Chapter 9 Algebra and calculator review Page 1 of 8 Chapter 9 Algebra and calculator practice Spring 2016 (1/16/16) Note: this course presumes a High School proficiency with Algebra. Based on this, I’ve selected only those parts of this chapter needed to review for: Chapter 5 Chapter 8 Chapter 10 Chapter 11 If you need more High School Algebra review, read all Chapter 9 especially sections 1, 2 in text pages 247 – 267 and more depending on your competence level. Seek a tutor available for Math 102 students. Some who need remedial work might consider Max 100 available as a lead-in course to this. Learn how to use your calculator. Each comes with a printed set of instructions, an online manual, and maybe an on-line help-desk. Chapter 9 Algebra and calculator review Page 2 of 8 Linear functions Functions - a function is an expression of dependence. A variable (y) is a function of another variable (x) written as an equation. Linear functions are drawn as straight lines. Examples: Your weekly pay (y) is a function of how many hours you worked (x). Your salary is $18 per hour… y = 18x Sales revenue (y) is a function of how many units sold (x). Each sale is $56 y = 56x Translate a verbal expression into a linear function: six more than a number x+6 six times a number 6x six more than a number is 10 x + 6 = 10 a number decreased by 13 is 6 times the number x - 13 = 6x Writing and solving a linear function Example: ABCD House cleaning service charges $20.00 fee, plus $32.50 per hour for labor. One particular service bill was $117.50. How many labor hours were charged? let n = number labor hours $32.50n = labor cost Service charge = $117.50 = $32.50n + $20.00 117.50 - 20.00 = 32.50n n = 117.50 - 20.00 = 3 32.50 Example: Your promotion to Broadcast Manager at WXYZ Action News requires you to plan ahead for next year’s TV crew expenses for on scene reporting. Your predecessor, familiar with budgeting, left the following algorithm for estimating annual budget increases solve for x in the equation 4x - 0.48 = 0.8x + 4 (linear function) 4x - 0.8x = 4 + 0.48 3.2 x = 4.48 x = 4.48 3.2 x = 1.4 budget will increase by 40% Chapter 9 Algebra and calculator review Page 3 of 8 Calculator work – learn your calculator for these problem types. (Recall policy regarding graphing calculators) Example: Solve: A = p(1 + rt) when p = 3,000 r = .018 t=2 A A A A = 3,000(1 + .018(2)) = 3,000(1 + .036) = 3,000(1.036) = 3,108 Example: Solve: A = p(1 + r/n) nt when p = 3,000 r = .018 n = 12 t=2 A = 3000(1 + .018/12) 12(2) A = 3000(1 + .0015) 24 A = 3000(1.0015) 24 A = 3000(1.036627885) = 3109.883655 Example: Solve for E when is 0.5 and n = 500 E =2 ( 1n E =2 .5(1-.5) 500 =2 ) = 2 .25 500 5.-04 on my calculator 5.-04 means 5.0 (10) -4 = .0005 yours might be shown differently = 2 .0005 = 2(.022360679) = .044721359 Chapter 9 Algebra and calculator review Page 4 of Graph a linear function A linear function is a straight line when drawn on coordinate axes. Any 2 points will describe the line. Example: x = 4 is a straight line with x having no dependence on y….x is always 4 7 6 5 4 3 2 1 x=4 x -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 1 2 3 4 5 6 7 Example: y = 4 is a straight line with y having no dependence on x….y is always 4 7 6 5 4 3 2 1 y=4 x -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 1 2 3 4 5 6 7 8 Chapter 9 Algebra and calculator review Page 5 of 8 Example: x + 2y = 2 For this course, use the intercepts method. There are 3 other methods, but the intercepts method is best for this course. Set x = 0, solve for y Set y = 0, solve for x x + 2y = 2 (0) + 2y = 2 2y = 2 y = 1 (0,1) x + 2y = 2 x + 2(0) = 2 x = 2 (2,0) y 3 2 1 (0, 1) (2, 0) x 1 2 3 4 5 6 x + 2y = 2 Example: x - 2y = 6 Set x = 0, solve for y Set y = 0, solve for x x - 2y = 6 (0) - 2y = 6 2y = -6 y = -3 (0,-3) x - 2y = 6 x - 2(0) = 6 x = 6 (6,0) y 3 2 1 x 1 2 3 4 5 6 x + 2y = 2 (0, -3) Chapter 9 Algebra and calculator review Page Practice problems page 272 17.) combine terms: 7x + 3y - 4x + 8y 3x + 11y 24.) combine terms: 4s + 3t + 8 - 2t 4s + t +8 32.) combine terms: 0.9(2.3x - 2) + 1.7(3.2x - 5) 2.07x - 1.8 + 5.44x - 8.5 7.51x -10.3 40.) solve for x: 12 = 3x + 6 12 - 6 = 3x 6 = 3x 2=x 50.) solve for r: r + 2r = 7 3 .3333333333333 is written as .33 .33r + 2r = 7 2.33 r = 7 r = 7/2.33 = 3 65.) Paint (1 gal. covers 825 ft2) needed for 6600 ft2 let x = gals. needed x = 6600 ft2 825 ft2/gal. x = 6600/825 = 8 gals. 68.) (There’s another 68 [later] but it’s a different problem) Bag of topsoil = 40 lbs. Bag of topsoil = 12 ft2 a.) how many lbs. = 480 ft2 40 lbs. = 12 ft2 no.bags = 480 ft2 = 40 bags 12 ft2/bag 40 bags = 40 lbs. (40 bags) = 1600 lbs. Bag 6 of 8 Chapter 9 Algebra and calculator review Page 7 of 8 Page 366 practice problems 81.) Solve: A = p(1 + rt) when p = 465 r = .0275 t = 1.25 A A A A = 465(1 + .0275(1.25)) = 465(1 + .034375) = 465(1.034375) = 480.98 143.) Solve: A = p(1 + r/n) nt when p = 7,000 r = .055 n = 12 t=3 A = 7000(1 + .055/12) 12(3) A = 7000(1 + .004583333333) 36 A = 7000(1.004583333333) 36 A = 7000(1.178948602) = 8252.640216 Page 237 practice problem 68.) (There’s another 68 [earlier] but it’s a different problem) Solve for E when = 0.4 and n = 1,000 E =2 ( 1n =2 .4(1-.4) 1000 =2 2.4-04 = 2 .00024 ) = 2 .24 1000 (on some calculators: 2.4-04 is shown 2.4E-4) = 2 (.015491933) = .030983866 Chapter 9 Algebra and calculator review Page 8 Practice problems page 277: 204,206 204.) Set x = 0, solve y Set y = 0, solve x 3x + 6y = 9 3(0) + 6y = 9 y = 9/6 = 1.5 (0, 1.5) 3x + 6y = 9 3x + 6(0) = 9 x = 9/3 = 3 (3, 0) y 1.5 1 3x + 6y = 9 0.5 x .5 206.) Set x = 0, solve y Set y = 0, solve x 6x - 3y = 9 6(0) - 3y = 9 y = 9/-3 = -3 (0, -3) 6x - 3y = 9 6x - 3(0) = 9 x = 9/6 = 1.5 (1.5, 0) 1 1.5 2 2.5 3 y 3 2 6x - 3y = 9 1 x -1 -2 -3 .5 1 1.5 2 2.5 3 of 8