An artist is using tiles and boards for a project. A tile has length 2/3 ft and width 2/3 ft. A board has length 1/2 yd and width 1/3 yd. what is the ratio of the length of the tile to the length of the board?

  4 : 9

Step-by-step explanation:

The requested ratio is ...

  tile length : board length = (2/3 ft) : (1/2 yd) = (8 in) : (18 in)

  = 8 : 18 = 4 : 9

To make a unitless ratio, both parts must have the same units. Here, we chose to express the lengths in inches. We could have used feet or yards as well. (2/3 ft)×(1 yard)/(3 ft) = 2/9 yd or (1/2 yd)(3 ft/yd) = 3/2 ft. You get the same ratio with any of these:

  (2/9 yd) : (1/2 yd) = (4 yd) : (9 yd) = 4 : 9 . . . . . multiply by 18

  (2/3 ft) : (3/2 ft) = (4 ft) : (9 ft) = 4 : 9 . . . . . multiply by 6

a 10 percent increase

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1