The third choice does not represent a proportional relationship because the y-intercept ≠ 0.
Hope that helped you.
Hey
Let the dimensions for the Print Region be M,N
Additional Margin is summed up to get :
New Dimensions of the Page = (M + 2)(N)
[ 2 inches - 1 inch on either side ]
Hence, the Area = [ MN + 2N ] = [ 95 + 2N ]
Note that 'N' has to be a factor of 95
=> Least Possible Area is achieved when N = 5
=> Dimensions of the Page = { 21 inches x 5 inches ]
Answer:
![\dfrac{203-183i}{169}](https://tex.z-dn.net/?f=%5Cdfrac%7B203-183i%7D%7B169%7D)
Step-by-step explanation:
![\dfrac{9-19i}{12-5i}=\dfrac{(9-19i)(12+5i)}{(12-5i)(12+5i)}=\dfrac{108+45i-228i-95i^2}{144-25i^2}\\\\=\dfrac{203-183i}{169}=\dfrac{203}{169}-\dfrac{183}{169}i](https://tex.z-dn.net/?f=%5Cdfrac%7B9-19i%7D%7B12-5i%7D%3D%5Cdfrac%7B%289-19i%29%2812%2B5i%29%7D%7B%2812-5i%29%2812%2B5i%29%7D%3D%5Cdfrac%7B108%2B45i-228i-95i%5E2%7D%7B144-25i%5E2%7D%5C%5C%5C%5C%3D%5Cdfrac%7B203-183i%7D%7B169%7D%3D%5Cdfrac%7B203%7D%7B169%7D-%5Cdfrac%7B183%7D%7B169%7Di)
The right answer is Option C : 5
Step-by-step explanation:
Let,
The numerator of fraction = x
The denominator of a fraction is 10 more than its numerator.
![\frac{x}{x+10}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%2B10%7D)
When 1/3 is added to this fraction,
![\frac{x}{x+10}+\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%2B10%7D%2B%5Cfrac%7B1%7D%7B3%7D)
the resulting fraction’s denominator is three times the denominator of the original fraction its numerator is 15 less than its denominator
![\frac{3(x+10)-15}{3(x+10)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%28x%2B10%29-15%7D%7B3%28x%2B10%29%7D)
Therefore, it becomes
![\frac{x}{x+10}+\frac{1}{3} = \frac{3(x+10)-15}{3(x+10)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%2B10%7D%2B%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B3%28x%2B10%29-15%7D%7B3%28x%2B10%29%7D)
Taking LCM on left side
![\frac{3x+(x+10)}{3(x+10)}=\frac{(3x+30)-15}{3(x+10)}\\\\\frac{3x+x+10}{3(x+10)}=\frac{3x+30-15}{x(x+10)}\\\\\frac{4x+10}{3(x+10)}=\frac{3x+15}{3(x+10)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B%28x%2B10%29%7D%7B3%28x%2B10%29%7D%3D%5Cfrac%7B%283x%2B30%29-15%7D%7B3%28x%2B10%29%7D%5C%5C%5C%5C%5Cfrac%7B3x%2Bx%2B10%7D%7B3%28x%2B10%29%7D%3D%5Cfrac%7B3x%2B30-15%7D%7Bx%28x%2B10%29%7D%5C%5C%5C%5C%5Cfrac%7B4x%2B10%7D%7B3%28x%2B10%29%7D%3D%5Cfrac%7B3x%2B15%7D%7B3%28x%2B10%29%7D)
Multiplying both sides by 3(x+10)
![3(x+10)*\frac{4x+10}{3(x+10)}=\frac{3x+15}{3(x+10)}*3(x+10)\\4x+10=3x+15\\4x-3x=15-10\\x=5](https://tex.z-dn.net/?f=3%28x%2B10%29%2A%5Cfrac%7B4x%2B10%7D%7B3%28x%2B10%29%7D%3D%5Cfrac%7B3x%2B15%7D%7B3%28x%2B10%29%7D%2A3%28x%2B10%29%5C%5C4x%2B10%3D3x%2B15%5C%5C4x-3x%3D15-10%5C%5Cx%3D5)
The numerator of original fraction is 5.
The right answer is Option C : 5
Keywords: fraction, addition
Learn more about fractions at:
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