1. Problem 4: Find the direct distance from home to work given a right triangle with legs 12 mi east and 9 mi north. 2. Use the Pythagorean theorem for right triangles: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are legs and $c$ is the hypotenuse. 3. Substitute $a=12$ mi and $b=9$ mi: $$c = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15$$ mi. 4. So, the direct distance is 15 miles. 5. Problem 5: Find the length of a guy wire from the top of a 32 ft building to a point 24 ft from the building on the ground. 6. Again, use the Pythagorean theorem with legs 32 ft (height) and 24 ft (ground distance): $$c = \sqrt{32^2 + 24^2} = \sqrt{1024 + 576} = \sqrt{1600} = 40$$ ft. 7. The wire must be 40 feet long. 8. Problem 6: Write a linear equation for total cost $y$ per day when renting a car with a fixed fee of 4500 plus 24 per km traveled $x$. 9. The linear equation is: $$y = 4500 + 24x$$ 10. To find the cost for 130 km, substitute $x=130$: $$y = 4500 + 24 \times 130 = 4500 + 3120 = 7620$$. 11. The total cost for one day traveling 130 km is 7620.