C. A function must have different elements in the Domain, but can have repeats in the range.
Answer:
b. (12, 485)
Step-by-step explanation:
We have been given the number of men receiving degrees (in thousands) is given by the equation
, and for women, the equation is
, where x is the number of years since 1970.
Let us find the coordinates of the point of intersection of both lines by equating our both equations as:
![14.3x+317=3.6x+443](https://tex.z-dn.net/?f=14.3x%2B317%3D3.6x%2B443)
![14.3x-3.6x+317=3.6x-3.6x+443](https://tex.z-dn.net/?f=14.3x-3.6x%2B317%3D3.6x-3.6x%2B443)
![10.7x+317=443](https://tex.z-dn.net/?f=10.7x%2B317%3D443)
![10.7x+317-317=443-317](https://tex.z-dn.net/?f=10.7x%2B317-317%3D443-317)
![10.7x=126](https://tex.z-dn.net/?f=10.7x%3D126)
![\frac{10.7x}{10.7}=\frac{126}{10.7}](https://tex.z-dn.net/?f=%5Cfrac%7B10.7x%7D%7B10.7%7D%3D%5Cfrac%7B126%7D%7B10.7%7D)
![x=11.7757](https://tex.z-dn.net/?f=x%3D11.7757)
Upon substituting x=11.7757 in our equations we will get,
![y=3.6x+443](https://tex.z-dn.net/?f=y%3D3.6x%2B443)
![y=3.6*11.7757+443](https://tex.z-dn.net/?f=y%3D3.6%2A11.7757%2B443)
![y=42.39252+443](https://tex.z-dn.net/?f=y%3D42.39252%2B443)
![y=485.39252](https://tex.z-dn.net/?f=y%3D485.39252)
![y=14.3x+317](https://tex.z-dn.net/?f=y%3D14.3x%2B317)
![y=14.3*11.7757+317](https://tex.z-dn.net/?f=y%3D14.3%2A11.7757%2B317)
![y=168.3925+317](https://tex.z-dn.net/?f=y%3D168.3925%2B317)
![y=485.3925](https://tex.z-dn.net/?f=y%3D485.3925)
Upon rounding our answers to nearest whole number we will get,
![y=485.3925\approx 485](https://tex.z-dn.net/?f=y%3D485.3925%5Capprox%20485)
![x=11.7757\approx 12](https://tex.z-dn.net/?f=x%3D11.7757%5Capprox%2012)
Therefore, the point (12,485) will be the solution of our given equations and option b is the correct choice.
4/(x+1) = 3/x + 1/15
Should we make common denominators with everything, we get
4*15*x / [15x(x+1)] = 3*15*(x+1)/[15x(x+1)] + x(x+1)/[15x(x+1)]
Multiply both sides of the equation by the denominator to cancel them
60x = 45(x+1) + x(x+1)
60x = 45x + 45 + x^2 + x
x^2 - 14x + 45 = 0
(x-9)(x-5) = 0
The answer to this question is that the solutions are x=9 and x=5.
Answer:
![AC=25](https://tex.z-dn.net/?f=AC%3D25)
Step-by-step explanation:
From the given figure, it can be seen that
, thus ΔABC is an isosceles triangle.
Therefore,![AB=BC](https://tex.z-dn.net/?f=AB%3DBC)
⇒![5x+5=7x-1](https://tex.z-dn.net/?f=5x%2B5%3D7x-1)
Solving the above equation, we get
⇒![5x-7x=-1-5](https://tex.z-dn.net/?f=5x-7x%3D-1-5)
⇒![-2x=-6](https://tex.z-dn.net/?f=-2x%3D-6)
⇒![x=3](https://tex.z-dn.net/?f=x%3D3)
Now, substituting the value of x in AC, we have
⇒![AC=6x+7](https://tex.z-dn.net/?f=AC%3D6x%2B7)
⇒![AC=6(3)+7](https://tex.z-dn.net/?f=AC%3D6%283%29%2B7)
⇒![AC=18+7](https://tex.z-dn.net/?f=AC%3D18%2B7)
⇒![AC=25](https://tex.z-dn.net/?f=AC%3D25)
Thus, the length of the side AC of the given triangle is 25 units.