6. Jim's house is 5.1 miles from the mall
7. Jim's house is closer to the mall by 0.3 miles.
8. The total distance of the round trip is 5.7 miles + 5.7 miles = 11.4 miles.
Since Jim's car has 25 miles until it runs out of gas and the round trip is 11.4 miles, Jim would be able to make it from his house to the grocery store and back without stopping for gas.
9. Jim had traveled 5.4 miles / 2 = 2.7 miles when his wife called.
10. The park is within 5 miles of Jim's house.
6. How many miles is Jim's house from the mall?
To find the distance between Jim's house and the mall, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of Jim's house are (12, 11) and the coordinates of the mall are (7, 10). Plugging these values into the distance formula, we get:
distance = sqrt((7 - 12)^2 + (10 - 11)^2)
distance = sqrt(25 + 1)
distance = sqrt(26)
distance = 5.1 miles (rounded to the nearest tenth)
Therefore, Jim's house is 5.1 miles from the mall
7. Is Jim's house closer to the mall or the bank? How many miles closer is it?
To find which point is closer to Jim's house, we can calculate the distance between Jim's house and each point and compare the results.
The distance between Jim's house and the bank is:
distance = sqrt((14 - 12)^2 + (16 - 11)^2)
distance = sqrt(4 + 25)
distance = sqrt(29)
distance = 5.4 miles (rounded to the nearest tenth)
Therefore, Jim's house is closer to the mall by 0.3 miles.
8. Jim is at his house, and his car has 25 miles until it runs out of gas. Would Jim be able to make it from his house to the grocery store and back without stopping for gas? Explain.
To find out if Jim can make it from his house to the grocery store and back without stopping for gas, we need to calculate the total distance of the round trip.
The distance between Jim's house and the grocery store is:
distance = sqrt((16 - 12)^2 + (15 - 11)^2)
distance = sqrt(16 + 16)
distance = sqrt(32)
distance = 5.7 miles (rounded to the nearest tenth)
Therefore, the total distance of the round trip is 5.7 miles + 5.7 miles = 11.4 miles.
Since Jim's car has 25 miles until it runs out of gas and the round trip is 11.4 miles, Jim would be able to make it from his house to the grocery store and back without stopping for gas.
9. Jim left his house and drove to the bank. On his way back home, Jim's wife called when he was exactly halfway home. How many miles had Jim traveled when his wife called?
To find the distance Jim had traveled when his wife called, we can divide the total distance between Jim's house and the bank by 2.
The distance between Jim's house and the bank is:
distance = sqrt((14 - 12)^2 + (16 - 11)^2)
distance = sqrt(4 + 25)
distance = sqrt(29)
distance = 5.4 miles (rounded to the nearest tenth)
Therefore, Jim had traveled 5.4 miles / 2 = 2.7 miles when his wife called.
10. Jim is hoping that a park will be built within 5 miles of his house. If a park is built at the coordinates (12, 10), does that meet Jim's criteria? Explain.
To find out if the park is within 5 miles of Jim's house, we can calculate the distance between the park and Jim's house.
The distance between the park and Jim's house is:
distance = sqrt((12 - 12)^2 + (10 - 11)^2)
distance = sqrt(1)
distance = 1 mile (rounded to the nearest tenth)
Therefore, the park is within 5 miles of Jim's house.