<span>4x+2y=10
x-y=13
x=13+y
4(13+y)+2y=10
52+4y+2y=10
52+6y=10
6y=-42
y=-7
x=13+y=13-7=6
</span>
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:
Wayne bought 72 blueberries.
Step-by-step explanation:
To combine the fractions, convert all of the fractions to a denominator of 24.
3/8 * 3/3 = 9/24
1/6 * 4/4 = 4/24
5/12 * 2/2 = 10/24
Now add together the fractions
9/24 + 4/24 + 10/24 = 23/24
He used 23/24 of his blueberries, or 69 of them.
To find the total amount of blueberries, divide 69 by 23, then multiply that number b 24.
69 / 23 = 3
3 * 24 = 72
Wayne bought 72 blueberries.
