Odd-Numbered Answers to Exercise Set 1.1: Numbers

Transcription

1 Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since = ) 9 9 (l). (since = ) 9 9 (m). (since 9 = ). (a) Rational; Irrational Rational; (d) Rational; (e) Rational; (f) Rational; (g) Rational; (h) Rational; (i) Irrational (j) Rational; (k) Irrational 9 9. Odd, Negative, Integer, Rational, Real 9. Positive, Irrational, Real. (a), 0,, π,,, (d),., 0. (e) (f) (g), (h) 0,,. (i), 0,, (j) All numbers in the set:,., 0., 0,, π,,, (k),., 0., 0,,, (l), π (m) None. is the only number that is both prime and even.. Answers vary. Some possible answers are:,, 0., 0., 0., (Note: Any repeating decimal is a rational number. There are methods for changing repeating decimals to fractions which will not be learned in this course.) 9. Answers vary. Some possible answers are:,,,,, π, e, Does not exist. Does not exist. True. True 9. False. The number 0 is a whole number but not a natural number.. True. False. A repeating decimal such as 0. = is a 9 nonterminating decimal, but is a rational number..,,,., 9.,,,,, 9.,, 0. Undefined Y N N N N Natural N Y N N N Whole N Y N N N Integer N Y N Y N Rational N Y Y Y Y Irrational N N N N N Prime N N N N N Composite N N N N N Real N Y Y Y Y MATH 00 Fundamentals of Mathematics

2 Odd-Numbered Answers to Exercise Set.: Numbers. <. >. =. > 9. >. <. <. =. (a) (d) (e) 9. (a) 9 Undefined (d) (Note: = ) (e). (a) 0. Numbers ordered from least to greatest: 9 0,,,, 0., 0.9 The above numbers plotted on a number line: 0 University of Houston Department of Mathematics

3 Odd-Numbered Answers to Exercise Set.: Integers. (a) (d) (e). (a) (d). (a) (d) (e) (f) (g) (h). (a) (d) (e) (f) 0 (g) (h) 9 (i) (j) (k) (l) 0 (m), or 0. (n) Undefined (o). (a) < > > (d) = 9. (a) 0 Undefined 0 (d) (e) (f) (g) (h) (i) (j) Undefined (k) (l) 0. (a) 0 0 (d) (e) (f). (a) (d) MATH 00 Fundamentals of Mathematics 9

4 Odd-Numbered Answers to Exercise Set.: Fractions. (a) GCD: LCM:. (a) GCD: LCM: 0. (a) GCD: LCM:. (a) GCD: LCM: 0. (a) 9. (a) 0. (a) (a) GCD: LCM: 90. (a). (a) GCD: LCM: 0. (a). (a). (a). (a). (a) 9 9. (a). (a). (a) (a). (a) = = 9. (a). (a) 0. (a). (a) = 0 9 =. (a) 9 9. (a) = 0 0. (a). (a). (a) University of Houston Department of Mathematics

5 Odd-Numbered Answers to Exercise Set.: Exponents and Radicals. (a) (d). k m. < 9. a b. >. < 9. (a) 9 (d) (e) 9 (f) (g) (h) 9 (i) (j) (k) (l) (m) (n) (o). (a) 0., or. (a). (a).. 9a b. (a) 9 =. (a) = 9. (a) = = 9 =. (a) 9 = = = 9. (a) 9. (a). (a). (a) = = =. (a). (a). (a). (a) 9. (a) = ( ) = = = ( ) = ( ). (a) =. (a) 9 x y z yz 9. (a). (a) Not a real number. (a). (a) Not a real number. (a) 9. (a) Not a real number. (a) 9 x y z z 9 x y. 0 x MATH 00 Fundamentals of Mathematics

6 Odd-Numbered Answers to Exercise Set.: Order of Operations. (a) P: Parentheses E: Exponents M: Multiplication D: Division A: Addition S: Subtraction Whichever appears first Whichever appears first. (a) (d) (e) (f). (a) (d) (a) (d) (e) (f) 9. (a) (d) 0. (a) 9 (d) (e) (f). (a) 0,000. (a) 0. (a) University of Houston Department of Mathematics

7 Odd-Numbered Answers to Exercise Set.: Solving Linear Equations. x =. x =. x =. x = 9. x =. x =. x = =. x =. x = 9. x =. x =. x = 0. x =. x = MATH 00 Fundamentals of Mathematics

8 Odd-Numbered Answers to Exercise Set.: Interval Notation and Linear Inequalities. (a) x > (, ). (a) x (, ] 9 0. (, ). (, ]. (, 0) ( 0, ) 9. {,, }. {,, }. {, }. (a) x (, ) (, ). (a) x < (, ) 9. (a) x [, ). (a) x (, ) (, ). (a) x and x 9 (, ) (, ) (, ). (, ). (, ] 9. (, ] (, ) (, ). (a) x < (, ). (a) x (, ] 9. (a) x [, ). (a) x < (, ). (a) x > (, ). (a) x [, ). (a) x (, ] 9 0 University of Houston Department of Mathematics

9 Odd-Numbered Answers to Exercise Set.: Interval Notation and Linear Inequalities 9. (a) x > (, ). (a) x [, ). (a) x < 0 [, ). (a) x, i.e. x [,] 0. (a) 0 < x < ( 0, ) 0 9. b (since 9 is not less than ), and d (since - is not greater than -). (a) + 0.x 0, where x represents the # of miles driven. x., so you can drive a maximum of miles and still be reimbursed in full.. You would need to talk for more than minutes in order for Plan to be more cost-effective than Plan. MATH 00 Fundamentals of Mathematics

10 Odd-Numbered Answers to Exercise Set.: Absolute Value and Equations. x = ±. No solution (since the absolute value of any quantity is always 0, and therefore cannot be negative). x = ±. x =, x = 9 9. x = ±. x =, x =. x = ±. x =, x = 9. x =, x = 9. x =, x =. No solution (since the absolute value of any quantity is always 0, and therefore cannot be negative). x =, x = University of Houston Department of Mathematics