Pregunta
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Write an expression that represents 72 divided by \( n \) plus 4 . What is the value of \( y \) ? Circle the correct answer. \[ y=47 \quad y=53 \] Use the distributive property to create an equivalent expression to \( 54+18 x \) Simplify the expression. \[ 7 y+4 x+4-2 x+8 \] What is the coefficient of \( x \) ? What is the constant?

Ask by Chadwick Jimenez. in the United States
Mar 13,2025

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The expression representing 72 divided by \( n \) plus 4 is \( \frac{72}{n} + 4 \). Without additional information, the value of \( y \) cannot be determined. Using the distributive property on \( 54 + 18x \) gives \( 18x + 54 \). Simplifying \( 7y + 4x + 4 - 2x + 8 \) results in \( 7y + 2x + 12 \). The coefficient of \( x \) is 2, and the constant term is 12.

Solución

To represent 72 divided by \( n \) plus 4, we can write the expression as: \[ \frac{72}{n} + 4 \] To find the value of \( y \), we need to determine which of the given options is correct. However, without additional information or context, we cannot determine the value of \( y \) based on the expression provided. Moving on to the next part of the problem, we are asked to use the distributive property to create an equivalent expression to \( 54 + 18x \). The distributive property states that for any real numbers \( a \), \( b \), and \( c \), the following equation holds: \[ a(b + c) = ab + ac \] Applying the distributive property to \( 54 + 18x \), we get: \[ 54 + 18x = 18x + 54 \] Now, let's simplify the expression \( 7y + 4x + 4 - 2x + 8 \) by combining like terms: \[ 7y + 4x + 4 - 2x + 8 = 7y + 2x + 12 \] The coefficient of \( x \) in the simplified expression is 2, and the constant term is 12.

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The Deep Dive

To represent 72 divided by \( n \) plus 4, you can write the expression as \( \frac{72}{n} + 4 \). Now, when it comes to the value of \( y \), if you're looking at \( y=47 \) and \( y=53 \), the correct answer is not clear without additional context or conditions to determine which value applies. Using the distributive property on \( 54 + 18x \) gives you \( 18(x + 3) \) since \( 54 = 18 \times 3 \). Now, simplifying the expression \( 7y + 4x + 4 - 2x + 8 \) leads us to \( 7y + (4 - 2)x + (4 + 8) \), simplifying that gives \( 7y + 2x + 12 \). The coefficient of \( x \) is \( 2 \) and the constant is \( 12 \).

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