1. If \(3x = 4y = 5z\), then what is the ratio \(x : y : z =\) _____?

2. If the roots of the equation \(ax^2 + bx + c = 0\) \((a \ne 0)\) are reciprocals of each other, then \(c =\) _____________.

3. If \((a + b) : \sqrt{ab} = 2 : 1\), then \(a : b =\) ______.

4. If a rectangular prism has the number of faces \(= x\), the number of edges \(= y\), and the number of vertices \(= z\), then \(z - \cfrac{y}{x} =\) _____.

5. If \(a:b=3:2\) and \(b:c=3:2\), then \((a+b):(b+c) =\)_____.

6. If \(\angle A\) and \(\angle B\) are complementary angles, then \(\angle A + \angle B =\) _____.

7. If \(3x = 5\sin\theta\) and \(4y = 5\cos\theta\), then which of the following relations is correct?

(a) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=1\) (b) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=0\) (c) \(\cfrac{9x^2}{25}-\cfrac{16y^2}{25}=1\) (d) \(\cfrac{16x^2}{25}+\cfrac{9y^2}{25}=1\)