Answers:
x = 6 and P = 128
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Explanation:
The tangents CT and CU are equal to each other. The rule is that tangent segments that meet at a common point are the same length.
Let's solve for x
CT = CU
3x = 18
x = 18/3
x = 6
Because CT = 18, this makes BC = BT+TC = 12+18 = 30
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For similar reasoning as mentioned earlier, we can say tangents BT and BV are the same length. This means BV = 12.
Segment CD = 52 and CU = 18, which makes UD = CD-CU = 52-18 = 34
From there, we can say segment DV = 34 also. This leads to BD = BV+VD = 12+34 = 46
Triangle BCD has the three sides
The perimeter is
P = sum of the three sides
P = (side1)+(side2)+(side3)
P = BC + CD + BD
P = 30+52+46
P = 82+46
P = 128
We want to expand (2x + y²)⁵.
From Pascal's Triangle (shown below), the coefficients of the expansion are
1,5,10,10,5,1.
n=0: 1
n=1: 1 1
n=2: 1 2 1
n=3: 1 3 3 1
n=4: 1 4 6 4 1
n=5: 1 5 10 10 5 1
Therefore the third term in the expansion is
10*(2x)³*(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴
Alternatively, the third term is
₅C₃ (2x)³(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴
Answer: 80x³y⁴
9514 1404 393
Answer:
y = 5
Step-by-step explanation:
The given points lie on the horizontal line ...
y = 5
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You could write this as 0x+1y=5, but the conventions regarding coefficients of 0 and 1 would have this simplified to y=5.
