Benjamin Franklin advised Americans to eat and drink to excess because there was a lot of food in America.

Which of the following represents the golden ratio, using a line segment which has been divided into a short length (a) and a long length (b) as shown below?   

Insert a geometric mean between 3 and 48.

 Insert a geometric mean between 3 and 27. 

Subdivide a line segment of length 180 cm into the ratio of 3:5. State both the short and the long lengths.

Use the quadratic formula to solve for x:  2×2 – 4x – 30 = 0

Solve the proportion. Round your answer to one decimal point and type just the numeric value below. 

 Insert a geometric mean between 3 and 12. 

Use the quadratic formula to solve for x :  2×2 + 10x – 28 = 0

Insert a geometric mean between 6 and 24.