# College Algebra Essentials by Julie Miller

By Julie Miller

While Julie Miller started writing her winning developmental math sequence, one in all her fundamental pursuits was once to bridge the distance among preparatory classes and school algebra. For millions of scholars, the Miller/O’Neill/Hyde (or M/O/H) sequence has supplied an exceptional beginning in developmental arithmetic. With the Miller university Algebra sequence, Julie has carried ahead her transparent, concise writing variety; powerful pedagogical positive aspects; and whole author-created technological package deal to scholars during this direction area.

the most targets of the school algebra sequence are three-fold:

-Provide scholars with a transparent and logical presentation of -the easy innovations that might organize them for endured examine in mathematics.

-Help scholars enhance logical pondering and problem-solving abilities that may gain them in all facets of life.

-Motivate scholars by means of demonstrating the importance of arithmetic of their lives via sensible purposes.

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Additional resources for College Algebra Essentials

Sample text

Skype Purchase Capillary Size Saturn Temp. 0 ϫ 10 Ϫ6 m ϭ Ϫ3 ϫ 102 ЊF For a number written in scientific notation, the power of 10 is sometimes called the order of magnitude. If two numbers differ by one order of magnitude, one number is on the order of 10 times larger than the other. If they differ by two orders of magnitude, then one number is 100 times larger than the other. 0 ϫ 105). This is an order of magnitude difference of 2. This means that the celebrity earns 100 times more money than the general surgeon.

A 81 9 d. 1Ϫ9 is not a real number. The principal square root of 4 is 2, because 2 Ն 0 and (2)2 ϭ 4. 3 1 Ϫ125 ϭ Ϫ5 because (Ϫ5)3 ϭ Ϫ125. 49 7 7 7 2 49 ϭ because Ͼ 0 and a b ϭ . A 81 9 9 9 81 No real number when squared equals Ϫ9. 1 Sets and the Real Number Line 11 Skill Practice 8 Simplify. 3 b. 1 Ϫ8 a. 1100 c. 9 A 121 d. 1Ϫ16 6. Apply the Order of Operations Many expressions involve multiple operations. In such a case, it is important to follow the order of operations. Order of Operations Step 1 Simplify expressions within parentheses and other grouping symbols.

EXAMPLE 9 Simplify. Simplifying an Expression Involving Nested Grouping Symbols 7 Ϫ {8 ϩ 4[2 Ϫ (5 Ϫ 8)2]} Solution: 7 Ϫ {8 ϩ 4[2 Ϫ (5 Ϫ 8) 2]} ϭ 7 Ϫ {8 ϩ 4[2 Ϫ (Ϫ3) 2]} ϭ 7 Ϫ [8 ϩ 4(2 Ϫ 9)] Simplify within the inner parentheses. Continue simplifying within the inner parentheses. Simplify (Ϫ3)2 to get 9. Simplify (2 Ϫ 9) to get (Ϫ7). ϭ 7 Ϫ [8 ϩ 4(Ϫ7)] ϭ 7 Ϫ (8 Ϫ 28) ϭ 7 Ϫ (Ϫ20) ϭ 27 Skill Practice 9 Simplify. Multiply before adding or subtracting. Simplify within parentheses. Subtract. 50 Ϫ {2 Ϫ [11 ϩ 3(Ϫ1 Ϫ 3)2]} TECHNOLOGY CONNECTIONS Nested Parentheses on a Calculator or Spreadsheet Answers 8.