A bottle of soda water is grasped by the neck and swung briskly in a circle .Near which portion of the bottle do the bubbles collect ?a. Near the neck b. near the bottom c. near the centre of the bottle d. bubbles remain distributed uniformly throughout the volume of the bottle

Sure, here are some step-by-step solutions with LaTeX tags intact: 1. Simplify the expression: $3(x-4)+2(x+5)$$\begin{array}{rl}3(x-4)+2(x+5)& =3x-12+2x+10\\ & =5x-2\end{array}$ 2. Solve the equation for $x$: $4x-5=11$$\begin{array}{rl}4x-5& =11\\ 4x& =16\\ x& =4\end{array}$ 3. Find the slope of the line passing through the points $(2,3)$ and $(5,9)$$\begin{array}{rl}\text{slope}& =\frac{\text{change in }y}{\text{change in }x}\\ & =\frac{9-3}{5-2}\\ & =\frac{6}{3}\\ & =2\end{array}$ 4. Factor the expression: $x^2-9$$\begin{array}{rl}{x}^2-9& =(x+3)(x-3)\end{array}$ 5. Solve the system of equations: $\begin{array}{rl}2x+y& =5\\ x-y& =3\end{array}$$\begin{array}{rl}2x+y& =5\\ x& =y+3\\ 2(y+3)+y& =5\\ 3y& =-1\\ y& =-\frac{1}{3}\\ x& =-\frac{8}{3}\end{array}$ I hope these step-by-step solutions are helpful for students using Filo App!