)

According to the order of operations, we follow the PEMDAS/BODMAS rules:

  1. Parentheses/Brackets
  2. Exponents/Orders
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

In the given expression \([15 + (-5)] + 6/2\), the first simplification involves the operation inside the brackets.

So, we start with \(15 + (-5)\):

  1. Simplify inside the brackets: \[ 15 + (-5) = 10 \]

After this simplification, the expression becomes: \[ 10 + 6/2 \]

Thus, the first simplification that would need to take place (according to the order of operations) is: Simplifying \(15 + (-5)\) inside the brackets.

Consider the following expression: 4+(−6)⋅2/−(−3) ^2
. What is the simplified denominator

To simplify the expression \(4 + (-6) \cdot 2 / -(-3)^2\), we will focus on simplifying the denominator, which is \(-(-3)^2\).

  1. Evaluate \((-3)^2\): \[ (-3)^2 = 9 \]

  2. Then apply the negative sign: \[ -(-3)^2 = -9 \]

Thus, the simplified denominator is \(-9\).