The threat of rain didn’t … her stroll through the grounds. Even the first drops were no …, and she continued her walk. A. hinder … incentive B. thwart … refuge C. impede … deterrent D. permit … provocation E. prevent … enticement
The correct answer is C. impede ... deterrent. We know that the person in the sentence continued her walk, so the words must indicate that the rain (even the first drops) didn't stop her from walking. A. The first word "hinder" would fit, but "incentive" isn't relevant either way to the situation in the sentence. Incentive means something that would compel someone to act a certain way, and we're looking for a word that means the opposite--it would stop someone from doing something. B. Same as A. "Thwart" would fit in the sentence, but "refuge" doesn't fit with what we're trying to say. C. Both words fit, this is the right answer. "Impede" means to stop, and a "deterrent" is something that causes someone not to do something. D. "Permit" is the opposite of what we want, and "provocation" doesn't fit at all. This answer is the furthest from being correct. E. "Prevent" would work, because it also means to stop. "Enticement" has the same problem as "incentive" in answer choice A, it means the opposite of the word we need for that blank.
A student gave me the following paragraph as part of a paper he needed help editing: A moment where I was able to realize that we were a community clearly was when we went ice skating in Bryant Park. To my surprise, everyone knew how to ice skate so well, and there was me who in the first 2 minutes fell sixteen times on the ground. When people from the program started to see my struggle they came over and helped me out. Instead of thinking about one another, the other students made it a point to help me and learn how to ice skate. This could be amplified in other situations, where we would help one another out, in the benefit to see others succeed. I was surrounded by the most positive and empathic people in my life.
With my help, the student was able to transform the paragraph into this: When we went ice-skating in Bryant Park, I realized for the first time that the people in the program were a community. To my surprise, everyone already knew how to ice skate well. That is, except me--I fell sixteen times in the first two minutes. When people from the program noticed me struggling, they came over and helped me, letting me lean on their shoulders until I felt comfortable enough to skate on my own. Instead of thinking about themselves, the other students made the selfless effort to help me learn how to ice skate. Similar things happened throughout the program--students would help one another for no reason except the joy of seeing one another succeed. During the program, I honestly felt that I was surrounded by the most positive and empathic people I had ever known in my life.
((x^2)/(x^2-1)) / ((3x)/(x-1)) Divide and simplify.
Instead of dividing the fraction, we can change the division symbol to multiplication and flip the second fraction, which gives us an equivalent equation. That gives us this instead. ((x^2)/(x^2-1)) * ((x-1)/(3x)) Next, we should see if there are any pieces that we can factor. x^2-1 can be factored into (x+1)(x-1), so we'll do that. ((x^2)/((x+1)(x-1))) * ((x-1)/(3x)) Next, let's see if there's anything that will cancel out. We can cancel either up and down (if a term is in the numerator and denominator of the same fraction) or diagonally (if a term is in the numerator of one fraction and the denominator of another). We cannot cancel across. In this case, we can cancel two things. We can cancel an x out of x^2 in the first fraction and 3x in the second. That gives us this: ((x)/((x+1)(x-1))) * ((x-1)/(3)) We can also cancel out (x-1) in both fractions. ((x)/(x+1)) * (1/3) That's as far as we can simplify, so now we should multiply. Fractions multiply across, so the numerators multiply and the denominators multiply. x/(3(x+1)) That's as simplified as we can get, so we're done!