Search results with tag "Odd integers"
QUADRATIC WORD PROBLEMS - Lancaster High School
www.lancasterschools.orgConsecutive Odd Integers: 1. Find two consecutive odd integers whose product is 99. 2. A certain number added to its square is 30. Find the number. 3. The square of a number exceeds the number by 72. Find the number. 4. Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second. ...
1.1 The Real Number System - UH
www.math.uh.eduAn integer is odd if it can be written in the form 2n −1, where n is an integer (if 2 is not a factor). Example: 2, 0, 8, -24 are even integers and 1, 57, -13 are odd integers. 4. The rational numbers are the numbers that can be written as the ratio of two integers. All
Set Theory Problems Solutions - MIT
web.mit.eduThe set of all positive even integers b) {…, -3, -1, 1, 3,…} The set of all odd integers c) {n | n = 2m for some y } The set of all positive even integers (using the convention that 0 is not a natural number) d) {x | x=2n and x=2k for some n, k } The set of all positive multiples of 6
Even/odd proofs: Practice problems Solutions
faculty.math.illinois.edu4. Cool application, II: Quadratic equations with no integer/rational solutions: (a) Prove the following: If a;b;c are odd integers, then the equation ax2 + bx+ c = 0 has no integer solution. [This is the equation considered at the beginning of Chapter 2 of the text and it is a nice illustration of the power of \parity arguments".
Chapter 3, Rings
www.math.hawaii.eduThe set of odd integers is not a ring. We can also work with matrices whose elements come from any ring we know about, such as Mn(Zr). Example. Let R = M2(Z2). This is a nite (16 elements) noncommutative ring with identity 1R = 10 01 and zero element 0R = 00 00 . We give an example to show it is noncommutative: 10 00 01 00 = 01 00
Translating English Words Into Algebraic Expressions
grayson.eduThe sum of two consecutive odd integers (x) + (x + 2) Reference: Paul D. Nolting, Ph.D., Winning at Math, 1997. 1989 by Academic Success Press, Inc. Translating English Terms Into Algebraic Symbols Sum + Add + In addition + More than + Increased + In excess + Greater + Decreased by - Less than - ...