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 Quadratic_Equations/551010: The sum of the two roots of a quadratic equation is 5 and their product is -6. What could be the equation?1 solutions Answer 359328 by ankor@dixie-net.com(15646)   on 2011-12-30 08:37:57 (Show Source): You can put this solution on YOUR website!The sum of the two roots of a quadratic equation is 5 and their product is -6. What could be the equation? : let the two roots be a and b a + b = 5 b = (5-a) and ab = -6 so we have a(5-a) = -6 5a - a^2 = -6 0 = a^2 - 5a - 6 could be the equation Factors to (a-6)(a+1)= 0 two solutions a=6, then b=-1 a=-1 then b=6
 Numbers_Word_Problems/550913: If x is an even number, what is the quotient of the next greater even number divided by the next greater odd number?1 solutions Answer 359264 by ankor@dixie-net.com(15646)   on 2011-12-29 21:36:28 (Show Source): You can put this solution on YOUR website!How about:
 Linear-equations/550909: Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this. 5√-1/321 solutions Answer 359262 by ankor@dixie-net.com(15646)   on 2011-12-29 21:33:09 (Show Source): You can put this solution on YOUR website!If a root cannot be simplified, state this. 5√-1/32 Get rid of the neg using : rewrite the fraction to extract the square root of 1/64
 Money_Word_Problems/550937: I deposit 2800 at 4% for 1 year how much will I earn at the end of year? what would be my account balance at end of year? 1 solutions Answer 359261 by ankor@dixie-net.com(15646)   on 2011-12-29 21:23:00 (Show Source): You can put this solution on YOUR website!I deposit 2800 at 4% for 1 year how much will I earn at the end of year? Since it is for just one year, just multiply I = .04(2800) I = \$112 earned in 1 yr : what would be my account balance at end of year? add the interest to the principal 2800 + 112 = \$2912
 Linear_Equations_And_Systems_Word_Problems/550952: a teacher is buying school supplies company A is offering a discount for every dollar spent where as Company B is giving a higher discount for ever dollar spent over 20 dollars determine which is a better deal. i cant figure out how to put both of the into an equation form and i dont know if i should use substituion method or elimination because i dont know how much the teacher spent or how much the discount is1 solutions Answer 359250 by ankor@dixie-net.com(15646)   on 2011-12-29 20:23:55 (Show Source): You can put this solution on YOUR website!a teacher is buying school supplies company A is offering a discount for every dollar spent where as Company B is giving a higher discount for ever dollar spent over 20 dollars determine which is a better deal : You are right there is so little information here, that it almost useless. The only thing that you can say for sure is: Co. A is the better deal for any amt \$20 or less. : After that, the amt of the discounts determine how much more than \$20 is Co. B a better deal. : A poor problem indeed, obviously contrived to torment the students.
 Linear_Equations_And_Systems_Word_Problems/550918: Emma, Jackson, and Nicholas have been selling raffle tickets to raise money for the math club. Emma sold 5 less than twice as many tickets as Nicholas. Jackson sold 10 more than twice as many as Nicholas. Together the three sold 180 tickets. How many did each student sell?1 solutions Answer 359246 by ankor@dixie-net.com(15646)   on 2011-12-29 20:11:30 (Show Source): You can put this solution on YOUR website!Emma, Jackson, and Nicholas have been selling raffle tickets to raise money for the math club. : Write an equation for each statement: : Emma sold 5 less than twice as many tickets as Nicholas. e = 2n-5 : Jackson sold 10 more than twice as many as Nicholas. j = 2n + 10 : Together the three sold 180 tickets. e + j + n = 180 From the 1st two statements we can substitute for e and j (2n-5) + (2n+10) + n = 180 2n + 2n + n - 5 + 10 = 180 5n + 5 = 180 5n = 180-5 n = n = 35 tickets solve by Nicholas : I'll let you find e and j, see that all three add up to 180 How many did each student sell?
 Linear-equations/550917: y-4=-1/2(x-6) into standard form?1 solutions Answer 359234 by ankor@dixie-net.com(15646)   on 2011-12-29 18:11:26 (Show Source): You can put this solution on YOUR website!y-4 = -1/2(x-6) into standard form? : y - 4 = -.5x + 3 +.5x + y = 3 + 4 .5x + y = 7 Get rid of the decimal, mult by 10 5x + 10y = 70 is the standard form
 Word_Problems_With_Coins/550874: A change purse contains a total of 100 nickels and dimes. The total value of the coins is \$7. How many coins of each type does the purse contain? Solve and write a system of equations to model the situation.1 solutions Answer 359226 by ankor@dixie-net.com(15646)   on 2011-12-29 17:51:43 (Show Source): You can put this solution on YOUR website!A change purse contains a total of 100 nickels and dimes. n + d = 100 n = (100-d) : The total value of the coins is \$7. .05n + .10d = 7.00 replace n in with (100-d) .05(100-d) + .10d = 7.00 5 - .05d + .10d = 7.00 -.05d + .10d = 7 - 5 .05d = 2 d = d = 40 dimes : I'll let you find the number of nickels. check the solutions in the \$\$ equation :
 Evaluation_Word_Problems/550804: A motor boat travels at the rate of 50kph down the river. If the current of the river is 5kph, how far can it travel up the river in 2 hours? 1 solutions Answer 359223 by ankor@dixie-net.com(15646)   on 2011-12-29 17:04:10 (Show Source): You can put this solution on YOUR website!A motor boat travels at the rate of 50kph down the river. If the current of the river is 5kph, how far can it travel up the river in 2 hours? : Find the speed of the boat in still water 50 - 5 = 45 mph : Find the distance (d) up river in two hrs d = 2(45-5) d = 80 km
 Geometry_Word_Problems/550688: using the Golden Ratio. If the pool is 110 feet wide, about how long should it be?1 solutions Answer 359216 by ankor@dixie-net.com(15646)   on 2011-12-29 16:45:55 (Show Source): You can put this solution on YOUR website!using the Golden Ratio. If the pool is 110 feet wide, about how long should it be? : Using the inverse of the golden ratio to find the longer dimension 1.618 * 110 = 177.98 ~ 178 ft long
 Money_Word_Problems/550858: Kyla wants to save \$8000 in 10 years she has three options determine the total amount that Kyla most deposit for each option monthly deposits paying 3% interest compounded monthly sn=a(r^n-1)/r-1 8000(1.0025^120-1/1.0025-1 8000x(0.349353/0.0025 8000x139.74 8000/139.74=x x=57.25 quarterly deposits paying 3% interest compounded quarterly sn=a(r^n-1/r-1 8000(1.0075^30-1/1.0075-1 8000x0.2512717/0.0075 8000x33.50 8000/33.50=x x=238.80 I believe that the problem is in order. Though, i feel that my answer is coming up short. Can someone help explain what im doing wrong? 1 solutions Answer 359198 by ankor@dixie-net.com(15646)   on 2011-12-29 16:19:40 (Show Source): You can put this solution on YOUR website!: Kyla wants to save \$8000 in 10 years she has three options determine the total amount that Kyla most deposit for each option monthly deposits paying 3% interest compounded monthly sn=a(r^n-1)/r-1 8000(1.0025^120-1/1.0025-1 8000x(0.349353/0.0025 8000x139.74 8000/139.74=x x=57.25 I check this using the annuity feature on the Ti83, and it is correct : quarterly deposits paying 3% interest compounded quarterly sn=a(r^n-1/r-1 8000(1.0075^30-1/1.0075-1 8000x0.2512717/0.0075 8000x33.50 8000/33.50=x x=238.80 On this one I think you made a mistake, it should be 40 periods, you have 30 x=172.24
 �t�e�s�t/550849: Solve the following question by completing the square: (n)^(2)+5n-6=0 Write the answer in both exact form and approximate form rounded to the hundredths place.1 solutions Answer 359188 by ankor@dixie-net.com(15646)   on 2011-12-29 15:58:41 (Show Source): You can put this solution on YOUR website!(n)^(2)+5n-6=0 completing the square n^2 + 5n + ___ = 6 find the value that completes the square (.5*5)^2 = 6,25, add to both sides n^2 + 5n + 6.25 = 6 + 6.25 : (n + 2.5)^2 = 12.25 find the square root of both sides n + 2.5 = +/- n + 2.5 = +/- 3.5 two solutions n = -2.5 + 3.5 n = 1 and n = -2.5 - 3.5 n = -6
 Bodies-in-space/550880: I need to pack round objects into a rectangular box. The box is a fixed length of 20" and fixed width of 10". If the part is a round cylinder of 3.5" diameter, how many can I get in the box? If the part is 4.5", how many can I get in the box? I'm really asking: "What is the formula to determine this?"1 solutions Answer 359182 by ankor@dixie-net.com(15646)   on 2011-12-29 15:44:44 (Show Source): You can put this solution on YOUR website!need to pack round objects into a rectangular box. The box is a fixed length of 20" and fixed width of 10". If the part is a round cylinder of 3.5" diameter, how many can I get in the box? If the part is 4.5", how many can I get in the box? : Assuming you mean the cylinder has 3.5" diameter and is 4.5" long Each part will occupy a rectangular area 3.5 by 4.5 If you place two rows of 5, side by side, a total of 10 can be placed in the box
 Rectangles/550847: Area of rectangle = 480 yards 1 side of fecne needed is 50 yards of wire what is the amount of fencing needed to build other three sides please provide formula and equation1 solutions Answer 359179 by ankor@dixie-net.com(15646)   on 2011-12-29 15:26:13 (Show Source): You can put this solution on YOUR website!Area of rectangle = 480 square yards 1 side of fence needed is 50 yards of wire what is the amount of fencing needed to build other three sides : Find the other side of the area = 9.6 yds : The dimensionof the rectangle: 50 by 9.6, find the total of the other three sides 9.6 + 9.6 + 50 = 69.2 to fence the remaining 3 sides
 Unit_Conversion_Word_Problems/550850: Please help me with this word problem: An alien rocketship is traveling at a speed of 20 inches per minute. At this speed, how many feet will it travel in one minute? Round to the nearest thousandth.1 solutions Answer 359145 by ankor@dixie-net.com(15646)   on 2011-12-29 12:16:45 (Show Source): You can put this solution on YOUR website!An alien rocketship is traveling at a speed of 20 inches per minute. At this speed, how many feet will it travel in one minute? Round to the nearest thousandth. : = 1.667 ft/min
 Numbers_Word_Problems/550817: If the reciprocal of (x-2) is (x+2) what is the greatest possible value of x Express your answer in simplest radical form i dont know how to solve it or what to do i tried quadratics but did not work1 solutions Answer 359123 by ankor@dixie-net.com(15646)   on 2011-12-29 09:55:55 (Show Source): You can put this solution on YOUR website!If the reciprocal of (x-2) is (x+2) what is the greatest possible value of x Express your answer in simplest radical form : Let's just solve for x and see what happens : = x + 2 1 = (x+2)(x-2) 1 = x^2 - 2x + 2x - 4 1 = x^2 - 4 0 = x^2 - 4 -1 0 = x^2 - 5 Therefore x = +/- the greatest possible value then: x =
 Age_Word_Problems/550805: The age of a man is 10 years more than three times his brother's age. Find the age of each if 5 years from now he will be 4 years more than twice his brother's age. 1 solutions Answer 359117 by ankor@dixie-net.com(15646)   on 2011-12-29 08:58:21 (Show Source): You can put this solution on YOUR website!The age of a man is 10 years more than three times his brother's age. m = 3b + 10 : Find the age of each if 5 years from now he will be 4 years more than twice his brother's age. m + 5 = 2(b+5) + 4 m + 5 = 2b + 10 + 4 m = 2b + 14 - 5 m = 2b + 9 Replace m with (3b+10) 3b + 10 = 2b + 9 3b - 2b = 9 - 10 b = -1; obviously this is not a valid problem
 Age_Word_Problems/550668: Diane is half the age of her brother 6 years ago. Represent Diane's age if her brother is y years old.1 solutions Answer 359116 by ankor@dixie-net.com(15646)   on 2011-12-29 08:46:57 (Show Source): You can put this solution on YOUR website!Diane is half the age of her brother 6 years ago. Represent Diane's age if her brother is y years old. : d = (y-6)
 Money_Word_Problems/550601: Jose invested \$10,000 in two accounts. One account paid 2% more than the other account. He invested the same amount in both accounts. If he received \$800 dollars in interest, what percent interest did the lower paying account pay?1 solutions Answer 359068 by ankor@dixie-net.com(15646)   on 2011-12-28 21:41:20 (Show Source): You can put this solution on YOUR website!Jose invested \$10,000 in two accounts. One account paid 2% more than the other account He invested the same amount in both accounts. If he received \$800 dollars in interest, what percent interest did the lower paying account pay? : From the give information, we know \$5000 was invested in each account : Total interest We will use the decimal equiv here let x = the % interest in the lower paying account then (x+.02) = the % of the higher paying account : 5000x + 5000(x+.02) = 800 5000x + 5000x + 100 = 800 10000x = 800 - 100 10000x = 700 x = x = .07 which is 7% is the lower paying rate : : See if that check out .07(5000) + .09(5000) = 800
 Money_Word_Problems/550729: On Monday, Jim had x dollars. On each subsequent day, he has half the money compared to the previous day, How many dollars does Jim have n weeks after Monday? A. (1/2) ^n x B. (1/2)^n (7x) C. (1/2)^7n x D. (1/2)^x n E. (1/2)^7x n Please explain step by step thanks.1 solutions Answer 359067 by ankor@dixie-net.com(15646)   on 2011-12-28 21:28:59 (Show Source): You can put this solution on YOUR website!On Monday, Jim had x dollars. On each subsequent day, he has half the money compared to the previous day, How many dollars does Jim have n weeks after Monday? : x amt is halved every day therefore the number of halving operations = 7n the above value is multiplied by the original amt x * x; (the C answer)
 test/550702: The solution to" the product of 5 and the quantity decreased by 10 is 40" ?1 solutions Answer 359066 by ankor@dixie-net.com(15646)   on 2011-12-28 21:18:54 (Show Source): You can put this solution on YOUR website!The solution to" the product of 5 and the quantity decreased by 10 is 40" ? : Let x = "the quantity" then 5(x-10) = 40 5x - 50 = 40 5x = 40 + 50 5x = 90 x = 90/5 x = 18 : : See if that checks out: 5(18-10) = 40
 Linear-equations/550740: I need help please!!!! Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this -x + 4y = 0.5 -3x – 6y = 10.51 solutions Answer 359043 by ankor@dixie-net.com(15646)   on 2011-12-28 19:43:14 (Show Source): You can put this solution on YOUR website!-x + 4y = 0.5 -3x – 6y = 10.5 : Multiply the 1st equation by -30, the 2nd equation by 10, this gets rid of the decimals and sets it up for elimination : +30x - 120y = -15 -30x - 60y = 105 -----------------------adding eliminates x, find y -180y = 90 y = y = -.5 : Find x, replace y with -.5 in the 2nd original equation -3x – 6y = 10.5 -3x – 6(-.5) = 10.5 -3x + 3 = 10.5 -3x = 10.5 - 3 -3x = 7.5 x = x = -2.5 : see if these two values x=-.5 and y=-2.5 check out in the 1st equation -x + 4y = 0.5 -(-2.5) + 4(-.5) = .5 2.5 - 2 = .5 confirms our solution
 Travel_Word_Problems/550660: a new airplane can travel at speeds up to 4,680 miles per hour. how many miles can the airplane travel in 10 seconds?1 solutions Answer 358963 by ankor@dixie-net.com(15646)   on 2011-12-28 13:14:09 (Show Source): You can put this solution on YOUR website!new airplane can travel at speeds up to 4,680 miles per hour. how many miles can the airplane travel in 10 seconds? : * 10 = 13 mi in 10 sec
 Travel_Word_Problems/550591: A boat travels 60 miles downstream in The same time it takes to go 36 miles upstream. The speed of The boat in still water is 15 mph greater than The speed of The current. Find The speed of The current.1 solutions Answer 358902 by ankor@dixie-net.com(15646)   on 2011-12-28 08:51:53 (Show Source): You can put this solution on YOUR website!A boat travels 60 miles downstream in The same time it takes to go 36 miles upstream. The speed of The boat in still water is 15 mph greater than The speed of The current. Find The speed of The current. : Let x = speed of the current and (x+15) = speed of the boat in still water then x + (x+15) = 2x+15; the effective speed down stream and (x+15) - x = 15 mph; the effective speed upstreams : Write a time equation; time = dist/speed : downstr time = upstr time = Cross multiply 36(2s+15) = 60 * 15 72s + 540 = 900 72s = 900 - 540 72s = 360 s = s = 5 mph is the rate of the current : : Confirm this solution, The speed of the boat in still water = 15 + 5 = 20 mph The speed with the current: 20 + 5 = 25 mph The speed against the current: 20 - 5 = 15 mph : Find the time each way, they should be equal 60/25 = 2.4 hrs 36/15 = 2.4
 Equations/550223: out of four pipes when 1,2,3 pipes are opened tank filled in 12 minutes; when 2,3,4 pipes opened time taken is 15 minutes;when 1 and 4 are opened it taken 20 minutes. How much time will take when all the four pipes are opened? 1 solutions Answer 358795 by ankor@dixie-net.com(15646)   on 2011-12-27 17:26:42 (Show Source): You can put this solution on YOUR website!out of four pipes when 1,2,3 pipes are opened tank filled in 12 minutes; when 2,3,4 pipes opened time taken is 15 minutes; when 1 and 4 are opened it taken 20 minutes. How much time will it take when all the four pipes are opened? : Let the 4 pipes be: a, b, c, d Let a full tank = 1 : "1,2,3 pipes are opened tank filled in 12 minutes" + + = 1 : "2,3,4 pipes are opened tank filled in 15 minutes" + + = 1 : Multiply the 1st equation by 5, the 2nd equation by 4, results + + = 5 + + = 4 -------------------------subtraction eliminates b and c - = 1 then "1,4 pipes are opened tank filled in 20 minutes" + = 1 multiply this equation by 3 add to the above equation + = 3 - = 1 -----------------------adding eliminates d find a = 4 4a = 120 a = 120/4 a = 30 min when the pipe 1 fills it alone then + = 1 = 1 - = d = 3*20 d = 60 min when pipe 4 fills it alone : Let's treat pipes 2&3 as a single pipe, call it bc + = 1 .4 + = 1 = 1 - .4 = .6 .6bc = 12 bc = 12/.6 bc = 20 min pipes 2&3 alone : "How much time will it take when all the four pipes are opened? + + = 1 multiply by 60 2t + 3t + t = 60 6t = 60 t = 10 minutes all pipes together : : see if this checks out using the 2nd original equation "2,3,4 pipes are opened tank filled in 15 minutes" + = .75 + .25 = 1 :
 Exponential-and-logarithmic-functions/550301: if one of the solutions to quadractic function is 1+i square root 2, what is the b value in the qudractic polynomial?1 solutions Answer 358735 by ankor@dixie-net.com(15646)   on 2011-12-27 12:32:47 (Show Source): You can put this solution on YOUR website!if one of the solutions to quadratic function is 1+i square root 2, what is the b value in the quadractic polynomial? : a complex solution of quadratic function is usually paired with it's conjugate and
 Quadratic_Equations/550389: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr.1 solutions Answer 358708 by ankor@dixie-net.com(15646)   on 2011-12-27 09:58:09 (Show Source): You can put this solution on YOUR website!n express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr. : let s = speed of the express then (s-12) = speed of the other train : Write a time equation, time = dist/speed : Other train time - Express train time = 1 hr - = 1 Multiply by s(s-12) s(s-12)* - s(s-12)* = s(s-12) Cancel the denominators and you have 240s - 240(s-12) = s^2 - 12s : 240s - 240s + 2880 = s^2 - 12s combine like terms and arrange as a quadratic equation 0 = s^2 - 12s - 2880 you can use the quadratic equation but this will factor to (s+48)(s-60) = 0 s = 60 km/hr is the the express train : : check this by finding the times of each 240/48 = 5 hrs 240/60 = 4 hrs
 Triangles/550189: While golfing , Sahar hits a tee shot from T toward a hole at H , but the ball veers 23 degrees and lands at B. The scorecard says that H is 270m from T. If Sahar walks 160m to the ball (B) , how far is the ball from the hole?1 solutions Answer 358637 by ankor@dixie-net.com(15646)   on 2011-12-26 19:58:11 (Show Source): You can put this solution on YOUR website!While golfing , Sahar hits a tee shot from T toward a hole at H , but the ball veers 23 degrees and lands at B. The scorecard says that H is 270m from T. If Sahar walks 160m to the ball (B) , how far is the ball from the hole? : This is a side/angle/side problem, use the law of cosines a^2 = b^2 + c^2 -2(bc)cos(A) in our problem A = 23 degrees a = side opposite of 23 degrees (distance from B to the hole) b = 270 c = 160 : a^2 = 270^2 + 160^2 -2(270*160)*cos(23) a^2 = 72900 + 25600 - 2(43200)*.9205 a^2 = 98500 - 79531.6 a = a = 137.7 meters from B to the hole
 �t�e�s�t/550212: If the population of a city doubles every 20 years, how long does it take to triple? (state this is logarithmic form and find solution) please, i really need your help! Thanks in advance1 solutions Answer 358633 by ankor@dixie-net.com(15646)   on 2011-12-26 19:35:41 (Show Source): You can put this solution on YOUR website!If the population of a city doubles every 20 years, how long does it take to triple? (state this is logarithmic form and find solution) : An exponential formula Ao*2^(t/20) = A where Ao = initial amt A = resulting amt in t time If Ao = 1, then A = 3 2^(t/20) = 3 using nat logs we have *ln(2) = ln(3) = t = * 20 t = 31.7 yrs : : Check this on a calc, enter: 2^(31.7/20) results: 3.000
 Quadratic_Equations/550222: if a man travels at the speed of 40km/hr then he reaches the office 5min late and if he travels at the speed 50km/hr then he reaches 3min early,find the distance and time?1 solutions Answer 358611 by ankor@dixie-net.com(15646)   on 2011-12-26 17:24:04 (Show Source): You can put this solution on YOUR website!if a man travels at the speed of 40km/hr then he reaches the office 5 min late and if he travels at the speed 50km/hr then he reaches 3 min early, find the distance and time? : Let d = distance to the office Let t - normal travel time to reach the office on time : change 5 min to hrs. 5/60 = 1/12 hrs change 3 min to hrs: 3/60 = 1/20 hrs : write a time equation for each scenario : = t+; 5 min late and = t - : 3 min early : get rid of the denominators and rearrange both equations = t+ Multiply by 120, results 3d = 120t + 10 3d - 120t = 10 and = t - multiply by 100, results 2d = 100t - 5 2d - 100t = -5 : Multiply the 1st rearranged eq by 2, multiply the 2nd eq by 3: 6d - 240t = 20 6d - 300t = -15 ----------------subtraction eliminates d, find t +60t = 35 t = t = 35 min is the normal time : Find d using the 5 min late equation (40 min travel time):(dist = speed * time} *40 = 26.67 km is the distance : Confirm this using the 3 min early equation (32 min travel time) * 50 = 26.67 km here also : Dist = 26.67 km, normal travel time 35 min
 Polynomials-and-rational-expressions/550129: Essay: Show all work. A school designer wants to create a whiteboard with the optimal dimensions to enhance learning. It is determined that if one side of the whiteboard is x + 4y inches, the other side should be x^2 + 4xy - 6y^2 inches. Write an algebraic expression for the area of such a whiteboard, simplify it, and include correct units with your solution. 1 solutions Answer 358543 by ankor@dixie-net.com(15646)   on 2011-12-26 08:48:51 (Show Source): You can put this solution on YOUR website!one side of the whiteboard is x + 4y inches, the other side should be x^2 + 4xy - 6y^2 inches : . . . x^2 + 4xy - 6y^2 . . . X. . . . . x + 4y --------------------------- . . . 4x^2y + 16xy^2 - 24y^3 . x^3 + 4x^2y - 6xy^2 ------------------------------ . x^3 + 8x^2y + 10xy^2 - 24y^3 = the area of the board :