Tutor profile: Helena B.
A right triangle has a perimeter of 24 inches with a base of 6 in, a height of x in, and the remaining hypotenuse with a length of y in. 1) Express the area (A) of the triangle with x and y still unknown. 2) Knowing that this triangle is a right triangle, solve x and y. What is the area of the triangle?
1) Formula for the area of a triangle is A = (0.5)(base)(height). In this case, base = 6, and height = x. So therefore, the area is = (0.5)(6 in)(x in) = 3x in^2. 2) We can apply the Pythagorean theorem to this triangle, knowing that the most basic Pythagorean triangle has a base of 3 in, a height of 4 in, and a hypotenuse of 5. Knowing that the base of this current triangle is 6 in, there is a factor of 2 between them. So therefore, we can multiply the length of all the legs of the basic Pythagorean triangle by 2. 3 in * 2 = 6 in (given) 4 in (height) * 2 = 8 in → x = 8 in 5 in (hypotenuse) * 2 = 10 in → y = 10 in We can double check this by comparing the numbers we have to the given perimeter. The perimeter is 24 in, and we can add up all the lengths of the sides of the triangle: (6 + 8 + 10) in = 24 in. So therefore, we can find the area from our formula we derived in the first part now knowing the value of x: A = (3)(8) in^2 = 34 in ^2.
How can you check if your thesis statement (i.e. the main argument of your paper) makes sense and is properly supported?
There are several ways to tell if your thesis statement is suitable for the paper that you are writing-- I outline them below, and make sure to ask yourself these questions before embarking on your paper writing journey. 1) Is my thesis arguable-- meaning, is the argument that I am making something that can be argued in the first place? For instance, you can argue "Orange juice is the most nutritious juice that currently exists!" And support it with information about orange juice's sugar content, vitamin C content, etc. But you cannot argue that "Orange juice has sugar in it." Of course it does! That is not necessarily something that can be disputed, because naturally, fruit juice will have sugar. Remember that a thesis is like an opinion-- people can respond with an alternative point of view to your argument. 2) Is my thesis original? Whether you're writing in the humanities, history, literature, sciences, everyone's coming up with new ideas all the time. It is always important, and part of your preliminary research into the topic that you want to write about, that what you're arguing or showing is new! Of course, research is never 100% original, but you want to contribute something that will add to a story-- not repeat something again. Also, plagiarism is a very serious concern in all academia, and presenting someone's idea as your own is morally dishonest and, in most cases, illegal. 3) Is my thesis researchable? Sometimes you might have a brand-new idea and you might go to research your topic, but nothing is there... Of course, adventuring into the unknown might be appealing, but oftentimes, you do not have that opportunity nor the time! Make sure that there are some more voices to the conversation when you are beginning, whether through journals, newspaper publications, media (video, music, print sources)-- it will help you know that there are other sources to bounce off of. 4) Is my thesis clear enough to readers? A thesis is typically one to two or three sentences on average-- that's not a lot of space! But you want to refine and be clear in what you want to argue. You have the rest of your paper to remind readers of your main point and to give supporting points. Oftentimes in writing, less is more!
Mary's child, Robert, has a condition called "red-green colorblindness" where he cannot tell the difference between the colors red and green. But the interesting fact is that Mary is not colorblind, Robert's father (Joe, also Mary's husband) is not colorblind, and neither of Mary's parents are colorblind either. How is this possible? Knowing that red-green colorblindness is an X-linked recessive trait: 1) Provide the genotypes of Robert, Mary, Joseph, and Mary's parents (who are grandma and grandpa in this case) 2) Identify if any of the above people are carriers for the trait.
1) Mary is XX*. Robert is X*Y. Joe is XY. Mary's mom is XX*. Mary's dad is XY. Where (*) denotes a recessive trait attached to a certain chromosome. 2) In this case, Mary's mom and Mary are carriers for the trait.
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