The first partner in the handshake can be any one of 15 people.
The second partner can be any one of 14 people.
So the total number of possible arrangements is (15 x 14) = <u>210</u> .
<em><u>BUT . . . .</u></em>
If Mr. Smith and Mr. Jones are shaking hands, it doesn't matter which one is the first partner and which one is the second partner ... It's the same handshake either way.
That number of ' <u>210</u> ' up above counted both ways separately. The real number of handshakes <em>between different people</em> is half of that 210/2 = <em>105 handshakes</em>.
Answer:
10 hours
Step-by-step explanation:
Let
represent the distance the train heading north has traveled
Let
represent the distance the train heading south has traveled
Let
represent the number of hours that has passed
![N=25t\\S=35t](https://tex.z-dn.net/?f=N%3D25t%5C%5CS%3D35t)
![600=N+S](https://tex.z-dn.net/?f=600%3DN%2BS)
![600=25t+35t\\600=60t\\t=10](https://tex.z-dn.net/?f=600%3D25t%2B35t%5C%5C600%3D60t%5C%5Ct%3D10)
Solving the given system of equations we get solution set: {(4,0),(0,4)}
Option B is correct.
Step-by-step explanation:
We need to find the solution set of the following equations:
![x+y=4\\x^2+y^2=16](https://tex.z-dn.net/?f=x%2By%3D4%5C%5Cx%5E2%2By%5E2%3D16)
Let:
![x+y=4\,\,\,eq(1)\\x^2+y^2=16\,\,\,eq(2)](https://tex.z-dn.net/?f=x%2By%3D4%5C%2C%5C%2C%5C%2Ceq%281%29%5C%5Cx%5E2%2By%5E2%3D16%5C%2C%5C%2C%5C%2Ceq%282%29)
Finding value of x from eq(1) and putting in equation (2)
![x=4-y\\Putting\,\,in\,\,eq(2):\\(4-y)^2+y^2=16\\(16-8y+y^2)+y^2=16\\16-8y+y^2+y^2-16=0\\2y^2-8y=0\\Using\,\,quadratic\,\,equation\,\,to\,\,find\,\,value\,\,of\,\,y:\\y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a=2,\,\,b=-8\,\,,c=0\\Putting\,\,values:\\y=\frac{8\pm\sqrt{64}}{4}\\y=\frac{8\pm8}{4}\\y=\frac{8+8}{4}\,\,and\,\,y=y=\frac{8-8}{4}\\y=4\,\,and\,\,y=0](https://tex.z-dn.net/?f=x%3D4-y%5C%5CPutting%5C%2C%5C%2Cin%5C%2C%5C%2Ceq%282%29%3A%5C%5C%284-y%29%5E2%2By%5E2%3D16%5C%5C%2816-8y%2By%5E2%29%2By%5E2%3D16%5C%5C16-8y%2By%5E2%2By%5E2-16%3D0%5C%5C2y%5E2-8y%3D0%5C%5CUsing%5C%2C%5C%2Cquadratic%5C%2C%5C%2Cequation%5C%2C%5C%2Cto%5C%2C%5C%2Cfind%5C%2C%5C%2Cvalue%5C%2C%5C%2Cof%5C%2C%5C%2Cy%3A%5C%5Cy%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5Ca%3D2%2C%5C%2C%5C%2Cb%3D-8%5C%2C%5C%2C%2Cc%3D0%5C%5CPutting%5C%2C%5C%2Cvalues%3A%5C%5Cy%3D%5Cfrac%7B8%5Cpm%5Csqrt%7B64%7D%7D%7B4%7D%5C%5Cy%3D%5Cfrac%7B8%5Cpm8%7D%7B4%7D%5C%5Cy%3D%5Cfrac%7B8%2B8%7D%7B4%7D%5C%2C%5C%2Cand%5C%2C%5C%2Cy%3Dy%3D%5Cfrac%7B8-8%7D%7B4%7D%5C%5Cy%3D4%5C%2C%5C%2Cand%5C%2C%5C%2Cy%3D0)
Putting values of y=4 and y=0 in equation(1), to find values of x:
Putting y=4
![x+y=4\\x+4=4\\x=4-4\\x=0](https://tex.z-dn.net/?f=x%2By%3D4%5C%5Cx%2B4%3D4%5C%5Cx%3D4-4%5C%5Cx%3D0)
So, one solution is (0,4)
Putting y=0
![x+y=4\\x+0=4\\x=4](https://tex.z-dn.net/?f=x%2By%3D4%5C%5Cx%2B0%3D4%5C%5Cx%3D4)
So, other solution is: (4,0)
Hence Solving the given system of equations we get solution set: {(4,0),(0,4)}
Option B is correct.
Keywords: System of equations
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Answer:
5(3x+4y)
Step-by-step explanation:
5 hours 65 miles per hour= 5x65=325