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 Expressions-with-variables/93320: This question is from textbook algebra 1 I NEED HELP ON THIS PROBLEM. I DON'T UNDERSTAND HOW TO FIGURE IT OUT. THANKS1 solutions Answer 67960 by ankor@dixie-net.com(15639)   on 2007-08-19 18:52:59 (Show Source): You can put this solution on YOUR website!Hey friend, you have to submit the actual problems; we do not have access to the book you are referring to.
 Quadratic_Equations/93321: Between 1992 and 1998 the percent of college freshman who planned to eventually get some type of medical degree can be approximated by s=-0.2369^2 + 1.425x + 6.905 where s represents the number of students and x represents the year. X=0 corresponds to 1992. In what year did this percentage reach a maximum? Sorry, not from a text Thanks in advance1 solutions Answer 67959 by ankor@dixie-net.com(15639)   on 2007-08-19 18:46:09 (Show Source): You can put this solution on YOUR website!I made the 1st term into -.2369x^2, it makes more sense that way. : Between 1992 and 1998 the percent of college freshman who planned to eventually get some type of medical degree can be approximated by s=-0.2369x^2 + 1.425x + 6.905 where s represents the number of students and x represents the year. X=0 corresponds to 1992. In what year did this percentage reach a maximum? : s = -0.2369x^2 + 1.425x + 6.905 : Since this is a quadratic equation in the form ax^2 + bx + c, we can find the axis of symmetry using the formula x = -b/(2a); a = -.2369, b = +1.425 : x = -1.425/(2*-.2369) x = -1.425/-.4738 x = +3.0 : Substitute 3 for x in the original equation and find the vertex, that value will be the max s. : s = -.2369(3^2) + 1.425(3) + 6.905 : s = -.2369(9) + 4.35 + 6.905 : s = -2.13 + 4.35 + 6.91 : s ~ 9 added to 1992 ~ 2001 : Did this help?
 Evaluation_Word_Problems/93322: Two people with flu visit a campus. The number of days T it took for the flu viruses to infect n people is given by: T=-1.43Ln(10,000-n/4998n) how many days will it take to infect 500 people? Sorry, not from a text Thanks in advance1 solutions Answer 67957 by ankor@dixie-net.com(15639)   on 2007-08-19 18:15:17 (Show Source): You can put this solution on YOUR website!Two people with flu visit a campus. The number of days T it took for the flu viruses to infect n people is given by: T=-1.43Ln(10,000-n/4998n) how many days will it take to infect 500 people? : Assume you mean: T = -1.43 * : Enter this into your calc: T = -1.43 * : T = -1.43 * : Enter into your calc: -1.43 * : ans: 7.968 ~ 8 days
 expressions/93252: Simplify completely: ( x + 7 )/( x - 7 ) divided by (x2 - 49 )/( 7 - x ) 1 solutions Answer 67930 by ankor@dixie-net.com(15639)   on 2007-08-19 14:56:01 (Show Source): You can put this solution on YOUR website!Simplify completely: ( x + 7 )/( x - 7 ) divided by (x2 - 49 )/( 7 - x ) : ------------ : We can rewrite (7-x) to -1(x-7) and factor (x^2-49), (difference of squares) ------------ : Cancel out the (x-7)'s in the dividing fraction ------------ : Invert the dividing fraction and multiply * - = -; canceled (x+7)'s ; How about this, did it make sense to you?
 Graphs/93196: Can someone please help me solve this problem? Function for x -3x+4y=11 Thank you1 solutions Answer 67928 by ankor@dixie-net.com(15639)   on 2007-08-19 14:35:31 (Show Source): You can put this solution on YOUR website!Function for x -3x + 4y = 11 : -3x = -4y + 11; subtract 4y from both sides: : +3x = +4y - 11; multiplied by -1, (to get a positive x) : x = (4/3)y - (11/3); divided equation by 3 : Did this help?
 Rectangles/93266: I am having trouble with this word problem. Find an expression that represents its perimeter. Length Width How do I solve this problem? Please help me.1 solutions Answer 67927 by ankor@dixie-net.com(15639)   on 2007-08-19 14:06:33 (Show Source): You can put this solution on YOUR website!Find an expression that represents its perimeter. (2x+1)/(5) Length (4)/(3x+1) Width : We know that perimeter = 2L + 2W, therefore we have: + : Multiplying what's inside the brackets: + : Arrange over a single common denominator and we have: = = = : That's about all you can do with it: : Could you follow what we did here? Any questions?
 Linear_Algebra/93264: i have absolutely no idea what this means. can someone please help me with this question?: find the equation of the linear functions that has a slope of -3 and 1 solutions Answer 67897 by ankor@dixie-net.com(15639)   on 2007-08-19 09:55:38 (Show Source): You can put this solution on YOUR website!i have absolutely no idea what this means. can someone please help me with this question?: find the equation of the linear functions that has a slope of -3 and f(2)=6 : Using the form y = mx + b : Slope is given as -3 so we have y = -3x + b : f(2) = 6 means when x = 2, y = 6 : In our equation, substitute 2 for x, and 6 for y to find b -3(2) + b = 6 -6 + b = 6 b = 6 + 6 b = 12; The equation is: y = -3x + 12 : CAn be writtten: f(x) = -3x + 12 : Check our reasoning: You can see that: f(2) = -3(2) + 12 = 6 : Did this help?
 Equations/93199: Can someone help solve this word problem? P(x)=2.25x-7,000 a.)What is profit if 2,000 units are sold. b.)What is profit if 5,000 units are sold. c.)What is the break even points for sale? Thank you.1 solutions Answer 67839 by ankor@dixie-net.com(15639)   on 2007-08-18 16:09:46 (Show Source): You can put this solution on YOUR website!P(x)=2.25x-7,000 a.)What is profit if 2,000 units are sold. Substituting 2000 for x in the given equation P(x) = 2.25(2000) - 7000 P(x) = 4500 - 7000 P(x) = -2500; not a profit at all, lost \$2500 ; b.)What is profit if 5,000 units are sold. P(x) = 2.25(5000) - 7000 P(x) = 11250 - 7000 P(x) = \$4250 profit : c.)What is the break even points for sale? Break-even point is when profit (or loss) = 0 2.25x - 7000 = 0 2.25x = +7000 x = 7000/2.25 x = 3111 units is about the break-even point : Not that hard to understand, was it?
 Equations/93197: I am having trouble. Can someone please help? f(x)=4x-3 f(-1) Thank you.1 solutions Answer 67833 by ankor@dixie-net.com(15639)   on 2007-08-18 14:00:29 (Show Source): You can put this solution on YOUR website!f(x)=4x-3 f(-1); this means you substitute -1 for x : f(-1) = 4(-1) - 3 f(-1) = -4 - 3 f(-1) = -7
 Equations/93200: I am confused with this problem. Can someone help? f(x)=5x-1 Find the followinf for f(a-2. Thanks.1 solutions Answer 67832 by ankor@dixie-net.com(15639)   on 2007-08-18 13:56:06 (Show Source): You can put this solution on YOUR website!f(x)=5x-1 Find the following for f(a-2) : Just substitute (a-2) for x in the original equation. f(a-2) = 5(a-2) - 1 Multiply what's inside the brackets: f(a-2( = 5a - 10 - 1 : f(a-2) = 5a - 11
 Equations/92998: Simplify: (16-x^2) / (x^3-2x^2-8x)1 solutions Answer 67785 by ankor@dixie-net.com(15639)   on 2007-08-17 19:20:29 (Show Source): You can put this solution on YOUR website!(16-x^2) / (x^3-2x^2-8x) : Convert (16-x^2) to -1(x^2 - 16), then we have = = = = : Could you follow this OK?
 Graphs/92908: I have 2 questions that I cannot come up with a solution, Could you kindly help me. 1. Draw L1 hrough (-4,0)and (0,6). What is the slope of any line parallel to L1? Draw L2 tjrough the origin and parallel to L1. 2. y=1/3x+1/2 Thank you1 solutions Answer 67779 by ankor@dixie-net.com(15639)   on 2007-08-17 16:20:48 (Show Source): You can put this solution on YOUR website!I have 2 questions that I cannot come up with a solution, Could you kindly help me. 1. Draw L1 through (-4,0)and (0,6). It should look like this: : : What is the slope of any line parallel to L1? Parallel lines have the same slope. Equation for this line: y = (6/4)x + 6 Slope (m) = = : Draw L2 through the origin and parallel to L1. Equation for this line y = (6/4)x : : 2. y=1/3x+1/2; assume you want this graphed graph it from x = -6 to x = +4, should look like this: : : Did this help?
 Trigonometry-basics/92864: This question is from textbook Finite Mathematics The solution to the system of equations below is: 3x+4y=-6, x-5y=171 solutions Answer 67777 by ankor@dixie-net.com(15639)   on 2007-08-17 15:45:30 (Show Source): You can put this solution on YOUR website!3x + 4y = -6 x - 5y = 17 : Multiply 2nd equation by 3 and subtract from the 1st equation: 3x + 4x = -6 3x -15y = 51 ------------- subtracting eliminates x 0x +19y = -57 y = -57/19 y = -3 : Find x using the 1st equation: 3x + 4(-3) = -6 3x - 12 = -6 3x = -6 + 12 3x = 6 x = 2 : Check solutions in the 2nd equation 2 - 5(-3) = 17 2 + 15 = 17 : Did this make sense to you? Any questions?
 Surface-area/92987: HOW DO YOU FIND THE ALTITUDE OF A TRIANGLE THAT HAS A BASE OF 7 INCHES AND A SURFACE AREA OF 21 SGUARE INCHES?1 solutions Answer 67776 by ankor@dixie-net.com(15639)   on 2007-08-17 15:31:52 (Show Source): You can put this solution on YOUR website!HOW DO YOU FIND THE ALTITUDE OF A TRIANGLE THAT HAS A BASE OF 7 INCHES AND A SURFACE AREA OF 21 SGUARE INCHES? : You know the area of a triangle: .5*b*h = A : Substitute for b and A: .5*7*h = 21 3.5h = 21 h = 21/3.5 h = 6 inches is the altitude : Check the area using these values A = .5 * 7 * 6 A = 21 sq inches
 Trigonometry-basics/92859: This question is from textbook Finite Mathematics The soultion to the system of equations below is: x+2y-z=-3, 2x-y+3z=14, x+4y-2z=81 solutions Answer 67775 by ankor@dixie-net.com(15639)   on 2007-08-17 15:24:05 (Show Source): You can put this solution on YOUR website!The soultion to the system of equations below is: Eq1: x + 2y - z =-3, Eq2:2x - y + 3z =14, Eq3: x +4y - 2z = 8 : Multiply eq1 by -2 and add to eq3 -2x - 4y + 2z = 6 x + 4y - 2z = 8 -------------------adding eliminates y & z -x +0y + 0z = 14 x = -14 : Add all three equations, eliminates z x + 2y - z =-3, 2x - y + 3z =14, x +4y - 2z = 8 -------------------- 4x + 5y + 0z = 19 4x + 5y = 19 : x = -14, substitute -14 for x in the above and find 4(-14) + 5y = 19 -56 = 5y = 19 5y = 19 + 56 5y = 75 y = 75/5 y = +15 : I'll let you find z; check solutions in one of the original equations
 Travel_Word_Problems/93043: The Brodskys drove to the mountains at 60km/h. they returned at 40km/h. The return trip took 2 hours longer than the trip to the mountains. How long did it take them to get home?1 solutions Answer 67771 by ankor@dixie-net.com(15639)   on 2007-08-17 14:56:48 (Show Source): You can put this solution on YOUR website!The Brodskys drove to the mountains at 60km/h. they returned at 40km/h. The return trip took 2 hours longer than the trip to the mountains. How long did it take them to get home? : Let t = time to make the trip home Then (t-2) = time to make the trip to the mts. : The distances there and back are equal. Make an distance equation from that fact dist = speed * time : dist out = dist back 60(t-2) = 40t ; 60t - 120 = 40t : 60t - 40t = +120 : 20t = 120 : t = 120/20 : t = 6 hrs : : Check our solution by find the distances, they should be equal 60 * 4 = 240 40 + 6 = 240 : How about this? make sense to you? Any questions?
 Equations/93015: Please help me solve this problem m=x+3y/2 find y1 solutions Answer 67767 by ankor@dixie-net.com(15639)   on 2007-08-17 14:05:22 (Show Source): You can put this solution on YOUR website!Please help me solve this problem m = x + 3y/2; find y : Multiply equation by 2 to get rid of the denominator, results: 2m = 2x + 3y : 2m - 2x = 3y; subtracted 2x from both sides or 3y = 2m - 2x : y = (2/3)m - (2/3)x; divided both sides by 3
 Geometry_Word_Problems/93071: The length of a rectangle exceeds its width by 2 feet. If each dimension was increased by 3ft., the area would increased by 51 square feet.. Find the original dimensions.1 solutions Answer 67766 by ankor@dixie-net.com(15639)   on 2007-08-17 13:51:47 (Show Source): You can put this solution on YOUR website!The length of a rectangle exceeds its width by 2 feet. If each dimension was increased by 3 ft., the area would increased by 51 square feet.. Find the original dimensions. : Let x = the width Then (x+2) = the length and Area = x(x+2) : If the dimensions are increase by 3 ft, then (x+3) = new width (x+5) = new length and New Area = (x+3)(x+5) : Problem equation New area - old area = 51 sq/ft : (x+3)(x+5) - x(x+2) = 51 x^2 + 8x + 15 - x^2 - 2x = 51 x^2 - x^2 + 8x - 2x + 15 = 51 6x = 51 - 15 6x = 36 x = 36/6 x = 6 ft. width of the original rectangle 6 + 2 = 8 ft, length of the original rectangle : : Check our solution 6 + 3 = 9 ft, width of the new rectangle 6 + 5 = 11 ft, length of the new rectangle : 11*9 - 8*6 = 99 - 48 = 51
 Linear_Equations_And_Systems_Word_Problems/93012: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities1 solutions Answer 67701 by ankor@dixie-net.com(15639)   on 2007-08-16 20:57:28 (Show Source): You can put this solution on YOUR website!A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities. : Let x = standard p.h; y = deluxe p.h : The labor equation: 12x + 20y =< 800 : put equation in the general (y=) form to plot the graph: 20y =< 800 - 12x y =< 800/20 - (12/20)x y =< 40 - .6x : : The production capacity equation: x + y =< 50 Put this in the "y=" form also y <= 50 -x : Existing order constraints x => 10 and y => 15 : Plot these using the equation givens. y = 40 - .6x; (purple line) y = 50 - x; (green line) y = 15; Note that y = 15 is a horizontal line going thru y = 15; black line x = 10 is a vertical line going thru x = 10, I am unable to put this in : I assume you know how to make up an x/y table and plot a graph, if you can't, let me known and we will go thru the graphing routine : Here is the graph: : When you draw your graph (or print this one) draw a vertical line thru x = 10 This will complete the area of feasibility which is: : 1.At or below, the purple line or the green line whichever is lower. 2.At or above the black horizontal line 3.At or to the right of the vertical line which you will add to the graph : Does this all make sense to you?
 Miscellaneous_Word_Problems/93010: This is not from a book but I am having difficulties with this question. The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers? Any explanation would be helpful. Thank you. 1 solutions Answer 67695 by ankor@dixie-net.com(15639)   on 2007-08-16 19:55:26 (Show Source): You can put this solution on YOUR website! Just write what it says: : "The difference of two numbers is 27." One number = x the 2nd number = (x-27) : "The second is 1 less than 3 times the first. x - 27 = 3x - 1 : What are the two numbers? x - 3x = -1 + 27 -2x = +26 x = 26/-2 x = -13 : 2nd number: -13 - 27 = -40 : Check using the statement "The second is 1 less than 3 times the first." -40 = 3(-13) - 1
 Mixture_Word_Problems/92898: Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of each should she use?1 solutions Answer 67626 by ankor@dixie-net.com(15639)   on 2007-08-16 10:42:45 (Show Source): You can put this solution on YOUR website!Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of each should she use? : Let x = amt of pure anti-freeze required Then (20-x) = amt of 40% solution required: : The percent equation: .40(20-x) + 1.0(x) = .50(20) 8 - .4x + x = 10 .6x = 10 - 8 .6x = 2 x = 2/.6 x = 3.33 qt of pure anti freeze and 20 - 3.33 = 16.67 qt of 40% solution : : Check our solution .4(16.67) + 3.33 = .5(20) 6.668 + 3.33 = 9.998 ~ 10 :
 Linear_Equations_And_Systems_Word_Problems/92912: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. sorry but I am so lost on this one, thank you 1 solutions Answer 67625 by ankor@dixie-net.com(15639)   on 2007-08-16 10:24:43 (Show Source): You can put this solution on YOUR website!This problem came up a few days ago. I assume you are not the same person who submitted then. This is what I submitted then, hope it will help you. : A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. : x = no. of scarves; y = no. of sweaters: : The labor inequality: 2x + 14y =< 40 Arrange in the general (y=) form so we can graph it: 14y =< 40 - 2x y =< (40/14) - (2/14)x y =< 20/7 - (1/7)x; green line : The production inequality: x + y = 5 y = 5 - x; purple line : Plot these two inequalities (I assume you know how to plot a graph, if not you can email me at ankor@dixie-net.com and I will add the procedure to do that.) : your graph should look like this: : The area of feasibility would be at or below either line, whichever is lower It's assumed that x and y => 0
 Human-and-algebraic-language/92903: A father walks 36miles in 12hours while his son covers the same distance on a bicycle at twice the fathers rate of speed. at this rate, how many miles would the bicycle rider travel in 9hours.1 solutions Answer 67623 by ankor@dixie-net.com(15639)   on 2007-08-16 10:18:23 (Show Source): You can put this solution on YOUR website!A father walks 36 miles in 12 hours while his son covers the same distance on a bicycle at twice the father's rate of speed. at this rate, how many miles would the bicycle rider travel in 9 hours. : Remember speed = dist/time The problem: twice father's speed times 9 hrs 2() * 9 = 2 * 3 * 9 = 54 mi :
 Polynomials-and-rational-expressions/92886: If the sides of a square are increased by 3 in, the area is increased by 39 in. What were the dimensions of the original square1 solutions Answer 67591 by ankor@dixie-net.com(15639)   on 2007-08-15 21:43:11 (Show Source): You can put this solution on YOUR website!If the sides of a square are increased by 3 in, the area is increased by 39 in. What were the dimensions of the original square : Side of original square = x Area of original square = x^2 : Side of new square = (x+3) Area of new square = (x+3)^2 : The problem equation: New square area - original square area = 39 sq/in (x+3)^2 - x^2 = 39 : x^2 + 6x + 9 - x^2 = 39; FOILed (x+3)(x+3) : 6x + 9 = 39; x^2's eliminated : 6x = 39 - 9 ; x = 30/6 : x = 5 in, the dimension of original square : : Check using the area: 8^2 - 5^2 = 64 - 25 = 39 : Did this make sense to you? Not that hard, right?
 Miscellaneous_Word_Problems/92812: A small copany produces both doll houses and sets of doll furniture. The doll houses take 3hrs of labor to produce, and the furniture sets take 8hrs. The labor available is limited to 400hrs per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequlities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities.1 solutions Answer 67589 by ankor@dixie-net.com(15639)   on 2007-08-15 21:21:12 (Show Source): You can put this solution on YOUR website!This same problem came up recently. This is what I submitted then, perhaps it will help you. : A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities. : x = number of doll houses; y = furniture sets : The labor constraint: 3x + 8y =< 400 Arrange in the general (y=) form so we can plot the graph 8y =< 400 - 3x y =< (400/8) - (3/8)x y =< 50 - (3/8)x : The production constraint: x + y =< 100 y =< 100 - x : Min house constraint: x => 20 : Min furniture constraint y => 10 : Plot the Labor equation; I assume you know how to substitute for x and find y x | y ------- 0 | 50 8 | 47 32 | 38 : Plot the production restraint x | y ------ 0 |100 20 | 80 50 | 50 : x => 20 is at or to the right of a vertical line going thru x=20 : y => 10 is at or above a horizontal line going thru y = 10 : Look something like this: You have to draw in the vertical line at x = 20 : Area of feasibility: 1. At or below the green or purple lines which ever is lowest 2. At or above the horizontal line 3. At or to the right of vertical line at x=20 which you have to draw in : Any question about this?
 Polynomials-and-rational-expressions/92834: I am not sure how to solve this problem. I am having trouble putting it in simplist form. How do you solve this expression. ____________________ 1 solutions Answer 67570 by ankor@dixie-net.com(15639)   on 2007-08-15 19:06:31 (Show Source): You can put this solution on YOUR website!You can't solve it (no = sign), just simplify it. : ------------------ : Both the numerator & denominator can be factored: ------------------ : Note that (2r-5s)'s will cancel, leaving you with: ----------- : Did this make sense to you?
 Linear-equations/92813: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hrs of labor to produce, and the sweaters take 14 hrs. The labor available is limited to 40 hrs per week, and the total production capacity is 5 times per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. 1 solutions Answer 67567 by ankor@dixie-net.com(15639)   on 2007-08-15 18:44:14 (Show Source): You can put this solution on YOUR website!A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. : x = no. of scarves; y = no. of sweaters: : The labor inequality: 2x + 14y =< 40 Arrange in the general (y=) form so we can graph it: 14y =< 40 - 2x y =< (40/14) - (2/14)x y =< 20/7 - (1/7)x : The production inequality: x + y = 5 y = 5 - x : Plot these two inequalities (I assume you know how to plot a graph, if not you can email me and I will add the procedure to do that.) : your graph should look like this: : The area of feasibility would be at or below either line, whichever is lower It's assumed that x and y => 0