$Factories 5x^2-16x-3$

$$\begin{gathered} Karan pays \$153.00 for a DVD player which has been discounted \\ 15\%.what was the original price of the DVD\hspace{0.17em}player? \end{gathered}$$

$Solve \left|2\mathcal{x}+1\right| =7$

$Solve 3-2\mathcal{x} \le 5$

$Find integers \mathcal{x} and \mathcal{y} such that {(\sqrt{7}-2)}^2=\mathcal{x}+\mathcal{y}\sqrt{7}$

$The point A(4,12), B(8,6) and C(-4,k) are collinear. Find the value of k.$

$$\begin{gathered} solve {\mathcal{x}}^2=10\mathcal{x} \\ write down a quadratic equation with roots \\ 3+\sqrt{2 } and 3-\sqrt{2.} \end{gathered}$$

$Find the equation of the curve which is always 3 units from (2,-3)$

The region bounded by the curve $\mathcal{y}=\tan \mathcal{x}$, the $\mathcal{x}$-axis and the line $\mathcal{x}=\frac{\mathrm{\pi }}{4}$ x = π 4 is rotated about the $\mathcal{x}$-axis. Find, in terms of $\mathrm{\pi }$, the volume of the solid of revolution.

$$\begin{gathered} simplify \frac{{\mathcal{x}}^2-4\mathcal{x}}{\mathcal{x}-4} \\ if \sqrt{75}+\sqrt{80}-\sqrt{12}==\sqrt[4]{c}+\sqrt[a]{4,} find a and c. \end{gathered}$$

(i) Given that ${\log }_a$ 10=2-094 and ${\log }_a$ 2=0.6309, find ${\log }_a$ 500.

(ii) Find $\underset{x\to 3}{\lim }\frac{x^2-9}{x-3}$

(iii) Find the values of k for which x² + kr +2 is positive definite.

$$\begin{gathered} a partical is initially at rest at origin moves in stright line with velocity \\ v=6-2t m/s to the nearest meter the total dis\tan ce travelled in first \\ 6 secounds is \\ \left(A\right) 0m \\ \left(B\right) 6m \\ \left(C\right) 9m \\ \left(D\right) 18m \end{gathered}$$