Sarah Owens Asst. 2 13. 1/2 ? 0 = 1/2 > 0 16. -3 ? -5/2 = -3 < -5/2 19. 1/2 ? 0.5 = 1/2 = 0.5 22. 1/4 ? 0.25 = 1/4 = 0.25 25. x is less than 2 = x < 2 28. x is greater than or equal to 2 = x > 2 ___ 31. x > -1 on the number line (_______________________ everything above -1 is greater -1 34. d(C,A) = using this / for the absolute value sign --- /0-(-3)/ = 3 37. d(A,E) = /-3(3)/ = 6 x = -2 y = 3 40. 3x + y = 3(-2)+3 = -6+3 = -3 42. -2x + xy = -2(-2) + (-2)(3) = -4 + 6 = 10 46. 2x - 3 2(-2)-3 -4 - 3 1 ________ = _________ = _______ = ____ y 3 3 3 x = 3 y = -2 49. /x/+/y/ = /3/ + /-2/ = 3+2 = 5 52. /y/ = /-2/ = 2 = 1 _____ ______ ___ y 2 2 55. //4x/ - /5y// = /4(3)/ - /5(-2)/ = /12/ - /-10/ = 12 - /10/ = 2 a. x=3 b. x=1 c. x=0 d. x = -1 58. x^2 + 1 3^2 + 1 9 + 1 10 None of these should be excluded from the domain _________ = _________ = ______ = __ x 3 3 3 1^2 + 1 1 + 1 2 ________ = ______ = ____ = 2 1 1 1 0^2 + 1 0 + 1 1 ________ = ________ = ___ = 1 0 0 0 -1^2 + 1 -1 + 1 2 _________ = ________ = ___ = -2 -1 -1 -1 61. x^2 3^2 9 9 None of these should be excluded from the domain ______ = _____ = ____ = _____ x^2 + 1 3^2 +1 9+1 10 1^2 1 1 ______ = _____ = ____ 1^2 + 1 1+1 2 0^2 0 0 ______ = _____ = _____ 0^2 +1 0+1 1 -1^2 -1 -1 _______ = ________ = _______ -1 +1 -1 + 1 2 64. -9x^2 - x + 1 = -9(3^2)-3+1 -27^2-4 -729-4 725 ______________ = __________ = __________ = _______ 3^3+3 9+3 12 12 -9(1^2)-1+1 -9^2 - 1+1 81 - 2 79 ____________ = _______________ = _________ = _____ 1^3 + 1 1+1 2 2 -9(0)^2 - 0+1 0^2 - 0 + 1 0-1 1 ________________ = _______________ = ________ = ____ = 1 0^3 + 0 0-0+1 1 1 -9(-1) - -1=1 9 - 1 + 1 8 + 1 9 ________________ = ______________ = _________ = _____ -1^3 + -1 -2 -2 -2 67. Determine the domain of the variable x in each expression x ????? ______ x+4 70. Convert degrees farenheit into degrees celcius to find the celcius measure of each farenheit temperature. Formula = C = 5/9 (F-32) F = 212 degrees ?????? Simplify each expression --- 73. (-4)^2 = 16 79. (3-^2)-1 = 3(^-2)(^-1) = 3^-2 = 9 82. The square root of 36 is 6 85. (8x^3)^2 = 8x^2 = 64x^6 (for the 6 I multiplied the 3x2) 88. (x^-1 Y)^3 ????????? 90. x^-2 y ________?????????? xy^2 93. (3x^-1)^-2 ????????? ___________ (4y^-1) x = 2 y = -1 96. -3x^-1y = -3(2)^-1(-1) = -9(-1) = 9 99. (xy)^2 = 2(-1)^2 = -2^2 = -4 102. (square root x)^2 = (square root 2) = 2 105. x^y = 2^1 108. 4X^3 + 3x^2 - x + 2 (x = 1 and x = 2) 4(1)^3 + 3(1) - 1 + 2 = 4^3 + 3^2 - 3 = 64 + 9 - 3 = 73 - 3 = 70 4(2)^3 + 3(2)^2 - 1 + 2 = 8^3 + 6^2 - 3 = 512 + 36 - 3 = 548 - 3 = 545 111. (8.2)^6 = 304,006.671 114. (2.2)^-5 = .0194037913 117. (-8.11)^-4 = 0.000 Write in Scientific notation 120. 32.14 = 3214 x 10^2 122. 0.00421 = 42.1 x 10^-3 125. 0.000423 = 4.23 x 10^-4 Write each as a decimal 128. 9.7 x 10^3 = 9700. 131. 1.1 x 10^8 = 1.10,000,000 134. 6.453 x 10^-1 = .6453 137. The circumference C of a circle is the product of pi and its diameter d = C = pi x d 140. The perimeter P of an equilateral triangle is 3 times the length x of one side. = P = 3 times x 143. The volume V of a cube is the cube of the length x of a side = V = x^3 146. Balancing a checkbook Beginning balance - $210.00 Deposit - + 80.00 Wrote check - -120.00 Deposit - + 25.00 Wrote checks - $60 and $32 - 92.00 Service charge - - 5.00 Balance at the end of the month - $ 98.00 150. ???????? 153. Express this wavelength as a decimal. 5 x 10^-7 = 0.0000005 meter 156. Express this width using scientific notation - 0.05 centimeter 5 x 10^-2 158. ??????? 161. Is there a positive real number closest to 0? No there is no positive real number closest to 0. "