X is equal to 15 explanation is that you subtract 180 for 165 to find x which is equal to 15
|x| this means absolute value making what ever number in the inside positive UNLESS you have a negative out front. Ex |8|=8. -|8|=-8. |-8|=8
Mary's house is approximately 49.73 miles from her grandmother's house.
The distances the three drove were;
Mary drove for 49.73 miles, Theo drove 50 miles and Nancy drove 53.299 miles.
Explanation:
- The given triangle has a 13 mile long adjacent side, a 48 mile long opposite side and the distance of Mary's route is the hypotenuse. As we have two sides of the triangle, we can solve for the length of the other side by using Pythagoras' theorem.
- Assume the hypotenuse of the triangle measures x miles. According to Pythagoras theorem, x = √(13² + 48²) , x = √169 + 2,304 x = √2,473 = 49.729. Rounding this off, we get Mary's route was 49.73 miles long.
- Nancy drove √2,840 miles = 53.2916 miles.
- So Mary drove the shortest distance of 49.73 miles, second shortest was Theo who drove for 50 miles and the longest was Nancy who drove for 53.299 miles.
No, the two lines do NOT intersect because they are parallel lines (see the attached image). Both lines have a slope of 2, or 2/1. Recall that slope = rise/run. So this means that we go up 2 and over to the right 1. Lines with the same slope but different y intercepts means that they are parallel. Parallel lines never cross.
In short, the final answer is choice D.