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All Textbook Solutions for College Algebra

Solve the linear equation in one variable: 2x+1=9 .Solve the equation in one variable: 2(3x1)+x=14x .Solve the rational equation: 23x=1416x.Solve the rational equation: 52x+34x=74.Solve 32x+1=43x+1. State the excluded values.Solve the rational equation: 2x2+1x+1=1x2x2.Find the slope of the line that passes through the points (2,6)and(1,4) .Given m=4 , find the equation of the line in slope-intercept form passing through the point (2,5) .Find the equation of the line in standard from with slope m=13 and passing through the point (1,13).Find the equation of the line passing through (5,2)and(2,2) .Graph the two lines and determine whether they are parallel, perpendicular, or neither: 2yx=10and2y=x+4.Find the equation of the line parallel to 5x=7+y and passing through the point (1,2) .What does it mean when we say that two lines are parallel?What is the relationship between the slopes of perpendicular lines (assuming neither is horizontal nor vertical)?How do we recognize when an equation, for example y=4x+3 , will be a straight line (linear) when graphed?What does it mean when we say that a linear equation is inconsistent?When solving the following equation: 2x5=4x+1 explain why we must exclude x=5andx=1 aspossible solutions from the solution set.For the following exercises, solve the equation for x. 6.7x+2=3x9 For the following exercises, solve the equation for x. 7.4x3=5 For the following exercises, solve the equation for x. 8.3(x+2)12=5(x+1)For the following exercises, solve the equation for x. 9.125(x+3)=2x5 For the following exercises, solve the equation for x. 10.1213x=43 For the following exercises, solve the equation for x. 11.x334=2x+312 For the following exercises, solve the equation for x. 12.23x+12=316 For the following exercises, solve the equation for x. 13.3(2x1)+x=5x+3 For the following exercises, solve the equation for x. 14.2x334=x6+214 For the following exercises, solve the equation for x. 15.x+24x13=2 For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 16.3x13=16 For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 17.23x+4=x+2x+4 For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 18.3x2=1x1+7(x1)(x2)For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 19.3xx1+2=3x1 For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 20.5x+1+1x3=6x22x3 For the following exercises, solve each rational equation for x. State all x-values that are excluded from the solution set. 21.1x=15+32x For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 22. (0,3) with a slope of 23 For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 23. (1,2) with a slope of 45 For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 24. x-intercept is 1, and (2,6)For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 25.y-intercept is 2, and (4,1)For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 26. (3,10)and(5,6)For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 27. (1,3)and(5,5)For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 28. parallel to y=2x+5 and passes through the point (4,3)For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form. 29. perpendicular to 3y=x4 and passes through the point (2,1) .For the following exercises, find the equation of the line using the given information. 30. (2,0)and(2,5)For the following exercises, find the equation of the line using the given information. 31. (1,7)and(3,7)For the following exercises, find the equation of the line using the given information. 32. The slope is undefined and it passes through the point (2,3) .For the following exercises, find the equation of the line using the given information. 33. The slope equals zero and it passes through the point (1,4) .For the following exercises, find the equation of the line using the given information. 34. The slope is 34 and it passes through the point (1,4) .For the following exercises, find the equation of the line using the given information. 35. (1,3)and(4,5)For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. 36.y=2x+7 y=12x4 For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. 37.3x2y=5 6y9x=6 For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. 38.y=3x+14 y=3x+2 For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither. 39.x=4y=3 For the following exercises, find the slope of the line that passes through the given points. 40. (5,4)and(7,9)For the following exercises, find the slope of the line that passes through the given points. 41.(3,2)and(4,7)For the following exercises, find the slope of the line that passes through the given points. 42.(5,4)and(2,4)For the following exercises, find the slope of the line that passes through the given points. 43.(1,2)and(3,4)For the following exercises, find the slope of the line that passes through the given points. 44.(3,2)and(3,2)For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 45.(1,3)and(5,1)(2,3)and(0,9)For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 46.(2,5)and(5,9)(1,1)and(2,3)For the following exercises, express the equations in slope intercept form (rounding each number to the thousandths place). Enter this into a graphing calculator as Yl, then adjust the yminand ymaxvalues for your window to include where the y-intercept occurs. State your yminand ymaxvalues. 47. 0.537x2.19y=100 For the following exercises, express the equations in slope intercept form (rounding each number to the thousandths place). Enter this into a graphing calculator as Yl, then adjust the yminand ymaxvalues for your window to include where the y-intercept occurs. State your yminand ymaxvalues. 48. 4,500x200y=9,528 For the following exercises, express the equations in slope intercept form (rounding each number to the thousandths place). Enter this into a graphing calculator as Yl, then adjust the ymin and ymax values for your window to include where the y-intercept occurs. State your ymin and ymax values. 49. 20030yx=70 Starting with the point-slope formula yy1=m(xx1) , solve this expression for x in terms of x1,y,y1,andm .Starting with the standard form of an equation Ax+By=C , solve this expression for y in terms of A, B, C,and x. Then put the expression in slope-intercept form.Use the above derived formula to put the following standard equation in slope intercept form: 7x5y=25.Given that the following coordinates are the vertices of a rectangle, prove that this truly is a rectangle by showing the slopes of the sides that meet are perpendicular. (1,1),(2,0),(3,3),and(0,4)Find the slopes of the diagonals in the previous exercise. Are they perpendicular?The slope for a wheelchair ramp for a home has to be 112 . If the vertical distance from the ground to the door bottom is 2.5 ft, find thedistance the ramp has to extend from the home in order to comply with the needed slope.If the profit equation for a small business selling x number of item one and y number of item two is p=3x+4y find the y value when =453andx=75 .For the following exercises, use this scenario: The cost of renting a car is $45/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y=45+0.25x, where x is the number of miles traveled. 57.What is your cost if you travel 50 mi?For the following exercises, use this scenario: The cost of renting a car is $45/wkplus $0.25/mi traveled during that week. An equation to represent the cost would be y=45+0.25x, where x is the number of miles traveled. 58. If your cost were $63.75, how many miles were you charged for traveling?For the following exercises, use this scenario: The cost of renting a car is $45/wkplus $0.25/mi traveled during that week. An equation to represent the cost would be y=45+0.25x, where x is the number of miles traveled. 59. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is 36, find the numbers.Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. What are the company’s monthly expenses?On Saturday morning, it took Jennifer 3.6 h to drive to her mother’s house for the weekend. On Sunday evening, due to heavy traffic, it took Jennifer 4 h to return home. Her speed was 5 mi/h slower on Sunday than on Saturday. What was her speed on Sunday?Find the dimensions of a rectangle given that the perimeter is 110 cm and the length is 1 cm more than twice the width.A game room has a perimeter of 70 ft. The length is five more than twice the width. How many ft2of new carpeting should be ordered?To set up a model linear equation to fit real-world applications, what should always be the first step?Use your own words to describe tins equation wherenis a number: 5(n+3)=2n If the total amount of money you had to invest was $2,000 and you deposit x amount in one investment, how can you represent the remaining amount?If a man sawed a 10-ft board into two sections and one section was nft long, how long would the other section be in terms of n?If Bill was traveling v mi/h, how would you represent Daemons speed if he was traveling 10 mi/h faster?For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. 6. Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. 7. Beth and Ann are joking that their combined ages equal Sam’s age. If Beth is twice Ann’s age and Sam is 69 yr old, what are Beth and Ann’s ages?For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. 8. Ben originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to 28. How many applications did each boy originally fill out?For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.l0/min for calls. 9. Find the model of the total cost of Company A’s plan, using m for the minutes.For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.l0/min for calls. 10. Find the model of the total cost of Company B’s plan, using m for the minutes.For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.l0/min for calls. 11. Find out how many minutes of calling would make the two plans equal.For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.l0/min for calls. 12. If the person makes a monthly average of 200 min of calls, which plan should for the person choose?For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly tee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use P for the number of devices that need data plans as part of their cost. 13. Find the model of the total cost of the Family Plan.For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly tee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use P for the number of devices that need data plans as part of their cost. 14. Find the model of the total cost of the Mobile Share Plan.For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly tee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use P for the number of devices that need data plans as part of their cost. 15.Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly tee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use P for the number of devices that need data plans as part of their cost. 16. If a family has 3 smart phones, which plan should, they choose?For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a yearfrom the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it shewants to put in a CD that pays 7%. 17. If we let xbe the amount the woman invests in the 15% bond, how much will she be able to invest in the CD?For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a yearfrom the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it shewants to put in a CD that pays 7%. 18. Set up and solve the equation for how much the woman should invest in each option to sustain a $6,000 annual return.For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. 19.Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart?Ben starts walking along a path at 4 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 6 mi/h. How long will it be before Amanda catches up to Ben?Fiora starts riding her bike at 20 mi/h. After a while, she slows down to 12 mi/h, and maintains that speed for the rest of the trip. The whole trip of 70 mi takes her 4.5 h. For what distance did she travel at 20 mi/h?A chemistry teacher needs to mix a 30% salt solution with a 70% salt solution to make 20 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?Paul has $20,000 to invest. His intent is to earn11% interest on his investment. He can invest part of his money at 8% interest and part at 12% interest. How much does Paul need to invest in each option to make get a total 11% return on his $20,000?For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wkplus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven. 24. Write the model equation for the cost of renting a truck with plan A.For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wkplus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven. 25. Write the model equation for the cost of renting a truck with plan B.For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wkplus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven. 26. Find the number of miles that would generate the same cost for both plans.For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wkplus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven. 27. If Tim knows he has to travel 300 mi, which plan should he choose?For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 28. A=P(1+rt) is used to find the principal amount Pdeposited, earning r%interest, for t years. Use this to find what principal amount PDavid invested at a 3% rate for 20 yr it A=8,000 .For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 29. The formula F=mv2R relates force (F), velocity (v), mass (m) , and resistance (R). Find R when m=45,v=7,andF=245 For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 30. F=ma indicates that force (F) equals mass (m)times acceleration (a). Find the acceleration of a mass of 50 kg if a force of 12 N is exerted on it.For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular. 31. Sum=11r is the formula for an infinite series sum. If the sum is 5, find r.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula,you will use it to solve a question. 32. Solve for W: P=2L+2W For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 33. Use the formula from the previous question to find the width, W,of a rectangle whose length is 15 and whose perimeter is 58.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula,you will use it to solve a question. 34. Solve for f:1p+1q=1f For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 35. Use the formula from the previous question to find fwhen p=8andq=13 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 36.Solve for min the slope-intercept formula: y=mx+b For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 37. Use the formula from the previous question to find m when the coordinates of the point are (4,7)andb=12 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 38. The area of a trapezoid is given by A=12h(b1+b2). Use the formula to find the area of a trapezoid with h=6,b1=14,andb2=8 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula,you will use it to solve a question. 39. Solve for h: A=12h(b1+b2)For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 40. Use the formula from the previous question to find the height of a trapezoid with A=150,b1=19,andb2=11 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 41. Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find the length and width. Use the perimeter formula P=2L+2W.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 42. Distance equals rate times time, d=rt . Find the distance Tom travels if he is moving at a rate of 55 mi/h for 3.5 h.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 43.Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of 60 mi/h for 6.75 h.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 44. What is the total distance that two people travel in 3 h if one of them is riding a bike at 15 mi/h and the other is walking at 3 mi/h?For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 45. If the area model for a triangle is A=12bh, find the area of a triangle with a height of 16 in. and a base of 11 in.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula,you will use it to solve a question. 46. Solve for h: A=12bh For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 47. Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of 15 and an area of 215.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 48. The volume formula for a cylinder is V=r2h . Using the symbol in your answer, find the volume of a cylinder with a radius, r, of 4 cm and a height of 14 cm.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 49. Solve for h: V=r2h For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 50. Use the formula from the previous question to find the height of a cylinder with a radius of 8 and a volume of 16 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 51. Solve for r: V=r2h For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 52. Use the formula from the previous question to find the radius of a cylinder with a height of 36 and a volume of 324 .For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 53. The formula for the circumference of a circle isC=2r. Find the circumference of a circle with a diameter of 12 in. (diameter=2r) . Use the symbol in your final answer.For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question. 54.Solve the formula from the previous question for . Notice why is sometimes defined as the ratio of the circumference to its diameter.Express 24 in standard form.Plot the complex number 4i on the complex plane.Subtract 2+5ifrom34i .Find the product: 12(52i).Multiply: (34i)(2+3i) .Find the complex conjugate of 3+4i .Evaluate: i18 Explain how to add complex numbers.What is the basic principle in multiplication of complex numbers?Give an example to show that the product of two imaginary numbers is not always imaginary.What is a characteristic of the plot of a real number in the complex plane?For the following exercises, evaluate the algebraic expressions. 5. If y=x2+x4 , evaluate y given x=2i .For the following exercises, evaluate the algebraic expressions. 6. If y=x32 , evaluate y given x=i .For the following exercises, evaluate the algebraic expressions. 7. If y=x2+3x+5 , evaluate y given x=2+i.For the following exercises, evaluate the algebraic expressions. 8. If y=2x2+x3 , evaluate y given x=23i .For the following exercises, evaluate the algebraic expressions. 9.If y=x+12x, evaluate y given x=5i .For the following exercises, evaluate the algebraic expressions. 10. If y=1+2xx+3, evaluate y given x=4i .For the following exercises, plot the complex numbers on the complex plane. 11. 12i.For the following exercises, plot the complex numbers on the complex plane. 12. 2+3i.For the following exercises, plot the complex numbers on the complex plane. 13. i.For the following exercises, plot the complex numbers on the complex plane. 14. 34i.For the following exercises, perform the indicated operation and express the result as a simplified complex number. 15.(3+2i)+(53i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 16.(24i)+(1+6i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 17.(5+3i)(6i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 18.(23i)(3+2i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 19.(4+4i)(6+9i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 20.(2+3i)(4i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 21.(52i)(3i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 22.(62i)(5)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 23.(2+4i)(8)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 24.(2+3i)(4i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 25.(1+2i)(2+3i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 26.(42i)(4+2i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 27.(3+4i)(34i)For the following exercises, perform the indicated operation and express the result as a simplified complex number. 28.3+4i2 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 29.62i3 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 30.5+3i2i For the following exercises, perform the indicated operation and express the result as a simplified complex number. 31.6+4ii For the following exercises, perform the indicated operation and express the result as a simplified complex number. 32.23i4+3i For the following exercises, perform the indicated operation and express the result as a simplified complex number. 33.3+4i2i For the following exercises, perform the indicated operation and express the result as a simplified complex number. 34.2+3i23i For the following exercises, perform the indicated operation and express the result as a simplified complex number. 35.9+316 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 36.4425 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 37.2+122 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 38.4+202 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 39. i8 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 40. i15 For the following exercises, perform the indicated operation and express the result as a simplified complex number. 14. i22 For the following exercises, use a calculator to help answer the questions. 42. Evaluate (1+i)kfork=4,8and12. Predict the value if k=16 .For the following exercises, use a calculator to help answer the questions. 43. Evaluate (1i)kfork=2,6and10. Predict the value if k=14 .For the following exercises, use a calculator to help answer the questions. 44. Evaluate (l+i)k(li)kfork=4,8,and12 , Predict the value for k=16 .For the following exercises, use a calculator to help answer the questions. 45. Show that a solution of x6+1=0is 32+12i.For the following exercises, use a calculator to help answer the questions. 46. Show that a solution of x81=0is 22+22i.For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 47.1i+4i3 For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 48.1i111i21 For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 49. i7(1+i2)For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 50. i3+5i7 For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 51.(2+i)(42i)(1+i)For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 52.(1+3i)(24i)(1+2i)For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 53.(3+i)2(1+2i)2 For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 54.3+2i1+i+(4+3i)For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 55.4+ii+34i1i For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 56.3+2i1+2i23i3+i Factor and solve the quadratic equation: x25x6=0.Solve the quadratic equation by factoring: x24x21=0 Solve by factoring: x225=0 .Solve using factoring by grouping: 12x2+11x+2=0.Solve by factoring: x3+11x2+10x=0.Solve the quadratic equation using the square root property: 3(x4)2=15 .Solve by completing the square: x26x=13 .Solve the quadratic equation using the quadratic formula: 9x2+3x2=0.Use the Pythagorean Theorem to solve the right triangle problem: Leg a measures 4 units, leg bmeasures 3units.Find the length of the hypotenuse.How do we recognize when an equation is quadratic?When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form ax2+bx+c=0 we may graph the equation y=ax2+bx+c and have no zeroes (x-intercepts).When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?In the quadratic formula, what is the name of the expression under the radical sign b24ac, and how does it determine the number of and nature of our solutions?Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.For the following exercises, solve the quadratic equation by factoring. 6. x2+4x21=0 For the following exercises, solve the quadratic equation by factoring. 7. x29x+18=0 For the following exercises, solve the quadratic equation by factoring. 8. 2x2+9x5=0 For the following exercises, solve the quadratic equation by factoring. 9. 6x2+17x+5=0 For the following exercises, solve the quadratic equation by factoring. 10. 4x212x+8=0 For the following exercises, solve the quadratic equation by factoring. 11. 3x275=0 For the following exercises, solve the quadratic equation by factoring. 12. 8x2+6x9=0 For the following exercises, solve the quadratic equation by factoring. 13. 4x2=9 For the following exercises, solve the quadratic equation by factoring. 14. 2x2+14x=16 For the following exercises, solve the quadratic equation by factoring. 15. 5x2=5x+30 For the following exercises, solve the quadratic equation by factoring. 16. 4x2=5x For the following exercises, solve the quadratic equation by factoring. 17. 7x2+3x=0 For the following exercises, solve the quadratic equation by factoring. 18.x39x=2 For the following exercise, solve the quadratic equation by using the square root property. 19. x2=36 For the following exercise, solve the quadratic equation by using the square root property. 20. x2=49 For the following exercise, solve the quadratic equation by using the square root property. 21. (x1)2=25 For the following exercise, solve the quadratic equation by using the square root property. 22. (x3)2=7 For the following exercise, solve the quadratic equation by using the square root property. 23. (2x+1)2=9 For the following exercise, solve the quadratic equation by using the square root property. 24. (x5)2=4 For the following exercise, solve the quadratic equation by using the square root property. 25. x29x22=0 For the following exercise, solve the quadratic equation by using the square root property. 26. 2x28x5=0 For the following exercise, solve the quadratic equation by completing the square. Show each step. 27. x26x=13 For the following exercise, solve the quadratic equation by competing the square. Show each step. 28.x2+23x13=0 For the following exercise, solve the quadratic equation by competing the square. Show each step. 29.2+z=6x2 For the following exercise, solve the quadratic equation by competing the square. Show each step. 30.6p2+7p20=0 For the following exercise, solve the quadratic equation by competing the square. Show each step. 31.2x23x1=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 32.2x26x+7=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 33.x2+4x+7=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 34.3x2+5x8=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 35.9x230x+25=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 36.2x23x7=0 For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve. 37.6x2x2=0 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 38.2x2+5x+3=0 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 39.x2+x=4 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 40.2x28x5=0 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 41.3x25x+1=0 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 42.x2+4x+2=0 For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No Real Solution. 43.4+1x1x2=0 For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the x-intercepts) by using 2ndCALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth. 44.Y1=4x2+3x2 For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the x-intercepts) by using 2ndCALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth. 45.Y1=3x2+8x1 For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the x-intercepts) by using 2ndCALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth. 46.Y1=0.5x2+x7 For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the x-intercepts) by using 2ndCALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth. 47. To solve the quadratic equation x2+5x7=4 , we can graph these two equations Y1=x2+5x7 Y2=4 and find the points of intersection. Recall 2nd CALC 5: intersection. Do this and find the solutions to the nearest tenth.For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the x-intercepts) by using 2ndCALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth. 48. To solve the quadratic equation 0.3x2+2x4=2 , we can graph these two equations Y1=0.3x2+2x4 Y2=2 and find the points of intersection. Recall 2ndCALC 5:intersection. Do this and find the solutions to the nearest tenth.Beginning with the general form of a quadratic equation, ax2+bx+c=0 , solve for xby using the completing the square method, thus deriving the quadratic formula.Show that the sum of the two solutions to the quadratic equation is ba.A person has agarden that has a length 10 feet longer than the width. Set up a quadratic equation to find the dimensions of the garden if its area is 119 ft.2. Solve the quadratic equation to find the length and width.Abercrombie and Fitch stock had a price given as P=0.2t25.6t+50.2 , where t is the time in months from 1999 to 2001. ( t=1 is January 1999). Find the two months in which the price of the stock was $30.Suppose that an equation is given p=2x2+280x1000 , where x represents the number of items sold at an auction and p is the profit made by the business that ran the auction. How many items sold would make this profit a maximum? Solve this by graphing the expression in your graphing utility and finding the maximum using 2ndCALC maximum. To obtain a good window tor the curve, set x [0,200] and y[0,10000]A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P=0.006A20.02A+120 . Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.The cost function for a certain company is C=60x+300 and the revenue is given by R=100x0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $300.A falling object travels a distance given by the formula d=5t+16t2ft , where t is measured in seconds. How long will it take for the object to traveled 74 ft?A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 ft2. Find the width of the walkway if the garden is 12 ft, wide by 15 ft. long.An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P=t2+13t+130,where1t6. Find the day that 160 students had the flu. Recall that the restriction on t is at most 6.Evaluate 6413.Solve the equation x32=125 .Solve: (x+5)32=8 .Solve by factoring: 12x4=3x2 .Solve the radical equation: x+3=3x1 Solve the equation with two radicals: 3x+7+x+2=1.Solve the absolute value equation: |14x|+8=13 .Solve using substitution: x48x29=0 .Solve: (x5)24(x5)21=0.Solve 3x+2x2+1x=2x22x.In a radical equation, what does it mean if a number is an extraneous solution?Explain why possible solutions must be checked in radical equations.Your friend tries to calculate the valut? 932 and keeps getting an ERROR message. What mistake is he or she probably making?Explain why |2x+5|=7 has no solutions.Explain how to change a rational exponent into the correct radical expression.For the following exercises, solve the rational exponent equation. Use factoring where necessary. 6. x23=16 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 7.x34=27 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 8.2x12x14=0 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 9.(x1)34=8 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 10.(x+1)23=4 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 11.x235x13+6=0 For the following exercises, solve the rational exponent equation. Use factoring where necessary. 12.x733x434x13=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 13. x3+2x2x2=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 14. 3x36x227x+54=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 15. 4y39y=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 16. x3+3x225x75=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 17. m3+m2m1=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 18. 2x514x3=0 For the following exercises, solve the following polynomial equations by grouping and factoring. 19. 5x3+45x=2x2+18 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions, 20. 3x12=0 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 21. x7=5 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 22. x1=x7 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 23. 3t+5=7 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions, 24. t+1+9=7 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions, 25. 12x=x For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 26. 2x+3x+2=2 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 27. 3x+7+x+2=1 For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 28. 2x+3x+1=1 For the following exercises, solve the equation involving absolute value. 29. 3x4=8 For the following exercises, solve the equation involving absolute value. 30. 2x3=2

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