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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.

(1 point)
Statement #
could be a correct interpretation of the coefficient of a term.

9 answers

In the equation \( C = 18 + 4x \), \( C \) represents the total cost, \( 18 \) represents a fixed cost (like a base fee), and \( 4x \) represents the cost that varies based on the number of books \( x \) that Tatiana purchases, where \( 4 \) is the coefficient of \( x \).

The coefficient \( 4 \) indicates that for each book purchased, she spends an additional $4.

Therefore, the correct interpretation of the coefficient \( 4 \) is:

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

Statement #2 is incorrect because it references the fixed cost, which is $18.00, not the per book fee.

So, the answer is:

Statement #1 could be a correct interpretation of the coefficient of a term.

Which of the following statements about the equation 2x−5=8+x is correct?

Statement #1: There are two constants in the equation.

Statement #2: x does not have a coefficient.

Statement #3: There are two terms in the equation.

(1 point)
Statement #
is correct.

Let's analyze the equation \(2x - 5 = 8 + x\):

  1. Statement #1: There are two constants in the equation.

    • The constants in this equation are \(-5\) and \(8\). Therefore, this statement is correct.

  2. Statement #2: x does not have a coefficient.

    • In the equation \(2x\) and \(x\) (which is \(1x\)) both have coefficients. Therefore, this statement is incorrect.

  3. Statement #3: There are two terms in the equation.

    • The equation has more than two terms when combining both sides, namely \(2x\), \(-5\), \(8\), and \(x\). So this statement is also incorrect.

Based on this analysis, the correct statement is:

Statement #1 is correct.

Which of the following options contains two coefficients and three terms?

Option #1: 2x−3=4−y

Option #2: 6+7y=5

Option #3: 9x=1−8x

(1 point)
Option #
contains two coefficients and three terms.

Let's analyze each option to identify the number of coefficients and terms:

  1. Option #1: \(2x - 3 = 4 - y\)

    • Terms: \(2x\), \(-3\), \(4\), and \(-y\), which totals 4 terms.
    • Coefficients: \(2\) (for \(x\)) and \(-1\) (for \(y\)), which totals 2 coefficients.
    • Conclusion: This option contains 2 coefficients and 4 terms.

  2. Option #2: \(6 + 7y = 5\)

    • Terms: \(6\), \(7y\), and \(5\), which totals 3 terms.
    • Coefficients: \(7\) (for \(y\)), which totals 1 coefficient.
    • Conclusion: This option contains 1 coefficient and 3 terms.

  3. Option #3: \(9x = 1 - 8x\)

    • Terms: \(9x\), \(1\), and \(-8x\), which totals 3 terms.
    • Coefficients: \(9\) (for \(x\)) and \(-8\) (for the second \(x\)), which totals 2 coefficients.
    • Conclusion: This option contains 2 coefficients and 3 terms.

Based on this analysis, Option #3 contains two coefficients and three terms.

So, the answer is:

Option #3 contains two coefficients and three terms.

Consider the expression [15+(−5)]+62 . What is the result of the first simplification that would need to take place, according to the order of operations?(1 point)

To simplify the expression \([15 + (-5)] + 62\) according to the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we start with the parentheses first.

The first simplification involves evaluating the expression inside the brackets:

\[ 15 + (-5) \]

Calculating this gives:

\[ 15 - 5 = 10 \]

Thus, the first simplification that takes place is simplifying \(15 + (-5)\) to \(10\).

Therefore, the result of the first simplification is \(10\).

Consider the following expression: 4+(−6)⋅2−(−3)2 . What is the simplified denominator?(1 point)

Let's simplify the given expression step-by-step to identify the simplified denominator. The expression is:

\[ 4 + (-6) \cdot 2 - (-3)^2 \]

  1. Evaluate \( (-6) \cdot 2 \): \[ (-6) \cdot 2 = -12 \]

  2. Evaluate \( (-3)^2 \): \[ (-3)^2 = 9 \] (Note: The square of a negative number is positive.)

  3. Substituting these values back into the expression: \[ 4 + (-12) - 9 \]

  4. Simplifying the expression:

    • First, perform the addition: \[ 4 - 12 = -8 \]
    • Then subtract \(9\): \[ -8 - 9 = -17 \]

In the context of this problem, if you are specifically asking for the simplified denominator (considering only denominators in a fraction context), there is no fraction present in the original expression, and thus there are no denominators to simplify.

If we assume you meant the simplified result of the expression, that value is: \[ -17 \]

If you're looking for something else regarding denominators or fractions, please provide further clarification so I can assist you accurately!