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Prove that the equivalence relation modulo m where m is an integer, forms a ring.
Also, does this same equivalence relation form a field and why?
For this proof, you are given that [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. We also know that for any two integers, a and b, that
[a]m + [b]m = [a + b]m and
[a]m[b]m = [ab]m
Assuming that all variables represent positive real numbers rewrite the following in simplified radical form
Provide a numerical answer to each of the following questions and also show the calculations you used to find the answers. How many different ways can 30 runners place in an Olympic qualifying marathon?
Use elimination or substitution method equations.
How does the knowledge of simplifying an expression help you, personally, to solve an equation efficiently? Give an example from your life in how knowing the reason why helped you with the process of solving a difficult situation or problem.
Evaluate the graph.
Find the solution for x
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Use the technique as specified in this lecture under the section Completing the Square to Determine the solutions (roots) of the equation. Verify each root by plugging the root back into the equation and performing the computation
Problems on distance.
Exhibit that ordered pair which constitutes the vertex. Exhibit the y intercept. How many zeros does this expression have?
Suppose K is a Galois extension of F of degree p^n for some prime p and some n >= 1. Show that there are Galois extensions of F contained in K of degree p and p^(n-1).
In an exponential smoothing model, if the smoothing constant (alpha) were equal to 0, then. The forecast would never change.
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