1. Circle the equations that are true when \( \mathrm{x}=4 \) \( \begin{array}{ll}x-4=10 & 3 x=12 \\ x^{3}=12 & \frac{1}{3} x=12 \\ x^{2}=16\end{array} \)

To determine which equations are true when \( x = 4 \), we will substitute \( x \) with 4 in each equation and check if the left-hand side equals the right-hand side. 1. **Equation:** \( x - 4 = 10 \) - Substitute \( x = 4 \): \[ 4 - 4 = 0 \quad \text{(not equal to 10)} \] 2. **Equation:** \( 3x = 12 \) - Substitute \( x = 4 \): \[ 3(4) = 12 \quad \text{(true)} \] 3. **Equation:** \( x^3 = 12 \) - Substitute \( x = 4 \): \[ 4^3 = 64 \quad \text{(not equal to 12)} \] 4. **Equation:** \( \frac{1}{3}x = 12 \) - Substitute \( x = 4 \): \[ \frac{1}{3}(4) = \frac{4}{3} \quad \text{(not equal to 12)} \] 5. **Equation:** \( x^2 = 16 \) - Substitute \( x = 4 \): \[ 4^2 = 16 \quad \text{(true)} \] Now, let's summarize the results: - \( x - 4 = 10 \) is **false**. - \( 3x = 12 \) is **true**. - \( x^3 = 12 \) is **false**. - \( \frac{1}{3}x = 12 \) is **false**. - \( x^2 = 16 \) is **true**. Thus, the equations that are true when \( x = 4 \) are: - \( 3x = 12 \) - \( x^2 = 16 \)