Question

1. what is the rate of change from 1 minute to 3 minutes?
2. if ( m(x)=7.5x + 20 ), complete the table.
3. the 2025 class is sponsoring a school dance. the function ( p ) models the profit ( p(t) ), in dollars, they will earn for the numb they sell. describe what each equation means.

a) ( p(20)=-40 )
b) ( p(25)=0 )

Explanation:

Step1: Substitute \(x = 6\) into \(M(x)=7.5x + 20\)

Substitute \(x = 6\) into the function \(M(x)=7.5x + 20\).

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Step2: Substitute \(x = 10\) into \(M(x)=7.5x + 20\)

Substitute \(x = 10\) into the function \(M(x)=7.5x + 20\).

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Step3: Solve for \(x\) when \(M(x) = 200\)

Set \(M(x)=200\), so \(7.5x+20 = 200\).
First, subtract \(20\) from both sides: \(7.5x=200 - 20=180\).
Then divide both sides by \(7.5\): \(x=\frac{180}{7.5}=24\).

Answer:

When \(x = 6\), \(M(x)=65\); when \(x = 10\), \(M(x)=95\); when \(M(x)=200\), \(x = 24\).