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Linear-equations/459876: I am having problems with understanding how to solve equations that involve LCD. Such as 10/4y+6/2=2y-2. I don't understand the whole concept so if you could maybe tell me how I would go about solving that problem and explain each step so I know how to do it in future equations I would appreciate it. Thank you 1 solutions Answer 315520 by ankor@dixie-net.com(15638)   on 2011-06-11 18:29:12 (Show Source): You can put this solution on YOUR website! assume the problem is: y + = 2y - 2 the common denominator would be 4, multiply each term by 4 4*y + 4*= 4(2y) - 4(2) Cancel the denominators and you have 10y + 2(6) = 8y - 8 10y + 12 = 8y - 8 10y - 8y = -8 - 12 2y = -20 y = y = -10 : : See if that checks out, replace y with -10 in the original problem (-10) + = 2(-10) - 2 + 3 = -20 - 2 -25 + 3 = -22

test/459968: A car is driving from point A to point B at 50mph and from point B to point A at 60mph. The whole trip took 11hrs. How mach distance was driven in that time... 1 solutions Answer 315515 by ankor@dixie-net.com(15638)   on 2011-06-11 18:19:32 (Show Source): You can put this solution on YOUR website! A car is driving from point A to point B at 50mph and from point B to point A at 60mph. The whole trip took 11 hrs. How mach distance was driven in that time... : Let d = the one-way distance : Write a time equation: Time = dist/speed : A-B time + B-A time = 11 hrs + = 11 multiply by 300 300* + 300* = 300(11) Cancel the denominators, resulting in: 6d + 5d = 3300 d = d = 300 mi is the one-way dist : Total dist: 2(300) = 600 driven in 11 hrs

test/459945: Solve __8__ = __7__ y+2 y-9 The solution to y = ??? simplify answer, use integer or fraction. Thank you in advance for your assistance. Devoted, Minka. 1 solutions Answer 315482 by ankor@dixie-net.com(15638)   on 2011-06-11 14:47:25 (Show Source): You can put this solution on YOUR website! Solve : = : When you have single a fractions on each side of the equal side, you can cross multiply: 8(y-9) = 7(y+2) : 8y - 72 = 7y + 14 : 8y - 7y = 14 + 72 : y = 86 : : Check this in the original equation = = : How about this, is this stuff making sense to you now? Just knowing a few rules makes it possible to solve a lot of these problems.

test/459702: Solve the equation for M. f=-__GMn___ r^2 Thanks, Minka 1 solutions Answer 315475 by ankor@dixie-net.com(15638)   on 2011-06-11 14:00:20 (Show Source): You can put this solution on YOUR website! Solve the equation for M. f = : multiply both sides by r^2 and write it: -GMn = fr^2 : divide both sides by -Gn M = or M =

test/459700: Add ___X____ + _5_ x^2-2x-3 x+1 The sum is ? Thanks, Minka 1 solutions Answer 315468 by ankor@dixie-net.com(15638)   on 2011-06-11 13:31:13 (Show Source): You can put this solution on YOUR website! Assume the problem is: + : we can factor the 1st denominator to: + : Therefore the common denominator would be (x-3)(x+1), right? so we have : Multiply what's inside the brackets: = : you can factor out 3 if you want to:

Inequalities/459469: Simplify and reduce the expression to lowest terms. 25r 15r-3 ____ - _____ 10r+3 10r+3 Thank you from Minka 1 solutions Answer 315467 by ankor@dixie-net.com(15638)   on 2011-06-11 13:17:48 (Show Source): You can put this solution on YOUR website! Simplify and reduce the expression to lowest terms. - They have the same denominators so we can write it: When we remove the bracket it changes the signs because of the neg = = 1; (When denominator=numerator it's always one)

Inequalities/459466: Simplify by removing factors 36s^8 ______ = 42s^11 Thank you from Minka 1 solutions Answer 315465 by ankor@dixie-net.com(15638)   on 2011-06-11 13:08:39 (Show Source): You can put this solution on YOUR website! Simplify by removing factors reduce the numerical fraction, divide both by 6, resulting in Divide the top and bottom by s^8, using the law of exponents, we have we know s^0 = 1 so we have

Quadratic_Equations/459334: Hi Need help again. Does this equation x^2-10=0 have 1real solution 2imaginary solutions 2 real solutions Thanks Gina One more E=lc^2 solve for c 1 solutions Answer 315460 by ankor@dixie-net.com(15638)   on 2011-06-11 12:58:54 (Show Source): You can put this solution on YOUR website! Does this equation x^2 - 10 = 0 have 1real solution 2imaginary solutions 2 real solutions We can use the discriminant rules here, d = b^2 - 4*a*c in this equation a=1, b=0, c= -10 d = -4*1*-10 d =+40, a greater than 0 value, therefore 2 real solutions, right? : E=lc^2 solve for c divide both sides by l = c^2 therefore c =

Travel_Word_Problems/459887: A train covers a distance in 50 mins,if it runs at at the speed of 36km/hour on the avarage.The speed at which the trin must run into reduce the time of journey to 30 mins,will be? 1 solutions Answer 315453 by ankor@dixie-net.com(15638)   on 2011-06-11 12:44:19 (Show Source): You can put this solution on YOUR website! A train covers a distance in 50 mins, if it runs at at the speed of 36km/hour on the average. The speed at which the train must run into, reduce the time of journey to 30 mins, will be? : Let s = speed required to reduce speed to 30 min : Time varies inversely to speed, there for = Cross multiply 30x = 50*36 30x = 1800 x = x = 60 mph to reduce the time to 30 min : : Check this out using the actual distance dist = 36* dist = 30 mi : Time going 60 mph: t = 30/60 = .5 hr which is 30 min

Equations/459929: I'm 46 years old and trying to refresh my algebra x+1/6 = 4/3 Thanks 1 solutions Answer 315444 by ankor@dixie-net.com(15638)   on 2011-06-11 12:28:06 (Show Source): You can put this solution on YOUR website! x + = First get rid of those annoying fractions, mult by 6, resulting in: 6x + 1 = 2(4) Subtract 1 from both sides 6x = 8 - 1 6x = 7 divide both sides by 6 x = : : See if this works, replace x with 7/6 in the original equation + = Which is + = : : Hey, you're just a kid, I'm 74!

Graphs/459937: Solve the system of equations 8x + 4y = 8 -12x + 3y = 12 a) symbolically b) graphically c) numerically Can someone assist me with this. I need to see how the solution was arrived at. Thank you in advance for your assistance. Devoted, Minka. 1 solutions Answer 315441 by ankor@dixie-net.com(15638)   on 2011-06-11 12:20:30 (Show Source): You can put this solution on YOUR website! : Solve the system of equations 8x + 4y = 8 -12x + 3y = 12 : multiply the the 1st equation by 1.5, use elimination here 12x + 6y = 12 -12x+ 3y = 12 --------------adding eliminates x, find y 9y = 24 y = y = : Use the 2nd equation to find x, replace y with 8/3 -12x + 3() = 12 -12x + 8 = 12 -12x = 12 - 8 x = x = : therefore solution is: x = , y = Is this symbolically or numerically? I don't know. : But graphically, put both equations in the slope/intercept form 8x + 4y = 8 4y = -8x + 8 Divide by 4 y = -2x + 2; (red) and -12x + 3y = 12 3y = 12x + 12 divide by 3 y = 4x + 4, (green) : Graph these two equations, should look like this : Note the intersection is x = , y = : Minka is a great name!

Graphs/459714: Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 Please show all of your work 1 solutions Answer 315351 by ankor@dixie-net.com(15638)   on 2011-06-10 21:59:51 (Show Source): You can put this solution on YOUR website! Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 : Find the slope of the given equation, put it in the slope intercept form -9x - 2y = 10 -2y = 9x + 10 y has to be positive, mult by -1 2y = -9x - 10 Divide by 2 y = x - 5 : m1 = is the slope : The slope relationship of perpendicular lines: m1*m2 = -1. Find m2 *m2 = -1 m2 = : Find the equation using y - y1 = m(x - x1) m=, x1=-9, y1=9 y - 9 = (x - (-9)) y - 9 = (x + 9) y - 9 = x + 2 y = x + 2 + 9 y = x + 11

Radicals/459539: Multiply √11(√5-√10) Simplify your answer. Type an exact answer, using radicals as needed 1 solutions Answer 315347 by ankor@dixie-net.com(15638)   on 2011-06-10 21:46:13 (Show Source): You can put this solution on YOUR website! = =

Money_Word_Problems/459572: Please help me solve this problem. A land investment company purchase a parcel of land for $7200. After having sold all but 20 acres at a profit of $30 per acre over original cost per acre, the company regained the entire cost of the parcel. How many acres were sold? 1 solutions Answer 315343 by ankor@dixie-net.com(15638)   on 2011-06-10 21:29:46 (Show Source): You can put this solution on YOUR website! A land investment company purchase a parcel of land for $7200. After having sold all but 20 acres at a profit of $30 per acre over original cost per acre, the company regained the entire cost of the parcel. How many acres were sold? : Let x = no. of acres sold then (x+20) = total no. of acres in the parcel : Selling price - cost price = $30 - = 30 : multiply by x(x+20), results: 7200(x+20) - 7200x = 30x(x+20) 7200x + 144000 - 7200x = 30x^2 + 600x A quadratic equation 30x^2 + 600x - 144000 = 0 Simplify, divide by 30 x^2 + 20x - 4800 = 0 Factor this to (x+80)(x-60) = 0 positive solution x = 60 acres sold : : Check this (total acres 20 more, 80) - = $120 - $90 = $30; confirms our solution of x=60

Travel_Word_Problems/459165: The length of the rails used by a railroad is 30 feet. In years past, before railroads welded rails together, an audiable click could be heard each time the wheels of a railroad car passed over a point where rails were joined together. Old mr.neyland said that he could tell how fast a train was going by counting clicks as he looked at his pocketwatch. Approximately how long did Mr.Neyland have to count clicks for the number of clicks to equal the train's speed in miles per hour? 1 solutions Answer 315286 by ankor@dixie-net.com(15638)   on 2011-06-10 16:37:52 (Show Source): You can put this solution on YOUR website! The length of the rails used by a railroad is 30 feet. In years past, before railroads welded rails together, an audiable click could be heard each time the wheels of a railroad car passed over a point where rails were joined together. Old mr.neyland said that he could tell how fast a train was going by counting clicks as he looked at his pocketwatch. Approximately how long did Mr.Neyland have to count clicks for the number of clicks to equal the train's speed in miles per hour? : = 176 clicks in 1 mile : At 60 mph, a mile a minute, you would have to count 176 clicks in one minute. 60/176 * 60 ~ 20 sec : If you count 60 clicks in 20 sec, the speed is approx 60 mph : Perhaps we can we say that if you count the clicks in 20 seconds it will equal the speed in mph.

Functions/459321: If y varies inversely as x^2, and y=2 when x=4, what is the constant of variation? Thank you for the help :-) 1 solutions Answer 315025 by ankor@dixie-net.com(15638)   on 2011-06-09 16:16:05 (Show Source): You can put this solution on YOUR website! If y varies inversely as x^2, and y=2 when x=4, what is the constant of variation? : Let k = constant of variation : = y : Replace x & y: = 2 = 2 multiply both sides by 16 k = 16(2) k = 32 is the constant of variation and y = is the equation

Rectangles/459012: How do you find x and y of this rectangle when sides: AB = -2x DC = 7y + 1 AD = -x BC = 2y + 2 AB = DC AD = BC I know you use substitution, I'm just not sure how to... Thank you so much in advance! 1 solutions Answer 314901 by ankor@dixie-net.com(15638)   on 2011-06-08 22:03:36 (Show Source): You can put this solution on YOUR website! How do you find x and y of this rectangle when sides: AB = -2x DC = 7y + 1 AD = -x BC = 2y + 2 AB = DC AD = BC : Draw out a rectangle ABCD, label each side as given: Put the equations in the standard form AB=DC, therefore: -2x = 7y+1 -2x - 7y = 1 2x + 7y = -1; multiplied by -1 and AD=BC, therefore -x = 2y+2 -x - 2y = 2 x + 2y = -2 : Use these two equation for elimination 2x + 7y = -1 x + 2y = -2 multiply the 2nd equation by 2 2x + 7y = -1 2x + 4y = -4 ---------------Subtracting eliminates x, find y 3y = 3 y = 1 : You should be able to find x, check to make sure opposite sides are equal

Rate-of-work-word-problems/458867: It takes Rob 10 hours to clean an attic. Sam can clean the same attic in 11 hours. How long would it take them if they work together? Thank You!! 1 solutions Answer 314838 by ankor@dixie-net.com(15638)   on 2011-06-08 16:47:13 (Show Source): You can put this solution on YOUR website! It takes Rob 10 hours to clean an attic. Sam can clean the same attic in 11 hours. How long would it take them if they work together? : Let t = time if they work together Let the completed job = 1 (a clean attic) : A typical shared work equation : + = 1 multiply by a common denominator, 110 110* + 110* = 110(1) Cancel the denominators 11t + 10t = 110 : 21t = 110 t = t = 5.238 hrs or about 5 hrs 14.3 min

Equations/458869: The variables x and y vary directly. Use the given values to write an equation that relates x and y. x = 5, y = 25 Help me!! Due friday help me slove this problem asap!!! 1 solutions Answer 314836 by ankor@dixie-net.com(15638)   on 2011-06-08 16:40:03 (Show Source): You can put this solution on YOUR website! he variables x and y vary directly. Use the given values to write an equation that relates x and y. x = 5, y = 25 : Write it as y = kx Replace x and y to find k 25 = 5k k = k = 5 : y = 5x, is the equation that relates y to x : You can see when x=5, y=25 as given.

Quadratic-relations-and-conic-sections/458999: Please note that graphing is not allowed to solve this. If x^2+y^2=36 and (x^2/16)+(y^2/64)=1, then what are the values of x and y? 1 solutions Answer 314835 by ankor@dixie-net.com(15638)   on 2011-06-08 16:34:26 (Show Source): You can put this solution on YOUR website! If x^2 + y^2 = 36 and (x^2/16)+(y^2/64)=1, then what are the values of x and y? Get rid of the annoying fraction in the 2nd equation multiply by 64 and we have 4(x^2) + y^2 = 64 : Use elimination with the 1st equation just as it is 4x^2 + y^2 = 64 x^2 + y^2 = 36 ----------------subtraction eliminates y^2, find x^2 3x^2 = 28 x^2 = x = = : Find y, replace x^2 with in the 1st equation + y^2 = 36 y^2 = 36 - y^2 = - y = y = = :

logarithm/458858: 3x^2+48x=-24 solve the equation by completing the square. final answer should be completely simplified and in EXACT form 1 solutions Answer 314831 by ankor@dixie-net.com(15638)   on 2011-06-08 16:09:04 (Show Source): You can put this solution on YOUR website! 3x^2 + 48x = -24 : Simplify, divide be 3 x^2 + 16x = -8 : Complete the square x^2 + 16x + __ = -8 : To complete the square, divide the coefficient of x by 2 and square it. (8^2) add to both sides x^2 + 16x + 64 = -8 + 64 x^2 + 16x + 64 = 56 : Which is (x+8)^2 = 56 : The square root of both sides x + 8 = +/- Factor out the perfect square inside the radical x + 8 = +/- extract the {square x + 8 = +/- Two solutions x = and x =

Money_Word_Problems/458926: Please help me to solve this problem. Suppose that customers will purchase q unit of a product when the price is (80-q)/4 dollars each, how many units must be sold in order that sales revenue be $400? 1 solutions Answer 314829 by ankor@dixie-net.com(15638)   on 2011-06-08 15:52:41 (Show Source): You can put this solution on YOUR website! Suppose that customers will purchase q unit of a product when the price is (80-q)/4 dollars each, how many units must be sold in order that sales revenue be $400? : Revenue = price * no. of units purchased therefore * q = 400 : = 400 Multiply both sides by 4 80q - q^2 = 1600 Combine on the right 0 = q^2 - 80q + 1600 this factors to (q-40)(q-40) = 0 q = 40 units sold to have a revenue of $400 : : Check this out; find the price p = p = $10 40 * 10 = 400

Travel_Word_Problems/458996: : Distance between City A and City B is 60 kilometres. A driver should go from City A to City B for 1 hour. If first 30 kilometres the driver drives with 30 km/h what should be his speed during last 30 kilometres so he arrives in City B on time? 1 solutions Answer 314828 by ankor@dixie-net.com(15638)   on 2011-06-08 15:43:07 (Show Source): You can put this solution on YOUR website! Distance between City A and City B is 60 kilometres. A driver should go from City A to City B for 1 hour. If first 30 kilometres the driver drives with 30 km/h, what should be his speed during last 30 kilometres so he arrives in City B on time? : You can see this is not possible. The first 30 km at 30 km/hr, will take one hr So he has 0 time to drive the 2nd 30 km

Quadratic_Equations/458970: Hi everyone My problem is: Give exact and approximate solutions to three decimal places x^2+6x+9=25 Thanks you Gina 1 solutions Answer 314827 by ankor@dixie-net.com(15638)   on 2011-06-08 15:39:11 (Show Source): You can put this solution on YOUR website! My problem is: Give exact and approximate solutions to three decimal places x^2 + 6x + 9 = 25 x^2 + 6x + 9 - 25 = 0 x^2 + 6x - 16 = 0 This factors exactly to (x+8)(x-2) = 0 Two solutions x = -8 and x = +2 : An approximate solution would not be necessary.

Quadratic_Equations/458849: Write a quadratic equation with -3/4 and 4 as its roots. Wite the equation in form ax^2 + bx + c = 0, where a,b and c are intergers. 1 solutions Answer 314825 by ankor@dixie-net.com(15638)   on 2011-06-08 15:21:15 (Show Source): You can put this solution on YOUR website! Write a quadratic equation with -3/4 and 4 as its roots. : These two roots could be derived from the factors: (4x + 3) (x - 4) = 0 FOIL 4x^2 - 16x + 3x - 12 = 0 Combine like terms 4x^2 - 13x - 12 = 0

Linear-equations/458769: I got this incorrect on my homework assignment. Please show me how to do it! 1. Find the intersection point of the two straight lines: 3x - 4y = 5 and 2x + 3y =1. Answer in fractions reduced to the lowest terms. I said x= 51/51 and y= -7/17 but got it wrong. Please show me the steps. 1 solutions Answer 314808 by ankor@dixie-net.com(15638)   on 2011-06-08 13:19:55 (Show Source): You can put this solution on YOUR website! 1. Find the intersection point of the two straight lines: 3x - 4y = 5 and 2x + 3y = 1. Answer in fractions reduced to the lowest terms. : 3x - 4y = 5 2x + 3y = 1 : multiply the 1st eq by 3, multiply the 2nd eq by 4, resulting in: 9x - 12y = 15 8x + 12y = 4 --------------- adding eliminates y, find x 17x = 19 x = : Find x, multiply the 1st eq by 2, the 2nd equation by 3, results 6x - 8y = 10 6x + 9y = 3 ------------------Subtraction eliminates x, find y -17y = 7 y =

Functions/458523: A piece of wire 16 inches long is to be cut in two parts. Each piece will be bent in the shape of a square. Find the expression that represents the total area of the two squares made with the pieces of wire as a function of the length, x, of one of the pieces. 1 solutions Answer 314630 by ankor@dixie-net.com(15638)   on 2011-06-07 20:17:38 (Show Source): You can put this solution on YOUR website! A piece of wire 16 inches long is to be cut in two parts. Each piece will be bent in the shape of a square. Find the expression that represents the total area of the two squares made with the pieces of wire as a function of the length, x, of one of the pieces. : Other square side = simplified to (4-x) : total area A(x) = x^2 + (4-x)^2 A(x) = x^2 + 16 - 8x + x^2 A(x) = 2x^2 - 8x + 16

Mixture_Word_Problems/458653: I have a mixture problem that reads: A woman has made 6 quarts of an orange juice punch for a party. The punch contains 12% orange juice. She feels she may need more punch, but she has no more orange juice so she adds 1/2 quart of water to the punch. Find the percent of orange juice in the new mixture. 1 solutions Answer 314621 by ankor@dixie-net.com(15638)   on 2011-06-07 20:04:52 (Show Source): You can put this solution on YOUR website! A woman has made 6 quarts of an orange juice punch for a party. The punch contains 12% orange juice. She feels she may need more punch, but she has no more orange juice so she adds 1/2 quart of water to the punch. Find the percent of orange juice in the new mixture. : Let x = the per cent of orange juice in the new mixture : 12(6) = x(6+.5) 72 = 6.5x x = x = 11.077 percent orange juice now

Graphs/458510: Could someone please help me! Construct a table of values for the equation y=3/x if the replacement set for x is {-3,-1,6}. Thank you! Sarah 1 solutions Answer 314602 by ankor@dixie-net.com(15638)   on 2011-06-07 19:41:37 (Show Source): You can put this solution on YOUR website! Construct a table of values for the equation y=3/x if the replacement set for x is {-3,-1,6}. : This is easy y = For x=-3, replace x with -3 y = y = -1 : The table x | y -------- -3 |-1 : x=-1 y = y = -3 Add this pair to the table x | y -------- -3 |-1 -1 |-3 : x=6 y = y = .5 Add this pair to the table x | y -------- -3 |-1 -1 |-3 6 |.5

Travel_Word_Problems/458480: A man rode a bycycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking was 10 mph faster than his hiking rate, what was each rate? 1 solutions Answer 314565 by ankor@dixie-net.com(15638)   on 2011-06-07 16:39:42 (Show Source): You can put this solution on YOUR website! A man rode a bicycle for 12 mi and then hiked an additional 8 mi. The total time for the trip was 5 hr. If his biking was 10 mph faster than his hiking rate, what was each rate? : Let r = his hiking rate it says," biking was 10 mph faster than his hiking rate". therefore: (r+10) = his biking rate : Write a time equation, time = dist/speed : hike time + bike time = 5 hrs + = 5 : multiply by r(r+10) r(r+10)*8 + r(r+10)*12 = r(r+10)*5 : Cancel the denominators and you have: 8(r+10) + 12r = 5r(r+10) : 8r + 80 + 12r = 5r^2 + 50r : 20r + 80 = 5r^2 + 50r Combine on the right 0 = 5r^2 + 50r - 20r - 80 A quadratic equation 5r^2 + 30r - 80 = 0 simplify divide by 5 r^2 + 6r - 16 = 0 factors to (r+8)(r-2) = 0 the positive solution r = 2 mph is his hiking speed then 2 + 10 + 12 mph is his biking speed : : Check this by finding the times 12/12 + 8/2 = 5

Money_Word_Problems/458230: The word problem is....A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store but by sellimg each of the remaining mugs at $3 above the original cost per mug she made a total profit of $22. Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased. If the price for n mugs is $48, how can we express the cost per mug? 1 solutions Answer 314347 by ankor@dixie-net.com(15638)   on 2011-06-06 18:40:11 (Show Source): You can put this solution on YOUR website! A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store but by selling each of the remaining mugs at $3 above the original cost per mug she made a total profit of $22. Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased. If the price for n mugs is $48, how can we express the cost per mug? : Price paid for each mug = : No. of mugs sold = (n-2) : Selling price = + 3 ; Revenue should = cost + profit : Total revenue = 48 + 22 = $70: : #sold * Price sold = total revenue (n-2) * [ + 3] = 70 FOIL 48 + 3n - 96/n - 6 = 70 combine like terms 3n - 96/n + 48 - 6 - 70 = 0 3n - 96/n - 28 = 0 Multiply equation by n, forming a quadratic equation: 3n^2 - 28n - 96 = 0 Factor (3n +8)(n-12) = 0 Positive solution n = 12 mugs originally bought : Check Cost: 48/12 = $4 Sold: 10 * 7 = $70 (cost + profit)