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Quadratic_Equations/199215: The hypotenuse of a right triangle is 13cm. The sum of the lengths of the two other sides is 17cm. Find the unknown lengths. 1 solutions Answer 149697 by ankor@dixie-net.com(15648)   on 2009-06-07 15:03:19 (Show Source): You can put this solution on YOUR website! The hypotenuse of a right triangle is 13cm. The sum of the lengths of the two other sides is 17cm. Find the unknown lengths. : Let x = length of one side then (17-x) = length of the other side ; Using pythag x^2 + (17-x)^2 = 13^2 FOIL x^2 + (289 - 34x + x^2) = 169 Which is 2x^2 - 34x + 289 - 169 = 0 : 2x^2 - 34x + 120 = 0 Simplify, divide by 2 x^2 - 17x + 60 = 0 Factor (x-12)(x-5) = 0 x = 12, the other side is 5 or x = 5, the other side is 12

Word_Problems_With_Coins/199219: A jar contains a total of 85 coins, all of which are either DIMES OR QUARTERS. If the coins together are worth $15.40, how many of each type of coin are in the jar? Please help -- can't figure this one out. Thank you! 1 solutions Answer 149691 by ankor@dixie-net.com(15648)   on 2009-06-07 14:29:40 (Show Source): You can put this solution on YOUR website! A jar contains a total of 85 coins, all of which are either DIMES OR QUARTERS. If the coins together are worth $15.40, how many of each type of coin are in the jar? : Let d = number of dimes Let q = number of quarters ; It says,"A jar contains a total of 85 coins,"; therefore: d + q = 85 or d = (85-q); use for substitution : "If the coins together are worth $15.40,"; therefore: .10d + .25q = 15.40 : Substitute (85-q) for d in the above equation .10(85-q) + .25q = 15.40 8.5 - .10q + .25q = 15.40 -.10q + .25q = 15.40 - 8.5 .15q = 6.90 q = q = 46 quarters then d = 85 - 46 d = 39 dimes ; : Check solution, find the values .10(39) + .25(46) = 3.90 + 11.50 = 15.40

Linear-equations/199205: Students of a class are made to stand in rows.If four students are extra in a row there would be two rows less.If four students are less in a row there would be four more rows.Find the number of students in the class? 1 solutions Answer 149687 by ankor@dixie-net.com(15648)   on 2009-06-07 14:06:42 (Show Source): You can put this solution on YOUR website! Students of a class are made to stand in rows. If four students are extra in a row there would be two rows less. If four students are less in a row there would be four more rows. Find the number of students in the class? : let s = number students in a row let r = number of rows then No of students = rs ; "If four students are extra in a row there would be two rows less." (r-2)(s+4) = rs FOIL rs + 4r - 2s - 8 = rs rs - rs + 4r - 2s - 8 = 0 4r - 2s = 8 2r - s = 4; simplified, divided by 2 : "If four students are less in a row there would be four more rows." (r+4)(s-4) = rs rs - 4r + 4s - 16 = rs rs - rs - 4r + 4s = 16 -4r + 4s = 16 -r + s = 4; simplified, divided by 4 : Adding these two equations eliminates s 2r - s = 4 -r + s = 4 ------------- r = 8 rows : find s: -8 + s = 4 s = 4 + 8 s = 12 students in a row : Find the number of students in the class? 8 * 12 = 96 students : : See if that's true "If four students are extra in a row there would be two rows less." (12+4)*(8-2) = 16 * 6 = 96 and "If four students are less in a row there would be four more rows." (12-4)*(8+4) = 8 * 12 = 96

Expressions-with-variables/199204: This question is from textbook extended mathematics for IGCSE make K the subject of the formula [square root of (k-m)]/n=1/m 1 solutions Answer 149686 by ankor@dixie-net.com(15648)   on 2009-06-07 13:30:06 (Show Source): You can put this solution on YOUR website! make K the subject of the formula = Multiply both sides by n = Square both sides k - m = Add m to both sides k = m +

Radicals/199143: This question is from textbook Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the formula S = 16Ad-2/3.(-2/3 is the power or exponent whatever they want to call it) a) Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S. 1 solutions Answer 149685 by ankor@dixie-net.com(15648)   on 2009-06-07 13:15:37 (Show Source): You can put this solution on YOUR website! Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. : For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the formula : S = : a) Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. S = S = 12960 * .00122776 S = 15.9 knots : b) Write d in terms of A and S. = S : = : d =

Quadratic_Equations/199209: I need the quadratic equation for the following twice the square of a number is the same as eighttimes the same numbers 1 solutions Answer 149682 by ankor@dixie-net.com(15648)   on 2009-06-07 12:36:59 (Show Source): You can put this solution on YOUR website! I need the quadratic equation for the following: twice the square of a number is the same as eight times the same numbers : 2x^2 = 8x 2x^2 - 8x = 0

Money_Word_Problems/199173: Maria was reviewing investment results. The account balance at the start of the year was $6700. The account earned $619. She had 3 investments: Bond fund(5% return), balance fund(8% return), and aggressive fund(12% return). She had $300 fewer than she did in balance and bond combined. How much did she have invested in the aggressive fund? 1 solutions Answer 149681 by ankor@dixie-net.com(15648)   on 2009-06-07 12:33:23 (Show Source): You can put this solution on YOUR website! Maria was reviewing investment results. The account balance at the start of the year was $6700. The account earned $619. She had 3 investments: Bond fund(5% return), balance fund(8% return), and aggressive fund(12% return). She had $300 fewer than she did in balance and bond combined. How much did she have invested in the aggressive fund? : Three funds: a = bond (5%) b = balance (8%) c = aggressive (12%) : Total invested equation: a + b + c = 6700 : "Aggressive had $300 fewer than she did in balance and bond combined." c + 300 = a + b : Looking at these two equation, we can replace a + b with (c+300) c + 300 + c = 6700 2c = 6700 - 300 2c = 6400 c = c = $3200 in the Aggressive fund

Radicals/199141: This question is from textbook America’s Cup. Since 1988 basic yacht dimensions for the America’s Cup competition have satisfied the inequality L 1.25+ radical symbol over S- 9.8 radical symbol with 3on the side and D under the sign this < underline, and 16.296 after underline< sign where L is the boat’s length in meters (m), S is the sail area in square meters, and D is the displacement in cubic meters (www.sailing.com).Ateam of naval architects is planning to build a boat with a displacement of 21.44 cubic meters (m3), a sail area of 320.13 square meters (m2), and a length of 21.22 m. Does this boat satisfy the inequality? If the length and displacement of this boat cannot be changed, then how many square meters of sail area must be removed so that the boat satisfies the inequality? 1 solutions Answer 149673 by ankor@dixie-net.com(15648)   on 2009-06-07 10:43:11 (Show Source): You can put this solution on YOUR website! L 1.25+ radical symbol over S- 9.8 radical symbol with 3on the side and D under the sign this < underline, and 16.296 after underline < sign where L is the boat’s length in meters (m), S is the sail area in square meters, and D is the displacement in cubic meters (www.sailing.com).Ateam of naval architects is planning to build a boat with a displacement of 21.44 cubic meters (m3), a sail area of 320.13 square meters (m2), and a length of 21.22 m. Does this boat satisfy the inequality? If the length and displacement of this boat cannot be changed, then how many square meters of sail area must be removed so that the boat satisfies the inequality? : I think the formula should be Substituting for L, S, D = 21.22 + 1.25(17.892) - 9.8(2.778) = : 21.22 + 22.365 - 27.225 = 16.36, slightly above 16.296 : : If the length and displacement of this boat cannot be changed, then how many square meters of sail area must be removed so that the boat satisfies the inequality? 16.36 - 16.296 = .064; the amt that it is over specs : Find the reduced sail area: = 316.3 sq/ft to meet the rule formula That's a removal of 3.83 sq/ft : : Check using this sail area = 21.22 + 1.25(17.785) - 9.8(2.778) = : 21.22 + 22.231 - 27.225 = 16.226, which is less than 16.296

Polynomials-and-rational-expressions/199132: Express the function f(x)=-2x^3+6x^2-9/2x in factored form and show all work done in order to optain the factored form of the function, also find all zeros of f(x) and state its multiplicity. 1 solutions Answer 149617 by ankor@dixie-net.com(15648)   on 2009-06-06 14:47:14 (Show Source): You can put this solution on YOUR website! f(x)=-2x^3+6x^2-9/2x in factored form write it: -2x^3 + 6x^2 - 4.5x = 0 Factor out -1, changes the signs, makes it easier to factor -x(2x^2 - 6x + 4.5) = 0 Factor the quadratic -x(2x - 3)(x - 1.5) = 0 The zeros x = 0 and 2x = 3 x = +1.5 and x = +1.5

Points-lines-and-rays/199137: 7x-5y=1 solve for x solve for y and find the intercept for x&y and the slope 1 solutions Answer 149613 by ankor@dixie-net.com(15648)   on 2009-06-06 14:32:19 (Show Source): You can put this solution on YOUR website! 7x-5y=1 : solve for x Add 5y to both sides 7x = 5y + 1 Divide both sides by 7 x = y + : solve for y subtract 7x from both sides -5y = -7x + 1 Multiply both sides by -1 to get a positive y 5y = 7x - 1 Divide both sides by 5 y = x - : and find the intercept for x&y x intercept occurs when y = 0 x = (0) + x = 0 + x intercept = : Y intercept occurs when x = 0 y = (0) - y intercept = ; and the slope use the slope intercept form which is: y = mx + b: y = x - m = is the slope ; ; a graphical illustration will help it make sense to you Note the graph intercepts the x axis at 1/7 and intercepts the y axis at -1/5

Equations/199096: A. Perform the indicated operation and express the result in simplest form: 3x+24 over x+2 times x²-6x-16 over x²-64 B. Solve for x: x+4 over 2 plus 2x over 3 equals 9 1 solutions Answer 149587 by ankor@dixie-net.com(15648)   on 2009-06-05 21:27:55 (Show Source): You can put this solution on YOUR website! A. Perform the indicated operation and express the result in simplest form: * Factor, then everything cancels except 3 * = 3 ; : B. Solve for x: + = 9 Multiply by 6 6* + 6* = 6(9) cancel denominators, results: 3(x+4) + 2(2x) = 54 : 3x + 12 + 4x = 54 : 7x = 54 - 12 : 7x = 42 x = x = 6 : Check solution in original equation + = 9 + = 9 5 + 4 = 9 :

Polynomials-and-rational-expressions/199099: This question is from textbook Intermediate Algebra An Applied Approach The larger of two printers being used to print the payroll for a major corporation requires 30 min to print the payroll. After both printers have been operating for 10 min, the larger printer malfunctions. The smaller printer requires 40 more minutes to complete the payroll. How long would it take the smaller printer working alone to print the payroll? 1 solutions Answer 149576 by ankor@dixie-net.com(15648)   on 2009-06-05 18:38:21 (Show Source): You can put this solution on YOUR website! The larger of two printers being used to print the payroll for a major corporation requires 30 min to print the payroll. After both printers have been operating for 10 min, the larger printer malfunctions. The smaller printer requires 40 more minutes to complete the payroll. How long would it take the smaller printer working alone to print the payroll? : Let x = time (in minutes) required by the small printer working alone Let the completed job = 1 : Smaller printer will operate for 10 + 40 = 50 min : + = 1 : Multiply equation by 30x, results 10x + 30(50) = 30x 1500 = 30x - 10x 1500 = 20x x = x = 75 min, small printer alone : : Check solution: 10/30 + 50/75 = 1/3 + 2/3 = 1

Miscellaneous_Word_Problems/199087: This isn't the question, but here is the info provided: 1267 pop tabs= 1 pound 1 kg=2.2 pounds 0.88 cents per kg charged how many pop tabs are needed to make $1500? Is my answer 1,705 tabs correct? 1 solutions Answer 149551 by ankor@dixie-net.com(15648)   on 2009-06-05 15:42:25 (Show Source): You can put this solution on YOUR website! 1267 pop tabs= 1 pound 1 kg=2.2 pounds 0.88 cents per kg charged how many pop tabs are needed to make $1500? : Find the number of tabs in 1 kg: 2.2 * 1267 = 2787.4 tab in 1 kg : Write a ratio equation = Cross multiply: .88x = 1500 * 2787.4 .88x = 4181100 x = x = 4,751,250 tabs to make $1500

Geometric_formulas/199049: This question is from textbook geometry can you please help me solve ((( The are of a circle is 16pie. What is its circumference? ))) 1 solutions Answer 149540 by ankor@dixie-net.com(15648)   on 2009-06-05 15:17:34 (Show Source): You can put this solution on YOUR website! The area of a circle is 16pie. What is its circumference? : Use the area of a circle formula to find the radius (r): = A = divide both sides by pi = 16 Find the square root of both sides r = r = 4 : The circumference formula: c = 25.1327

Geometric_formulas/199043: This question is from textbook geometry can you please help me solve the following and write formula insert values and show calculations. (((Find the height of a trapezoid with bases 6ft and 10ft and area 32sq ft. ))) 1 solutions Answer 149530 by ankor@dixie-net.com(15648)   on 2009-06-05 14:52:33 (Show Source): You can put this solution on YOUR website! write formula insert values and show calculations. Find the height of a trapezoid with bases 6ft and 10ft and area 32sq ft. : The Area of a trapezoid formula h(b1 + b2) = A where b1 = 6 b2 = 10 A = 32 sq/ft : h(6 + 10) = 32 Get rid of the fraction multiply by 2, add the bases, results 16h = 64 h = h = 4 ft is the height : : You can check the solution using the area formula :

Linear_Equations_And_Systems_Word_Problems/199007: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labeled with coordinates. 1 solutions Answer 149528 by ankor@dixie-net.com(15648)   on 2009-06-05 13:43:11 (Show Source): You can put this solution on YOUR website! A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. : Find the equation using the format y = ax^2 + bx + c (c=0, we can ignore that) : Using the vertex x=60, y = 25 a(60^2) + 60b = 25 3600a + 60b = 25 : Using the x intercept x=120, y=0 a(120^2) + 120b = 0 14400a + 120b = 0 : Multiply the 1st equation by 2, subtract from the 2nd equation 14400a + 120b = 0 7200a + 120b = 25 --------------------subtraction eliminates b, find a 7200a = -25 a = a = -.00694 : Find b using the 2nd equation, substitute -.00694 for a 14400(-.00964) + 120b = 0 -100 + 120b = 0 120b = 100 b = b = .833 : y = -.00694x^2 + .8333x; the equation for this parabola : 10 ft from center: 60-10 = 50 = x y = -.00694(50^2) + .8333(50) y = -17.35 + 41.665 y = 24.3 ft high, 10 ft from center : 20 ft from center: 60-20 = 40 = x y = -.00694(40^2) + .8333(40) y = -11.1 + 33.3 y = 22.2 ft high. 20 ft from center : 40 ft from center: 60-40 = 20 = x y = -.00694(20^2) + .8333(20) y = -2.8 + 16.7 y = 13.9 ft high. 40 ft from center : : The graph of this equation: : Provide a sketch representing the situation and be sure it is clearly labeled with coordinates. Your sketch should resemble this graph, you should be able to label this now

Travel_Word_Problems/198981: The distance between two cities is ninety miles, and a woman drives from one city to the other at a rate of forty-five mph. At what rate must she return if the total travel time is three hours and forty minutes? 1 solutions Answer 149523 by ankor@dixie-net.com(15648)   on 2009-06-05 09:46:16 (Show Source): You can put this solution on YOUR website! The distance between two cities is ninety miles, and a woman drives from one city to the other at a rate of forty-five mph. At what rate must she return if the total travel time is three hours and forty minutes? : Let s = speed require to return in 3 hr 40 min : Write a time equation: Time = Dist/speed : Change time to hrs: 3 & 2/3 hrs = 11/3 hrs : To time + return time = 3 hr 40 min + = Multiply equation by 45s 45s* + 45s* = 45s* Cancel denominators, results 90s + 45(90) = 15s(11) 90s + 4050 = 165s 4050 = 165s - 90s 4050 = 75s s = s = 54 mph required on the return trip ; : Check solution 90/45 + 90/54 = 2 + 1.67 = 3.67 hrs ~ 3 hr 40 min

Angles/198960: measure of angle FDE= (2x+7) and measure of angle CDE= (10x-1) and measure of angle FDC= 66 degrees. Find the measure of angle FDE and CDE. 1 solutions Answer 149456 by ankor@dixie-net.com(15648)   on 2009-06-04 16:24:03 (Show Source): You can put this solution on YOUR website! measure of angle FDE= (2x+7) and measure of angle CDE= (10x-1) and measure of angle FDC= 66 degrees. Find the measure of angle FDE and CDE. ; From the given information; 1st angle + 2nd angle = 66 degrees : 2x + 7 + 10x - 1 = 66 12x + 6 = 66 12x = 66 - 6 12x = 60 x = x = 5 : Then FDE: 2(5) + 7 = 17 and CDE: 10(5) - 1 = 49 ------------------------ and then FDC = 66 degrees

Geometric_formulas/198805: 1 solutions Answer 149419 by ankor@dixie-net.com(15648)   on 2009-06-04 10:16:47 (Show Source): You can put this solution on YOUR website! if you had a rectangle that is less than 2 times as long as it is wide, what is the formula to calculate the largest diameter of 2 equal sized circles, that you could create from this rectangle : Let x = the width then length < 2x and "largest diameter of 2 equal sized circles that you could create from this rectangle " 2d < 2x d < x

Linear-systems/198941: {-2x + y=-1 {x + y= 5 1 solutions Answer 149418 by ankor@dixie-net.com(15648)   on 2009-06-04 10:05:06 (Show Source): You can put this solution on YOUR website! -2x + y=-1 x + y = 5 multiply the 1st equation by - 1 and you have 2x - y = 1 x + y = 5 --------------additions eliminates y, find x 3x = 6 x = x = 2 : Find y by substituting 2 for x in the 2nd equation 2 + y = 5 subtract 2 from both sides y = 5 - 2 y = 3 : : Check solutions in the 1st equation -2x + y = -1 -2(2) + 3 = -4 + 3 = -1; confirms our solutions ; Not that hard, right?

Quadratic_Equations/198912: A picture frame dimesions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat? 1 solutions Answer 149417 by ankor@dixie-net.com(15648)   on 2009-06-04 09:40:11 (Show Source): You can put this solution on YOUR website! A picture frame dimensions are 20cm by 30cm. If a mat was put inside the frame that decreases the picture area by 264cm^2, how wide is the mat? : Let x = width of the mat : Find the overall area of the picture and frame: 20 * 30 = 600 sq/cm : The dimension of the picture inside the mat (20-2x)by(30-2x) Foil to find the area: A = 600 - 100x + 4x^2 : Overall area - picture area = 264 sq/cm 600 - (4x^2 - 100x + 600) = 264 : Remove the brackets (change signs) arrange as a quadratic eq -4x^2 + 100x + 600 - 600 - 264 = 0 -4x^2 + 100x - 264 = 0 Multiply eq by -1 4x^2 - 100x + 264 = 0 Simplify divide by 4 x^2 - 25x + 66 = 0 Factor (x - 22)(x - 3) = 0 Reasonable solution x = 3 cm is the width of the mat ; : Check solution Find the area of the picture (2x=6), subtract from the overall dimensions 14 * 24 = 336 then 600 - 336 = 264; confirms our solution

Travel_Word_Problems/198883: A man travels from Town x to town y at an average rate of 50mph and returns at an average rate of 40pmh. he takes 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from town x to town y. 1 solutions Answer 149376 by ankor@dixie-net.com(15648)   on 2009-06-03 20:55:16 (Show Source): You can put this solution on YOUR website! A man travels from Town x to town y at an average rate of 50mph and returns at an average rate of 40pmh. he takes 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from town x to town y. : Let d = dist of town x to town y : Write a time equation: Time = dist/speed : To time + return time = 45 mph time + 1/2 hr + = + : Multiply equation by 1800: 1800* + 1800* = 1800* + 1800* Cancel the denominators, results: 36d + 45d = 40(2d) + 900 : 81d = 80d + 900 81d - 80d = 900 d = 900 mi from town x to town y ; : The solution in original time equation (round trip = 1800 mi) 900/50 + 900/40 = 1800/45 + 1/2 18 + 22.5 = 40 + .5

Linear_Equations_And_Systems_Word_Problems/198713: Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to amke an open-top box under these conditions: I. Each box must be made by cutting small squares from each corner of a cardboard sheet. II. The box must have a volume of 48 in^3 III. The amount of cardboard waste must be minimized. What is the appropriate side length for the small squares that would be cut from the cardboard sheet? 1 solutions Answer 149271 by ankor@dixie-net.com(15648)   on 2009-06-02 21:43:44 (Show Source): You can put this solution on YOUR website! Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to make an open-top box under these conditions: : I. Each box must be made by cutting small squares from each corner of a cardboard sheet. Let the side of the small square = x then the dimension of the box: (8.5-2x) by (11-2x) by x FOIL x(93.5 - 17x - 22x +4x^2) A volume equation V = 4x^3 - 39x^2 + 93.5x : ; II. The box must have a volume of 48 in^3 4x^3 - 39x^2 + 93.5x = 48 4x^3 - 39x^2 + 93.5x - 48 = 0 : : III. The amount of cardboard waste must be minimized. Graph the above equation to find the values of x: What is the appropriate side length for the small squares that would be cut from the cardboard sheet? : The smaller solution: x ~.7"; would give us the smallest removed squares ; ; : Check our solution: 2x = 1.4 (8.5-1.4) * (11-1.4) * .7 = 7.1 * 9.6 * .7 = 47.4 ~ 48

Functions/198727: Please HELP!! A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)= -16t^2 + 30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)= -8t + 15. Can the gull catch the crab before the crab hits the water? Thanks! 1 solutions Answer 149231 by ankor@dixie-net.com(15648)   on 2009-06-02 18:53:07 (Show Source): You can put this solution on YOUR website! A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)= -16t^2 + 30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)= -8t + 15. Can the gull catch the crab before the crab hits the water? : When the gull catches the crab, they will be at the same height, so we can say: Gull ht = crab ht -8t + 15 = -16t^2 + 30 16t^2 - 8t + 15 - 30 = 0 16t^2 - 8t - 15 = 0 Factors to (4t - 5)(4t + 3) = 0 Positive solution 4t = 5 t = 1.25 sec they will be at the same height (5 ft) : A graph would would show this

absolute-value/198697: if one-half a number is subtracted from five-sixth of the number, the difference is 6. what is this number 1 solutions Answer 149223 by ankor@dixie-net.com(15648)   on 2009-06-02 17:55:06 (Show Source): You can put this solution on YOUR website! if one-half a number is subtracted from five-sixth of the number, the difference is 6. what is this number : x - x = 6 The common denominator x - x = 6 x = 6 x = 6 Multiply both sides by 3 x = 3(6) x = 18

Quadratic_Equations/198591: Solving Problems with Quadratic Equations 17. Sherri sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is $10 per photograph, and she usually sells about 30 photographs. Sherri finds that, for each reduction in price of $0.50, she can sell an additional two photographs. a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue. b) At what price will Sherri's revenue be $150? c) At what price will her maximum revenue occur? d) At what price will her revenue be $0? e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)? Thanksssssss 1 solutions Answer 149216 by ankor@dixie-net.com(15648)   on 2009-06-02 17:09:15 (Show Source): You can put this solution on YOUR website! regular price is $10 per photograph, and she usually sells about 30 photographs. Sherri finds that, for each reduction in price of $0.50, she can sell an additional two photographs. : Let x = ea 50 cent reduction & also = ea photograph increase : a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue. Revenue = price * pictures sold Rev = (10-.5x)*(30+2x) FOIL f(x) = 300 + 20x - 15x - x^2 f(x) = -x^2 + 5x + 300 : ; b) At what price will Sherri's revenue be $150? -x^2 + 5x + 300 = 150 -x^2 + 5x + 300 - 150 = 0 -x^2 + 5x + 150 = 0 Multiply equation by -1 (easier to factor) x^2 - 5x - 150 = 0 Factors to: (x-15)(x+10) = 0 Positive solution; x = 15 Price: 10 - .5(15) = $2.50 for $150 revenue ; Revenue Check: 2.50(30+2(15)) = $150 : : c) At what price will her maximum revenue occur? Find the axis of symmetry of the equation: y = -x^2 + 5x + 300 x = x = x = 2.5 price(10-.5(2.5)) = 8.75 : : d) At what price will her revenue be $0? -x^2 + 5x + 300 = 0 x^2 - 5x - 300 = 0 (x-20)(x+15) = 0 x = 20 Price: 10 - .5(20) = $0 ; : e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)? b: x=15 price reductions; about $150 c: you can see max rev occurs when x = 2.5 d: x=20, rev = 0

Exponents/198692: x to the power of 2/3 divided by x to the power of 1/3 is equal to 4 what is x? 1 solutions Answer 149203 by ankor@dixie-net.com(15648)   on 2009-06-02 15:45:05 (Show Source): You can put this solution on YOUR website! x to the power of 2/3 divided by x to the power of 1/3 is equal to 4 what is x? : = 4 Subtract exponents when you divide like terms : = 4 : = 4 ; Cube both sides: x = 64 : : Check solution on calc; enter: (64^(2/3))/(64^(1/3)) = 4

Exponential-and-logarithmic-functions/198661: I need help solving: log(3x-2)^4=12 1 solutions Answer 149202 by ankor@dixie-net.com(15648)   on 2009-06-02 15:33:52 (Show Source): You can put this solution on YOUR website! I need help solving: log equiv of exponents Divide both sides by 4 which is 3x - 2 = 1000 3x = 1000 + 2 3x = 1002 x = x = 334 : : Check solution on a calc; enter: log((3(334)-2)^4) = 12

Linear_Algebra/198623: x+2y-z=3 2x-y+z=3 3x-4y+2z=-1 1 solutions Answer 149197 by ankor@dixie-net.com(15648)   on 2009-06-02 15:10:30 (Show Source): You can put this solution on YOUR website! x + 2y - z = 3 2x - y + z = 3 3x -4y + 2z = -1 : Multiply the 1st equation by 2, add to the 3rd equation 2x + 4y - 2z = 6 3x - 4y + 2z = -1 --------------------Addition eliminates y and z, find x: 5x = 5 x = 1 : Replace x with 1 in the first two equations 1 + 2y - z = 3 2(1) - y + z = 3 : 2y - z = 3 - 1 -y + z = 3 - 2 : 2y - z = 2 -y + z = 1 --------------addition eliminates z, find y y = 3 : Use the 3rd equation to find z: 3x -4y + 2z = -1 3(1) - 4(3) + 2z = -1 3 - 12 + 2z = -1 -9 + 2z = -1 2z = -1 + 9 2z = 8 z = 4 : : Check solutions in the 2nd equation; x = 1; y = 3; z = 4 2x - y + z = 3 2(1) - 3 + 4 = 3 2 - 3 + 4 = 3

Quadratic_Equations/198658: factorise: 1) 5m2-45n2 2)10m2n2-7mn-12 3) 9a2-(3a-2b)2 4)12x2+35xy+18y2 1 solutions Answer 149173 by ankor@dixie-net.com(15648)   on 2009-06-02 10:58:05 (Show Source): You can put this solution on YOUR website! 1) 5m^2-45n^2 Factor out 5 5(m^2 - 9n^2) Factor difference of squares 5(m - 3n)(m + 3n) : 2)10m^2n^2 - 7mn - 12 mn(10mn - 7) - 12 : 3) 9a^2-(3a-2b)^2 9a^2 - (9a^2 - 12ab + 4b^2);square 3a-2b 9a^2 - 9a^2 + 12ab - 4b^2;removing brackets changes the signs 12ab - 4b^2 4b(3a- b) : 4)12x^2 + 35xy + 18y^2 This can be factored (4x + 9y)(3x + 2y)

Mixture_Word_Problems/198580: Find the cost of liter of solution when you have 70L of cranberry juice that costs $1.20 and 130L of apple juice that costs $0.80. 1 solutions Answer 149144 by ankor@dixie-net.com(15648)   on 2009-06-01 21:41:18 (Show Source): You can put this solution on YOUR website! Find the cost of liter of solution when you have 70L of cranberry juice that costs $1.20 and 130L of apple juice that costs $0.80. : Let x = the cost of the mixture : Resulting total: 70 + 130 = 200L : 200x = 1.20(70) + .80(130) : 200x = 84 + 104 x = x = $.94 cost per liter