1. **State the problem:** Find the magnitude of the vector $\vec{v} = (-3, -10)$. The magnitude of a vector $\vec{v} = (x, y)$ is given by the formula: $$|\vec{v}| = \sqrt{x^2 + y^2}$$ 2. **Apply the formula:** Substitute $x = -3$ and $y = -10$ into the formula: $$|\vec{v}| = \sqrt{(-3)^2 + (-10)^2}$$ 3. **Calculate the squares:** $$|\vec{v}| = \sqrt{9 + 100}$$ 4. **Sum inside the square root:** $$|\vec{v}| = \sqrt{109}$$ 5. **Calculate the square root:** $$|\vec{v}| \approx 10.4403$$ 6. **Round to the nearest hundredth:** $$|\vec{v}| \approx 10.44$$ **Final answer:** The magnitude of the vector $\vec{v}$ is approximately **10.44**.