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## Kenneth G.'s Resources

The vertex of the parabola is at (4,-1).  Knowing the vertex alone will not determine a parabola.  Assume the parabola's equation is f(x) = ax2 + bx + c.   The x-coordinate of the vertex is x = -b/2a = 4, so that b = -8a.   (4,-1) is on the parabola, so...

The base cause of the Berlin Crisis was that the Soviets were loosing valuable professionals and other citizens who emigrated across the boarder in Berlin because people did not want to live under Soviet rule.  (reference: http://en.wikipedia.org/wiki/Berlin_Crisis_of_1961)

There are multiple answers to this question because a finite number of terms do not precisely determine the sequence.  For example, one could fit a polynomial f(x) of degree 10 to this sequence so that f(i) was equal to the ith term.     However here is another approach   First...

This is a multiple-choice question - the type you find on standardized tests like the SAT. Your approach should be to answer the question as quickly as possible without worrying about understanding details. Rule #1: On a multiple-choice question, your first step is not to work the problem...

This is a multiple-choice question - the type you find on standardized tests like the SAT.  Your approach should be to answer the question as quickly as possible without worrying about understanding details.   Rule #1:  On a multiple-choice question, your first...

Michael,   You are correct, it's not an identity.     You've created a counterexample, which is a valid way to prove that something is false.     By the way, was this presented to you as an identity? Or is the idea to find which x makes it a true...

Heidi,   You asked "Are legs of a trapezoid always, sometimes, or never congruent?"      What does it mean for two lines to be congruent?  It means the are the same length, period!     What are you referring to by the term "legs"...

Image 431k

This file is an alternative to the spreadsheet AvgCardTotal if the user does not have software that can read Microsoft Excel files.

This spreadsheet is referenced by the problem in Answers section called "Probability of the sum of three random cards from...

There are 22,100 ways to select 3 cards from a deck of 52 cards.  This spreadsheet image shows the total number of combinations of cards that will yield each sum from 3 to 30, and then computes the actual expected value of the total of the three cards: http://www.wyzant.com/resources/files/259851/avgcardtotal_png...

If I am understanding the problem, we have triangle ABC where  CB is 45 units, BA is 43 units, and CA = b is unknown.   Also angle at vertex B is 88 degrees.  The requirement is to find the other components of the triangle.   -----------------------------------------------------------------------   We...

The sum of the three angles in any triangle is 180 degrees. Triangle ABC is a right triangle with the right angle at vertex A. Point D is on the line AC so that the like BD bisects angle B So line BD divides the triangle ABC into two triangles, ABD and DBC, and the angle at vertex...

P(A∩B) = P(A) P(B)  by the definition of independence = P(A) (1-P(B'))   since P(B) = 1- P(B') = P(A) - P(A) P(B')   So,   (1)   P(A) P(B') = P(A) - P(A∩B)    Since A∩B'  =  A - A∩B and A∩B ⊂ A,    (2)...

start with the identity tan2θ + 1 = sec2θ   substituting, 2(sec2θ - 1) = 5 secθ + 10  giving an equation in secθ.   substituting x = secθ   2(x2 - 1) = 5x + 10,   2x2 -5x -12 = 0   Using the quadratic formula,  x...

Strategy is king on tests like the SAT, GRE or ACT.   After preparation, the most important thing to getting the highest score is to develop a strategy long before you take the test.   The reason for the importance of strategy is that these tests are timed.   What changes when a test is timed?  What changes is there is a premium on answering as many questions as possible... read more

This answer was really intended as an answer to the comment on Robert's answer.   I believe the wyzant reference quoted in the comment is incorrect.  To see this, let's first take the sample pentagon at at http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons...

The sum of interior angles of a regular polygon with n sides is (n-2)*180.  The sum of the interior angles of a pentagon is  3 x 180 degrees, or 540 degrees.     There are 5 interior angles in a pentagon, so 540/5 = 108 degrees in each angle.

The number of degrees in each angle of a regular polygon with n sides is 180(n-2)/n .   180(n-2)/n = 156,  180(n-2) = 156n,     So 24n = 360,  n = 360/24  = 15 sides

Assumptions make up the basic fabric of Mathematics.  Every problem in mathematics makes assumptions.   As a student, when you see a problem on a test or in homework, the first thing you need to do is figure out what assumptions the question writer has in mind.  It may be that a problem has multiple solutions, and knowing the assumptions will allow you a better chance... read more

This is a confusing problem because it can be read in a number of ways.  Depending on how you read it, you don't  know a lot of things.  For example,   (1) The problem says that "you" paid \$1 per ticket for 1000 tickets.  It does not say that "you"...