I suppose the claim is for
.
When , we have
, and of course 5 divides 5.
Assume the claim holds for , that
. We want to use this to show it holds for
, that
.
We have
Since , we can write
for some integer
. Then
which is clearly divisible by 5. QED
Answer: 24
Step-by-step explanation:
Given : A metallurgist wants to study four different fluxes, two different base metals, and three different amounts of energy input.
i.e. 4 different choices for fluxes.
2 different choices for base metals.
3 different choices for amounts of energy input.
If each run of the experiment involves a choice of one flux, one base metal, and one amount of energy input.
Then , the number of runs are possible :-
Hence, there are 24 different runs are possible .
The value of x on the number line is 24 and - 40
A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.
The given equation is
Solving the equation:
Now we take the two separate values of x:
either x=-8+32 or x=-8-32
or,x=24 or x=-40
The value of x is 24 and - 40.
To learn more about number line:
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