You can graph a line using the y=mx+b equation. The first thing you do is graph the b. The b is the y intercept. This is wear the line goes through the graph. The m is the slope. Let's say the cost for a taxi ride is $.50 per mile and you also have to pay a base fee. Let's say the base fee is $3.00. Let's say that you took a 20 mile cab ride. This is the x, also known as the independent variable. 20*.50 is 10. You know add the b to the mx which in this case is 10. The cost would have been $13. Now to graph this, you start off at 3 which is your b. you go up 1, then over 2. Rise over run. 1/2 gives you .5 which is your slope.
Another example of y=mx+b could be when you are buying insurance. It costs $5 just to get insurance from Progressive. This is the y-intercept. Then on top of that you have to pay $10 for every $100 you are covered. Therefore, the m would be 10. Now lets plug in some numbers. let's say you want $10000 coverage. You would have to pay $1000 for the coverage plus the $5 base fee for getting insurance.
3.14159265358979323846264338327950288419716939937510582 are the first few numbers of Pi. Pi is the ratio of the diameter of a circle to the circumference of the circle. The formula for the circumference of a circle is Pi times the diameter if the diameter of a circle is 4 inches. Then the circumference of the circle is 4Pi. To determine the area of a circle is Pi * radius^2. If the diameter is 4 inches, then the radius of the circle is 2 inches. If you square 2, you get 4. Therefore, the area of the circle is 4Pi.
Note: the circumference of a circle is not always equal to area of a circle. It varies based on the diameter and radius of a circle. Pi was discovered by Babylonians about 4000 years ago. Since I am in Algebra, I do not know what Mrs. Moon or Mr. Dorman have taught you about Pi.
I will explain each and everyone on of the variables In the equation y=mx+b which is used to determine a line's slope. In the equation y=mx+b, the x is the independent variable and the y is the dependent variable. This means that to get the y, the y needs to know what x is. The y depends on the x, but the x does not depend on the y; so x is the independent variable. B is the y intercept. A y intercept is where a line passes through a point in which the dependent variable is 0. The M is the slope. The slope is the angle and direction the line is pointing from left to right.
Let's say you are buying pizzas. The cost for one pizza is $10. This is the m. Let's say you want to donate a $1 to red cross and put it in the donation box. This is the b. Now the equation looks like this Y(Dependent Variable)=$10(Slope) * X (Independent Variable) + 1 (Y Intercept). All you have to do now is plug in the number of pizzas you buy. Let's say you bought 10 pizzas. Plug it in for X. Now the equation is Y=10*10+1. Now, you just need to solve. The cost for the pizzas and donation together is $101. This is an example of how Y=MX+B works.
The cost of a 12 pack of Mountain Dew cost 11.99. This means the cost for one soda would be $1 based on the price. This can contains 8 ounces. If you divide 1 by 8, you get 0.125. In money, this is 12.5 cents. The cost for a 1 liter bottle of soda online is about $6 dollars. A one liter bottle contains 33.8 ounces. The cost for a one ounce is about 10 cents. Another factor to consider when you are buying is to include the fact that the 12 pack gets charged Crv, which cost 10 cents per can, therefore the cost of the 12 pack is increased to 11.99.
Therefore, the better deal would be to buy one liter bottles since the cost is less per ounce, and if you would buy a liter of soda using the first amount would be about $4.23, and the cost for the second amount would be $3.38. The difference between these two cost is $0.85. Clearly, the better deal is the second one, and you are being ripped off if you buy the 12 pack.
I remember substitution the most. Substitution is when you have two equations, and you want to find the solution ( intersecting points on a graph). If the first equation was y=2x-5, and the second equation was y=-4x+7. If y=2x-5, and y also equals -4x+7, then -4x+7 must equal 2x-5. So it would be turned into a balance problem. -4x+7=2x-5 would be the balance equation. To find x and y's values you have to use this method. The first step in this equation would be to get rid of -4x. How do you get rid of a negative number? You get rid of a negative number adding it's absolute value which is +4x, and if we add 4x to one side, we also have to add it to the other side. Now the equation looks like this 7=6x-5. Now we want to have 6x by itself, so we will get rid of -5 by adding 5. Remember, if you add to one side, you also have to add to the other side. Now the equation looks like this 12=6x. We do not want to know what 6x equals, we want to know what 1x equals. We will now divide both sides by 6 which will give us 2=x. We will now plug in 2 for x. Now the original equation looks like this y=2(2)-5. 2*2 is 4, and 4-5 is -1; y is -1. The point where they will intersect on a graph is (2,-1).
When we were reviewing this in Algebra, many kids reactions were that they had forgotten how to substitute. I was one of the kids who were most confused.After Mr. Erickson reintroduced this concept to us, it all made sense.
The math concept that I had the most trouble with is substitution. We used pictures and how we can use pictures to substitute. I had a lot of trouble with it because I wasn't used to using pictures to substitute. To substitute in Algebra, you just plug in what you are substituting. Doing this with pictures was harder. It took me a while to figure out how to do it visually with pictures and how to do it using Algebra. This concept was introduced to us on 12-14-12. What helped me understand; was practicing substitution more. Everything else in Algebra came pretty easy to me, and I had no problems. According to Mr.Erickson; this was the easy half of Algebra.
Pythagorean Theorem... What is Pythagorean Theorem? I actually do not know what Pythagorean Theorem is. Based on the quick research I just did, it means that in a right triangle; the right angle has 90 degrees, and the other two sides have a sum of 90 degrees. Another way to understand it is using the formula a 2 + b 2 = c 2. If the first side is 3. Than it is 3^2. If the second is 4, that it is 4^2. So far we have 3^2 + 4^2. This means that the third side must be 5^2. Now we have 3^2+4^2=5^2. Simpler, this means 9+16=25. This is all I am able to understand, if there is more to this, please leave a comment because I am not exactly sure I know what Pythagorean Theorem is.
If it is 64^2 , then it would be 64 * 64. The first 64 is length, and the second 64 is height. If we work by centimeters, than it would be 64 centimeters high, and 64 centimeters over. This makes it squared. If you work backwards, it would be a square root. Root means origin. That means the origin of the squared number. If you square 64, it means you are multiplying 64 by 64. This gives us the number 4096. The square root of 4096 is 64. Squaring and finding square roots are the inverse of the other.
I am not exactly sure what it is trying to say. So if you do know please leave a comment. But what I think it means is that in the example 5^-2. 5 is squared by -2. It is that number out of 1. I would do 5*5 which is 25. I would then put 1 over 25. I think that this is how you are supposed to be solving this equations. We have not yet talked about this in Algebra so I do not guarantee that this is the best way to do it, but it still works so for know this the solution that I use. If there is a better way to do it, please let me know in the comments.
Exponents are just an easier way of writing multiplactin. For example, if it 5 squared by 10. 5 squared by 10 is just an easier way of writing 5*5*5*5*5*5*5*5*5*5. We use exponents because we are lazy. We choose not to write all of it, so we just square it instead of writing 5*5*5*5*5*5*5*5*5*5. We use exponents to save time. We use exponents when we are talking about how much land there is. It could be 16 feet squared. 16 feet squared is 256 feet. Instead of 16*16 we do 16 feet squared.
RSS Feed