Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
====================================================
Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
------------------------
Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Answer:
Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)
Step-by-step explanation:
To understand better how we arrived at the aforementioned algorithm, we take it step by step
a, Construct a min-heap of the minimum elements from each of "k" lists.
The creation of this min-heap will cost O (k) time.
b) Next we run delete Minimum and move the minimum element to the output array.
Each extraction takes O (log k) time.
c) Then insert into the heap the next element from the list from which the element was extracted.
Now, we note that since we extract n elements in total, the running time is
O (n log k+ k) = O (n log k).
So we can conclude that :
Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)
Discount points are normally a type of prepaid interests that lowers the interest on subsequent payments for mortgage borrowers pay.
Each of the points is given by:
1 point = 1% of the mortgage value.
Therefore,
Cost of discount points = 0.01*519,000*3 = $15,570
Cost of origination points = 0.01*519,000*2 = $10,380
In this regard, option B. is the correct answer on the cost of discount and origination points respectively.
