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# Recent problems solved by 'rapaljer'

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 Rational-functions/213456: A Prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll. The troll demanded payment of one-half of the apples plus two more. the prince gave him the apples and continued on home. The prince was then stopped by a second troll who demanded one- half of the apples plus two more, the prince did as he was told and continued on home. Stopped by a third troll he demanded the prince give him one- half of the apples plus two more. The prince did as asked and sadly continued on home only having two golden apples left. How many apples did he pick to begin with?1 solutions Answer 161263 by rapaljer(4667)   on 2009-09-14 11:45:59 (Show Source): You can put this solution on YOUR website!Let x = total number of apples The first troll demands half of his apples plus 2, so after leaving the first troll, the prince has apples The 2nd troll demands half of what is left and 2 more, so now the prince has The 3rd troll demands half of what is left and 2 more, so now the prince has And this equals exactly 2 apples! Now, work this backwards by adding +2 to each side: Multiply both sides by 2: (1/4)x-3=8 Add +3 to each side: (1/4)x=11 Multiply both sides by 4: x=44 apples. Check: If the prince starts with 44 apples, the first troll gets 22 +2 =24 apples. The prince is left with 20. The second troll demands 10+2, which leaves the prince with 8. The third troll demands 4 apples plus 2, leaving the prince with 2 apples. Very nice problem!! Poor princess!! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Inequalities/213424: solve the following linear inequality. write the solution in interval notation 3x-(4-2x)+21 solutions Answer 161256 by rapaljer(4667)   on 2009-09-14 11:09:53 (Show Source): You can put this solution on YOUR website!3x-(4-2x)+2 < x-(3x-5)+1 3x-4+2x+2 < x-3x+5+1 5x-2 < -2x+6 7x<8 x<8/7 R^2
 Volume/213419: What is the volume of a paper cup with a diameter of 2 inches and 5 tall converted to centimeters.1 solutions Answer 161249 by rapaljer(4667)   on 2009-09-14 10:29:22 (Show Source): You can put this solution on YOUR website! r=1, h=5 =5.23 cubic inches approximately To convert to cubic centimeters, multiply by the conversion factor 2.54^3 cubic centimeters approximately R^2
 Coordinate-system/213421: This question is from textbook college algebra 1 solutions Answer 161247 by rapaljer(4667)   on 2009-09-14 10:21:39 (Show Source): You can put this solution on YOUR website!No problem stated???
 Graphs/213429: f(x)=-3x^2 make a table and a graph 1 solutions Answer 161245 by rapaljer(4667)   on 2009-09-14 10:17:18 (Show Source): You can put this solution on YOUR website!f(x)=-3x^2 If x=0, then f(x)=0 If x=1, then f(x) = -3(1)^2=-3 If x=2, then f(x) =-3(2)^2=-12 If x=-1, then f(x)=-3(-1)^2=-3 If x=-2, then f(x)=-3(-2)^2=-12 R^2
 Inequalities/213454: please help me solve 1 solutions Answer 161241 by rapaljer(4667)   on 2009-09-14 10:11:23 (Show Source): You can put this solution on YOUR website!Do you mean graph y=-x+3?? The y intercept is 3 and the slope is -1. Start by going UP the y-axis 3 units, and put a point at (0,3). From this point, the slope is -1/1, so go DOWN 1, go RIGHT one unit, and put the second point. Connect the dots. It should look like this: R^2
 Probability-and-statistics/213458: If the odds in favor of the Rangers winning the game are 7 to 5, what is the probability that they will win?1 solutions Answer 161240 by rapaljer(4667)   on 2009-09-14 10:06:57 (Show Source): You can put this solution on YOUR website!Odds in favor of winning =7/5 This means number of favorable outcomes is 7 Number of unfavorable outcomes is 5 Therefore the total outcomes is 12 Probability = = R^2
 Complex_Numbers/213433: Select the correct upper limit, lower limit, and the range of tolerance for the measurement listed. 4.75 ± 0.05 1 solutions Answer 161224 by rapaljer(4667)   on 2009-09-14 09:15:13 (Show Source): You can put this solution on YOUR website!The upper limit is 4.75+.05= 4.80 The lower limit is 4.75-.05=4.70 R^2
 Quadratic_Equations/213436: Solve by factoring: 16x2 - 14x + 1 = -6x I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.1 solutions Answer 161219 by rapaljer(4667)   on 2009-09-14 09:01:53 (Show Source): You can put this solution on YOUR website!16x^2 -14x+1=-6x This is a quadratic equation, so start by setting it equal to zero by adding +6x to each side: 16x^2 -14x+6x +1=-6x+6x 16x^2 -8x+1=0 This is perfect square trinomial, so it factors like this: (4x_____)(4x_____)=0 (4x-1)(4x-1)=0 4x-1=0 4x=1 x=1/4 In this exercise, you may need additional help with solving quadratic equations. However, the underlying problem may be being able to factor this trinomial. Either way, I have pages on my website that may be helpful to you. If you need additional help with "Factoring" or "Solving Quadratic Equations", check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and look for the appropriate sections in Chapter 2. My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Age_Word_Problems/213442: I havea problem and couldn't find a similar problem: 2 years ago a father was 4 times as old as his son. 3 years from now the father will be only 3 times as old as the son. how old is each now? can you find a problem at least similar to this one? thank you, Destiny1 solutions Answer 161216 by rapaljer(4667)   on 2009-09-14 08:54:15 (Show Source): You can put this solution on YOUR website!Let x = age of son now y= age of father now x-2= age of son 2 years ago y-2 = age of father 2 years ago x+3 = age of father 3 years from now y+3= age of father 3 years from now y-2=4(x-2) y+3=3(x+3) y-2=4x-8, so y = 4x-6 y+3=3x+9, so y=3x+6 Now, since y=4x-6 and y=3x+6, 4x-6=3x+6 x=12 Age of son now y=3x+6 y=3(12)+6 y=36+6=42 Age of father now Check: 2 years ago, son was 10 and father was 40--(four times as old!) 3 years from now, the son will be 15 and father will be 45--(three times as old!!) I would love to recommend my website to you on this, but I just don't have anything like this on it!!! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Complex_Numbers/213439: The waterbeds Myron sells have an average size of 22.5 cubic feet. One cubic foot of water weighs 62.4 pounds. What is the weight of one waterbed? 1 solutions Answer 161212 by rapaljer(4667)   on 2009-09-14 08:44:22 (Show Source): You can put this solution on YOUR website!Just multiply the number of cubic feet times the weight of each cubic foot. That would be 22.5*62.4 =1406.25 pounds. R^2
 Functions/213443: This question is from textbook College Algebra in Context What is the domain of y = rqst(4x + 1)1 solutions Answer 161210 by rapaljer(4667)   on 2009-09-14 08:40:23 (Show Source): You can put this solution on YOUR website!To find the domain of a function, make sure DENOMINATORS are NOT ZERO, and RADICANDS (whatever is inside the square root!) must be GREATER THAN OR EQUAL TO ZERO!! In this case , so If you need additional help with Domain and Range, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Math in Living Color." Click on "College Algebra", and look for "Section 2.07, Functions, Domain, and Range." My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Graphs/213444: Suppose that a circle has an equation of the form x^2 + y^2 =r^2, r>0. What is the center of the circle? What is the radius of the circle? I am lost since there aren't any numbers to plug into the equation....1 solutions Answer 161208 by rapaljer(4667)   on 2009-09-14 08:32:27 (Show Source): You can put this solution on YOUR website!The center is at (0,0) and the radius is r. That's it!! If you need additional help with Circles, you may want to check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Math in Living Color." Click on "College Algebra", and look for Section 2.04 "The Circle" at this link. My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Geometry_Word_Problems/213410: a carpenter has a wooden dowel that is 72 cm long. she wants to cut it into 2 pieces so that one is 5 times as long as the other. what are the lentghs of the two pieces?1 solutions Answer 161192 by rapaljer(4667)   on 2009-09-14 00:20:37 (Show Source): You can put this solution on YOUR website!Let x = smaller piece 5x= larger piece x+5x=72 6x=72 x=12 cm smaller piece 5x=5(12)=60 cm larger piece Check: 12 +60=72 It checks! If you need additional help with Word Problems, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and you will find a couple of sections near the end of Chapter 1 on "Word Problems". My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Radicals/213407: simplify the square root of 8 over 27 thank you so much!1 solutions Answer 161191 by rapaljer(4667)   on 2009-09-14 00:07:25 (Show Source): You can put this solution on YOUR website! If you need additional help with square roots, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and you will find a couple of sections near the end of Chapter 5 on "Radicals". My non-traditional explanation should be easier to understand than your textbook! See also my "MATH IN LIVING COLOR", "Intermediate Algebra", "Chapter 3". R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Rational-functions/213408: Write your own equation for a rational function with two vertical asymptotes. At which values of x are the vertical asymptotes found? Then, write your own equation for a rational function with a singular point (or "hole"). At which value of x is this hole found? Please explain.1 solutions Answer 161190 by rapaljer(4667)   on 2009-09-13 23:58:04 (Show Source): You can put this solution on YOUR website!Two vertical asymptotes: . The asymptotes are at x= 2 and x=-2 Rational function with a hole in the graph . The hole is at x=2, asymptote at x=-2 R^2
 Functions/213192: This question is from textbook Algebra Concepts and Applications Find the domainof x - 2y = 1 if the rainge is {-2,0,5,8}.1 solutions Answer 161161 by rapaljer(4667)   on 2009-09-13 20:19:38 (Show Source): You can put this solution on YOUR website!x-2y=1 x=2y+1 If y = -2, then x=2*-2+1=-4+1=-3 If y=0, then x=1 If y =5, then x=2*5+1 = 10+1=11 If y=8, then x=2*8+1=16+1=17 Domain = {-3,1,11,17} R^2
 Equations/213216: State whether any conclusions can be made using the true statement , x = 3 If 4 x is greater than or equal to 12, then y = 6x 1 solutions Answer 161159 by rapaljer(4667)   on 2009-09-13 20:16:52 (Show Source): You can put this solution on YOUR website!Did you leave something out of this? There must have been something about y that you didn't mention in the problem. It seems that the y came out of nowhere! R^2
 Radicals/213328: I need help simplifying the square root of three sevenths. please show work.1 solutions Answer 161158 by rapaljer(4667)   on 2009-09-13 20:14:57 (Show Source): You can put this solution on YOUR website! R^2
 Functions/213193: This question is from textbook Algebra Concepts and Applications Solve y = -2x+7 if the domain is {-2,0,4,7}.1 solutions Answer 161156 by rapaljer(4667)   on 2009-09-13 20:05:35 (Show Source): You can put this solution on YOUR website!Domain is the set of all x values, which would be {-2,0,4,7}, so y = {11,7,-1,-7}. If x= -2, then y=-2*-2+7=4+7=11. If x=0, then y= 7. If x=4, then y=-2*4+7=-8+7=-1. If x=7, then y=-2*7 +7 ==14+7=-7 R^2
 Linear_Algebra/213317: Use the Pythagorean Theorem to find the slant height of the face of the unit pyramid with edge 11 cm. 1 solutions Answer 161154 by rapaljer(4667)   on 2009-09-13 20:03:51 (Show Source): You can put this solution on YOUR website!You need more information to solve this. R^2
 Numbers_Word_Problems/213318: how do u find a consecutive integer? i dont get it.1 solutions Answer 161150 by rapaljer(4667)   on 2009-09-13 20:01:06 (Show Source): You can put this solution on YOUR website!For consecutive integers, use x, x+1, x+2, etc. For consecutive even or consecutive odd integers, use x, x+2, x+4, etc. If you need additional help with Word Problems, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and you will find a couple of sections near the end of Chapter 1 on "Word Problems". My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Equations/213302: solve for D: e = K(D-d)/f1 solutions Answer 161138 by rapaljer(4667)   on 2009-09-13 18:55:14 (Show Source): You can put this solution on YOUR website!e = K(D-d)/f Since most folks don't particularly like FRACTIONS, I recommend you multiply both sides by the denominator f. ef=K(D-d) Next, remove the parentheses using the distributive property: ef =KD - Kd To solve for D, you need to get the D term alone on the right side. Do this by adding +Kd to each side: ef+Kd = KD Finally, to get D by itself, divide both sides by K: By the way, don't DARE divide out the K's, since the K in the numerator is in a TERM!! If you need additional help with Literal Equations, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "MATH IN LIVING COLOR." The topic of Literal Equations can be found at ALL three levels. For "College Algebra" look in Chapter 1. For "Intermediate Algebra" look in Chapter 2, and in "Basic Algebra" look in Chapter 3. My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Miscellaneous_Word_Problems/213294: This question is from textbook I think i did this one correctly but i want to make sure since it is for a project in math class: An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 lbs for the first 5 feet and 5 lbs for every inch over 5 feet tall." Under this description, what height corresponds to a recommended weight of 135 lbs? If an overweight woman (225 lbs and 5 feet 8 inches tall) plans on going on a diet in which she will lose 5 lbs every two weeks, how many weeks before she is back down to her recommended weight? I did 100=5 feet, 5 lbs for every inch over 35 lbs / 5 lbs = 7 inches 5 foot 7 inches for 135 lbs 5 foot = 100 lbs + (5lbsX 8) = 40 + 100 = 140 lbs for 5 foot 8 inches as the recommended weight for this lady 225 lbs needs to get to 140 lbs 225 lbs - 140 lbs = 85 lbs difference, the woman needs to lose 85 lbs 5/2 = 2.5 lbs every week lost 85 lbs / 2.5 lbs = 34 weeks I hope i got this right, i would appricate any feedback.1 solutions Answer 161124 by rapaljer(4667)   on 2009-09-13 18:27:29 (Show Source): You can put this solution on YOUR website!Looks right to me!! R^2
 Miscellaneous_Word_Problems/213285: This question is from textbook Structure and Method Book 1 Todd has 48 words to spell for a puzzle. As an incentive, his mother offers to pay him 10 cents for each word he spells correctly, if Todd will pay her 6 cents for each word he spells incorrectly. If Todd makes \$1.92, how many words does he spell correctly?1 solutions Answer 161122 by rapaljer(4667)   on 2009-09-13 18:23:32 (Show Source): You can put this solution on YOUR website!Let x= number of words Todd spells correctly 48-x = number of words that he misses In order to avoid the decimals, let's solve this in "cents". Does that make "cents" to you??? It means that he gets 10 cents for correct words, he pays -6 cents for words missed, and there is a total income of 192 cents. Here is the equation: 10*x -6(48-x) = 192 10x - 288 + 6x = 192 16x- 288=192 16x= 192 +288 16x = 480 x=30 words correct 48-30=18 words missed Check: 30*\$.10 -18*\$.06 = &1.92 \$3.00-\$1.08=\$1.92 It checks!!! If you need additional help with Word Problems, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and you will find a couple of sections near the end of Chapter 1 on "Word Problems". My non-traditional explanation should be easier to understand than your textbook! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 logarithm/213272: Write 2lnx + lny - ln(z-3) as a single log expression. 1 solutions Answer 161116 by rapaljer(4667)   on 2009-09-13 18:14:04 (Show Source): You can put this solution on YOUR website!2lnx + lny - ln(z-3) If you need additional help with logarithms, check out my website by doing a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of the search list, and choose the link on my homepage "Basic, Intermediate and College Algebra: One Step at a Time." Click on "College Algebra", and you will find an entire Chapter, Chapter 4, on Logarithms. My non-traditional explanation should be easier to understand than your textbook! In addition, I have two videos that are freely available on my website. From my Homepage, click on the link "Rapalje Videos", look for "College Algebra" and then "Logarithms." The videos are a few years old, and the calculator technology is out of date, but this is an explanation that should be easier for you to understand. R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Equations/213283: Solve equation for x and put the equation in x= form. 2xy=3y+5xy And this one I really don't get, 4+t/3x+2 = 6m+171 solutions Answer 161110 by rapaljer(4667)   on 2009-09-13 18:05:33 (Show Source): You can put this solution on YOUR website!Get the x terms on one side by subtracting 5xy from each side: 2xy=3y+5xy 2xy -5xy=3y -3xy=3y Divide both sides by -3y to get the x isolated: R^2
 Angles/213155: This question is from textbook geometry (4x-2y)+70=180 this is two supplementary angles, one is (4x-2y)degrees and the other is 70 degrees. I know they equal 180 degrees when added together. how do i solve for x and for y1 solutions Answer 161053 by rapaljer(4667)   on 2009-09-13 11:41:31 (Show Source): You can put this solution on YOUR website!When there are two variables without any other conditions given, you can't solve for x and y. The best you can do is to solve for y in terms of x or x in terms of y. 4x-2y +70=180 4x-2y = 110 4x-110=2y 2x-55=y y=2x-55 R^2
 Quadratic_Equations/213152: A cylindrical can has a volume of 128pi cm^3 and is 8cm tall. What is its radius?1 solutions Answer 161052 by rapaljer(4667)   on 2009-09-13 11:36:59 (Show Source): You can put this solution on YOUR website! Divide both sides by or Reject the negative value. Radius = 4 cm. R^2
 Graphs/212128: log subscript 7 (7^5) simplify1 solutions Answer 161026 by rapaljer(4667)   on 2009-09-13 09:49:18 (Show Source): You can put this solution on YOUR website! When you have a log base b of b raised to the power, the answer is always the power! That's what a logarithm is!! Final answer is the exponent, Please see my own website for an entire explanation and videos on logarithms. R^2
 Probability-and-statistics/213137: This question is from textbook Estimate the following sums or differences. 1 4/5 - 3 9/10 - 6 1/71 solutions Answer 161024 by rapaljer(4667)   on 2009-09-13 09:43:24 (Show Source): You can put this solution on YOUR website!Approximately 2-4-6=-8 R^2