\( 1 \leftarrow \begin{array}{l}\text { Let } \mathbf{u}=\langle 2,7\rangle \text { and } \mathbf{v}=\langle 4,2\rangle \text {. Express } 2 \mathbf{u}+9 \mathbf{v} \text { in the form }\langle a, b\rangle \text {. } \\ \begin{array}{l}2 \mathbf{u}+9 \mathbf{v}=\langle\square, \square\rangle \\ \text { (Simplify your answers.) }\end{array}\end{array} \)

To express \( 2\mathbf{u} + 9\mathbf{v} \) in the form \(\langle a, b \rangle\), follow these steps: 1. **Given Vectors:** \[ \mathbf{u} = \langle 2, 7 \rangle \quad \text{and} \quad \mathbf{v} = \langle 4, 2 \rangle \] 2. **Calculate \( 2\mathbf{u} \):** \[ 2\mathbf{u} = 2 \times \langle 2, 7 \rangle = \langle 2 \times 2, 2 \times 7 \rangle = \langle 4, 14 \rangle \] 3. **Calculate \( 9\mathbf{v} \):** \[ 9\mathbf{v} = 9 \times \langle 4, 2 \rangle = \langle 9 \times 4, 9 \times 2 \rangle = \langle 36, 18 \rangle \] 4. **Add the Results:** \[ 2\mathbf{u} + 9\mathbf{v} = \langle 4, 14 \rangle + \langle 36, 18 \rangle = \langle 4 + 36, 14 + 18 \rangle = \langle 40, 32 \rangle \] **Final Answer:** \[ 2\mathbf{u} + 9\mathbf{v} = \langle 40, 32 \rangle \]