The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length(in cm) of PQ?
1). 6
2). 9
3). 12
4). 18
If $x^{2}+ y^{2} + z^{2}$ = xy + yz + zx, then what is the value of $\frac{(7x + 3y - 5z)}{5x}$?
1). 0
2). 1
3). 5
4). $\frac{33}{5}$
If $x - 3 +\left[\frac{1}{(x - 3)}\right]$ = 4, what is the value of $(x - 3)^{3} +\left[\frac{1}{(x - 3)^{3}}\right]$?
1). 14
2). 18
3). 52
4). 76
If $\frac{x}{y}$ = $\frac{4}{9}$, then what is the value of $\frac{(7x^{2} - 19xy + 11y^{2})}{y^{2}}$?
1). $\frac{59}{81}$
2). $\frac{100}{27}$
3). $\frac{319}{81}$
4). $\frac{313}{81}$
If x(2x + 3) = 90 and $7y^{-\frac{1}{2}} + 2y^{-\frac{1}{2}}$ = $y^{\frac{1}{2}}$ (x and y are positive numbers), then what is the value of $x^{2} + y^{2}$?
1). 45
2). 109
3). 117
4). 126