Triangle LMN is plotted on a coordinate plane. It is then dilated by a factor of 2 using the origin as the center of dilation, and translated 5 units left and 3 units up. How is this sequence of transformations written in coordinate notation to correctly map triangle LMN to its image, triangle L'M'N' ?

A. ( x , y )→(2 x + 3, 2 y - 5)

B. ( x , y )→(2 x - 5, 2 y + 3)

C. ( x , y )→(2 x + 5, 2 y + 3)

D. ( x , y )→(2 x + 3, 2 y + 5)

Li buys supplies so he can make and sell key chains. he begins to make a profit only after he sells 4 key chains. what point on the graph makes the most sense in this situation?

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.