1. **State the problem:** A hill on a dirt bike course is 5 feet tall. The valley below the hill is as deep as the hill is tall. We need to find the integer representing the location of the bottom of the valley and compare it to the height of the hill. 2. **Understand the problem:** The hill's height is +5 feet. The valley is as deep as the hill is tall, so its depth is also 5 feet but below zero. 3. **Find the valley's location:** Since the valley is 5 feet deep below zero, its location is at $$-5$$. 4. **Compare the valley to the hill:** The valley's depth $$-5$$ is the negative of the hill's height $$+5$$, meaning the valley is equally deep as the hill is tall but in the opposite direction. **Final answer:** The bottom of the valley is at $$-5$$, which is the negative of the hill's height $$5$$. --- 1. **Evaluate the expression:** $$-[-(-7)]$$ 2. **Simplify inside the brackets:** $$-7$$ is inside the innermost bracket. 3. **Apply the negative sign:** $$-(-7) = 7$$ 4. **Now the expression is:** $$- [7] = -7$$ **Final answer:** $$-7$$