a) The linear function that runs through the point \( (-2 ; 3) \) and has a gradient of \( -\frac{2}{3} \) b) The linear function \( \frac{1}{2} y-x=3 \) using the dual intercept method. c) Given \( y=-x^{2}+6 x-5 \). Plot the \( x \) and \( y \) intercepts, the axis of symmetry and the turning point and then link the points to form the graph.

Solve the system of quadratic inequalities: \[ \begin{array}{c}\mathrm{y}>\mathrm{x}^{2}-1 \\ \mathrm{y} \leq-\frac{1}{3} \mathrm{x}^{2}+5\end{array} \]

The ratio of Ben's age to Ali's age is \( 3=2 \). Their total age is 140 years now What is Alils age?

The function \( f(x)=2 x^{2}-5 x+2 k-1 \) does not intersect the \( x- \) axis. Find the range of values of \( k \)

Find the points of intersection for the system \[ \begin{array}{l}\mathrm{y} \geq 2 \mathrm{x}^{2}+3 \mathrm{x}-20 \\ \mathrm{y} \leq \mathrm{x}^{2}+\mathrm{x}-5\end{array} \]

Solve the system of quadratic inequalities: \[ \begin{array}{l}y<x^{2}-4 \\ y>-x^{2}+2\end{array} \]