The years when the Russo-Japanese war had not yet happened is the year of 1903 and before
Let x represents years, the inequality system is x < 1904
Answer:
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Step-by-step explanation:
Answer:
The answer is 61.
Step-by-step explanation:
Let, the numbers are: x, (x+2), (x+4)
Now, x+x+2+x+4 = 183
3x + 6 = 183
3x = 177
x = 59
So, second number would be: (x+2) = (59+2) = 61
Answer:
4 cents
Step-by-step explanation:
4.50 divide by is .9 and 7.52 divide by 8 is .94
Answer:
Step-by-step explanation:
Our equations are
![y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\](https://tex.z-dn.net/?f=y%20%3D%20-3x%5E2%20%2B%20x%20%2B%2012%5C%5Cy%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5Cy%20%3D%20x%5E2%20%2B%207x%20-%2011%5C%5Cy%20%3D%20-x%5E2%20-%208x%20-%2016%5C%5C)
Let us understand the term Discriminant of a quadratic equation and its properties
Discriminant is denoted by D and its formula is
![D=b^2-4ac\\](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%5C%5C)
Where
a= the coefficient of the ![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
b= the coefficient of ![x](https://tex.z-dn.net/?f=x)
c = constant term
Properties of D: If D
i) D=0 , One real root
ii) D>0 , Two real roots
iii) D<0 , no real root
Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .
Let us start with
![y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\](https://tex.z-dn.net/?f=y%20%3D%20-3x%5E2%20%2B%20x%20%2B%2012%5C%5Ca%3D-3%20%2C%20b%20%3D1%20%2C%20c%20%3D12%5C%5CD%3D1%5E2-4%2A%28-3%29%2A%2812%29%5C%5CD%3D1%2B144%5C%5CD%3D145%5C%5CD%3E0%20%5C%5C)
Hence we have two real roots for this equation.
![y = 2x^2 - 6x + 5\\](https://tex.z-dn.net/?f=y%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5C)
![y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D](https://tex.z-dn.net/?f=y%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5Ca%3D2%2Cb%3D-6%2Cc%3D5%5C%5CD%3D%28-6%29%5E2-4%2A2%2A5%5C%5CD%3D36-40%5C%5CD%3D-4%5C%5CD%3C0%5C%5C)
Hence we do not have any real root for this quadratic
![y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20%2B%207x%20-%2011%5C%5Ca%3D1%2Cb%3D7%2C-11%5C%5CD%3D7%5E2-4%2A1%2A%28-11%29%5C%5CD%3D49%2B44%5C%5CD%3D93%5C%5C)
Hence D>0 and thus we have two real roots for this equation.
![y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20-%208x%20-%2016%5C%5Ca%3D-1%2Cb%3D-8%2Cc%3D-16%5C%5CD%3D%28-8%29%5E2-4%2A%28-1%29%2A%28-16%29%5C%5CD%3D64-64%5C%5CD%3D0%5C%5C)
Hence we have one real root to this quadratic equation.