= -4/2 Step-by-step explanation: xp=x1 +k (x2-x1) = -3+1/3 (2- -3) = -3 + 1/3 (5/1) = -3 + 5/3 = -9/3 +5/3 = -4/2 Sorry, it doesn't look the best:)
The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
