Get 100 Jahre Mathematisches Seminar der Karl-Marx-Universitaet PDF

By H.; Beckert, H. Schumann

Show description

Read Online or Download 100 Jahre Mathematisches Seminar der Karl-Marx-Universitaet Leipzig PDF

Similar mathematics books

Extra resources for 100 Jahre Mathematisches Seminar der Karl-Marx-Universitaet Leipzig

Sample text

You can use a variable to represent an unknown quantity. For example, if you earn x dollars per hour and your friend earns $2 more than you per hour, then x ϩ 2 represents the amount in dollars per hour earned by your friend. When you combine variables and numbers using multiplication, division, addition, and subtraction, as well as powers and roots, you get an algebraic expression. We are often interested in finding the value of an algebraic expression for a given value of a variable. This is known as evaluating an algebraic expression and is illustrated in the next example.

Example 3 Multiplication of Monomials Multiply (Ϫ2x 2)(4x 7). ᭤Solution (Ϫ2x 2)(4x 7) ෇ (Ϫ2)(4)(x 2x 7) Commutative and associative properties of multiplication ෇ Ϫ8x 9 Multiply coefficients and add exponents of same base ✔ Check It Out 3: Multiply (4x 4)(Ϫ3x 5). ■ ■ Algebra and Geometry Review To multiply binomials, apply the distributive property twice and then apply the rules for multiplying monomials. Example 4 Multiplying Binomials Multiply (3x ϩ 2)(Ϫ2x Ϫ 3). ᭤Solution (3x ϩ 2)(Ϫ2x Ϫ 3) ෇ 3x(Ϫ2x Ϫ 3) ϩ 2(Ϫ2x Ϫ 3) Apply distributive property Note that the terms 3x and 2 are each multiplied by (Ϫ2x Ϫ 3).

25. −4 −3 − 2 −1 0 1 2 3 4 x 26. −4 −3 −2 −1 0 1 2 3 4 x 27. −4 −3 − 2 −1 0 1 2 3 4 x 28. −4 −3 −2 −1 0 1 2 3 4 x 29. −4 −3 − 2 −1 0 1 2 3 4 x 30. −4 −3 −2 −1 0 1 2 3 4 x 31. −4 −3 − 2 −1 0 1 2 3 4 x 32. −4 −3 −2 −1 0 1 2 3 4 x In Exercises 33–38, fill in the table. Inequality 33. 36. 37. 38. Graph 4 Յ x Յ 10 (Ϫϱ, 6) 34. 35. Interval Notation Ϫ3 Յ x Ͻ 0 (Ϫ5, 10͔ − 2 0 2 4 6 8 10 12 14 x − 8 − 7 − 6 − 5− 4 − 3− 2 − 1 0 In Exercises 67–76, evaluate each expression without using a calculator. 67. 9 Ϫ 3(2) Ϫ 8 68.

Download PDF sample

100 Jahre Mathematisches Seminar der Karl-Marx-Universitaet Leipzig by H.; Beckert, H. Schumann


by Charles
4.1

Rated 4.48 of 5 – based on 47 votes