Answer:
ZM = 8
WM = 12
XZ = 7
XN = 21
LZ = 20
Step-by-step explanation:
The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.
The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.
ZM = (2/3)WM (centroid theorem)
Therefore: WZ = (1/3)WM
WM = 3WZ = 3 * 4 = 12
ZM = (2/3) * WM = 2/3 * 12 = 8
ZN = (2/3)XN (centroid theorem)
XN = (3/2)ZN = 3/2 * 14 = 21
XN = 21
XZ + ZN = XN
XZ + 14 = 21
XZ = 7
LZ = (2/3)LY (centroid theorem)
Therefore: ZY = (1/3)LY
LY = 3ZY = 3 * 10 = 30
LZ = (2/3) * LY = 2/3 * 30 = 20
Step-by-step explanation:
2,5 and 7 are the three integers
(n+5)^2=48
sqrt both sides
n+4=+/-4√3
minus 4 both sides
n=-4+/-4√3
-4+4√3>0 so this cannot be the value of n
n=-4-4√3
the number is -4-4√3
9. 1/2 x 8 x 10 = 40 in²
10. 1/2 x 7 x 9 = 31.5 yd²
11. 1/2 x 12 x 8 = 48 cm²
12. 1/2 x 3 x 16 = 24 ft²
Answer: 8.50 dollars
The result is positive, so this is a gain (instead of a loss)
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Explanation:
Focus on the "stock JKL" row only when it comes to the percentages we'll use. We need to convert them to decimal form
15% ---> 0.15
65% ---> 0.65
20% ---> 0.20
I just moved the decimal point over 2 spots, or you can divide by 100 (eg: 15% = 15/100 = 0.15)
Multiply each of these values by their corresponding loss or gain. Use negative numbers for losses
15% chance of losing $25 ---> 0.15*(-25) = -3.75
65% chance of winning $5 ---> 0.65*(5) = 3.25
20% chance of winning $45 ---> 0.20*(45) = 9
Now add up those results: -3.75+3.25+9 = 8.50