
Number Theory Review for Exam 1 ERRATA On Problem 3 on the
... 1. Show that there are only finitely many primes of the form n2 − 9 where n is a positive integer. Note that n2 − 9 = (n − 3)(n + 3). So, if n2 − 9 is prime, then n − 3 is 1 and n + 3 is n2 − 9. I.e. n = 4. So if n > 4, n2 − 9 is not prime. 2. Find all PPT’s of the form (a) (15, y, z) We need to fin ...
... 1. Show that there are only finitely many primes of the form n2 − 9 where n is a positive integer. Note that n2 − 9 = (n − 3)(n + 3). So, if n2 − 9 is prime, then n − 3 is 1 and n + 3 is n2 − 9. I.e. n = 4. So if n > 4, n2 − 9 is not prime. 2. Find all PPT’s of the form (a) (15, y, z) We need to fin ...
Determine whether each trinomial is a perfect square trinomial. Write
... The resulting polynomial is not a perfect square or a difference of squares. Try to factor using the general factoring pattern. In the trinomial, a = 3, b = –17 and c = 24, so m + p is negative and mp is negative. Therefore, m and p must have different signs. List the factors of 3(24) or –60 with a ...
... The resulting polynomial is not a perfect square or a difference of squares. Try to factor using the general factoring pattern. In the trinomial, a = 3, b = –17 and c = 24, so m + p is negative and mp is negative. Therefore, m and p must have different signs. List the factors of 3(24) or –60 with a ...
Euclidean Algebra - Rosshall Academy
... First use the Euclidean algorithm to find the greatest common divisor ...
... First use the Euclidean algorithm to find the greatest common divisor ...
Math A Regents Exam 0604 Page 1 The test scores for 10
... [3] Appropriate work is shown, but one computational error is made. or [3] Seventh test score = 96, but only the median or the mode is found correctly, but appropriate work is shown. or [3] 91.5, 92, and 96, and appropriate work is shown, but the median and mode are not labeled or are labeled incorr ...
... [3] Appropriate work is shown, but one computational error is made. or [3] Seventh test score = 96, but only the median or the mode is found correctly, but appropriate work is shown. or [3] 91.5, 92, and 96, and appropriate work is shown, but the median and mode are not labeled or are labeled incorr ...
Math7 Final Exam Quick Review
... • 40/70 + 7/70 = 47/70 * Reduce the fraction to its simplest form, if possible. Strategy #3: Multiply the denominators of the two fractions. The product is the new common denominator. 7.) 3/5 + 5/6 = 1 13/30 How did we arrive at the answer? ...
... • 40/70 + 7/70 = 47/70 * Reduce the fraction to its simplest form, if possible. Strategy #3: Multiply the denominators of the two fractions. The product is the new common denominator. 7.) 3/5 + 5/6 = 1 13/30 How did we arrive at the answer? ...
2-8 Page 119 9-27 odd 39
... Graph the inequality |y| > |x|. Test various values of x and y, both negative and positive, to see if they make the inequality true. ...
... Graph the inequality |y| > |x|. Test various values of x and y, both negative and positive, to see if they make the inequality true. ...
Equation

In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.