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9² = 12² + 15² - 2 (12) (15) cos (B)
81 = 144 + 225 - 360 cos(B)
81 = 369 - 360 cos (B)
360 cos (B) = 369 - 81
360 cos (B) = 288
cos (B) = 0.8
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Answer: Cosine B = 0.8
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12² = 15² + 9² - 2 (15)(9) cos (A)
144 = 225 + 81 - 270 Cos A
144 = 306 - 270 Cos A
270 Cos A = 162
Cos A = 3/5 or 0.6
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Answer: Cosine Angle A = 3/5
Answer:
This is not a solvable question, since the least amount of money you can have with this combination is $4.20.
Step-by-step explanation:
Let q = quarters
Let d = dimes
Equation: 0.1d + 0.25q = 3.00
Maximum amount of dimes: 0.1d *42 = 4.2d
Answer:
60cm²
Step-by-step explanation:
The area of a rhombus is: A=d1×d2/2, where d1 and d2 are its diagonals.
A=10×12/2=60cm²
The question is asking 15+2*9=? so to do this first multiply 2*9 which = 18 and then add 15, 18+15= 33
Prove:
Using mathemetical induction:
P(n) = 
for n=1
P(n) =
= 6
It is divisible by 2 and 3
Now, for n=k, 
P(k) = 
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) = 
P(k+1) = 
P(k+1) = 
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) =
is divisible by 2 and 3 for all positive integer n.