The fibonacci sequence is a series of numbers that usually starts with 0 or 1. The next number is the sum of the two before. 0,1,1,2,3,5,8,13,21.. and so on.
A Government subsidized loan is a loan from the government. They pay the interest on the loan when you are in school, but when you graduate you pay the loan. A Government unsubsidized loan is
Asymptotes and holes are similar because both have to make the bottom of the fraction equal zero. They are different because holes cancel out with and equation on the top to create a hole in the graph.
To reduce the square root of 500 using Mr.Kelly's method, you take 500 and divide it by the smallest number.500 /2 is 250. then divide 250 by the smallest number. 250/2 is 125. 125/5 is 25. 25/5 is 5. 5/5 is 1. this gives you 10 square root of 5. This way is better because a calculator will give you a number with a bunch of decimals. 10 square root of 5 is a better answer than 22.36067977. Using a calculator to get a decimal number would work better for science, when you need an exact number.
To find an inverse function, you replace all the x's with y's and all y's with x's. To verify that two functions are inverse, you solve the equations.
x^y * x^z = x^yz
This equation is sometimes true. For example, if y=3 and z=5, the answer would be x^8 because you add the exponents together. However, if y=2 and x= 2 it would work because 2+2 Quadratic equations always look like ax^2+bx+c=0. When graphed, these equations make either a U or an upside-down U. There are 4 ways to solve these equations. Graphing, Completing the Square, Factoring, and using the quadratic formula. For Graphing, you just type the equation into desmos. My favorite method is completing the square, it seems to be the easiest way to solve.
x²-20x+100. First you subtract the 100 to the other side. x²-20x = -100 then you divide the number in front of the x in half, and add to both sides. x²-20x-10=-90 Then you take the half of the x number and put in the parentheses. (x-10)²=-90. And continue to solve by taking the square root of both sides. Another way to solve is factoring. Using the equation x²+20x+100=0. Find two numbers that add together to get -20 and multiplied together to get 100. (x-10) (x-10) Then, you set the equation equal to 0. so x-10=0 and x-10=0 and solve for x. x=10. The last way to solve is using the quadratic formula. x=-b + or - the square root of b² - 4ac all over 2a. in the equation x²-20x+100, a=1 b=-20 and c=100 plug the numbers in and you get x=20+ or - the square root of -20²-4(1)(100) all over 2(1) simplify . Overall, learning the ways to solve a quadratic equation in school is very important. Scientists use the quadratic formula to determine the path of a missile ( or a ball, but who really cares about the ball, not important), where it will reach its peak, and where it will land. This is very important because if you fire off a missile aimed for an enemy and you don't know exactly how far it can go, things could get very dangerous and unpredictable. :-) There are two steps to factoring the equation:
x3 + 3x2 -54x=0 all of the variables have an x value, so you start with the x outside the parentheses by dividing each by x so x (x2+3x-54 ) you can factor this more. Find two numbers that add together to get 3x and multiplied together to get -54. -6 and 9 work. so x(x-6)(x+9) you can check your work by foiling x(x2+9x-6x-54) which is what we started with. :-) Factoring and solving are similar because you use both to break down the problem to simpler numbers y=|x| y=|x| +1 y=|x|+2 y=|x|+3 y=|x|-2 y=|x+1| y=|x-2| 1. when you add a positive number after the function in the equation, in makes the y intercept what ever number you added. 2. When you add a negative number to the equation after the function, it makes the Y intercept the negative number 3.when adding a positive number to the function, it makes the x intercept a negative 4. when subtracting a number, it makes the x intercept positive 5. y=|x|x-1 when multiplying by -1, it makes the graph go downwards
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