A car travels sixty miles per hour. How long would it take this car to travel 210 miles?
First, let's take a look at our variables. 1 hour= 60 miles. ? hour= 210 miles. This would be a simple ratio problem since we are comparing. We have one missing variable: how long in hours it takes to travel 210 miles. In completing a ratio, we always put the same measurement across from each other, either on top or on bottom. I am choosing to put my hours on top since they are a smaller number. I will put one of my hours as a variable because I do not know it's measurement yet. I will put my miles on the bottom because they are known. 1 hour x hours ---------- = ----------------- 60 miles 210 miles An easy way to complete this problem is to cross multiple. First, I will multiple (60 miles) ( x hours). I will add this onto my left hand side, whereas my (1 hour) (210 miles) will be on my right hand side. Below is a clearer picture of what this will look like: (60 miles) (x hours) = (1 hour) (210 miles) I will remove my measurements to make multiplying easier. (60) (x) = (1) (210) 60x = 210 Here I will divide 60 by each side 60x = 210 ------ -------- 60 60 x= 3.5 x=3.5 miles. So, in conclusion, we can see that it will take a car 3.5 hours to travel 210 miles.
If 12x= 6x- 18, what does x+ 20 equal?
By looking at our first problem, we can see that we can get our variable x by itself. I will move our 6x to the left hand side to join with our 12x. What we do to one side, we have to do to the other. 12x= 6x -18 -6x -6x 6x= -18 Since we want x by itself, I am going to divide both sides by 6 to isolate our x since he wants to be alone. 6x = -18 -------------- 6 6 x= -3. Our answer will be a negative three because a negative 18 divided by our 6 will be a negative 3. Our answer is a negative because we have one numeral that is a negative, and one that is a positive. In other cases, if we have both numbers either negative or positive, our answer will result in a positive. I know you're problem asking why do two negatives equal a positive? These two negatives cancel out producing a positive number. To conclude our problem, we will substitute -3 in for the x in our second equation. x+20= ? -3+20 = 17. And there we go!
What is the difference between topic and concept?
Often, these terms get used as synonyms, but they are not. Concepts pertain to the bigger picture. They aren't ideas that can be explained easily or with one essay or described in one five paged essay as they are general. Ideas such as culture, identity, etc are concepts. It is not easy to explain these, and there are many perspectives that go into describing what all goes into the idea. Topics are more straight forward and specific. They can be easily narrowed to events such as Civil War or the War of 1812. A teacher may ask you to write an essay on the topic of allusion in Moby Dick. Surely there can be pages upon pages of writing, but it is a very specific topic.