1. **State the problem:** We need to find the value of $v$ using the formula $v = u + 10t$ when $u = -23$ and $t = 7$. 2. **Write the formula:** The formula given is: $$v = u + 10t$$ This formula means that $v$ is equal to the initial value $u$ plus 10 times the value of $t$. 3. **Substitute the values:** Substitute $u = -23$ and $t = 7$ into the formula: $$v = -23 + 10 \times 7$$ 4. **Calculate the multiplication:** $$v = -23 + 70$$ 5. **Add the numbers:** $$v = 47$$ **Final answer:** The value of $v$ is 47.