Answer:
17. 6
18. 18 (as shown)
19. 10/3 = 3 1/3
20. 20/3 = 6 2/3
Step-by-step explanation:
17. For this, you can subtract the given length GB=12 from the length you found for problem 18, BF=18. Doing that tells you FG = 18-12 = 6, as you have marked on the diagram.
19. As with median BF, the point G divides it into two parts that have the ratio 1:2. The distance from G to D is the shorter of the distances, so you have ...
... GD = (1/3) CD = (1/3)·10 = 10/3
... GD = 3 1/3
20. You can subtract GD from CD to get CG, or you can multiply CD by 2/3. The result is the same either way.
... CG = CD -GD = 10 -3 1/3
... CG = 6 2/3
_____
<em>Comment on centroid and median</em>
The centroid (G) divides each median into parts in the ratio 1:2. Hence the shorter of those parts is half the length of the longer one, or 1/3 the total length of the median.
The longer of the parts is double the length of the shorter one, or 2/3 the total length of the median.
Your marking of median BF seems to show an understanding of these relationships. (Total length: 18; length of parts: 6 and 12.)
Answer:
-15x^2 +8x -1
Step-by-step explanation:
(3x – 1)(-5x + 1)=
3x(-5x) + 3x(1) - 1(-5x) -1 =
-15x^2 +3x +5x -1 =
-15x^2 +8x -1
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Answer:
T=-20
Step-by-step explanation:
first get rid of the 7
1. T/4=-5
then multiply by 4 to isolate T
2. T=-20
Writing the equation that governs this situation:
-3C - (2.5C/hr)x = -18C
Simplifying, -3 - 2.5x = -18, or 3 + 2.5x = 18
Combining like terms: 2.5x = 18-3 = 15
Then x = 15/2.5 = 6. The temp. will reach -18C after 6 hours.
From second equation y = 8 - x so
7x + 2(8 - x) = -14
5x = -14 - 16 = -30
x = -6
and y = 8 - -6 = 14
Answer x=-6,y=14
