The X value of a Vertex of a parabola is equal to -b/2a.
So h = 5, and k = 5^2-5(5)+1 = 1.
The next one you should split into 2 fractions. The 5*4! is equivelant to 5!. 5!/7! = 1/42 (6*7). Now multiply by two, and you get 1/21.
4^x is equivelant to 2^2x. When you have +1 on an exponent, it means to multiply by the base once more. 10.7*2 = 21.4
In the expansion question, try expanding (a+b)^2, then (a+b)^3 etc. The answer will always be one more than the exponent. Which in this case will be 7.
Deficient, Abundant, and perfect numbers are all related.
Perfects are numbers whose divisors (including 1) add up to the number itself. Take 6 for example. 1+2+3 = 6. YOU MUST MEMORIZE the first 3 --> 6, 28, 496.
Abundants are numbers whose factors add to more than the number. These are numbers that are divisable by perfects. 18 for example is abundant, as is 56.
Deficents are numbers whose factors add to less than the number, like 15 or 14.
Transcendential numbers are a class of irrational numbers that includes pi and e. These are numbers that are uncountable infinite. You can't simplify them with fractions, and people like memorize several digits of them. Yeah.
The last one in a product of the roots question
Given a quadratic a^2 +b + c, the sum of the roots is equal to -b/a. (ALWAYS) The product is equal to the last term divided by the first term or c/a. If the power of a polynomial is odd, the product is negative. The sum of roots is always -b/a.
4. the expansion of polynomial with power n has n+1 terms. Ergo 7 terms
5,6&8. Given a natural number K, if the sum of K's integral divisors (excluding K itself but not 1) add up to K, then K is perfect (e.g. 6=1+2+3); if the sum is less, K is deficient; if more, abundant. The first 3 perfect numbers were 6 (# of days in which God is said to have created the world), 28 (# of days in a lunar month) and 496 (whatever it is)
7. Transcendental numbers are those irrational number that can never be a solution to a polynomial of any degree with rational coefficients. e and pi are both transcendental, so is ln2, and sin2, and some others. But if you see squareroots or any radicals, it's not transcendental
8. write the cubic eqn in standard form ax^3+bx^2+cx+d=0. The product of the roots is -d/a. Ergo 5/2
Lol, Zack's beat me to it. However, I don't think Zack's solutions to number 1 and 2 are correct. And I don't think my understanding of number 3 is correct, either, lol.
Arg! On 2 I saw 5*4! + 5*4!/7! I'm an idiot. On 1... I didnt divide 5 by 2 in coming up with -b/2a. Arg. I need to check my answers before I post. And on #3 I thought it was an exponential problem.
