The length of one side of an equilateral triangle is x - 3. First, express the perimeter as a sum. Next, express the perimeter as a product. Then show that the two expressions are equivalent.

Is the square root of 4 plus the square root of 16 rational?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

On a cm grid, point p has coordinates (3,-1) and point q has coordinates (-5,6) calculate the shortest distance between p and q give your answer to 1 decimal place