What are the "benefits of failure" according to rowling? why do you think she discusses these?

Read the excerpt below and answer the question. she dwelt among the untrodden ways beside the springs of dove, a maid whom there were none to praise and very few to love: a violet by a mossy stone half hidden from the eye! --fair as a star, when only one is shining in the sky. she lived unknown, and few could know when lucy ceased to be; but she is in her grave, and, oh, the difference to me! (wordsworth, “she dwelt among the untrodden ways”) which option explains a meaning implied by the use of the adjective untrodden in the excerpt? the maid was lost in the woods. the maid lived in a rural setting. the maid was a nature spirit. the maid suffered a life without joy.

(1) fire extended humans’ geographical boundaries by allowing them to travel into regions that were previously too cold to explore. (2) it also kept predators away, allowing early humans to sleep securely. (3) fire, in fact, has been a significant factor in human development and progress in many ways. (4) other obvious benefits of fire are its uses in cooking and in hunting. (5) probably even more important, however, is that learning to control fire allowed people to change the very rhythm of their lives. (6) before fire, the human daily cycle coincided with the rising and setting of the sun. (7) with fire, though, humans gained time to think and talk about the day’s events and to prepare strategies for coping with tomorrow. the sentence that expresses the main idea is: (type the number of the sentence. then click “go.”)

Shape 1 and shape 2 are plotted on a coordinate plane. which statement about the shapes is true? a. shape 1 and shape 2 are not congruent.b. a translation will prove that shape 2 is congruent to shape 1.c. a rotation and a translation will prove that shape 2 is congruent to shape 1.d. a reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.