1.Graph the system of linear inequalities on the coordinate plane. y => -1/2x + 2 1/2y< 1/5x + 6( a) Shade the solution to the system of inequalities.(b) Pick a point and show your solution is correct.

2.Discuss in detail Question: Now consider equations of the form x-a sqrt bx+c , where a, b, and c are all positive integers and b >1.(a) Make equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution.(b) What must be true about the value of bx + c to ensure that there is a real number solution to the equation? Explain.

4.You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest candle designs, the Brick and the Egyptian. The original Brick was a cube 8 cm on a side. The original Egyptian was a pyramid 21 cm tall with a square base 10 cm on a side. Improvements in the manufacturing process have made it possible to change the design of these candles for a fresh new look and improved profit.

Question: Now make your own original candle design based on solid figures. Draw the candle in the space below and label the drawing with dimensions. Then write the equation for the volume of the candle in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in standard form.