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# Recent problems solved by 'rapaljer'

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 Rational-functions/66437: What is the GCF for the polynomial -10x3y4 - 16x5y2? 1 solutions Answer 47401 by rapaljer(4667)   on 2007-01-14 23:23:31 (Show Source): You can put this solution on YOUR website!The GCF is the largest common factor of . To find the powers of x and y, always use the LOWEST power of each factor. R^2 at SCC
 Quadratic-relations-and-conic-sections/66491: How do I go about converting this equation to the standard form in order to graph the conic section? 4x^2-16x+9y^2+18y=0 I know I am supposed to complete the square...Thanks a bunch.1 solutions Answer 47400 by rapaljer(4667)   on 2007-01-14 23:10:38 (Show Source): You can put this solution on YOUR website!Conic Sections Summary -- If the coefficients of and are of the same sign, but unequal coefficients, then the graph will be an ELLIPSE. If both coefficients are the same sign with equal coefficients, it will be a CIRCLE. If coefficients are of opposite sign, then it will be a HYPERBOLA. A PARABOLA results when there is an but no or a but no . The preferred method of solving such a problem is the method of completing the square: You must first factor out the coefficients of x^2 and y^2 like this: This is an ellipse. The standard form for an ellipse is in a form = 1, so divide both sides of the equation by 25 to set it equal to 1. Finally invert the coefficients of 4 and 9 in order to write this: That would be standard form for an ellipse! The center is at (2,-1), with the "radius" extending units in the x direction, and units in the y direction. R^2 at SCC
 Expressions-with-variables/66448: if 5^21*4^11=2*10^n what is value of n1 solutions Answer 47399 by rapaljer(4667)   on 2007-01-14 23:06:26 (Show Source): You can put this solution on YOUR website! Therefore n= 21 R^2 at SCC P.S. Nice problem!!
 Trigonometry-basics/66622: x^4 when x=2 and y=-81 solutions Answer 47398 by rapaljer(4667)   on 2007-01-14 23:01:54 (Show Source): You can put this solution on YOUR website! where x=2 simply means . R^2 at SCC
 Linear-systems/66675: 3y = 4x =0 1 solutions Answer 47397 by rapaljer(4667)   on 2007-01-14 22:58:38 (Show Source): You can put this solution on YOUR website!3y=0, so y = 0 4x= 0, so x = 0 (0,0) R^2 at SCC
 Linear-equations/66715: This question is from textbook Algebra 1 How do i write the question?1 solutions Answer 47396 by rapaljer(4667)   on 2007-01-14 22:57:02 (Show Source): You can put this solution on YOUR website!We don't have a book, so we have no idea what the question is! You'll have to give something to work with here . . . R^2 at SCC
 Linear_Equations_And_Systems_Word_Problems/66702: –3(10x – 3) + 10(3x – 3) = x – 71 solutions Answer 47395 by rapaljer(4667)   on 2007-01-14 22:55:23 (Show Source): You can put this solution on YOUR website!–3(10x – 3) + 10(3x – 3) = x – 7 -30x + 9 + 30x - 30 = x-7 -21= x-7 Add + 7 to each side: -21+7= x - 7 + 7 -14 = x R^2 at SCC
 Numbers_Word_Problems/66719: 3x – 2y = 6 Solve for x1 solutions Answer 47394 by rapaljer(4667)   on 2007-01-14 22:51:42 (Show Source): You can put this solution on YOUR website!3x - 2y = 6 First you must get the x term alone, in this case, on the left side, by adding +2y to each side: 3x= 6+2y Next, divide each side by 3: There are other ways to solve this equation that are equally correct. You might have written it like this: or R^2 at SCC
 Radicals/66724: The algebra questions reads the square root of x minus 8 is equal to the square root of 13 plus x. Please help me solve this!1 solutions Answer 47393 by rapaljer(4667)   on 2007-01-14 22:45:36 (Show Source): You can put this solution on YOUR website!Do you mean ?? If so, then square both sides of the equation: There is no solution to this equation. Perhaps I misunderstood what you meant. Did you perchance mean: or maybe ?? Maybe you can indicate with parentheses exactly what is supposed to be inside the square root symbols. R^2 at SCC
 Expressions-with-variables/66730: This question is from textbook pretice hall mathematics ALGEBRA 1 Suppose you try to solve systems of linear equations using substitution and get x=8.How many solutions does each system have?1 solutions Answer 47392 by rapaljer(4667)   on 2007-01-14 22:39:33 (Show Source): You can put this solution on YOUR website!If the system is linear, and x=8, then there is a unique solution. There will be one and only one solution to the system! R^2 at SCC
 Linear-equations/66744: Between which two sets of data is there NOT a linear relationship? Answer Choices: A) a number x and the square of that number y B) the number of hours worked x and the amount of money earned y at \$6 per hour C) the number of sides x that a regular polygon has and the number of interior angles y that the polygon has D) number of people entering a museum at a cost of \$1 per person and the total amount of money collected by admission fees1 solutions Answer 47391 by rapaljer(4667)   on 2007-01-14 22:18:00 (Show Source): You can put this solution on YOUR website!The variable x compared to is obviously NOT a linear relationship!! R^2 at SCC
 Linear-systems/66745: Given the following system of equations, which statement is true? y=1/4x+2 x=8y-12 Answer Choices: A) y=8y-12+2 B) y=2y-1 C) x=1/4x+2 D) y=8y-121 solutions Answer 47390 by rapaljer(4667)   on 2007-01-14 22:15:38 (Show Source): You can put this solution on YOUR website!Assuming that you meant The correct answer is B) R^2 at SCC
 Expressions-with-variables/66748: You decide to market your own custom computer system. You must invest \$5874 in computer hardware and spend \$4.85 to buy and package each disk. If each program sells for \$13.75, how many copies must you sell to break even? Here are the multiple choice answers: A. 660 copies B. 316 copies C. 315 copies D. 659 copies1 solutions Answer 47389 by rapaljer(4667)   on 2007-01-14 22:11:33 (Show Source): You can put this solution on YOUR website!Profit = Selling Price - Cost for each disk Profit = 13.75 - 4.85 = \$8.90 Let x = number of disks to break even Then, 8.90x= 5874 copies. The correct answer is A) R^2 at SCC
 Functions/56078: This is a question on inverse functions. Let y=f(x)=5x^3+8 The question wants the answer in the form y= cube root a(x)+b. where a and b are coefficients. I have come up with 1/5 for coeffcient a and I am thinking -(8/5) for coefficient b, but it does not seem to work.1 solutions Answer 38062 by rapaljer(4667)   on 2006-10-13 14:34:25 (Show Source): You can put this solution on YOUR website!As I explained in the previous exercise, I interchange the x and y, and solve for y. y = 5x^3 + 8 Step 1: Interchange the x and y: x = 5y^3 + 8 Step 2: Solve for y: x-8 = 5y^3 Take the cube root of each side: This is what I got!! I think you are correct!! Why do you think it does not work??? R^2 at SCC
 Rational-functions/56080: Given f(x)=3x+4 Find f -1(x)1 solutions Answer 38061 by rapaljer(4667)   on 2006-10-13 14:25:53 (Show Source): You can put this solution on YOUR website!There are a few different ways to do this, and I don't want to conflict with your teacher or your textbook, but I like to find the inverse function in TWO steps: 1. Interchange the x and y, and 2. Solve for y. So, y = 3x+4 Step 1: Interchange the x and y: x= 3y +4 Step 2: Solve for y: x-4 = 3y Divide both sides by 3: . So, or R^2 at SCC
 Radicals/56102: Please help me to check if I have the correct solution. sqrtx^4y^3. when I simplify it I get x^2y sqrt y1 solutions Answer 38059 by rapaljer(4667)   on 2006-10-13 14:18:25 (Show Source): You can put this solution on YOUR website!You got it!!! R^2 at SCC
 Graphs/56096: graph the inequality please: 2x + 3y > 6 1 solutions Answer 38058 by rapaljer(4667)   on 2006-10-13 14:17:34 (Show Source): You can put this solution on YOUR website!First graph the equation 2x+3y = 6, which has x intercept: y=0, x= 3; and y intercept: x=0, y=2. Draw a DOTTED line, since you do NOT want to include the line, and shade the area ABOVE the line, since it is a POSITIVE Y coefficient, with a ">" symbol. Here is the line: You will have to make this a DOTTED line and SHADE ABOVE THE LINE. Unfortunately, I don't know how to do this in algebra.com notation! R^2 at SCC
 logarithm/56100: 3) using the formula R=0.17 + 0.44 log N, determine how many choices would result in a reaction time of 0.42 seconds. Round your answer to the nearest whole number. I started the formula as: .42=0.17 + 0.44 log N 1 solutions Answer 38057 by rapaljer(4667)   on 2006-10-13 14:06:56 (Show Source): You can put this solution on YOUR website! .42=0.17 + 0.44 log N Subtract 0.17 from each side: .42-.17 = 0.44 log N .25= 0.44 log N Divde both sides by .44 .568 = log N To "undo" log, raise both sides to the 10 power, which is N= 3.6998, which rounded to the nearest whole number is 4. R^2 at SCC
 Money_Word_Problems/56012: what is the difference, money-wise, between a half-dozen dozen dollar bills and six dozen donzen dimes? Chip and Dale collected 32 acrons on monday and stored them with their acorn supply. After Chip fell asleep, Dale ate half the acorns. This pattern continued through friday night, with 32 acrons being added and half being eaten on saturday morning, chip counted the acrons and found that they had only 35. how many acorns had they started with on monday1 solutions Answer 37973 by rapaljer(4667)   on 2006-10-12 20:11:19 (Show Source): You can put this solution on YOUR website!A half-dozen dozen dollar bills would be 6 dozen dollar bills or \$72. Six dozen dozen dimes would be 6 * 144 dimes or 864 dimes. The value of this is of course \$86.40. The difference would be \$14.40, or I guess you could say a dozen dozen dimes. *********************************************************************************************************** On the Chip and Dale problem, the problem is not entirely clear to me, but I'll give it my best interpretation. Let x = the original number of acorns. According to the problem, they added 32 acorns to their supply, giving them a total of x+32 acorns. Next, Dale ate half of the acorns after Chip fell asleep. I will assume that it was still Monday when Dale first ate half of the acorns. This means that he ate half and that left of the acorns. On Tuesday he ate half of what was left, leaving half: . On Wednesday, he ate half and left half, leaving . On Thursday, he ate half and left half, leaving . On Friday, he ate half and left half, leaving . On Saturday, he ate half and left half, leaving . The equation for all of this, since after Saturday morning there were 35 acorns left is this: Multiply both sides by 64: Subtract 32 from each side: Check: Add 2208 +32 = 2240 acorns on Monday afternoon. If Dale ate half on Monday, this leaves 1120 acorns on Monday night. Tuesday = 560 Wednesday = 280 Thursday = 140 Friday = 70 Saturday = 35 It checks!! *********************************************************************************************************** Hey, HERE'S AN EVEN BETTER WAY TO SOLVE THE ACORN PROBLEM, and it doesn't even require ALGEBRA!! You can start with the acorns at the end of the week, which was 35 at the end of Saturday. Realizing that half were eaten each day, this means that at the beginning of Saturday, there were 35*2 = 70 acorns. Likewise at the beginning of each day, there would have been: Saturday 35*2 = 70 Friday 70*2 = 140 Thursday = 140*2 = 280 Wednesday = 280*2 = 560 Tuesday = 560 *2 = 1120 Monday = 1120*2 = 2240 Now, undo the 32 acorns that they added on Monday before half were eaten (by subtracting!), and you have 2208 acorns to begin with. R^2 at SCC
 real-numbers/55970: What other sets of real numbers are there other than the set of real numbers, its subsets and find five examples of the set(s)?1 solutions Answer 37972 by rapaljer(4667)   on 2006-10-12 20:04:37 (Show Source): You can put this solution on YOUR website!For a detailed explanation, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for Basic Algebra, then Samples from Basic Algebra: One Step at a Time, then Chapter 1, then Section 1.01 Number Systems. Meanwhile, these are the systems of numbers leading up to the Real Number System. 1. Natural Numbers = 1, 2, 3, 4, etc. It's "natural" to count on your fingers! 2. Whole Numbers= 0, 1, 2, 3, 4, etc. 3. Integers = 0, 1, 2, 3, 4, etc, also -1, -2, -3, -4, etc. 4. Rational Nunbers = any number that can be expressed as a "ratio" of two integers. This includes whole numbers, integers, fractions, terminating and repeating decimals, etc. 5. Irrational Numbers= numbers like , , , etc. The rational and irrational numbers have NO members in common, and together they form the real number system. R^2 at SCC
 Equations/55993: Can you please help my son with this problem it is not in a text book 1/3x=1/21 solutions Answer 37969 by rapaljer(4667)   on 2006-10-12 19:55:46 (Show Source): You can put this solution on YOUR website! Multiply both sides of the equation by 3 to get the x alone, and you get or 1 1/2 R^2 at SCC
 Exponents-negative-and-fractional/55975: y-3/5 - 1 = y-5/41 solutions Answer 37962 by rapaljer(4667)   on 2006-10-12 18:16:35 (Show Source): You can put this solution on YOUR website!y-3/5 - 1 = y-5/4 y-8/5 = y - 5/4 If you subtract y from each side, you get -8/5=-5/4, which is a FALSE statement. It can NEVER be true, so there is NO SOLUTION!! R^2 at SCC
 Equations/55979: 1/5(10x-15)=1/4(8-4x)+4 This is not in a text book. I worked it an came up with X-1/3. Is this correct? I want to make sure i'm doing it correct? Thanks a lot1 solutions Answer 37959 by rapaljer(4667)   on 2006-10-12 18:14:05 (Show Source): You can put this solution on YOUR website!I got x=3. Add +x to each side, then +3 to each side to get all the variables on the left side and the numbers on the right. That gives you 3x=9 x=3 R^2 at SCC
 Polynomials-and-rational-expressions/54932: Please help me wit this problem: Find the exact solution to the equation 3^x+5=9^x1 solutions Answer 37138 by rapaljer(4667)   on 2006-10-06 11:24:03 (Show Source): You can put this solution on YOUR website!Im assuming that you mean . Therefore, R^2 at SCC
 Equations/54956: Can someone help me on this equation? I need to complete the order pair so that each is a solution for the given equation: 3x + 4y = 12 pair 1 is (8/3,) pair 2 is (0,) Thanks, Sher1 solutions Answer 37136 by rapaljer(4667)   on 2006-10-06 11:12:39 (Show Source): You can put this solution on YOUR website!3x + 4y = 12 If x=8/3, then 3*8/3+4y = 12 8+4y=12 4y=4 y=1 (8/3,1) If x=0, then 3*0+4y=12 4y=12 y=3 (0,3) R^2 at SCC
 Expressions-with-variables/54957: Can someone help me on this equation? I need to find two solutions for this equation: Celsius temperature readings can be converted to Fahrenheit readings using the formula F= 9/5C + 32. What is the Fahrenheit temperature that corresponds to each of the following Celsius temperatures: 0 , 15, and 100? Thanks, Sher1 solutions Answer 37134 by rapaljer(4667)   on 2006-10-06 11:09:17 (Show Source): You can put this solution on YOUR website!F= 9/5C + 32 F=9/5*0+32=32 F=9/5*15+32 =9*3 +32=27+32=59 F=9/5*100+32 =9*20+32=180+32=212 R^2 at SCC
 Percentage-and-ratio-word-problems/54951: no book What was the percentage increase in the age 75+ population of Europe from 1970 to 1995? 22,762 in 1970 38,139 in 1995 Thank you for your help!!!!1 solutions Answer 37129 by rapaljer(4667)   on 2006-10-06 10:36:57 (Show Source): You can put this solution on YOUR website!First, find the amount of increase, . Next divide by the original amount . Finally, change this decimal to a percent by moving the decimal two places to the right: .67555575= 67.56% (approximately). R^2
 Travel_Word_Problems/54953: Speed: A boat travels 36 miles down a river in 3 hours. If it takes the boat 9 hours to travel the same distance going up the river, what is the speed of the boat? What is the speed of the current of the river?1 solutions Answer 37128 by rapaljer(4667)   on 2006-10-06 10:32:56 (Show Source): You can put this solution on YOUR website!Let x = speed of the boat in still water y = speed of the current of the river x+y = rate downstream x-y = rate upstream Distance = Rate * Time, so x+y==12 Downstream x-y==4 Upstream Add these two equations together: 2x = 16, so x = 8 mph in still water x+y = 12, where x = 8, y = 4 mph current. R^2 at SCC
 logarithm/54933: PLEASE HELP ME WITH THIS PROBLEM: Write the expression LOGa (y+5)+2 LOGa(x+1) as logarithm.1 solutions Answer 37120 by rapaljer(4667)   on 2006-10-06 09:00:09 (Show Source): You can put this solution on YOUR website! = = Hey, I've got a GREAT handout on logarithms, but it's not on my website. I can send a copy to anyone who needs one. Send me a mailing address, and I'll put one in the mail to you!! R^2 at SCC
 logarithm/54935: PLEASE HELP ME SOLVE THIS PROBLEM; Given that LOGa (x)=3.58 and LOGa (y) = 4.79, find LOGa(y/x)1 solutions Answer 37117 by rapaljer(4667)   on 2006-10-06 08:54:15 (Show Source): You can put this solution on YOUR website!By the law of logarithms, R^2 at SCC
 Exponential-and-logarithmic-functions/54886: Please help w/ the following: Evaluate: ln( 1/^5 radical e) Thank you.1 solutions Answer 37116 by rapaljer(4667)   on 2006-10-06 08:50:40 (Show Source): You can put this solution on YOUR website!I'm not sure you stated this problem the way you meant for it to be stated, and I may be way off base with this, but I'm going to try it anyway. I think the problem you meant to ask is. Tell me if this is what you meant to ask? If so, then remember that and that . Put these together and you have This last statement in reverse, using "e" to replace the x, looks like this: Now, . R^2 at SCC