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Linear_Equations_And_Systems_Word_Problems/178909: Dear Sir I would be glad if you can help me to resolve the below problems that has been bothering me for awhile. Thanks Jackie King e-mail address; smsltd@starhub.net.sg 1) Jane had 156 red and yellow beads in the ratio 7:6. After she gave away an equal number of each type of bead, the number of red and yellow beads left was in the ratio 7:3. (a) Did the fraction of the red beads that Jane had increases, decreases, or remain the same? (b) How many beads did she give away altogether? 2) In Mariam’s aquarium there are swordtails and guppies, 25% of the fishes are swordtails. She then buys an equal number of swordtails and puts them into the aquarium. (a) Will the percentage of fishes in the aquarium which are guppies increases, decrease or remain the same? (b) What percentage of the fishes will be guppies? My queries in the above the two questions are: In question 1 (a) does the ‘fraction’ asked refers to the new base after “she gave away an equal number of each type of bead “ or referring the same base before giving away. If the answer is related to the new base then my question is how we can compare two fractions coming from different wholes; I could not find any mathematical meaning in this situation. Similar query in question two in which I wonder which ‘whole’ the question refers to; before or after. In addition, the quantity “an equal number of swordtails” refers to the same amount of 25% of the fishes. Lastly, what principles do the examiner what to test in the above two questions. I would appreciate very much if you would provide me the method how you would work the solutions to the above questions. Furthermore, what happen if we keep increasing or increasing the “equal amount to put in or taken away”? Is there some kind of relationship that we can deduce from these two problems? 1 solutions Answer 133912 by ankor@dixie-net.com(15622)   on 2009-01-28 13:35:01 (Show Source): You can put this solution on YOUR website! 1) Jane had 156 red and yellow beads in the ratio 7:6. After she gave away an equal number of each type of bead, the number of red and yellow beads left was in the ratio 7:3. : (a) Did the fraction of the red beads that Jane had increases, decreases, or remain the same? : Try it and see, we know that 156/13 = 12 therefore there are: 7*12 = 84 red 6*12 = 72 yellow decimal equiv of red beads 84/156 = .538 Give away two of each, reducing the total to 152 decimal equiv of red beads: 82/152 = .539, fraction of red beads has increased : : (b) How many beads did she give away altogether? ; let amt of each given away = x = Cross multiply 3(84-x) = 7(72-x) 252 - 3x = 504 - 7x -3x + 7x = 504 - 252 4x = 252 x = x = 63 ea given away : Check this: = = : : 2) In Mariam’s aquarium there are swordtails and guppies, 25% of the fishes are swordtails. She then buys an equal number of swordtails and puts them into the aquarium. : (a) Will the percentage of fishes in the aquarium which are guppies increases, decrease or remain the same? : Lets say there are 25 swords in the tank which contains 100 fish (75 are gups) then, the decimal amt of guppies will be .75 (75%) Add 25 more swords, total fish = 125, no. of guppies remain at 75 so we have: = .60 (60%) so it decreases (b) What percentage of the fishes will be guppies? 60% : : Hopefully I straightened this out. Let me know Carl

Numeric_Fractions/178921: 4/7 of the school's faculty are women; 4/5 of the male faculty are married; and 9 of the male faculty are unmarried. How many faculty members are there? 1 solutions Answer 133869 by ankor@dixie-net.com(15622)   on 2009-01-28 10:04:24 (Show Source): You can put this solution on YOUR website! 4/7 of the school's faculty are women; 4/5 of the male faculty are married; and 9 of the male faculty are unmarried. How many faculty members are there? : let x = no. members : if of the males are married, then are unmarried and = 9 therefore total males = 5*9 = 45 : x = x + 45 multiply equation by 7 to get rid of the denominator (what was I thinking?!) 7x = 7*x + 7(45) cancel denominators 7x = 4x + 315 : 7x - 4x = 315 : 3x = 315 x = x = 105 members : : Check solution: married males: 45-9 = 36 105 + 36 + 9 = 60 = 36 + 9 = 105

Functions/178908: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear. 1 solutions Answer 133867 by ankor@dixie-net.com(15622)   on 2009-01-28 09:40:33 (Show Source): You can put this solution on YOUR website! Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear. : Make coordinates from the given information x1=2, y1=120 x2=3, y2=60 : Find the slope (m), where m = : m = m = = -60 : write the equation using the point/slope formula [y-y1 = m(x-x1)] y - 120 = -60(x - 2) y - 120 = -60x + 120 y = -60x +120 + 120 y = -60x + 240 Translate this to your problem where x=p, y=C C(p) = -60p + 240 : : you can check this by substituting 2 for p and ensuring that C(p) = 120 do the same for p=3

Equations/178794: Carlos can walk 8 miles in the same time it takes him to jog 12 miles. His jogging rate is 5 miles per hour faster than his walking rate. At what rate does he walk? 1 solutions Answer 133824 by ankor@dixie-net.com(15622)   on 2009-01-27 21:43:55 (Show Source): You can put this solution on YOUR website! can walk 8 miles in the same time it takes him to jog 12 miles. His jogging rate is 5 miles per hour faster than his walking rate. At what rate does he walk? : let r = his walking rate then (r+5) = his jogging rate : It says the times are equal, write a time equation; time = : jogging time = walking time = cross multiply and you have 12r = 8(r+5) 12r = 8r + 40 12r - 8r = 40 4r = 40 r = 10 mph is his walking speed (unrealistic) and 15 mph is his jogging speed (also unrealistic, that's a 4 min mile!) ; : Check to see of the times are equal 12/15 = .8 hr 8/10 = .8 hr; confirms our solution

Radicals/178834: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers 1 solutions Answer 133822 by ankor@dixie-net.com(15622)   on 2009-01-27 21:24:51 (Show Source): You can put this solution on YOUR website! Two positive numbers x, y : differ by 11, x-y = 11 or x = (y+11) : their square roots differ by 1. = 1 : Find the numbers : Substitute (y+11) for x in the above equation = 1 : = + 1 : Square both sides y + 11 = ( + 1)^2 ; FOIL the right side: y + 11 = y + + 1 : y - y + 11 - 1 = : 10 = : Square both sides: 100 = 4y y = y = 25 then x = 25 + 11 x = 36 : This satisfies the problem as you can see

Inequalities/178601: 1. Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area that Jenny has visualized 1 solutions Answer 133802 by ankor@dixie-net.com(15622)   on 2009-01-27 20:11:58 (Show Source): You can put this solution on YOUR website! a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area. : let x = length of the third side then (x-3) = length of the 1st side and (x+2) = length of the 2nd side ; : Add the three sides to get the given perimeter (x-3) + (x+2) + x = 32 x + x + x - 3 + 2 = 32 3x - 1 = 32 3x = 32 + 1 3x = 33 x = x = 11 ft is the third side ; I'll let you determine the other two sides, make sure they add up to 32.

Miscellaneous_Word_Problems/178841: A man left an estate of $64,000 to three children. The eldest child received 3 times as much as the youngest. The middle child received $14,000 more than the youngest. How much did each child get? thanks so much 1 solutions Answer 133801 by ankor@dixie-net.com(15622)   on 2009-01-27 20:01:37 (Show Source): You can put this solution on YOUR website! A man left an estate of $64,000 to three children. The eldest child received 3 times as much as the youngest. The middle child received $14,000 more than the youngest. How much did each child get? thanks so much. : Let x = amt received by the youngest : Write an equation for each statement: : "The eldest child received 3 times as much as the youngest." eldest amt = 3x : "The middle child received $14,000 more than the youngest." middle amt = (x+14000) ; How much did each child get? : we know the three amts add up to 64000 3x + (x+14000) + x = 64000 3x + x + x = 64000 - 14000 5x = 50000 x x = $10,000 amt rec'd by the youngest and 10000 + 14000 = $24,000 amt rec'd by the middle child and 3(10000) = $30,000 amt rec'd by the eldest : : you can check our solution by finding the total of the 3 amts

Human-and-algebraic-language/178845: a sign has a area of 60ft squared. if the width of is 4 ft shorter then the length, what are the dimensions of the sighn? 1 solutions Answer 133800 by ankor@dixie-net.com(15622)   on 2009-01-27 19:51:38 (Show Source): You can put this solution on YOUR website! a sign has a area of 60ft squared. if the width of is 4 ft shorter then the length, what are the dimensions of the sign? : let x = width of the sign then (x+4) = length of the sign ; : W * L = area x(x+4) = 60 : x^2 + 4x = 60 ; x^2 + 4x - 60 = 0; a quadratic equation Factor this to: (x+10)(x-6) = 0 positive solution is what we want here x = 6 ft is the width then 6 + 4 = 10 ft is the length : : Check solution by finding the area: 10 * 6 = 60 sq/ft

Equations/178796: Maria jogs 15 miles and bicycles back. The total trip requires 3 hours. If she bicycles twice as fast as she jogs, how fast does she bicycle? 1 solutions Answer 133799 by ankor@dixie-net.com(15622)   on 2009-01-27 19:42:56 (Show Source): You can put this solution on YOUR website! Maria jogs 15 miles and bicycles back. The total trip requires 3 hours. If she bicycles twice as fast as she jogs, how fast does she bicycle? : Let s = jogging speed then 2s = biking speed : Write a time equation; time = : time jogging + time riding = 3 hrs + = 3 multiply equation by 2s : 2s* + 2s* = 2s(3) cancel out the denominators 2(15) + 15 = 6s : 30 + 15 = 6s : 45 = 6s s = s = 7.5 mph is the jogging speed then 2(7.5) = 15 mph is the biking speed ; : Check solution by finding the times 15/7.5 = 2 hr 15/15 = 1 hr ------------ total = 3 hrs. confirms our solution

absolute-value/178650: This question is from textbook Algebra for College Students Amtrak's annual passenger revenue for the years 1985-1995 is modeled approximately by the formula R=-60/x-11/+962 where R is the annual revenue in millions of dollars and x is the number of years since January 1, 1980 (Association of American Railroads, Washington, DC, Railroad Facts, Statistics of Railroads of Class 1, annual). In what years was the passenger revenue $722 million? 1 solutions Answer 133737 by ankor@dixie-net.com(15622)   on 2009-01-27 15:53:47 (Show Source): You can put this solution on YOUR website! Amtrak's annual passenger revenue for the years 1985-1995 is modeled approximately by the formula R=-60/x-11/+962 where R is the annual revenue in millions of dollars and x is the number of years since January 1, 1980 : Assume the equation is: R = -60|x-11| + 962 : In what years was the passenger revenue $722 million? ; Replace R with 722 : -60|x-11| + 962 = 722 -60|x-11| = 722 - 962 -60|x-11| = -240 : Remove the absolutes and solve two equation (we will have two solutions): -60x + 660 = -240 -60x = -240 - 660 -60x = -900 x = x = +15 years or 1995 and -60x + 660 = +240 -60x = 240 - 660 -60x = -420 x = x = +7 years or 1987

Miscellaneous_Word_Problems/178754: Question 1) A square flower bed in Michelle's garden is to be enlarged by adding 3 feet on each side. If the larger square has an area of 169 square feet, what is the length of the original square? 1 solutions Answer 133735 by ankor@dixie-net.com(15622)   on 2009-01-27 15:28:53 (Show Source): You can put this solution on YOUR website! A square flower bed in Michelle's garden is to be enlarged by adding 3 feet on each side. If the larger square has an area of 169 square feet, what is the length of the original square? : Let s = length of the side of the original square then (s+6) = length of the enlarged square when 3' is added to each side : Area of new square given as 169 sq/ft (s+6)^2 = 169 FOIL s^2 + 12s + 36 = 169 : s^2 + 12s + 36 - 169 = 0 : s^2 + 12s - 133 = 0 Factor this to (s-7)(s+19) = 0 Positive solution s = 7' is the side of the original square : ; Check solution: (7+6)^2 = new area 13^2 = 169

Miscellaneous_Word_Problems/178716: Please help. An artist wants her painting to be in the shape of a golden rectangle. If the length of the painting is 36 inches, then what should be the width? L/W = W/L-W 1 solutions Answer 133733 by ankor@dixie-net.com(15622)   on 2009-01-27 15:10:05 (Show Source): You can put this solution on YOUR website! An artist wants her painting to be in the shape of a golden rectangle. If the length of the painting is 36 inches, then what should be the width? : Using the Golden Rectangle ratio of width/length which ~ .618...: .618 * 36 = 22.25 inches : Or you can solve the given equation = L = 36, Find W = Cross Multiply W^2 = 36(36-W) : W^2 = 1296 - 36W : W^2 + 36W - 1236 = 0 : Using the quadratic formula, the positive solution should = 22.25" also

Miscellaneous_Word_Problems/178715: Please help. Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner? 1 solutions Answer 133704 by ankor@dixie-net.com(15622)   on 2009-01-27 11:28:16 (Show Source): You can put this solution on YOUR website! Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner? : Let x = side of the square to be cut off : Box dimension : (11-2x) by (14-2x) by x : Base as given = 80 sq/in, therefore (11-2x) * (14-2x) = 80 FOIL 154 - 22x - 28x + 4x^2 = 80 : 154 - 50x + 4x^2 - 80 = 0 Arranged as a quadratic equation: 4x^2 - 50x + 74 = 0 Simplify divide by 2 2x^2 - 25x + 37 = 0 Solve this using the quadratic formula: in this equation a=2, b=-25, c=37 : : Two solutions x = 10.785 and x = 1.715 inches (the solution that makes sense) ; : Check solution (11-2(1.715)) * (14-2(1.715)) = (11-3.43) * (14-3.43) = 80.0

Polynomials-and-rational-expressions/178577: Thanks for the help ;) Multiply and them simplify if possible 3a^2+7ab+2b^2 a^2-ab _____________ . ______ a^2+2ab 3a^+ab 1 solutions Answer 133640 by ankor@dixie-net.com(15622)   on 2009-01-26 21:56:49 (Show Source): You can put this solution on YOUR website! I assume it's: * Factor, then cancel: a, (3a+b), and (a+2b) * =

Exponential-and-logarithmic-functions/178647: A square is inscribed in a circle. If the length of the diagonal of the square is 6.4 cm, What is the area of the shaded region.( The shaded region is inside the circle ad outside the square box.) 1 solutions Answer 133617 by ankor@dixie-net.com(15622)   on 2009-01-26 20:00:53 (Show Source): You can put this solution on YOUR website! A square is inscribed in a circle. If the length of the diagonal of the square is 6.4 cm, What is the area of the shaded region.( The shaded region is inside the circle ad outside the square box.) : find the area of the circle, subtract the area of the square : circle, r = 3.2 cm A = pi*3.2^2 A = 32.167 sq cm ; Find the dimensions of the square: 2s^2 = 6.4^2 2s^2 = 40.96 s^2 = 20.48, which is the area of a square : 32.167 - 20.48 = 11.69 is the shaded area

Linear-equations/178328: From a base elevation of 7200 ft, a mountain peak in Colorado rises to a summit elevation of 14598 ft over a horizontal distance of 15848 ft find the grade of the peak? 1 solutions Answer 133545 by ankor@dixie-net.com(15622)   on 2009-01-26 16:21:34 (Show Source): You can put this solution on YOUR website! From a base elevation of 7200 ft, a mountain peak in Colorado rises to a summit elevation of 14598 ft over a horizontal distance of 15848 ft find the grade of the peak. ; Find the height of the peak above the base of the mountain 14598 - 7200 = 7398 ft : Percent grade = rise/run * 100 : * 100 = 46.68% grade

Triangles/178376: In triangle ABC, linr CD is both the median and the altitude to side AB. If AB=5x+3, AC=2x=8, and BC=3x+5, what is the perimeter of triangle ABC? 1 solutions Answer 133537 by ankor@dixie-net.com(15622)   on 2009-01-26 15:34:06 (Show Source): You can put this solution on YOUR website! In triangle ABC, line CD is both the median and the altitude to side AB. If AB=5x+3, AC=2x+8, and BC=3x+5, what is the perimeter of triangle ABC? : If the median is the same as the altitude, this triangle has two equal sides, namely, AC and BC, therefore: 2x + 8 = 3x + 5 8 - 5 = 3x - 2x x = 3 : AB: 5(3) + 3 = 18 AC: 2(3) + 8 = 14 BC: 3(3) + 5 = 14 ------------------ the perimeter: 46

Geometry_Word_Problems/178300: A photo is 4 inches longer than its width. A 3 inch border is placed around the photo making the total area around the photo and border 165 square inches. What are the dimensions of the photo 1 solutions Answer 133533 by ankor@dixie-net.com(15622)   on 2009-01-26 15:19:13 (Show Source): You can put this solution on YOUR website! A photo is 4 inches longer than its width. A 3 inch border is placed around the photo making the total area around the photo and border 165 square inches. What are the dimensions of the photo? : Let x = width of the photo then (x+4) = length of the photo : draw this out showing the 3" border around the photo, label the photo width as x and the length as (x+4), and you will see the dimensions of the rectangle including the 3" border are (x+6) by (x+4+6) or (x+10) : Overall area given as 165 sq/in so we have: Length * width = 165 sq/in (x+10)*(x+6) = 165 FOIL x^2 + 6x + 10x + 60 = 165 : x^2 + 16x + 60 - 165 = 0 : x^2 + 16x - 105 = 0; our old friend, the quadratic equation! Factors to (x+21)(x-5) = 0 positive solution is what we want here: x = 5" is the width of the photo and 5 + 4 = 9" is the length ; ; Check solution by confirming the overall area: (5+6)*(9+6) = 11 * 15 = 165

Mixture_Word_Problems/178565: what quantity x of an 80% solution must be added to a 15% solution to produce 600mL of a 40% solution 1 solutions Answer 133521 by ankor@dixie-net.com(15622)   on 2009-01-26 14:34:54 (Show Source): You can put this solution on YOUR website! what quantity x of an 80% solution must be added to a 15% solution to produce 600mL of a 40% solution : mix x amt with (600-x) amt : .8x + .15(600-x) = .4(600) .8x + 90 - .15x = 240 .8x - .15x = 240 - 90 .65x = 150 x = x = 230.77 ml of 80% solution : : Check solution: (600 - 230.77 = 369.23 ml of 15% solution: .8(230.77) + .15(369.23) = .4(600) 184.62 + 55.38 = 240

Graphs/178536: can someone please help me with this problem Draw l1 through (-4, 0) and (0, 6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1 1 solutions Answer 133503 by ankor@dixie-net.com(15622)   on 2009-01-26 12:36:44 (Show Source): You can put this solution on YOUR website! Draw l1 through (-4, 0) and (0, 6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1 : Find the slope using the given coordinates: m = x1=-4; y1=0 x2=0; y2=6 m = = = : find the equation by using the point/slope equation: y-y1 = m(x-x1) y - 0 = (x -(-4)) y = (x + 4)) y = x + 6 : Graph this equation (L1): : Parallel lines have the same slope in this case : The parallel line thru the origin (0,0) would be y = x add to the graph L2

Equations/178524: Hi. An artist wants to frame a picture with a frame 2 inches wide. How wide will the framed picture be if the artist uses 70 inches of framing material? Thanks. H.C. 1 solutions Answer 133492 by ankor@dixie-net.com(15622)   on 2009-01-26 08:58:42 (Show Source): You can put this solution on YOUR website! An artist wants to frame a picture with a frame 2 inches wide. How wide will the framed picture be if the artist uses 70 inches of framing material? : Since the don't indicate otherwise, I assume the picture is a square. Let s = one side of the square frame then 4s = 70 s = s = 17.5; one side of the frame : Picture size: 17.5 - 2(2") = 13.5 inches

Linear-systems/178257: Write a system of two equations in two unknowns for each problem. Solve each system by substitution. The width of a rectangualr painting is two -thirds of its length. If the perimeter is 28ft, then what are the length and width? 1 solutions Answer 133458 by ankor@dixie-net.com(15622)   on 2009-01-25 21:41:52 (Show Source): You can put this solution on YOUR website! The width of a rectangular painting is two-thirds of its length. If the perimeter is 28ft, then what are the length and width? : Write an equation for each statement; : "The width of a rectangular painting is two-thirds of its length. W = L : " If the perimeter is 28ft," 2L + 2W = 28 : then what are the length and width? : Substitute L for W in the perimeter equation, Find L: 2L + 2(L) = 28 2L + L = 28 multiply eq by 3 to get rid of that annoying denominator, results: 6L + 4L = 3(28) : 10L = 84 L= L = 8.4 ft : Find W (8.4) = 5.6 ft : : Check solution: 2(8.4) + 2(5.6) = 16.8 + 11.2 = 28 ft

Rate-of-work-word-problems/178509: On a 255 mile trip gary traveled at an average of 70 mph, got a speeding ticket, and then traveled at 60 mph for the remainder of the trip. If the entire trip took 4.5 hours and the speeding ticket stop took 30 minutes, how long did gary speed before he got stopped? 1 solutions Answer 133456 by ankor@dixie-net.com(15622)   on 2009-01-25 21:26:00 (Show Source): You can put this solution on YOUR website! On a 255 mile trip Gary traveled at an average of 70 mph, got a speeding ticket, and then traveled at 60 mph for the remainder of the trip. If the entire trip took 4.5 hours and the speeding ticket stop took 30 minutes, how long did Gary speed before he got stopped? : Let t = time driven at 70 mph The total driving time was 4 hrs, therefore: (4-t) = time at 60 mph : Write a distance equation; dist = speed * time ; Dist at 70 + dist at 60 = 255 : 70t + 60(4-t) = 255 : 70t + 240 - 60t = 255 : 70t - 60t = 255 - 240 : 10t = 15 t = t = 1.5 hrs at 70 mph : : check solution (time at 60 mph: 4 - 1.5 = 2.5hrs) 1.5(70) + 2.5(60) = 105 + 150 = 255 mi confirms our solution

Geometric_formulas/178408: Two trains are start from the same point and travel in. Train A travels East at an average speed of 75 mph and train B travels West at an average speed of 60 mph. How long will it take for the trains to be 297 miles apart? 1 solutions Answer 133441 by ankor@dixie-net.com(15622)   on 2009-01-25 20:34:07 (Show Source): You can put this solution on YOUR website! Two trains are start from the same point and travel in. Train A travels East at an average speed of 75 mph and train B travels West at an average speed of 60 mph. How long will it take for the trains to be 297 miles apart? ; Let t = time in hrs to be 297 mi apart ; Write a distance equation; dist = speed * time ; Train A dist + Train B dist = 297 mi 75t + 60t = 297 : 135t = 297 t = t = 2.2 hrs to be 297 mi apart : : Check solution: 75*2.2 + 60*2.2 = 165 + 132 = 297

Miscellaneous_Word_Problems/178251: Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is high. The other has a wider, high-definition screen, which is 1.8 times as wide as it is high. The diagonal measure of the wider screen is 17 inches more than the diagonal measure of the smaller. What is the height of the screens, correct to the nearest 0.1 inch? 1 solutions Answer 133383 by ankor@dixie-net.com(15622)   on 2009-01-25 15:19:09 (Show Source): You can put this solution on YOUR website! Two television monitors sitting beside each other on a shelf in an appliance store have the same screen height. One has a conventional screen, which is 7 inches wider than it is high. The other has a wider, high-definition screen, which is 1.8 times as wide as it is high. The diagonal measure of the wider screen is 17 inches more than the diagonal measure of the smaller. What is the height of the screens, correct to the nearest 0.1 inch? : Let x = height of both screens: : Conventional screen dimensions: (x+7) by x HD screen dimensions: 1.8x by x : Find x by writing an equation of the diagonals (hypotenuse) of the screens HD diagonal = Conventional diagonal + 17 inches = + 17 : = + 17 : - - 17 = 0 To avoid a tremendous amt of math, graph this equation: : Note the positive intercept occurs at x~34" or 34.4" on a Ti83 : Check solution by finding the diagonals using x = 34.4 HD = 70.8 Convent = 53.8 ------------------------------------------ This will give us a difference of: 17.0" : : I'll let you find the actual width of the two screens:

Radicals/178341: solve algebraically and show your potential solutions √(x+2) -x=0 b.∛x -5=3 c.X3/2 = 27 1 solutions Answer 133357 by ankor@dixie-net.com(15622)   on 2009-01-25 13:29:35 (Show Source): You can put this solution on YOUR website! √(x+2) -x=0 b.∛x -5=3 c.X3/2 = 27 : = 0 : = x square both sides and you have x + 2 = x^2 A quadratic equation: x^2 - x - 2 = 0 Factors to (x-2)(x+1) = 0 two solutions x = +2 x = -1 Check both solutions in original equation = 0 and = 0 does not = 0 : x = 2 is the only solution : : ∛x - 5 = 3 : ∛x = 3 + 5 : ∛x = 8 x = 2 : : = 27 find the cube root of both sides = 3 which is: = 3 Square both sides x = 9 : : Check on a good calc: enter 9^(3/2) = 27

Linear_Equations_And_Systems_Word_Problems/178255: A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will amount to 54,150 . The variable costs will be 12.50 per book. The publisher will sell the finished product to bookstores at a price of $25.00 per book. How many books must the publisher print and sell so that the production costs will equal the money obtained from sales? 1 solutions Answer 133293 by ankor@dixie-net.com(15622)   on 2009-01-24 21:49:07 (Show Source): You can put this solution on YOUR website! A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will amount to 54,150 . The variable costs will be 12.50 per book. The publisher will sell the finished product to bookstores at a price of $25.00 per book. How many books must the publisher print and sell so that the production costs will equal the money obtained from sales? ; Let x = no. of books : Cost = 12.50x + 54150 : Revenue = 25x : Rev = cost 25x = 12.5x + 54150 25x - 12.50x = 54150 12.5x = 54150 x = x = 4332 books need to be sold to cover production costs : : Check: c = 12.50(4332) + 54150 c = 54150 + 54150 c = 108300 : r = 25(4332) r = 108300

Mixture_Word_Problems/178278: Soybean meal is 16% protein and cornmeal is 8% protien, how many pounds of each should be mixed together in order to get 320lb mixture that is 13% protein? 1 solutions Answer 133287 by ankor@dixie-net.com(15622)   on 2009-01-24 20:57:43 (Show Source): You can put this solution on YOUR website! Soybean meal is 16% protein and cornmeal is 8% protien, how many pounds of each should be mixed together in order to get 320lb mixture that is 13% protein? : let x = amt of soy The total will be 320, therefore: (320-x) = amt of corn : .16x + .08(320-x) = .13(320) : .16x + 25.6 - .08x = 41.6 : .16x - .08x = 41.6 - 25.6 : .08x = 16 x = x = 200 lb of soy then 320 - 200 = 120 lb of corn : : Check solution: .16(200) + .08(120) = .13(320) 32 + 9.6 = 41.6

Money_Word_Problems/178315: This question is from textbook Math its Power and Utility Please help me, I have been trying to solve this for 2 days. Jerry has just received an inheritance of $50,000, and he would like to use it to help him with his retirement. Since Jerry is 25 years old, he figures that the $50,000 can be invested for 40 years before he will need to use it for retirement. Jerry wants to know what interest rate would be necessary for the $50,000 to grow to provide an amount so that he can have a monthly income of $4,000 earned from the interest only. Assume that Jerry is able to invest in real estate and can earn a 12% return on his investment. I=Prt; first I found out the amount Jerry would have after 40 years at 12% interest. I=50000.00(.12)(40) I=240,000.00 Then I took the 240,000.00 and used the same formula: I=Prt 4000.00=240,000.00(r)(1/12) 12*4000.=240,000.00(r)(1/12)*12 48000.00=240,000.00r (divide both sides by 240,000.00 I=.20 or 20% I am doing this class online and so when I input the answer it tells me if the answer is correct or not. I don't understand what I am doing wrong. PLEASE HELP ME I AM DESPERATE AT THIS POINT!!!! Thank you so much in advance!! 1 solutions Answer 133285 by ankor@dixie-net.com(15622)   on 2009-01-24 20:24:47 (Show Source): You can put this solution on YOUR website! Jerry has just received an inheritance of $50,000, and he would like to use it to help him with his retirement. Since Jerry is 25 years old, he figures that the $50,000 can be invested for 40 years before he will need to use it for retirement. Jerry wants to know what interest rate would be necessary for the $50,000 to grow to provide an amount so that he can have a monthly income of $4,000 earned from the interest only. Assume that Jerry is able to invest in real estate and can earn a 12% return on his investment. : I.m not sure what you are doing here, see if this makes sense to you : First find out how much required to produce $4000 a month interest at 12% : 12% per yr is 1% per month so we have p*r*t = 4000 t = 1 r = .01 find p p * .01 * 1 = .01p = 4000 p = p = $400,000 will be the required amt ; Now we want to find out what interest rate will produce $400,000 in 40 yrs with $50,000 initial investment. Assume it's compounded annually Ao(1+r)^t = A where A = final amt (400000) Ao = initial amt (50000) t = time (40 yrs) r = interest rate (decimal) : 50000(1+r)^40 = 400000 (1+r)^40 = (1+r)^40 = 8 40*log(1+r) = log(8); log equiv of exponents 40*log(1+r) = .90309 log(1+r) = log(1+r) = .022577 Find the 10^x of each side 1 + r = 1.05336 r = 1.05336 - 1 r = .05336 ~ 5.3% interest will produce $400,000 after 40 yrs compounded annually : Sorry I got i mixed up with r, hope it didn't confuse you. Carl

Linear_Equations_And_Systems_Word_Problems/178306: This question is from textbook Intermediate Algebra Twice the sum of a number and 3 is the same as five times the number minus 1 minus four times the number. Find the number. 1 solutions Answer 133281 by ankor@dixie-net.com(15622)   on 2009-01-24 19:01:00 (Show Source): You can put this solution on YOUR website! let x = " a number" : Write an equation for the given statement : Twice the sum of a number and 3 is the same as five times the number minus 1 minus four times the number. 2x + 3 = 5x - 1 - 4x 2x + 3 = x - 1 2x - x = -1 -3 x = -4 : Check solution 2(-4) + 3 = 5(-4) - 1 - 4(-4) -8 + 3 = -20 - 1 + 16 -5 = -5

Expressions-with-variables/178231: 13) Solve 2/(x – 3) = 4/(x + 3) + 8/(x2 – 9) 14) Solve 13/(y – 1) – 3 = 1/(y – 1) 15) Solve (x + 3)/(x –1) = (x + 2)/(x – 3) thanks thanks thanks!!! 1 solutions Answer 133256 by ankor@dixie-net.com(15622)   on 2009-01-24 16:59:00 (Show Source): You can put this solution on YOUR website! 13) Solve = + Note that the third denominator is the "difference of squares"; factors to: = + this is includes the other two denominators multiply equation by (x-3)(x+3) 2(x+3) = 4(x-3) + 8 : 2x + 6 = 4x - 12 + 8 : 2x + 6 = 4x - 4 : 2x - 4x = -4 - 6 : -2x = -10 : x = +5 : always check solutions by substituting for the variable in the original equation : : 14) Solve – 3 = Multiply equation by (y-1), results: 13 - 3(y-1) = 1 : 13 - 3y + 3 = 1 ; -3y + 13 = 1 : -3y = 1 - 13 : -3y = -12 : y = +4 : : 15) Solve = Cross multiply and you have: (x+3)*(x-3) = (x-1)*(x+2) FOIL x^2 - 9 = x^2 + x - 2 : x^2 - x^2 - x = -2 + 9 : -x = +7 which is x = -7 : : Be sure to check all these solutions in the original equation