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Quadratic_Equations/184027: seven more then 11 times a number is 6 times the square of the number 1 solutions Answer 138121 by ankor@dixie-net.com(15661)   on 2009-02-27 14:30:13 (Show Source): You can put this solution on YOUR website! Just write an equation for what it says: seven more then 11 times a number is 6 times the square of the number 11x + 7 = 6x^2 : 0 = 6x^2 - 11x - 7; our old friend, the quadratic equation! : Unless they're trying to torment us, it should factor. (2x + 1) (3x - 7) = 0 Two solutions 2x = -1 x = and 3x = +7 x = x = 2 : : Check the 1st solution using x = -.5 in the original statement: "seven more then 11 times a number is 6 times the square of the number" 11(-.5) + 7 = 6(-.5)^2 -5.5 + 7 = 6(.25) +1.5 = +1.5 : You can check the the x = solution using a calc:

Systems-of-equations/184065: Okay I am so lost on this question, so any help will be greatly appreciated. Philip has 10 coins in his pocket. Philip has the same number of pennies as quarters and the same number of dimes as nickels. He also has one more nickel than he does pennies. If he has 97 cents, how many coins of each type does he have? 1 solutions Answer 138118 by ankor@dixie-net.com(15661)   on 2009-02-27 14:09:57 (Show Source): You can put this solution on YOUR website! Philip has 10 coins in his pocket. Philip has the same number of pennies as quarters and the same number of dimes as nickels. He also has one more nickel than he does pennies. If he has 97 cents, how many coins of each type does he have? : let p, n, d, q = no. of pennies, nickels, dimes and quarter respectively : Write an equation for each statement: : "Philip has 10 coins in his pocket." p + n + d + q = 10 : " Philip has the same number of pennies as quarters" p = q : " and the same number of dimes as nickels." d = n : "He also has one more nickel than he does pennies." n = (p + 1) : " If he has 97 cents," 1p + 5n + 10d + 25q = 97 : how many coins of each type does he have? : Using the given equations, replace p with q, and d with n in the 1st equation q + n + n + q = 10 2n + 2q = 10 simplify, divide by 2 n + q = 5 n = (5-q) good for substitution : Do the same in the total value equation 1q + 5n + 10n + 25q = 97 15n + 26q = 97 : Substitute (5-q) for n 15(5-q) + 26q = 97 75 - 15q + 26q = 97 11q = 97 - 75 11q = 22 q = q = 2 quarters : we know p = q, therefore p = 2 pennies : we also know n = p + 1, therefore n = 3 nickels : we know d = n, therefore d = 3 dimes : Check solution, in total coin equation 2 + 3 + 3 + 2 = 10 : You can check solution in total value equation 1q + 5n + 10n + 25q =

test/183994: 1.Double the sum of a number and 6 is the same as 15 more than triple the same number. Find the number 2.Four less than seven time is the same as nine times the number . Find the number 3.8-x(2) for x = -3 4.-2x(2) - 5z = x= -2 z = -4 1 solutions Answer 138116 by ankor@dixie-net.com(15661)   on 2009-02-27 13:47:07 (Show Source): You can put this solution on YOUR website! 1.Double the sum of a number and 6 is the same as 15 more than triple the same number. Find the number : Write an equation for what it says, let x = "the number" 2(x+6) = 3x + 15 2x + 12 = 3x + 15 12 - 15 = 3x - 2x -3 = x : check solution in the original statement: 2(-3+6) = 3(-3) + 15 2(3) = -9 + 15 : : 2.Four less than seven time is the same as nine times the number . Find the number : 7x - 4 = 9x 7x - 9x = +4 -2x = 4 x = x = -2 : Check solution 7(-2) - 4 = 9(-2) -14 - 4 = -18 : : Assume you mean: 3. 8 - x^2; for x = -3 8 - (-3)^2) 8 - (+9) 8 - 9 = -1 : : 4.-2x^2 - 5z = x= -2 z = -4 -2*(-2)^2 - 5(-4) = -2(4) - (-20) = -8 + 20 = +12

Pythagorean-theorem/183991: It gave me triangles to see if they had right angles. There were 4 of them. Then it asked me to find the sum be of the non-right angles and what i noticed. Then it asked me if i were to draw a different right triangle, what would the sum be of it's non-right angles and how i know? 1 solutions Answer 138105 by ankor@dixie-net.com(15661)   on 2009-02-27 11:39:25 (Show Source): You can put this solution on YOUR website! It gave me triangles to see if they had right angles. There were 4 of them. Then it asked me to find the sum be of the non-right angles and what i noticed. Then it asked me if i were to draw a different right triangle, what would the sum be of it's non-right angles and how i know? : You know that in any triangle, all three angles add up to 180 degrees, right? : You know that a right triangle has one 90 degree angle, that means the other two angles have to add up to 90 to give a total of 180 degrees. We can say that in any group of 4 right triangles, the total of the non-right angles, will have to be 4 * 90 = 360 degrees. right?

Graphs/184076: i dont know what the given lines of y1= -2/7x-2 and y2= 5/3x + 17/3 i dont know what the graph would look like, i dont have a graphing calculator, i can only use points with integer coordinates. 1 solutions Answer 138102 by ankor@dixie-net.com(15661)   on 2009-02-27 11:28:55 (Show Source): You can put this solution on YOUR website! I don't know what the given lines of y1 = -2/7x-2 and y2= 5/3x + 17/3. I don't know what the graph would look like, I don't have a graphing calculator, I can only use points with integer coordinates. ; We can choose which values for x we want to plot; let's use values that cancel the fraction and give integer values for x and y, if possible. : On the 1st equation y1 = x - 2 : find y1 when x = +7 y1 = (7) - 2 y1 = -2 - 2 y1 = -4 our 1st coordinate: 7,-4 : find y1 when x = -7 y1 = (-7) - 2 y1 = +2 - 2 y1 = 0 our 2nd coordinate: -7, 0 : plot/join these two points on graph paper +/-12 scale will work. should look like this : : The 2nd equation: y2 = x + : find y2 when x = +3 y2 = (3) + y2 = 5 + y2 = + y2 = y2 = 10 our 1st coordinate: +3, 10 : find y2 when x = -3 y2 = (-3) + y2 = -5 + y2 = + y2 = y2 = our 2st coordinate: -3, : plot/join these two points on the same graph paper. should look like this : The point of intersection x,y are not integers but we can't do anything about that. ; Did this make sense to you? Any questions?

Travel_Word_Problems/184082: A man rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km upstream as he takes in going same distance downstream. find the rate at which water is flowing. 1 solutions Answer 138093 by ankor@dixie-net.com(15661)   on 2009-02-27 10:21:21 (Show Source): You can put this solution on YOUR website! A man rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km upstream as he takes in going same distance downstream. find the rate at which water is flowing. : Let x = the rate water is flowing then (5+x) = boat speed downstream and (5-x) = boat speed upstream ; Let d = distance one way ; write a time equation; Time = : upstream time = 3 times downstream time = 3() = Cross multiply d(5+x) = 3d(5-x) : divide both sides d and eliminate it: 5 + x = 3(5 - x) ; 5 + x = 15 - 3x : x + 3x = 15 - 5 : 4x = 10 x = x = 2.5 km/hr is the rate of the current : : Check solution by finding the distances, should be equal: 5 + 2.5 = 7.5 3(5 - 2.5) = 7.5 :

Polynomials-and-rational-expressions/184077: I am having a problem with a word problem for my math class. The problem is: If a basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hang time function V=48T^2. Here is what the example says to do. To solve for T, first multiply by 1/48 to get T^2=20/48. Because hang time is positive, you can take the positive square root get T=squart20/48. I get that part, what I don't get is how did they get that T=squart20/48=0.6 seconds. How would I get the seconds if the equation is T=squart35/48? 1 solutions Answer 138092 by ankor@dixie-net.com(15661)   on 2009-02-27 09:45:41 (Show Source): You can put this solution on YOUR website! If a basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hang time function V=48T^2. : Use basic algebra rules to solve for T, (isolate T by itself on the left) write it: 48T^2 = V : Substitute 20 for T 48T^2 = 20 : Divide both sides by 48 T^2 = : Find the square root of both sides to change T^2 to just T T = : Enter into a calc, it will = .64549.. rounded to .6 sec ; You would do it exactly the same way if it were 35/48 : Does this make sense to you now?

Travel_Word_Problems/183983: It takes Mary 30 minuites to walk uphill 1 Km from her home to school, but it takes her only 10 minuites to walk from school to home along the same route. What is her average speed, in Km/hr, for the round trip? 1 solutions Answer 138056 by ankor@dixie-net.com(15661)   on 2009-02-26 20:59:55 (Show Source): You can put this solution on YOUR website! It takes Mary 30 minutes to walk uphill 1 Km from her home to school, but it takes her only 10 minutes to walk from school to home along the same route. What is her average speed, in Km/hr, for the round trip? : Round trip dist = 2 km : Change the times to hrs: 30/60 = hr 10/60 = hr : Total time = hr : Speed = When dividing, invert the dividing fraction and multiply: 2 * = = 3 km/h is the average speed : :

Equations/184000: This question is from textbook On her way to NY, Jenny spent the same amount for gasoline each time she stopped for gas. She paid 239.9 cents per gallon the first time; 249.9 cpg the second time and 259.9 cpg the third time. What was the average price per gallon to the nearest tenth of a cent for the gasoline that she bought? 1 solutions Answer 138049 by ankor@dixie-net.com(15661)   on 2009-02-26 20:32:27 (Show Source): You can put this solution on YOUR website! On her way to NY, Jenny spent the same amount for gasoline each time she stopped for gas. She paid 239.9 cents per gallon the first time; 249.9 cpg the second time and 259.9 cpg the third time. What was the average price per gallon to the nearest tenth of a cent for the gasoline that she bought? : Assign a value for each fill-up: 3000 cent : Find the number of gallon purchased each time: 1st time: = 12.505 gal 2nd time: = 12.005 gal 3rd time: = 11.543 gal ---------------------------------------- total number of gallons: 36.053 : To find the average price, divide the total cost (3*3000). by the total gallons: = 249.6 cents is the av cost per gallon

Equations/182975: The quotient of three times a number and 5 amounts to half the number increased by two. How do I write the equations or inequality to represent the unknowns? 1 solutions Answer 137424 by ankor@dixie-net.com(15661)   on 2009-02-21 16:33:19 (Show Source): You can put this solution on YOUR website! The quotient of three times a number and 5 amounts to half the number increased by two. How do I write the equations or inequality to represent the unknowns? : Let x = "the number" : = x + 2

Age_Word_Problems/182797: Mara's father is 12 years older than twice her age. If last year he was exactly three times her age, how old are each now? 1 solutions Answer 137298 by ankor@dixie-net.com(15661)   on 2009-02-20 13:42:09 (Show Source): You can put this solution on YOUR website! Let M = Mara's age now Let F = Father's age now : Write an equation for each statement: "Mara's father is 12 years older than twice her age." F = 2M + 12 : " If last year he was exactly three times her age," F - 1 = 3M F = 3M + 1 : how old are each now? : Substitute (2M+12) for F in the above equation: 2M + 12 = 3M + 1 12 - 1 = 3M - 2M M = 11 is Mara's present age then 2(11) + 12 = 34 yrs is Father's present age : : Check solution in the statement: "last year he was exactly three times her age," 34 - 1 = 3(11)

Linear-systems/182559: A merchant blends tea that sells for $2.85lb with tea that sells for $2.60lb to produce a 90lb mixture that sells for $2.75lb. How many pounds of each type of tea does the merchabt use in the blend? 1 solutions Answer 137057 by ankor@dixie-net.com(15661)   on 2009-02-18 15:39:16 (Show Source): You can put this solution on YOUR website! A merchant blends tea that sells for $2.85 lb with tea that sells for $2.60 lb to produce a 90 lb mixture that sells for $2.75 lab. How many pounds of each type of tea does the merchant use in the blend? : Let x = amt of $2.85 lb tea : It says the resulting amt will be 90 lb, therefore: (90-x) = amt of $2.60 lb tea : 2.85x + 2.60(90-x) = 2.75(90) : 2.85x + 234 - 2.6x = 247.5 : 2.85x - 2.60x = 247.5 - 234 : .25x = 13.5 x = x = 54 lb of $2.85 lb tea required then 90 - 54 = 36 lb of $2.60 lb required ; ; Check solution; 2.85(54) + 2.6(36) = 2.75(90) 153.9 + 93.6 = 247.5

Numbers_Word_Problems/182525: Q. (((One number is 1 more than another doubled. If their difference is 10, find the number (use algebra))). 1 solutions Answer 137040 by ankor@dixie-net.com(15661)   on 2009-02-18 13:44:09 (Show Source): You can put this solution on YOUR website! Let x = "one number" Let y = "another number" : "One number is 1 more than another doubled." x = 2y + 1 : If their difference is 10, find the number x - y = 10 : Substitute (2y+1) for x in the above equation, find y 2y + 1 - y = 10 2y - y = 10 - 1 y = 9 : x = 2y + 1 x = 2(9) +1 x = 19 is "the number" ; ; Check solution in the statement: "One number is 1 more than another doubled" 19 = 2(2) + 1

Miscellaneous_Word_Problems/182445: There are two intake pipes to a large storage tank. Using the smaller pipe alone, it takes twice as long to fill the tank as it does using the larger pipe alone. The tank can be filled in eight minutes if both pipes are used. How long will it take using only the smaller pipe? Explain your answer using mathematical models. 1 solutions Answer 136953 by ankor@dixie-net.com(15661)   on 2009-02-17 21:26:11 (Show Source): You can put this solution on YOUR website! There are two intake pipes to a large storage tank. Using the smaller pipe alone, it takes twice as long to fill the tank as it does using the larger pipe alone. The tank can be filled in eight minutes if both pipes are used. How long will it take using only the smaller pipe? Explain your answer using mathematical models. : Let t = time required by the smaller pipe alone (in minutes) ; It say the smaller pipe takes twice as long, therefore: .5t = time required by the larger pipe alone ; Let the completed job = 1 (a full tank) : Each pipe does a fraction of the job and the sum of those fractions = 1 : + = 1 multiply equation by t 2(8) + 8 = t 16 + 8 = t t = 24 minutes the small pipe alone : : Prove this: ( the larger pipe can fill it in 12 min alone) + = + = 1

Linear_Equations_And_Systems_Word_Problems/182346: A man is carrying rice on a journey. He passes through three custom stations. At the first he gives 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; and at the third, he gives up 1/4 of what remains. After passing through all three custom stations, he has 6 pounds less than he started with. How much rice ded he have when he started? 1 solutions Answer 136937 by ankor@dixie-net.com(15661)   on 2009-02-17 19:50:57 (Show Source): You can put this solution on YOUR website! A man is carrying rice on a journey. He passes through three custom stations. At the first he gives 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; and at the third, he gives up 1/4 of what remains. After passing through all three custom stations, he has 6 pounds less than he started with. How much rice did he have when he started? ; Let x = amt started with ; "the first he gives 1/3 of his rice;" the leaves him with x : "at the second he is allowed to keep 1/3 of what is left;" * x = x left : "at the third, he gives up 1/4 of what remains. (that means he kept 3/4) * x = x - 6 (he ended up with 6 lb less than when he started) x = x - 6 x = x - 6 Multiply equation by 6 x = 6x - 36 x - 6x = -36 -5x = -36 x = x = 7.2 lbs

Miscellaneous_Word_Problems/182345: Megan has $100 more than Andrew. After Megan spends $20 on groceries, she will still have 5 times as much money as Andrew. How much money does Andrew have? 1 solutions Answer 136934 by ankor@dixie-net.com(15661)   on 2009-02-17 19:30:25 (Show Source): You can put this solution on YOUR website! Megan has $100 more than Andrew. After Megan spends $20 on groceries, she will still have 5 times as much money as Andrew. How much money does Andrew have? : Let A = the money Andrew has then (A+100) = money Megan has : Write an equation for what it says: "Megan spends $20 on groceries, she will still have 5 times as much money as Andrew." (A+100) - 20 = 5A A + 100 - 20 = 5A A + 80 = 5A 80 = 5A - A 80 = 4A A = A = $20 Andrew has : : Check solution 120 - 20 = 5(20)

Miscellaneous_Word_Problems/182361: The amount of gold jewelry and other products is measured in karats (K), where 24K represents pure gold. The mark 14K on a chain indicates that the ratio between the mass of the gold in the chain and the mass of the chain is 14:24. If a gold ring is marked 18K and it weighs 0.4 oz, what is the value of the gold rinf if pure gold is valued at $300 per oz? 1 solutions Answer 136932 by ankor@dixie-net.com(15661)   on 2009-02-17 19:21:57 (Show Source): You can put this solution on YOUR website! The amount of gold jewelry and other products is measured in karats (K), where 24K represents pure gold. The mark 14K on a chain indicates that the ratio between the mass of the gold in the chain and the mass of the chain is 14:24. If a gold ring is marked 18K and it weighs 0.4 oz, what is the value of the gold ring if pure gold is valued at $300 per oz? : * .4 * 300 = $90.00

Graphs/182319: Adult tickets to the school musical are $5 and student tickets are $2. There are 300 seats in the auditorium where the musical is being performed. The goal for ticket sales for one performance is at least $900. Make a graph showing the number of each kind of ticket needed to be sold to rach the goal. List theree possilbe solutions. 1 solutions Answer 136930 by ankor@dixie-net.com(15661)   on 2009-02-17 19:16:18 (Show Source): You can put this solution on YOUR website! Adult tickets to the school musical are $5 and student tickets are $2. There are 300 seats in the auditorium where the musical is being performed. The goal for ticket sales for one performance is at least $900. Make a graph showing the number of each kind of ticket needed to be sold to reach the goal. : Let x = no. of adult tickets Let y = no. of student tickets : x + y =< 300 y = 300-x; graph this equation (purple line : 5x + 2y => 900 2y = 900-5x divide both sides by 2 y = 450 - 2.5x; graph this equation, (green line) The area of feasibility: At or above the green line (5x + 2y => 900) and At or below the purple line (x + y =< 300) List three possible solutions. : You can see the x values (adults) between 150 and 250 would satisfy x = 200 y = 300 - 200 y = 100 : 5(200) + 2(100) = $1200; 200 adults & 100 students is a good solution ; I'll let you choose two other solutions

logarithm/182284: I need help with assignment please.... Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Form each of the following: A linear equation in one variable A linear equation in two variables A quadratic equation A polynomial of three terms An exponential function A logarithmic function 1 solutions Answer 136882 by ankor@dixie-net.com(15661)   on 2009-02-17 15:20:22 (Show Source): You can put this solution on YOUR website! Give an example of an exponential function. f(x) = 2^x : Convert this exponential function to a logarithmic function. f(x) = x*log(2) : Plot the graph of both the functions and post to the discussion forum. Plot using x=0 to x=5 green is the logarithmic : Form each of the following: A linear equation in one variable 2x + 5 = 13 : A linear equation in two variables 2x + y = 13 : A quadratic equation y = x^2 + 5x + 6 : A polynomial of three terms x^2 + 5x = 6 : An exponential function f(x) = 4^x : A logarithmic function f(x) = x*log(4)

Equations/182369: How do I figure out this question? If sally paints a house in 4 hours and sam does the same house in 6 hours, how long will it take them both to do the same house? 1 solutions Answer 136870 by ankor@dixie-net.com(15661)   on 2009-02-17 14:55:58 (Show Source): You can put this solution on YOUR website! If sally paints a house in 4 hours and sam does the same house in 6 hours, how long will it take them both to do the same house? : A typical shared work problem : let t = time required when they work together Let the completed job = 1 (the painting of the house) : + = 1 Multiply equation by the LCM to get rid of the denominators 12* + 12* = 12(1) Results 3t + 2t = 12 5t = 12 t = t = 2.4 hrs working together or; .4 * 60 = 24 min, so 2 hrs 24 min : : Check solution in original equation: + = 1 .6 + .4 = 1

Age_Word_Problems/182293: Dan's father was forty years older when the son was 12 years old. How many years must be added to Dan's age so that he will be 8 years older than one-fourth of his father's age? 1 solutions Answer 136867 by ankor@dixie-net.com(15661)   on 2009-02-17 14:32:14 (Show Source): You can put this solution on YOUR website! Dan's father was forty years older when the son was 12 years old. How many years must be added to Dan's age so that he will be 8 years older than one-fourth of his father's age? : "Dan's father was forty years older when the son was 12 years old." : Father's age = 12 + 40 = 52 Dan's age = 12 : How many years must be added to Dan's age so that he will be 8 years older than one-fourth of his father's age? : Let x = no. of yr to be added : D + x = .25F + 8 Substitute the ages of F and D 12 + x = .25(52) + 8 12 + x = 13 + 8 x = 21 - 12 x = 9 yrs to be added ; : See if that is true in the statement: " 9 years must be added to Dan's age so that he will be 8 years older than one-fourth of his father's age? " 12 + 9 = .25(52) + 8 21 = 21

Functions/182249: This question is from textbook algebra and trigonometry The sum of two numbers is 20. If one number is x, then the other number is ____. Their product is p(x)= _____. Find the maximum value of p. Write a quadratic function to solve. 1 solutions Answer 136866 by ankor@dixie-net.com(15661)   on 2009-02-17 13:56:57 (Show Source): You can put this solution on YOUR website! The sum of two numbers is 20. If one number is x, then the other number is ____. It's quite obvious the other number = (20-x) ; Their product is p(x)= _____. p(x) = x(20-x) p(x) = -x^2 + 20x : : Find the maximum value of p. Find the axis of symmetry using the formula x = -b/(2a) x = x = x = +10 : Find max p(x), substitute 10 for x in the equation p(x) = -(10^2) + 20(10) p(x) = -100 + 200 p(x) = +100 : : Write a quadratic function to solve. -x^2 + 20x = 0 Factor out -x -x(x - 20) = 0 therefore: x = 0 and x = +20

Graphs/182139: I would appreciate the help with this problem, Given A. Find the x- and y-intercepts of the graph of the equation. B. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. I would be thankful for any help on atleast part A. I think that the y-intercept is undefined. Thanks 1 solutions Answer 136809 by ankor@dixie-net.com(15661)   on 2009-02-16 21:56:35 (Show Source): You can put this solution on YOUR website! Given y =(x^2-4)/x A. Find the x- and y-intercepts of the graph of the equation. You're right y intercept occurs when x = 0, that can't be (/0) so undefined Find the x intercept: (x^2 - 4)/x = 0 multiply both sides by x x^2 - 4 = 0 difference of squares, factors to: (x-2)(x+2) = 0 x = 2, -2 are the intercepts Looks like this B. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. : It is symmetrical with respect to the origin

Mixture_Word_Problems/182195: Television sets. What does it mean to refer to a 20 in TV st or a 25 in TV set? Such units refer to the diagnal of the screen. A 30 in TV set also has a width of 24 inches. What is its height? The hight of a 30 in TV would be?????? Please help me with this. I understand the measurment of the screen but don't understand how to get the height. 1 solutions Answer 136805 by ankor@dixie-net.com(15661)   on 2009-02-16 21:42:00 (Show Source): You can put this solution on YOUR website! Television sets. What does it mean to refer to a 20 in TV st or a 25 in TV set? Such units refer to the diagonal of the screen. A 30 in TV set also has a width of 24 inches. What is its height? The height of a 30 in TV would be?????? : Remember Pythagorus: a^2 + b^2 = c^2 c = the diagonal, and a and b are the width and height : A TV with a 30" screen and a width of 24" a = 24 c = 30 b = height : 24^2 + b^2 = 30^2 576 + b^2 = 900 b^2 = 900 - 576 b^2 = 324 b = b = 18" is the height of 30" TV : was this the help you needed?

Radicals/182132: This question is from textbook college algebra the problem is radical 3+2n + radical 2-2n =3, when i type radical it means the 3+2n and 2-2n are under the radical sign. i hope you can help me understand. 1 solutions Answer 136776 by ankor@dixie-net.com(15661)   on 2009-02-16 19:46:54 (Show Source): You can put this solution on YOUR website! the problem is radical 3+2n + radical 2-2n = 3, : + = 3 : = 3 - square both sides: 3 + 2n = (3 - )^2 FOIL the right side 3 + 2n = 9 - 6 + (2-2n) : 3 + 2n = 9 + 2 - - 2n : 3 + 2n = 11 - - 2n : 3 - 11 + 2n + 2n = - : 4n - 8 = - : square both sides, FOIL the left side 16n^2 - 64n + 64 = 36(2-2n) : 16n^2 - 64n + 64 = 72 - 72n : 16n^2 - 64n + 72n + 64 - 72 = 0 : 16n^2 + 8n - 8 = 0 Simplify, divide by 8 2n^2 + n - 1 = 0 Factors to (2n - 1)(n + 1) = 0 Two solutions: n = n = -1 : : Check both solution in original equation: n = .5 + = 3 + = 3 + = 3; a good solution : n = -1 + = 3 + = 3; also a good solution

Travel_Word_Problems/182159: John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing? 1 solutions Answer 136772 by ankor@dixie-net.com(15661)   on 2009-02-16 18:50:43 (Show Source): You can put this solution on YOUR website! John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing? ; Max area for a given perimeter is a square, therefore s = s = 12.247 ft Using natural numbers: square field 12 by 12 (only 48 m of fencing) But that is only 144 sq/m : If you have to have 150 sq/m and the dimensions have to be integers, 15 by 10 would be my answer. This requires 50 m of fencing

Graphs/182192: The question asks to create a graph of the followinf lines y=3/5x-4 y=-1/3x+2 and y=-5x-7 and indicate the points of intersection which i think i did because the next section says you should now have a triangle formed by the intersection of the three lines. Which i have graphed and it does make a triangle now it says to find the area of the triangle using two methods Method 1 A=1/2 bh Method 2 heron's formula the second one is stressing me out my instructor has not taught us this and i'm supposed to figure it out on my own but i just keep getting lost trying to find the area of the triangle.Any help will be greatly appreciated 1 solutions Answer 136755 by ankor@dixie-net.com(15661)   on 2009-02-16 16:49:55 (Show Source): You can put this solution on YOUR website! The question asks to create a graph of the followinf lines y=3/5x-4 y=-1/3x+2 and y=-5x-7 and indicate the points of intersection which i think i did because the next section says you should now have a triangle formed by the intersection of the three lines. Which i have graphed and it does make a triangle now it says to find the area of the triangle using two methods Method 1 A=1/2 bh Method 2 heron's formula : Hero's formula states (where a,b,c are lengths of the 3 sides) s = then the area of a triangle is given by: A = : you have to know the lengths of the 3 sides which you can find using the x/y coordinates of the three intersections and the the distance formula: d = ; does this help you?

Linear_Equations_And_Systems_Word_Problems/182080: hey guys this is a two part problem not doing so great on I could use your help please. 115. Kepler’s third law. According to Kepler’s third law of planetary motion, the ratio t^2/r^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units (AU), and T is the number of years it takes for one complete orbit of the sun. Jupiter orbits the sun in 11.86 years with an average radius of 5.2 AU, whereas Saturn orbits the sun in 29.46 years. Find the average radius of the orbit of Saturn. (One AU is the distance from the earth to the sun.) 116. Orbit of Venus. If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun? Use the information in question115 1 solutions Answer 136748 by ankor@dixie-net.com(15661)   on 2009-02-16 16:11:29 (Show Source): You can put this solution on YOUR website! 115. Kepler’s third law. According to Kepler’s third law of planetary motion, the ratio t^2/r^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units (AU), and T is the number of years it takes for one complete orbit of the sun. Jupiter orbits the sun in 11.86 years with an average radius of 5.2 AU, whereas Saturn orbits the sun in 29.46 years. Find the average radius of the orbit of Saturn. (One AU is the distance from the earth to the sun.) : = 1 As you can see by the data given about Jupiter = ~ 1 : to find the r of Saturn: 1 = 1 = therefore r^3 = 867.8916 r = 867.8916^(1/3) r = 9.54 au is the radius of the orbit of Saturn 116. Orbit of Venus. If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun? Use the information in question115 ; Find the yrs for Venus to complete 1 orbit = 1 = 1 t^2 = .3779 t = t = .6147 yrs or .6714 * 365 = 223.4 days

Rational-functions/182117: This question is from textbook Algebra2 Complete parts a-c for each quadratic equation a) find the value of the discriminant b) describe the number and type of roots c) find the exact solutions by using the Quadratic Formula 18) -12x^2+5x+2=0 1 solutions Answer 136724 by ankor@dixie-net.com(15661)   on 2009-02-16 13:27:15 (Show Source): You can put this solution on YOUR website! 18) -12x^2 + 5x + 2 = 0 : a) find the value of the discriminant discrim = b^2 - 4*a*c In this equation: a=-12; b=5; c=2, so we have d = 5^2 + 4 * -12 * 2 d = 25 - (-96) d = 25 + 96 d = +121 : b) describe the number and type of roots d > 0 therefore, two different real roots : c) find the exact solutions by using the Quadratic Formula we already found the value of the discriminant, so we can write it Two solutions: and

Linear-systems/182114: Hi I have 88 coins to the value of $11.40,I have some 5 cents,25 cents and three time more 10cents then 25 cents.How many of each tipe of coins do I have? How do I put it in a equation to solve it? Thanks Vasea 1 solutions Answer 136712 by ankor@dixie-net.com(15661)   on 2009-02-16 10:36:42 (Show Source): You can put this solution on YOUR website! I have 88 coins to the value of $11.40,I have some 5 cents, 25 cents and three time more 10 cents than 25 cents. How many of each type of coins do I have? : Let n = no. of nickels (5 cents) Let d = no. of dimes(10 cents) Let q = no. of quarters{25 cents) : Write an equation for each statement : "I have 88 coins" n + d + q = 88 : " to the value of $11.40," .05n + .10d + .25q = 11.40 : "three times more 10 cents then 25 cents." d = 3q : Using the 1st equation, replace d with 3q n + 3q + q = 88 n + 4q = 88 : Using the 2nd equation, do the same .05n + .10(3q) + .25q = 11.40 .05n + .30q+ .25q = 11.40 .05n + .55q = 11.40 : Multiply the above equation by 20, this makes .05 = 1; subtract (n + 4q = 88) n + 11q = 228 n + 4q = 88 -----------------subtraction eliminates n, find d 7q = 140 q = q = 20 quarters : Use n + 4q = 88 to find n n + 4(20) = 88 n + 80 = 88 n = 88 - 80 n = 8 nickels : we know d = 3q d = 3(20) d = 60 dimes : Check solution in the $ equation .05(8) + .10(60) + .25(20) = .40 + 6.00 + 5.00 = 11.40

Travel_Word_Problems/182118: Please help me solve this. I have no idea! At the beginning of a walk, Roberto and Juanita are 3.3 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other they meet in 1 hour. What are Roberto and Juanita's speeds? Thank you so much! 1 solutions Answer 136708 by ankor@dixie-net.com(15661)   on 2009-02-16 08:29:53 (Show Source): You can put this solution on YOUR website! At the beginning of a walk, Roberto and Juanita are 3.3 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other they meet in 1 hour. What are Roberto and Juanita's speeds? : Let x = R's speed Let y = J's speed : when they walk the same direction the speeds are subtracted when they walk toward each other the speeds are added : write a distance equation for each 11(x - y) = 3.3 and 1(x + y) = 3.3 : Simplify the 1st equation, divide by 11, then add to the 2nd equation; x - y = .3 x + y = 3.3 -------------adding eliminates y 2x = 3.6 x = x = 1.8 mph is R's speed : find y using x + y = 3.3 1.8 + y = 3.3 y = 3.3 - 1.8 y = 1.5 mph is J's speed : : Check solution in 1st original equation 11(1.8-1.5) = 11 * .3 = 3.3; confirms our solution