The answer would be the third choice as Geometry is essentially based on other proven theorems, axioms, and definitions.
ANSWER
![S_\infty= 686](https://tex.z-dn.net/?f=S_%5Cinfty%3D%20686)
EXPLANATION
The given infinite series is
![98 + 84 + 72 + \frac{432}{7} + ...](https://tex.z-dn.net/?f=98%20%2B%2084%20%2B%2072%20%2B%20%20%5Cfrac%7B432%7D%7B7%7D%20%20%2B%20...)
The sum to infinity of this series is given by the formula,
![S_\infty= \frac{a_1}{1 - r}](https://tex.z-dn.net/?f=S_%5Cinfty%3D%20%5Cfrac%7Ba_1%7D%7B1%20-%20r%7D%20)
where the first term of this infinite geometric series is
![a_1 = 98](https://tex.z-dn.net/?f=a_1%20%3D%2098)
and the common ratio is
![r = \frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7Ba_2%7D%7Ba_1%7D%20)
![r = \frac{72}{98} = \frac{6}{7}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B72%7D%7B98%7D%20%20%3D%20%20%5Cfrac%7B6%7D%7B7%7D%20)
We substitute these values to obtain,
![S_\infty= \frac{98}{1 - \frac{6}{7} }](https://tex.z-dn.net/?f=S_%5Cinfty%3D%20%5Cfrac%7B98%7D%7B1%20-%20%20%5Cfrac%7B6%7D%7B7%7D%20%7D%20)
We simplify the denominator to get,
![S_\infty= \frac{98}{\frac{1}{7} }](https://tex.z-dn.net/?f=S_%5Cinfty%3D%20%5Cfrac%7B98%7D%7B%5Cfrac%7B1%7D%7B7%7D%20%7D%20)
This simplifies to
1 is D, because if you wrote out all the choices as equations, you would get that A is 1/2 n - 3, B is also 1/2 n - 3, C is 1/2 - 3, and D is 1/2(n - 3)
2 is A, because 3 times her age minus 4 is 3x-4, with x as Marcys age
3 is C, because although 11 x 5 is 55, it says that 5 times a number is LESS than 55, so the answer is 10, or C
4 is B because the mode is 92, the mean is 122, and the median is 88, which would mean that mean>mode>median
18 answer 45 is the answer
Writing this info out symbolically:
x^2 + (x+5)^2 = 37
Expanding, x^2+x^2+10x +25=37, or 2x^2+10x-12=0.
Reducing, x^2+5x-6=0. factoring, (x-1)(x+6)=0
Solving for x: x-1=0 results in x=1; x=6=0 results in x=-6.
We want only a positive result, so choose x=1 and discard x=-6.