Investigate for what values of \( \lambda, \mu \) the system of equaions \( 2 x+3 y+5 z=9,7 x+ \) \( 3 y-2 z=8,2 x+3 y+\lambda z=\mu \), have (i) No Solution (ii) A Unique Solution (iii) An Infinite Number of Solutions.

Calculate the length of the third side of the following right-angled triangle. First draw a sough sketch of each of the triangles before you do any calculatic Round off your answers to two decimal places. \( \triangle A B C \) has \( A B=12 \mathrm{~cm}, B C=18 \mathrm{~cm} \) and \( \angle A=90^{\circ} \). Calculate \( A C \)

re il risultato della seguente espr \( \left(10 \cdot 10^{3} \cdot 10^{5}\right):\left(10^{8} \cdot 10\right)= \)

Simplify. \[ \sqrt{18 w^{12}} \]

For items \( 9-10 \), solve the right triangle whose hypotenuse is 20 m and one of whose legs is 16.40 m , given \( A=55^{\circ} 5^{\prime} \) 9. Find the value of the other leg. 10. What is the value of Angle B?

The POTW Input/Output Machine takes a number as input and adds 10 to the numb The machine then takes this sum and mult plies it by 2 . Finally, the machine takes this product, subtracts 30 from the number, an outputs this new number. Anala and Mei each input a positive intege into the machine. If the sum of their two ou puts is 130 , how many possibilities are the for the positive integer that Anala input int the machine?