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Emma D.'s Resources

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Hello Thorgerdur,    You can begin both problems by replacing 314 with its modular 7 representation: 314^163 = 6^163 mod 7   (a)  Note how powers of 6 repeat cyclically in the modular 7 number system: 6^1 = 6 mod 7 6^2 = 1 mod 7 6^3 = 6 mod...

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Hi Ana,  To visualize how the graph moves, rewrite y = (x - 3)^2 + 4 so that it is easier to compare with y = x^2.  old: y = x^2 new: (y' - 4) = (x' - 3)^2 Now you can see that the transformation changed y to (y' - 4) and x to (x' - 3).   y = y' - 4 ---->...

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Here is a graphical way to think of it.   Suppose you wanted to divide the number 1 by 0.  In other words, you want to find y = 1/x when x = 0.  Well, try graphing the function y = 1/x.  You will notice that to the left of x = 0, the value of y approaches negative infinity...

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Hi Maria,  One way to solve this problem is to use the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c.  Here a, b, c are the lengths of the sides, and A, B, C are the angles across from (not touching) the sides a, b, c respectively.   Since you are given b, c, and B, you could...

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Here is a way to remember that the angles of a triangle sum to 180 degrees. Imagine a squat triangle, with two very acute angles and one very obtuse angle.  If this triangle is very stout, then the acute angles are ~0 and the obtuse angle is ~180 degrees.