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
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<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: 18w^2 - 6w + 4
Explanation:
(4 + 7w^2) - (6w - 11w^2)
= 4 + 7w^2 - 6w + 11w^2
= 18w^2 - 6w + 4
Answer:
14/25
Step-by-step explanation:
p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25
Answer:
ABCD is a rectangle
Step-by-step explanation:
∵ A = (-5 , 0) , B = (2 , -6) , C = (8 , 1) , D = (1 , 7)
∵ The x-coordinate of the mid-point of AC = (-5 + 8)/2 =3/2
∵ The y-coordinate of the mid-point of AC = (0 + 1)/2 = 1/2
∴ The mid-point of AC = (3/2 , 1/2)
∵ The x-coordinate of the mid-point of BD = (2 + 1)/2 =3/2
∵ The y-coordinate of the mid-point of BD = (-6 + 7)/2 = 1/2
∴ The mid-point of BD = (3/2 , 1/2)
∴ The mid-point of AC = The mid-point of BD ⇒ (1)
∵ AC = √[(8 - -5)²+(1 - 0)² = √170
∵ BD = √[(1 - 2)²+(7 - -6)² = √170
∴ AC = BD ⇒ (2)
From (1) and (2)
AC and BD equal each other and bisects each other
∴ ABCD is a rectangle
Answer:
Jamar should hit the wall opposite to the side of the barrier(if there is a space), which will cause the ball to bounce off the wall at an angle and into Target.
