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Yes, there is. The planet is called Nibiru however it's further out than Pluto beyond the Kyper belt and the chance it'll make it through that without losing a large amount of mass is slim, then it has to pass the gas giants. If it can pass the gas giants without being sucked into one (The most likely of which would be Jupiter) then it still has to pass through the asteroid belt between Mars and Jupiter and if it can make it through all of that without being reduced to rubble or getting sucked into a gas giant it still has to be on a collision course with the Earth which is a rather small opportunity. All of this is assuming it broke from its orbit and moving on a path that'd go through the Earth's orbit. It's about as dangerous as a pebble on the ground.
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How does an indirect proof differ from a regular proof?
Given a proposition X, a regular proof known facts and logical arguments to show that X must be true. For an indirect proof, you assume that the negation of X is true. You then use known facts and logical arguments to show that this leads to a contradiction. The conclusion then is that the assumption about ~X being true is false and that is equivalent to showing that X is true.
How do you write two binomials whose product is a difference of squares?
The two binomials can be written as (x - a)(x + a), for any constant a. Proof: Expand using FOIL: (x - a)(x + a) = x2 + xa - xa - a2 Group: (x - a)(x + a) = x2 - a2 x2 - a2 is a difference of squares. Thus, the product of (x - a) and (x + a) is a difference of squares.
Why is 4 to the power 0 equal to 1?
for any non zero no. x, x^0=1 the proof is as follows, consider the two no.s x^m and x^n,where m and n are two non zero no.s. now let us assume without any oss of generality,that m>n,hence (x^m)/x^n=(x*x*x....m times)/(x*x*x...n times) now on the r.h.s, n no. of x in the denominator will cancel out n no. of x in the numerator(as x is non zero);leaving (m-n) no. of x in the numerator, i.e. (x^m)/(x^n)=x^(m-n) now letting m=n,we have x^m/x^m=x^(m-m) or, 1=x^0 hence the proof if x is also 0,i.e. 0 to the power 0 is undefined!
Is there Number that can be divided by all number?
No. And the proof is simple. Suppose there were such a number, X. Then X+1 is also a number and X+1 does not divide X.
How do you explain yourself in a math answer?
You explain yourself in a math answer by justifying your actions with the use of properties, definitions, theorems and axioms/postulates. This is called a "proof", and represents the foundation of modern mathematics. For example, here is a simple proof that FOILing two binomials is the same as polynomial multiplication: Consider the binomials (a*x + b) and (c*x +d) We know that: (a*x + b) * (c*x + d) = (a*x + b) * c*x + (a*x + b)*d by the Distributive Law of Multiplication. Applying the Distributive Law of Multiplication again a second time, we know that: (a*x + b) * c*x + (a*x + b) * d = a*x*c*x + b*c*x + a*x*d + b*d. Applying the Commutative Law of Multiplication and simplifying, we have: a*x*c*x + b*c*x + a*x*d + b*d = a*c*x^2 + b*c*x + a*d*x + b*d Applying the Commutative Law of Addition, we have: a*c*x^2 + b*c*x + a*d*x + b*d = a*c*x^2 + a*d*x + b*c*x + b*D Since "=" is an equivalence relation, we know the following by transitivity (if h = i and i = j then h = j): (a*x + b)*(c*x + d) = a*c*x^2 + a*d*x + b*c*x + b*d That is, the multiplication of two binomials is equal to the summation of the first terms multiplied, the outer terms multiplied, the inner terms multiplied and the last terms multiplied - hence FOIL (First Outer Inner Last). The above proof is an example of a "direct proof". We showed that two polynomials are equal to each other. THere are other methods for proving: Proof by Cases, Proof by Contradiction, Proof by Contrapositive, Proof by Induction and Proof by Logical Equivalency.
