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Quadratic_Equations/125441: What would the graph of the quadratic function with zeros 1/2 plus or minus sqrt7/3 look like ? 1 solutions Answer 92012 by ankor@dixie-net.com(15657)   on 2008-02-07 20:26:17 (Show Source): You can put this solution on YOUR website! What would the graph of the quadratic function with zeros 1/2 plus or minus sqrt7/3 look like ? : In order to graph it, you need the equation, find that: x = : x - = +/-; subtract from both sides : (x-)^2 = ; squared both sides : x^2 - 1x + = ; FOILed : x^2 - 1x + - = 0; Subtracted from both sides : x^2 - 1x + - = 0; use a common denominator : x^2 - 1x - = 0 : Plot this equation from x = -2 to x = +3, it should look like this: : Could you follow this OK?

Graphs/125401: Theater tickets are $8 for general admission (GA) and $5 for students (STD). During one evening 240 tickets were sold, and the receipts were $1680. How many of each type of ticket was sold? HELP!!!!!! 1 solutions Answer 92007 by ankor@dixie-net.com(15657)   on 2008-02-07 20:01:56 (Show Source): You can put this solution on YOUR website! Theater tickets are $8 for general admission (GA) and $5 for students (STD). During one evening 240 tickets were sold, and the receipts were $1680. How many of each type of ticket was sold? : Let x = no. of GA tickets Let y = no. of STD tickets : Translate these two statements to equations: : During one evening 240 tickets were sold," x + y = 240 or y = (240 - x); we can use this for substituting below : "tickets are $8 for general admission (GA) and $5 for students (STD).... the receipts were $1680." 8x + 5y = 1680 : How many of each type of ticket was sold? ; Substitute (240-x) for y in the above equation, find x: 8x + 5(240-x) = 1680 : 8x + 1200 - 5x = 1680; multiplied what's inside the brackets : 8x - 5x = 1680 - 1200 : 3x = 480 x = x = 160 Ga tickets : Find y: y = 240 - x y = 240 - 160 y = 80 STD tickets : : Check solution in the receipt$ equation 8(160) + 5(80) = 1280 + 400 = 1680 : Did I make this understandable? Think you can do these type of equations now?

Linear_Equations_And_Systems_Word_Problems/125444: How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get 20% mixture? 1 solutions Answer 91999 by ankor@dixie-net.com(15657)   on 2008-02-07 19:44:39 (Show Source): You can put this solution on YOUR website! How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get 20% mixture? : Let x = amt of pure acid required : This is to be mixed with 20 liters, therefore: The amt of the final mixture will = (x+20) : Pure acid will be 1.0x : .15(20) + 1.0x = .20(x+ 20) : 3 + 1x + .20x + 4 : 1x - .2x = 4 - 3 : .8x = 1 x = x = 1.25 liters of pure acid to produce a 20% mixture : : Check .15(20) + 1.25 = .20(21.25) 3 + 1.25 = 4.25; confirms our solution

Travel_Word_Problems/125584: a long distance runner, runs at an average velocity of 8mph. Two hours after Tanya leaves your house, you leave in your honda and follow the same route. If your average velocity is 40 mph, how long will it be before you catch up with Tanya? How far will you be from your home? 1 solutions Answer 91995 by ankor@dixie-net.com(15657)   on 2008-02-07 19:32:57 (Show Source): You can put this solution on YOUR website! a long distance runner, runs at an average velocity of 8mph. Two hours after Tanya leaves your house, you leave in your honda and follow the same route. If your average velocity is 40 mph, how long will it be before you catch up with Tanya? How far will you be from your home? : Let t = time required for you to catch up with T Then (t+2) = T's travel time when she is caught : One thing to remember in any of these "catch-up programs" is both of you travel the same distance, write a simple distance equation from this fact. : Distance = speed * time : Your dist = T's distance 40t = 8(t+2) : 40t = 8t + 16 : 40t - 8t = 16 : 32t = 16 t = t = hr for you to catch up : Find the distance using t = .5 hr for you and 2.5 hr for T 40 * .5 = 20 mi 8 * 2.5 = 20 mi also; confirms our solution

Inverses/125574: This question is from textbook Mathematics 10 1/2(x-5)=x/4 I have tried this question so many ways, my head hurts. I can't figure it out! I only need one example and I will be able to complete my homework, unfortunately the text book does not give me an example. I have plans to go into school early if you can't help, but I thought I would give this a shot. I like to work things out on my own, but this is review from last year and after not seeing math problems for a year I'm struggling. Thanks 1 solutions Answer 91991 by ankor@dixie-net.com(15657)   on 2008-02-07 19:22:53 (Show Source): You can put this solution on YOUR website! (x-5) = : The first thing you want to do here is get rid of the denominators multiply equation by a multiple of both denominators, that would 4 4*(x-5) = 4* Cancel out the denominators and you have: 2(x-5) = 1x : 2x - 10 = x; multiply what's inside the brackets : 2x - x = +10; basic algebra, add 10 to both sides, subtract x from both side : x = 10 : : Check in original equation; substitute 10 for x (10-5) = (5) = 2.5 = 2.5

Percentage-and-ratio-word-problems/125368: YOU HAVE SOLVED THIS PROBLEM BELOW ALREADY. BUT I DON'T UNDESTAND WHERE THE .88X COMES FROM. PLEASE SHOW ME HOW YOU ENDED UP WITH .88X TO SOLVE THIS EQUATION. X-.12=924 .88X=924 X=924/.88. You want to order a new computer. The manufacturer is offering a dicount of 12% off the original price of the computer. With the discount $924.What is the original price of the computer? 1 solutions Answer 91989 by ankor@dixie-net.com(15657)   on 2008-02-07 19:15:06 (Show Source): You can put this solution on YOUR website! You want to order a new computer. The manufacturer is offering a dicount of 12% off the original price of the computer. With the discount $924.What is the original price of the computer? : Let x = original price then .12x = the amt of the 12% discount : When you see x, it actually means 1x or 1.0x : So we have: original price - discount = $924 1.0x - .12x = 924 : .88x = 924; (You subtracted .12 from 1.00) : x = x = $1050 was the original price ; : Did this answer your question?

Linear_Equations_And_Systems_Word_Problems/125385: This question is from textbook Intermediate Algebra Review The demand for a certain toy is such that no one will purchase it once the price reaches $7. For every $0.02 decreases in price, 1 unit more will be sold. Write the price as a function of the number of units sold. How many toys would you expect to be sold if the price were set at $4.79? 1 solutions Answer 91988 by ankor@dixie-net.com(15657)   on 2008-02-07 19:03:29 (Show Source): You can put this solution on YOUR website! The demand for a certain toy is such that no one will purchase it once the price reaches $7. For every $0.02 decreases in price, 1 unit more will be sold. Write the price as a function of the number of units sold. : We need two sets of coordinates to find an equation x = price; y = no. sold This first set is given x = 7; y = 0 : Choose the 2nd set of coordinates, x = 6; y = 50, from the statement: "For every $0.02 decreases in price, 1 unit more will be sold. : Find the slope m = = = -50 : Find the equation using the point/slope formula: y - y1 = m(x - x1) x1 = 7; y1 = 0; m = -50 y - 0 = -50(x - 7) y = -50x + 350 : f(x) = -50x + 350 would be the equation: : : How many toys would you expect to be sold if the price were set at $4.79? Substitute 4.79 for x f(4.79) = -50(4.79) + 350 f(4.79) = -239.5 + 350 f(4.79) = 110.5 ~ 110 toys sold at $4.79

Quadratic_Equations/125320: What is the quadratic function that has a vertex at (-1,-3) and a y-intercept of -4? I think the answer is y=-(x+1)^2-3. Can someone please let me know if I am correct? 1 solutions Answer 91903 by ankor@dixie-net.com(15657)   on 2008-02-07 11:11:23 (Show Source): You can put this solution on YOUR website! What is the quadratic function that has a vertex at (-1,-3) and a y-intercept of -4? I think you are right : Would look like this:

Money_Word_Problems/125283: Can you please solve this problem? Anna, Jennifer, and Mia have certain sums of money. If Anna gives Jennifer $100, they will have the same amount; if Anna gives Mia $100, Mia will have twice as much as Anna; if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer. What sum has each? 1 solutions Answer 91878 by ankor@dixie-net.com(15657)   on 2008-02-06 21:37:40 (Show Source): You can put this solution on YOUR website! Anna, Jennifer, and Mia have certain sums of money. If Anna gives Jennifer $100, they will have the same amount; if Anna gives Mia $100, Mia will have twice as much as Anna; if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer. What sum has each? : Let a = Anna$; j = Jenn$; m = Mia$ : Write an equation for equation for each statement: : "If Anna gives Jennifer $100, they will have the same amount;" a - 100 = j + 100 or j + 100 = a - 100 j = a - 100 - 100 j = a - 200 : "if Anna gives Mia $100, Mia will have twice as much as Anna;" m + 100 = 2(a - 100) m + 100 = 2a - 200 m = 2a - 200 - 100 m = 2a - 300 : "if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer." m + 100 = 4(j-100) m + 100 = 4j - 400 m = 4j - 400 - 100 m = 4j - 500 : In the above equation, substitute (a-200) for j and (2a-300) for m; solve for a (2a-300) = 4(a-200) - 500 2a - 300 = 4a - 800 - 500 2a - 300 = 4a - 1300 -300 + 1300 = 4a - 2a 1000 = 2a a = a = $500 : m = 2a - 300 Substitute 500 for a m = 2(500) - 300 m = 1000 - 300 m = 700 : Use m = 4j - 500 to find j; substitute 700 for m 700 = 4j - 500 700 + 500 = 4j 1200 = 4j j = j = 300 : Anna had $500; Mia had $700 and Jenn had $300

Numbers_Word_Problems/125142: This question is from textbook beginning algebra If four times the sum of a number and 5 is divided by 3, the result is 16 1 solutions Answer 91821 by ankor@dixie-net.com(15657)   on 2008-02-06 16:04:55 (Show Source): You can put this solution on YOUR website! : Let x = the number and just write an equation for what it says: : If four times the sum of a number and 5, is divided by 3, the result is 16 = 16 Multiply equation by 3: 4(x + 5) = 3(16) : 4x + 20 = 48 : 4x = 48 - 20 : 4x = 28 x = x = 7 : : Check solution in original equation: = 16 = 16 = 16

Exponents-negative-and-fractional/125132: Hello If anyone can please try and solve this equation I don't even know where to start! Help! :( okay i realize that the LAST PART of this equation AFTER THE 1 written and shown to you incorrectly: it is supposed to be (3 over 4 ) 3/4 =1 (minus) - 3x-2 (over) / x+1. I don't know how to write this equation correctly as text. I apologize. Thank you and have blessed day!! 1 solutions Answer 91814 by ankor@dixie-net.com(15657)   on 2008-02-06 15:46:59 (Show Source): You can put this solution on YOUR website! Assume you mean: = 1 - Get rid of those annoying denominators; multiply the equation by 4(x+1): 4(x+1)* = 4(x+1)*1 - 4(x+1)* Cancel the denominators and you have: : 3(x+1) = 4(x+1) - 4(3x-2) : 3x + 3 = 4x + 4 - 12x + 8; multiply what's inside the brackets : 3x - 4x + 12x = 4 + 8 - 3; x's on the left, numerical values on the right : 11x = 9 x = : : Check solution in original equation: = 1 - = = 1 - = = 1 - : Invert the dividing fraction and multiply * = so we have: = 1 - ; confirms our solution

Equations/124754: I have 7 bags of marbles. There are 200 marbles in total. bag 1 + bag 2 = 57 marbles bag 2 + bag 3 = 83 marbles bag 3 + bag 4 = 71 marbles bag 4 + bag 5 = 43 marbles bag 5 + bag 6 = 66 marbles bag 6 + bag 7 = 43 marbles How many marbles are in each bag? 1 solutions Answer 91809 by ankor@dixie-net.com(15657)   on 2008-02-06 15:10:17 (Show Source): You can put this solution on YOUR website! I have 7 bags of marbles. There are 200 marbles in total. : Change the bag numbers to letters bag a + bag b = 57 marbles bag b + bag c = 83 marbles bag c + bag d = 71 marbles bag d + bag e = 43 marbles bag e + bag f = 66 marbles bag f + bag g = 43 marbles How many marbles are in each bag? : Try to get everything in terms of a b = -a + 57 : c = -b + 83 c = -(-a+57) + 83; substitute for b c = +a - 57 + 83 c = a + 26 : d = -c + 71 d = -(a+26) + 71; substitute for c d = -a - 26 + 71 d = -a + 45 : e = -d + 43 e = -(-a+45) + 43; substitute d e = +a - 45 + 43 e = a - 2 : f = -e + 66 f = -(a-2) + 66; substitute for e f = -a + 2 + 66 f = -a + 68 : g = -f + 43 g = -(-a+68) + 43 g = +a - 68 + 43 g = a - 25 : Substitute for b thru g in order = 200 a + (-a+57) + (a+26) + (-a+45) + (a-2) + (-a+68) + (a-25) = 200 : 4a - 3a + 57 + 26 + 45 - 2 + 68 - 25 = 200 : a + 169 = 200 a = 200 - 169 a = 31 marbles in bag 1 : Find the values b thru g by substituting for a: b = -31 + 57 = 26 in bag 2 c = 31 + 26 = 57 in bag 3 d = -31 + 45 = 14 in bag 4 e = 31 - 2 = 29 in bag 5 f = -31 + 68 = 37 in bag 6 g = 31 - 25 = 6 in bag 7 : Check our solutions using the above values: 31 + 26 + 57 + 14 + 29 + 37 + 6 = 200 total

Percentage-and-ratio-word-problems/125206: A certain sum of money y was divided into 3 portions in the ratio 1:2:3. If the difference between the maximum and minimum portions was Rs 4,000, find y? 1 solutions Answer 91770 by ankor@dixie-net.com(15657)   on 2008-02-06 08:20:19 (Show Source): You can put this solution on YOUR website! A certain sum of money y was divided into 3 portions in the ratio 1:2:3. If the difference between the maximum and minimum portions was Rs 4,000, find y? : Think of y divided into 6 parts: y, y and y : y - y = 4000 : Multiply equation by 6 to get rid of the denominators: 3y - y = 24000 : 2y = 24000 y = y = 12000

Travel_Word_Problems/124875: Smith bicycled 45 miles goin east from Durango and Jones bicycled 70 miles. Jones averaged 5 miles per hou more than Smith, and his trip took on-half hour longer than Smith's. How fast was each one traveling? 1 solutions Answer 91739 by ankor@dixie-net.com(15657)   on 2008-02-05 20:48:32 (Show Source): You can put this solution on YOUR website! Smith bicycled 45 miles going east from Durango and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took on-half hour longer than Smith's. How fast was each one traveling? : Let s = Smith's speed It says,"Jones averaged 5 miles per hour more than Smith," therefore: (s+5) = Jones' speed : Write a time equation: Time = Smiths time = Jones time - half an hour + Multiply equation by 2s(s+5) to get rid of the denominators 2s(s+5)* + 2s(s+5)* : Cancel out the denominators and you have: 2(s+5)*45 = 2s*70 - s(s+5) : 90s + 450 = 140s - s^2 - 5s : s^2 + 5s + 90s - 140s + 450 = 0 : s^2 - 45s + 450 = 0; Arranged as a quadratic equation : This factors to (s - 15) (s - 30) = 0 : s = 15, or s = 30; Check and you will see that either solution will work in the original equation : Probably s = 15 is more reasonable

Graphs/124905: Corporation Wally Mart allows each of its traveling employees an amount of money per day for a hotel room and food expenses. One employee travels for 4 days and 4 nights and is allotted $480 while another employee travels for 3 days and 2 nights and is allotted $270. a) Give the system of equations for solving this situation. b) Find the amount allowed for a hotel room and daily food expenses 1 solutions Answer 91738 by ankor@dixie-net.com(15657)   on 2008-02-05 20:15:01 (Show Source): You can put this solution on YOUR website! Let x = daily amt of hotel Let y = daily amt for food : a) Give the system of equations for solving this situation. : Write an equation for each statement: : "One employee travels for 4 days and 4 nights and is allotted $480" 4x + 4y = 480 : " another employee travels for 3 days and 2 nights and is allotted $270." 2x + 3y = 270 : : b) Find the amount allowed for a hotel room and daily food expenses : Multiply the 2nd equation by 2 and subtract the 1st equation from it 4x + 6y = 540 4x + 4y = 480 ------------------subtracting eliminates x, find y 0x + 2y = 60 y = y = $30 a day for food : Find x, substitute 30 for y in the 1st equation 4x + 4(30) = 480 4x + 120 = 480 4x = 480 - 120 4x = 360 x = x = $90 a night for hotel : Check solutions in the 2nd equation, substitute for x and y 2(90) + 3(30) = 180 + 90 = 270 as given : Did I explain this so you could understand what we did here? Any questions?

Numbers_Word_Problems/124791: There are some quarters and dimes in a piggy bank. There are 10 more quarters than the number of dimes, and their ratio is 3/2. How many quarters and dimes are there? 1 solutions Answer 91709 by ankor@dixie-net.com(15657)   on 2008-02-05 17:09:26 (Show Source): You can put this solution on YOUR website! There are some quarters and dimes in a piggy bank. There are 10 more quarters than the number of dimes, and their ratio is 3/2. How many quarters and dimes are there? : Let x = no. of dimes It says,"There are 10 more quarters than the number of dimes," therefore: (x+10) = no. quarters : It says,"their ratio is 3/2." : = Cross multiply and you have: : 3x = 2(x+10) : 3x = 2x + 20 : 3x - 2x = 20 : x = 20 dimes, and 30 quarters : =

Length-and-distance/124824: Convert a speed of 20.4 miles per second into its equivelant in kilometers per hour. 1 solutions Answer 91703 by ankor@dixie-net.com(15657)   on 2008-02-05 16:27:40 (Show Source): You can put this solution on YOUR website! Convert a speed of 20.4 miles per second into its equivelant in kilometers per hour. : It's useful to know the conversion factor of mph to km/h: Multiply by 1.609 You know there are 3600 seconds in 1 hour : Convert miles/sec to mph: : Mph = 20.4 * 3600 = 73,440 mph : Convert mph to km/h 1.609 * 73440 = 118,165 km/h

Linear-systems/124765: Find the slope of the line whose equation is 8x+7y=56? 1 solutions Answer 91694 by ankor@dixie-net.com(15657)   on 2008-02-05 16:06:59 (Show Source): You can put this solution on YOUR website! Find the slope of the line whose equation is 8x+7y=56? ; Put the equation into the slope/intercept format: y = mx + b : 8x + 7y = 56 : 7y = -8x + 56; subtracted 8x from both sides : y = x + ; divided both sides by 7 : y = x + 8; the slope/intercept form of the equation : The slope (m) will be

Human-and-algebraic-language/124902: there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the second equals the sum of the third and fourth numbers. find the numbers.: there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the second equals the sum of the third and fourth numbers. find the numbers. this is a grade 8 algebra question so no calculators so i need to understand how to get the answer from start to finish step by step. THANKS THANKS THANKS 1 solutions Answer 91685 by ankor@dixie-net.com(15657)   on 2008-02-05 15:36:52 (Show Source): You can put this solution on YOUR website! Rewrote the problem slightly : there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the first and the second equals the sum of the third and fourth numbers. find the numbers.: : Let the numbers be: w, x , y, z; in that order : Write an equation for each phrase/statement : " the first is twenty less the second, " w = x - 20 : "the third is one more than twice the first" y = 2w + 1 : "and the forth is four more than the third." z = y + 4 : "sum of the second equals the sum of the third and fourth numbers." w + x = y + z : find the numbers.: Get everything in terms of x w = (x-20) and y = 2w + 1 y = 2(x-20) + 1; substituted (x-20)for w y = 2x - 40 + 1 y = (2x-39) and z = y + 4 z = (2x-39) + 4: substitute (2x-39)for y z = (2x-35) And w + x = y + z Substitute for w, y, and z; and solve for x (x-20) + x = (2x-39) + (2x-35) 2x - 20 = 4x - 74 -20 + 74 = 4x - 2x 54 = 2x x = x = 27 : Find the other number w = 27 - 20 w = 7 : y = 2(27) - 39 y = 54 - 39 y = 15 : z = 2(27 - 35 z = 54 - 25 z = 19 : Determine if w + x = y + z; to confirm our solutions 7 + 27 = 15 + 19 34 = 34

Length-and-distance/124918: This question is from textbook Prentice Hall Mathmatics 2 I am trying to help my daughter better understand her math and how to find the answer. These are the practice questions. Thanks Rectangle ABCD shares BC (line above BC) with equilateral triangle BCE. The length of CD (line above CD) is 4 cm, and the length of DA (line above DA)is 3 cm.What is the length of BE (line above BE)? 1 solutions Answer 91672 by ankor@dixie-net.com(15657)   on 2008-02-05 14:54:39 (Show Source): You can put this solution on YOUR website! : If I am picturing this correctly, Line AD = BC = 3" because it is a rectangle BC is also one side of equilateral triangle (all sides =) Therefore BE = 3" also

Pythagorean-theorem/125032: I am trying to do my homework and do not understand the statement below. We can use the Pythagorean Theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem. 1 solutions Answer 91668 by ankor@dixie-net.com(15657)   on 2008-02-05 14:42:33 (Show Source): You can put this solution on YOUR website! Let's say you need to get up on a roof that is 18 ft off the ground and you need to buy a ladder to reach the roof. You want the ladder to rest on the ground 10 feet from the house (for safety reasons). : You can see that the side of the house. a point 10 feet from the house, and the ladder form a right triangle' Using Pythagorean theorem c^2 = a^2 + b^2 a = distance from the house 10' b = height to the roof 18' c = length of the ladder required : c^2 = 18^2 + 10^2 : c^2 = 324 + 100 : c^2 = 424 c = c = 20.5 ft : So we could say a 20' ladder would do the job : This is an every day example which enables you to avoid buying a ladder that is too short, or buying a longer ladder than you needed, which cost more.

Travel_Word_Problems/124782: Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed for each car for the 2-hour trip? 1 solutions Answer 91558 by ankor@dixie-net.com(15657)   on 2008-02-04 21:40:24 (Show Source): You can put this solution on YOUR website! Two cars started from the same point, and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed for each car for the 2-hour trip? : Let s = speed of the slower car then (s+8) = speed of the faster car : Write a distance equation; Distance = time * speed : 2s + 2(s+8) = 208 mi : 2s + 2s + 16 = 208 : 4s = 208 - 16 : 4s = 192 s = s = 48 mph av speed of the slower car then 48 + 8 = 56 mph av speed of the faster car : Check solutions by finding the distance 2(48) + 2(56) = 96 + 112 = 208

Polynomials-and-rational-expressions/124758: I need help with answering this problem. Thanks! Factor Completely: a(to the power of 4) -(minus) b(to the power of 4) 1 solutions Answer 91538 by ankor@dixie-net.com(15657)   on 2008-02-04 21:03:00 (Show Source): You can put this solution on YOUR website! Factor Completely: a(to the power of 4) -(minus) b(to the power of 4) : We can write it: (a^4 - b^4) : Recognize this as the "difference of squares"; factors to: (a^2 + b^2) (a^2 - b^2) : (a^2 - b^2) is also the difference of squares and factors to: (a + b)(a - b) : So you have (a^2 + b^2)(a - b)(a + b)

Linear-systems/124730: Wilma drove at an average speed of 50 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 45 mi/h. She returned home 40 hours after leaving. How many miles is City A from City B 1 solutions Answer 91509 by ankor@dixie-net.com(15657)   on 2008-02-04 19:04:08 (Show Source): You can put this solution on YOUR website! Wilma drove at an average speed of 50 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 45 mi/h. She returned home 40 hours after leaving. How many miles is City A from City B : First of all, let's just concern ourselves with the traveling time: Subtract the 10 hr stay from the total time (40 hr) she was gone; She had 30 hrs on the road : Let d = distance from A to B : Write a time equation: Time = : Time to B + time to A = 30 hrs + = 30 : Multiply equation by a multiple of both denominators, 450 would do it: 450* + 450* = 450(30) Cancel out the denominators and you have: : 9d + 10d = 13500 : 19d = 13500 d = d = 710.5 miles from A to B : : Check solution by finding the time each way and finding the total time: 710.5/50 = 14.2 hrs 710.5/45 = 15.8 hrs -------------------- Total time 30.0 hrs as given ; : Did I make this understandable? Any questions?

Mixture_Word_Problems/124726: For a certain experiment, a student requires 300 ml of a solution that is 13% HCl (hydrochloric acid). The storeroom has only solutions that are 10% HCl and 15% HCl. How many milliliters of each available solution should be mixed to get 300 ml of 13% HCl? Could you please explain to me how to solve this problem? 1 solutions Answer 91504 by ankor@dixie-net.com(15657)   on 2008-02-04 18:41:47 (Show Source): You can put this solution on YOUR website! For a certain experiment, a student requires 300 ml of a solution that is 13% HCl (hydrochloric acid). The storeroom has only solutions that are 10% HCl and 15% HCl. How many milliliters of each available solution should be mixed to get 300 ml of 13% HCl? : Let x = amt of 15% HCL the total resulting amt must be 300 ml, therefore: (300-x) = amt of 10% HCL : .15x + .10(300-x) =.13(300) : .15x + 30 - .10x = 39 : .15x - .10x = 39 - 30 : .05x = 9 x = x = 180 ml of 15% HCL then 300 - 180 = 120 ml of 10% HCL : : We can check our solution in the original equation .15(180) + .10(120) = .13(300) 27 + 12 = 39 : Did this make sense to you? Any questions?

Polynomials-and-rational-expressions/124607: I am working on solving linear and quadratic equations. I need help with this problem: I believe the CD:(y-2)(3y-2)(3y+2) Please help solve. Thanks. 1 solutions Answer 91485 by ankor@dixie-net.com(15657)   on 2008-02-04 16:40:38 (Show Source): You can put this solution on YOUR website! Assume you mean: + = Factor the denominators: + = : You're right about the common denominator, multiply each term by that: (y-2)(3y-2)(3y+2)* + (y-2)(3y-2)(3y+2)* = (y-2)(3y-2)(3y+2)* : Cancel out the denominators, leaving: (3y-2)(3y+1) + 9(y-2) = (3y+2)(2y-2) : FOIL (9y^2 - 3y - 2) + (9y-18) = 6y^2 - 2y - 4 : Combine like terms on the left 9y^2 - 6y^2 - 3y + 9y + 2y - 2 - 18 + 4 = 0 : 3y^2 + 8y - 16 = 0 : Factors to: (3y - 4)(y + 4) = 0 : 3y = +4 y = and y = -4 : : I checked the y=-4 solution in the original equation. : Did this help you?

Linear-equations/124548: I am so confused...I need to solve each system by the addition method, I am only understanding half of the process. 1 solutions Answer 91476 by ankor@dixie-net.com(15657)   on 2008-02-04 15:38:23 (Show Source): You can put this solution on YOUR website! : Are you sure you have this problem written correctly? Could it be: x + y = 5 : GEt rid of the denominators by multiplying equation by 12 12*x + 12*y = 12(5) : Cancel the denominators and you have: 3x + 4y = 60 : Multiply the 1st equation (x-y=6), by 4 and add to the above equation 3x + 4y = 60 4x - 4y = 24 ---------------- adding eliminates y 7x + 0y = 84 7x = 84 x = ; divided both sides by 7 x = 12 : Find y using x - y = 6; substitute 12 for y 12 - y = 6 -y = 6 - 12 -y = -6 y = +6; multiplied equation by -1 to get rid of the negatives : Now let's check our solutions in the original equations: *12 + *6 = 5 3 + 2 = 5; confirms our solution : : Did this unconfuse you? Any questions?

Polynomials-and-rational-expressions/124530: Perform the indicated operation. 1) cubed root of 9x squared TIMES cubed root of 3x 2) ( 2 squared root of 3 MINUS 3)(2 square root of 3 + 3) 1 solutions Answer 91475 by ankor@dixie-net.com(15657)   on 2008-02-04 15:24:58 (Show Source): You can put this solution on YOUR website! Perform the indicated operation. : 1) cubed root of 9x squared TIMES cubed root of 3x * can be combined, do the math, and note that 27x^3 is a perfect cube = = 3x : 2) ( 2 squared root of 3 MINUS 3)(2 square root of 3 + 3) ()() FOIL this 4(3) + 6 - 6* - 9 Note that the two radicals in the middle have opposite signs so they cancel, leaving: 12 - 9 = 3 : Did this make sense to you? Any questions?

Quadratic_Equations/124744: A professor started a project with a group of students, 60% of whom were boys. Due to sme unavoidable reasons, six girls could not turn up, so the professorhad to make some changes in the grou. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involvedin the project initially. 1 solutions Answer 91467 by ankor@dixie-net.com(15657)   on 2008-02-04 13:36:02 (Show Source): You can put this solution on YOUR website! A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially. : Let t = total number of students, .6t = number of boys originally : (.6t + 6) = actual number of boys (which the problem says became 75%) : From all this we have one simple equation: .6t + 6 = .75t .6t - .75t = -6 -.15t = -6 t = -6/-.15 t = +40 kids : .6 * 40 = 24 boys originally .4 * 40 = 16 girls "

Numbers_Word_Problems/124624: find the largest two-digit number which is equal to four times the sum of it's digits 1 solutions Answer 91463 by ankor@dixie-net.com(15657)   on 2008-02-04 12:33:39 (Show Source): You can put this solution on YOUR website! find the largest two-digit number which is equal to four times the sum of it's digits : We can find the relationship between the two digits with an equation: 10x + y = 4(x+y) 10x + y = 4x + 4y 10x - 4x = 4y - y 6x = 3y 2x = y; divided equation by 3 : We can see that x cannot = more than 4, if y is a single digit, therefore x = 4, y = 8; Largest 2 digit number is 48, that satisfied the problem

Graphs/124690: A runner is halfway(13 miles) thru the marathon and sees that he has been running for about 100 minutes. he realizes that in order to match his personal best he will have to run faster. his personal best time for 26 miles is 191 minutes. Q: what is the runner's rate (slope) during the second half of the race in minutes per mile? 1 solutions Answer 91410 by ankor@dixie-net.com(15657)   on 2008-02-03 21:56:20 (Show Source): You can put this solution on YOUR website! A runner is halfway(13 miles) thru the marathon and sees that he has been running for about 100 minutes. he realizes that in order to match his personal best he will have to run faster. his personal best time for 26 miles is 191 minutes. : Q: what is the runner's rate (slope) during the second half of the race in minutes per mile? : Since he has used up 100 min in 1st 13 mi, he has to do the last 13 mi in 91 min : Speed = Dist/time : s = = : He has to run a rate of 7 min per mile : Check: 13 * 7 = 91 min