<h3>Answer: x = 5</h3>
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Work Shown:
Angle Bisector Theorem
9/(2x-1) = 15/3x
9*3x = 15(2x-1) ... cross multiply
27x = 30x-15
27-30x = 30x-15-30x ... subtract 30x from both sides
-3x = -15
-3x/(-3) = -15/(-3) .... divide both sides by -3
x = 5
Answer: The unit rate is $5 per mug.
Step-by-step explanation:
To find the the unit rate, you will find the amount one mug will cost.
If there are 9 mugs then to get it to one, you will have to divide 9 by 9, and the same way you will have to divide 45 by 9.
45 / 9 = 5
Answer:
See explanation below.
Step-by-step explanation:
The prime numbers are bold:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31
a) We can see that as we go higher, twin primes seem less frequent but even considering that, there is an infinite number of twin primes. If you go high enough you will still eventually find a prime that is separated from the next prime number by just one composite number.
b) I think it's interesting the amount of time that has been devoted to prove this conjecture and the amount of mathematicians who have been involved in this. One of the most interesting facts was that in 2004 a purported proof (by R. F. Arenstorf) of the conjecture was published but a serious error was found on it so the conjecture remains open.
Step-by-step explanation:
height= 4b
length = 2 + b
volume = 60in³
or, l ×b × h = 60in³
or, (2+b) × b × 4b = 60in³
or, 4b²(2+b) = 60in³
or, 8b² + 4b³ = 60
or, 2b² + b³ = 15
or, b³ + 2b² -15= 0
b= 1.95
l= 2+1.95=3.95
h= 4×1.95 = 7.8
