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# Recent problems solved by 'rapaljer'

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 Numeric_Fractions/13301: Could u help me on finding the missing factors please1 solutions Answer 6647 by rapaljer(4667)   on 2005-09-29 22:31:26 (Show Source): You can put this solution on YOUR website!I don't see ANY factors in this problem!!! It looks to me like ALL the factors are missing!! R^2 at SCC
 Quadratic_Equations/13295: Simplifify 6x^2y^2 + 11xy + 4 all divided by 9x^2y^2 + 9xy - 4 I've tried and i cant get it to simplify, does it even simplify1 solutions Answer 6645 by rapaljer(4667)   on 2005-09-29 22:29:36 (Show Source): You can put this solution on YOUR website!You'll have to factor the numerator and denominator in order to reduce the fraction. It just so happens (by chance???) that they both factor as trinomials. It may be some tough factoring, but they do factor. You can divide out the factor of (3xy+4). Final answer: R^2 at SCC
 Numeric_Fractions/12283: (2x+3)/x + 4/(x-1) =0 Solve for x. I don't know if I'm on right track with this. I ended up with a quadratic and using formula got x=-2+or-sqrt7. Grateful for any advice1 solutions Answer 6631 by rapaljer(4667)   on 2005-09-29 20:10:24 (Show Source): You can put this solution on YOUR website!I don't know what you did to get your answer, but I didn't get that. First, this is an equation, and there are several ways to solve it. I think the easiest way to solve it, since it is equal to zero, add the second fraction to both sides and write this as a fraction equal to the negative of a fraction. As I said, this is NOT the only way, but I think it will be the easiest to explain and easiest to understand: Remember means that So, means that Multiplying it out: Set equal to zero by adding +4x to each side: As CHANCE would have it (yeah, right!) THE TRINOMIAL FACTORS!! First solution: Second solution: R^2 at SCC
 Equations/13223: If Loius's savings were increased by 4 times his savings, the result would be \$25,000. how much has he saved?1 solutions Answer 6619 by rapaljer(4667)   on 2005-09-29 18:39:45 (Show Source): You can put this solution on YOUR website!Let x= amount of his savings There may be two ways to interpret this: Were his saving increased BY 4 times his savings? I think that must mean that he ADDS 4x to his present savings of x. The equation is x + 4x = 25000 5x = 25000 x= \$5000 Check: If his savings of \$5000 are INCREASED BY 4 times this amount (which by the way is \$20,000), then the result is \$25,000. I'm almost sure this is the way the problem is intended to be interpreted. R^2 at SCC
 Linear-equations/13214: How would you solve y=-1/3+23/3 then graph it? 1 solutions Answer 6617 by rapaljer(4667)   on 2005-09-29 18:22:38 (Show Source): You can put this solution on YOUR website!Do you mean y= -1/3 x + 23/3??? If so, then you need to start with the y-intercept at the point 23/3, which is almost up to 8 units. From this point measure off a slope of -1/3. This is to say, it is a RISE of -1 and a run of 3. So from the point that you just graphed on the y axis, and measure DOWN 1 unit, then move 3 unit to the right, and put a point. Connect the two points and it should look like this: R^2 at SCC
 Percentage-and-ratio-word-problems/13219: Mr. Garza's annual income has gone from \$32,000 to \$48,000 in 6 years. By what percent has his annual income increased?1 solutions Answer 6616 by rapaljer(4667)   on 2005-09-29 18:08:17 (Show Source): You can put this solution on YOUR website!First find the amount of increase. Since the income went from \$32000 to 48000, this means that the amount of increase is \$16000. Percent of increase is always a comparison of the amount of increase to the ORIGINAL amount, which is \$32000. Percent of increase = = = = 50% R^2 at SCC
 Reduction-of-unit-multipliers/13213: Shandra combined the following juices to make fruit punch: 800ml applt juice, 500ml pineapple juice, 1,000ml of orange juice and 200ml of grape juice. What was the total amount of fruit punch made in liters?1 solutions Answer 6615 by rapaljer(4667)   on 2005-09-29 18:03:52 (Show Source): You can put this solution on YOUR website!First add up ALL the juice in ml. That would be 2500 ml. Then convert to liters. I use what I call the "Metric Line", starting from left to right with kilo, hecto, deca, basic unit (in this case liters), deci, centi, milli. When converting from one unit to another, you must move the decimal to the left or right, depending upon what you are converting to what. Count the number of units that you move from left to right or right to left, and move the decimal that many places to the left or right. In this case you are converting from milli to the basic unit (liters), which is moving 3 places to the left. You must therefore move the decimal three places to the left, so 2500 ml = 2.5 liters. R^2 at SCC
 Inequalities/12909: WHAT IS THE SOLUTION OF THE INEQUALITY 8-3x<-3(1+x)+1 a.all real numbers b.no real numbers c.x>2/3 d.x<-11/6 1 solutions Answer 6614 by rapaljer(4667)   on 2005-09-29 17:51:52 (Show Source): You can put this solution on YOUR website!8-3x<-3(1+x)+1 Use distributive property to remove the parentheses: 8-3x < -3- 3x + 1 Combine like terms on each side: 8-3x < -2 - 3x Add +3x to each side in an attempt to get all variable terms on the left side: 8-3x+3x < -1 - 3x + 3x 8 < -1 Since there are NO VARIABLES left in the equation, you can't solve for x as you do in most equations. In this case, all you have left is 8<-1, which is NOT TRUE. In fact, it is NEVER true. This means that no matter what x is, 8 will NEVER be less than -1. This means that there IS NO SOLUTION! The final answer is b. No Real Numbers. R^2 at SCC
 Circles/12974: Find the domain of y = √x –2 1 solutions Answer 6537 by rapaljer(4667)   on 2005-09-28 15:12:56 (Show Source): You can put this solution on YOUR website!I'm not sure exactly what you mean by this. If you mean which is technically what you have given, it means that x must be greater than or equal to zero. Domain is in interval notation: [0, infinity) If you meant , this means that x-2 must be greater than or equal to zero. If you add 2 to each side of the inequality, you get x must be greater than or equal to 2. Domain for this, in interval notation, would be [2, infinity). R^2 at SCC
 Circles/12975: Find the domain of y = 7x2 – 14/12x2 + 20 1 solutions Answer 6534 by rapaljer(4667)   on 2005-09-28 14:52:07 (Show Source): You can put this solution on YOUR website!Are you saying: y = If so, the domain consists of all values of x except that the denominator must NEVER be zero. The denominator consists of taking a value of x, squaring it, multiplying that result by 12 and then adding 20. By looking at this you can see that squaring a number will never be negative. Multiplying by 12 and then adding 20 will certainly always give you a positive, never a ZERO, result. Therefore the answer for domain is all real values, since the denominator can never be zero. R^2 at SCC
 Age_Word_Problems/12980: Kenneth's age is 5 yrs older than Alvin. Find there present ages if the product of Kenneth's age 4 yrs. from now and Alvin's age 5 yrs. ago is 51.1 solutions Answer 6532 by rapaljer(4667)   on 2005-09-28 14:24:46 (Show Source): You can put this solution on YOUR website!Let x = Alvin's age x+5 = Kenneth's age x+5 + 4 = x+9 = Kenneth's age 4 yrs from now x-5 = Alvin's age 5 years ago. Equation: Product of (Kenneth 4 years from now)x (Alvin 5 years ago) = 51 (x+9)(x-5) = 51 Guess what! It factors!! x= -12, x= 8 An age cannot be negative, so x= 8 Alvin's age x+5 = 13 Kenneth's age Check: In 4 years Kenneth will be 17, and 5 years ago, Alvin was 3. The product of 17*3 is 51. It checks. R^2 at SCC
 Expressions-with-variables/12987: i really need ur help solving this equation: 21x+3=1211 solutions Answer 6529 by rapaljer(4667)   on 2005-09-28 14:08:27 (Show Source): You can put this solution on YOUR website!21x+3=121 Add -3 to each side: 21x+3-3=121-3 21x = 118 Divide both sides by 21: What an UGLY answer! Life doesn't always come out even, does it? In this case, the fraction doesn't even reduce!! How sad!! R^2 at SCC
 Linear-systems/12985: Hello: I really need your help. I have tried all possible ways to solve this equation but I am confused on how to start to solve it. Here is the question: Find the point of intersection of the given straight lines. x - 4y = -2 x + 2y = 4 Please help me with this problem. Thank you.1 solutions Answer 6527 by rapaljer(4667)   on 2005-09-28 14:04:14 (Show Source): You can put this solution on YOUR website!There are several ways to do this. The elimination method usually works well when the equations are both in standard form, as in this case. x - 4y = -2 x + 2y = 4 In order to eliminate the x variable, multiply the first equation by -1, and rewrite the second equation as it is: -x + 4y = 2 x + 2y = 4 Now add these two equations together giving you 6y = 6 y=1 Substitute the y = 1 back into either equation, say the first one: x - 4y = -2 x - 4(1) = -2 x-4 = -2 Add 4 to each side: x-4+4 = -2 + 4 x=2 Check in the second equation, by letting x= 2 and y = 1: x + 2y = 4 2 + 2(1) = 4 It checks! R^2 at SCC
 Linear-systems/12580: I don't get qestion number 19 page 134 of algebra 11 solutions Answer 6398 by rapaljer(4667)   on 2005-09-26 02:01:12 (Show Source): You can put this solution on YOUR website!And YOU think the tutors at algebra.com are SO GOOD we can solve a problem just from the page number and the problem number? Maybe if you gave us the answer, we could tell you what the problem was??? Forgive my cynicism. It's late! Or is that EARLY?? R^2 clueless at SCC
 Functions/12592: hi can you help me with this -6/5<-4x1 solutions Answer 6397 by rapaljer(4667)   on 2005-09-26 01:58:04 (Show Source): You can put this solution on YOUR website!I personally think you are better off getting the variables to the LEFT side when solving inequalities, so add 4x to each side and add 6/5 to each side. 4x < 6/5 The divide both sides by 4, or what might work better in this case is to multiply both sides by 1/4: R^2 at SCC
 Geometry_Word_Problems/12577: The measures of two complementary angles are 12q-9 and 8q+14. Find the measures of the angles.1 solutions Answer 6396 by rapaljer(4667)   on 2005-09-26 01:42:45 (Show Source): You can put this solution on YOUR website!12q-9 + 8q+14 = 90 20q + 5 = 90 20q= 85 q = 85/20 = 4.25 The angles are 12q-9= 12(4.25) - 9 = 51-9= 42 degrees 8q + 14 = 8(4.25) + 14 = 34 + 14 = 48 degrees Check by adding 42 + 48 = 90 degrees. R^2 at SCC
 Expressions-with-variables/12584: I don't get how you do fractions like A/2+5=10 I get all confussed what do I do?1 solutions Answer 6395 by rapaljer(4667)   on 2005-09-26 01:37:39 (Show Source): You can put this solution on YOUR website!If you really don't like fractions, then multiply both sides by the denominator which is 2, and get rid of it: The 2 divides out in the first term, leaving: Now just subtract 10 from each side: R^2 at SCC
 Mixture_Word_Problems/12601: How many gallons of pure antifreeze must be added to 20 gallons of 25% antifreeze to get a mixture that is 40% antifreeze1 solutions Answer 6394 by rapaljer(4667)   on 2005-09-26 01:16:36 (Show Source): You can put this solution on YOUR website!Let x = amt of pure antifreeze to be added You are adding this to 20 gallons of 25% and you will end up a total mixture of x+ 20 at 40%. The equation is .25(20) + x = .40(x+20) 5 + 1.00x = .40x + 8 1.00x - .40x = 8 - 5 .60x = 3 Does it check?? (It is VERY late in Florida, here! I don't guarantee my work or my spelling at this hour!!}}} R^2 at SCC
 Quadratic_Equations/12588: I'm supposed to find a family of quadratic equations passing through the points (1,0) and (-1,-2), using the general form y=Ax^2+Bx+C. So far, here's what I got: 1) Plugged in both points to the general form, giving me 2 distinct equations: 0=A+B+C 0=A-B+C+2 2) Made them equal to each other, giving me B=1 3) Subbed B=1 into either equation to get A=-C-1 and C=-A-1 Now this is the point where I get stuck, since if I use both B=1 and A=-C-1 to get the final two variables, I end up with nothing. Please help, and thanks so much! -Bing1 solutions Answer 6393 by rapaljer(4667)   on 2005-09-26 00:54:36 (Show Source): You can put this solution on YOUR website!You are correct. Remember that you are trying to find a family of parabolas, which means that there are perhaps an infinite number of such parabolas. This is what happens when you have three unknowns and only two conditions (i.e., equations) to satisfy. Both equations come down to A + C = -1. So, let B=1, and solve for either C or A in terms of the other. Say, C= -A -1. The equation is the family of parabolas: , where A represents any non-zero number. Of course, if A = 0, then it is NOT a parabola. Any other value of A should give you points that include (1,0) and (-1,-2). For examples, let A = 1: Do both points satisfy this? If x =1, then y= 0, and if x=-1, then y =-2. Let A = 2: (((y = 2x^2 +x -3}}} Let A = -1: R^2 at SCC
 Polynomials-and-rational-expressions/12598: please help me solve these following questions: simplify the following radicals. : squar foot of 50=? squar foot of 325=? squar foot of 96=? squar foot of 256=?1 solutions Answer 6391 by rapaljer(4667)   on 2005-09-26 00:14:11 (Show Source): You can put this solution on YOUR website!What do you mean "squar foot"??? Do you mean square root?? To find a square root, you need to know the perfect squares, and find the largest perfect square that will divide evenly into the given number. The following ar examples of this concept. For additional explanation see my Lesson Plans in algebra.com on Square Roots, or see my website under Basic Algebra, Samples of Basic Algebra One Step at a Time, and Chapter 5. because that one comes out even: . R^2 at SCC
 Travel_Word_Problems/12597: A starts running at Speed 5 km/h at 8 am. after 30 minutes B starts running from the same point in the same direction at Speed 6 km/h. At what time, B will catch A. Sir I solved it like this. Pl. correct me where I was wrong. The answer is 11 am (3 hrs). Speed of A= 5 KM/h Distance travelled in 30 minutes= 2.5 kms. Relatve speed of B w.r.t. A = (6-5)= 1 km/h. Distance of 1 Km is covered in 1 hr by B. therefore gap of 2.5 kms will be covered by B in 1 * 2.5= 150 minutes (2 hrs 30 minutes) whereas the answer is 3 hrs. Pl. correct me. 1 solutions Answer 6389 by rapaljer(4667)   on 2005-09-26 00:06:36 (Show Source): You can put this solution on YOUR website!You are absolutely CORRECT!! You said that B will catch A in 2 hours 30 minutes, which IS at 11:00 a.m!! You must have forgotten that B started a half hour later than A, which would be starting at 8:30 a.m. for B. Three hours is the time for A to be caught! Two and a half hours is the time for B to do the catching!! BOTH happen at the same time--11:00 a.m.!! R^2 at SCC
 Numbers_Word_Problems/12585: A store keeper goes to the bank to get \$10 worth of change. He requests twicew as many quarters as half dollars, twice as many dimes as qurters, 3 times as many nickles as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?1 solutions Answer 6386 by rapaljer(4667)   on 2005-09-25 23:55:39 (Show Source): You can put this solution on YOUR website!Let x = number of half dollars 2x = number of quarters 2(2x) = 4x = number of dimes 3(4x) = 12x = number of nickels Total value, multiply number of coins times the value of each coin in cents, and the total value of the coins is \$10 or 1000 cents. (Doesn't it make "cents" to do it this way??) 50(x) + 25(2x) + 10(4x) + 5(12x) = 1000 50x + 50x + 40x + 60x = 1000 200x = 1000 x= 5 Half dollars 2x = 10 Quarters 4x = 20 Dimes 12x = 60 Nickels Check: Does it add up to \$10.00??? You tell me!! R^2 at SCC
 logarithm/12591: Please help with this problem: 3 log 3 x=5 (the second "3" is under the word "log"). I can't seem to follow the pattern on my textbook. I would love to see the steps to working out this problem. thanks!1 solutions Answer 6385 by rapaljer(4667)   on 2005-09-25 23:28:04 (Show Source): You can put this solution on YOUR website! There are probably several ways to go about this. I'd say to divide both sides by 3, and get Next use the basic definition of logarithms to convert to exponential form. Remember the definition says means ? In the same way, means that What you are trying to find is x, and that's it!! x = . Is that enough, or you could probably rewrite this as which means , but that's getting carried away if you ask me. Easier to calculate it and say approximately 6.24. R^2 at SCC
 Polynomials-and-rational-expressions/12380: no matter what i do, i can't figure this 1 out, please help 3y(2y-3)(3y-4)=01 solutions Answer 6290 by rapaljer(4667)   on 2005-09-23 16:39:59 (Show Source): You can put this solution on YOUR website!You have a product equal to zero: 3y(2y-3)(3y-4)=0 If a product of numbers equals to zero, then one of those numbers must be zero. Because this can be thought of as a product of three quantities, you can make three separate solutions: Solution #1. 3y = 0 Solution #2: 2y-3 = 0 2y= 3 Solution #3: 3y-4=0 3y = 4 R^2 at SCC
 Percentage-and-ratio-word-problems/12363: Please help me I need this by Monday, please!! :0) An investment of \$1500 paid interest of \$45 during a certain period. How much interest would an investment of \$2000 invested at the same rate for the same length of time pay?1 solutions Answer 6289 by rapaljer(4667)   on 2005-09-23 16:35:08 (Show Source): You can put this solution on YOUR website!Since the Interest paid is in proportion to the Investment, you can set up a proportion: Let x = interest earned on a \$2000 investment. = Remember means In the same way, means An easier way to look at it, since \$2000 is actually \$1500 plus one third of that amount, the interest earned will be the corresponding \$45 plus one third of that amount, or \$45 + 15 = \$60. R^2 at SCC
 Probability-and-statistics/12361: How many arrangements of the letters in the word olive can you make if each arrangement must use three letters? 1 solutions Answer 6288 by rapaljer(4667)   on 2005-09-23 14:18:53 (Show Source): You can put this solution on YOUR website!The key word is "arrangement" which means that the order is significant. This makes the problem a PERMUTATION, a permutation of the 5 letters in the word OLIVE taken 3 at a time. There are a lot of notations that can be used here, one of which, the easiest to type here, is P(5,3). It means to start with the first number 5, and start counting down. You must have THREE numbers (that is the second number), in the product: P(5,3) = 5*4*3 = 60 different arrangements. R^2 at SCC
 Exponential-and-logarithmic-functions/12356: im using substitution in algera2 and i cant figure this one out {4x - y = 22 { 2x + 3y = 4 1 solutions Answer 6283 by rapaljer(4667)   on 2005-09-23 12:12:53 (Show Source): You can put this solution on YOUR website!Solve for y in the first equation: 4x - y = 22 4x-4x - y = 22- 4x -y = -4x + 22 y = 4x - 22 Substitute into the second equation: 2x + 3y = 4 2x + 3(_____)=4 2x + 3(4x-22) = 4 2x + 12x - 66 = 4 14x =70 x=5 Substitute back into first equation to solve for y: y=4x -22 y=4*5 - 22 y=20-22 y=-2 Check in the second equation: 2x + 3y = 4 2(5)+3(-2) = 4 10-6= 4 It checks. R^2 at SCC
 Equations/12345: 5d+9-4d=51-5d1 solutions Answer 6282 by rapaljer(4667)   on 2005-09-23 12:00:57 (Show Source): You can put this solution on YOUR website!5d+9-4d=51-5d d +9 = 51 - 5d Add 5d to each side: d + 5d + 9 = 51 - 5d + 5d 6d + 9 = 51 Subtract 9 from each side: 6d + 9 - 9 = 51 - 9 6d = 42 d= 7 R^2 at SCC d= 7