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# Recent problems solved by 'rapaljer'

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 Graphs/42021: This question is from textbook Find the maximum value of y=-x^2+6x. Thank you. 1 solutions Answer 27170 by rapaljer(4667)   on 2006-06-13 23:52:30 (Show Source): You can put this solution on YOUR website!This is a parabola that opens downward, and the vertex (maximum point) will be at . In this case, vertex is at . If x = 3, then y = -3^2 + 6*3= -9 + 18 = 9. Maximum value is 9. Check it out with the graph: R^2 at SCC
 Divisibility_and_Prime_Numbers/42024: Write as a product of primes: 1,000 Thank you.1 solutions Answer 27169 by rapaljer(4667)   on 2006-06-13 23:46:00 (Show Source): You can put this solution on YOUR website!1000 R^2 at SCC
 Equations/42027: Find the slope of the line passing through the points (–8, –3) and (–2, 2). A) -5/6 B) -6/5 C) 5/6 D) 6/5 1 solutions Answer 27168 by rapaljer(4667)   on 2006-06-13 23:43:11 (Show Source): You can put this solution on YOUR website!Slope = = R^2 at SCC
 Complex_Numbers/42026: (-15.2)(-17.2)1 solutions Answer 27167 by rapaljer(4667)   on 2006-06-13 23:39:11 (Show Source): You can put this solution on YOUR website!What is the question? Perhaps you should clarify this and repost the question. R^2 at SCC
 Complex_Numbers/42025: -|-5|-|-3|=1 solutions Answer 27166 by rapaljer(4667)   on 2006-06-13 23:37:53 (Show Source): You can put this solution on YOUR website!-|-5|-|-3| - 5 - 3 -8 R^2 at SCC
 Complex_Numbers/42031: Why does the Trichotomy Property not apply to all complex numbers? Thank you 1 solutions Answer 27165 by rapaljer(4667)   on 2006-06-13 23:35:12 (Show Source): You can put this solution on YOUR website!Because the complex number system does NOT have an order relationship. Notice that the real numbers can be arranged on a numberline, so they can be placed in ORDER. Therefore, when comparing real numbers, each number on a real numberline must be equal to, greater than, or less than any other number. Since complex numbers cannot be "arranged in order, there are no such comparisions, and the Trichotomy Property does not apply. R^2 at SCC
 Equations/42035: Find all real or imaginary solutions to the equation. 49x^2+9 = 42x1 solutions Answer 27164 by rapaljer(4667)   on 2006-06-13 23:30:35 (Show Source): You can put this solution on YOUR website!49x^2+9 = 42x First set the equation equal to zero and place in descending powers of x: 49x^2 - 42x + 9 = 0 Factor it. (NOTE: It just happens to factor!!) {7x - 3)(7x - 3) = 0 7x = 3 x= 3/7 R^2 at SCC
 Money_Word_Problems/42037: The total profit (in dollars) for sales of x rowing machines is given by P(x) = 0.2 x^2 + 300x – 200. What is the profit if 500 are sold? For what value of x will the profit be at a maximum? 1 solutions Answer 27163 by rapaljer(4667)   on 2006-06-13 23:26:48 (Show Source): You can put this solution on YOUR website!I think you may have an error in the equation. Your P(x) equation for profit is a parabola that opens upward, since the coefficient of x^2 is positive. A parabola that opens upward has a MAXIMUM, not a MINIMUM value. Whatever it is, to find the profit if 500 are sold, just substitute the 500 into the value of x in the formula and calculate it. R^2 at SCC
 Graphs/42038: Graph the function and state the domain and range. y = 0.3x 1 solutions Answer 27162 by rapaljer(4667)   on 2006-06-13 23:21:35 (Show Source): You can put this solution on YOUR website! From the graph, you can see that this is a straight line in which x and y both extend from negative infinity to positive infinity. D: (-inf, inf) R: (-inf, inf) R^2 at SCC
 Graphs/42039: Graph the function and state the domain and range. y=4-x^2 1 solutions Answer 27161 by rapaljer(4667)   on 2006-06-13 23:20:00 (Show Source): You can put this solution on YOUR website! From the graph, you can see that x extends from left to right, from negative infinity to positive infinity. Y extends from negative infinity up to a maximum at y = 4. D: (-inf, inf) R: (-inf, 4] R^2 at SCC
 Polynomials-and-rational-expressions/41519: Can you please help. Perform the operations and simplify. Assume the variables represent positive real numbers. 1 solutions Answer 26819 by rapaljer(4667)   on 2006-06-10 10:24:40 (Show Source): You can put this solution on YOUR website! By FOIL : or R^2 at SCC
 Polynomials-and-rational-expressions/41488: I need help with the folowing problem: Find an equation of the inverse relation: y=3x^2-5x+91 solutions Answer 26818 by rapaljer(4667)   on 2006-06-10 10:12:33 (Show Source): You can put this solution on YOUR website!To find an inverse relation, interchange the x and y: Caylyne Dr. Rapalje's grand daughter
 Equations/41511: Hello! Can anyone help please? My question is: At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows: £7.48 men, £7.12 women and £0.45 children. How many children were there? I know the answer is 92 but I don't know how to work it out. Thanks marangeo 1 solutions Answer 26816 by rapaljer(4667)   on 2006-06-10 09:17:55 (Show Source): You can put this solution on YOUR website!There's not enough information sorry Caylyne Dr.Rapalje's grand daughter
 Divisibility_and_Prime_Numbers/41530: please help: the prime factors of 241 solutions Answer 26815 by rapaljer(4667)   on 2006-06-10 09:12:46 (Show Source): You can put this solution on YOUR website!A prime factor is a number that can only be divided by itself and one. These are like 2, 3,5,7,11,13,17,19,23,etc. Of these numbers only 2 and 3 can divide into 24. caylyne Dr.Rapalje's grand daughter
 Length-and-distance/38695: I am needing a step-by-step process on how to convert kilometers to miles. The problem is 4690 km to miles?1 solutions Answer 24234 by rapaljer(4667)   on 2006-05-20 23:30:54 (Show Source): You can put this solution on YOUR website!I think it is easiest to convert directly from km to miles. If you use the conversion of 1 km. = 0.62 miles, then 4690 km will be 4690 times what 1 km is. In other words, just multiply 4690 times 0.62, which gives you approximately 2908 miles. See also my website for an entire page on metric system. The link is http://www2.scc-fl.edu/rrapalje/Tech-Prep-Math/Metric%20System.htm. If this does not show up as a link, then click on my user name "rapaljer" anywhere in algebra.com, then look for Geometric Topics, then Metric System. R^2 at SCC
 Money_Word_Problems/38631: Find the final amount of the investment. \$10,000 invested at 6% compounded quarterly for 5 1/2 years. (end of problem) I've put this in my TI-83 calculator 20 times... and it still comes out 58,374.99. What am I doing wrong? I know the formula is A=P(1+r/t)^rt Can you help?1 solutions Answer 24173 by rapaljer(4667)   on 2006-05-20 10:31:34 (Show Source): You can put this solution on YOUR website!Did you take the 6% and divide by 4 giving you 1.5% or .015 per period? Did you take 5 1/2 years and multiply times 4 giving you 22 periods of compounding? If you do those two items, the rest should work out. I am getting this: R^2 at SCC
 Polynomials-and-rational-expressions/38627: This question is from textbook Beginning Algebra Factor by grouping. xa + 2bx - a - 2b Chapter 1.5 pg. 306 problem 18. Remove Largest Common Factor 14x^y - 35xy - 63x 1 solutions Answer 24172 by rapaljer(4667)   on 2006-05-20 10:24:52 (Show Source): You can put this solution on YOUR website!xa + 2bx - a - 2b x(a+2b) -1(a+2b) (a+2b)(x-1) Your second problem looks strange. Are you sure you meant x^y ??? If that is what you REALLY mean, then here goes. Factor out a common factor of 7 and x: 14x^y - 35xy - 63x Somehow, I don't think this is what you really meant, however. R^2 at SCC
 Exponential-and-logarithmic-functions/38630: solve the equation. Round your answers to the nearest hundredth. 9+1.95^x=40 1 solutions Answer 24171 by rapaljer(4667)   on 2006-05-20 09:57:47 (Show Source): You can put this solution on YOUR website!This is an exponential equation, so you will have to take the log or ln of each side of the equation to convert it from an exponential equation to an ordinary linear equation. First subtract 9 from each side: Now, take the ln of each side. By the way, taking the log of each side works equally well and gives exactly the same answer! By the third law of logarithms Divide each side by ln 1.95: = 5.142 approximately. Final answer rounded to nearest tenth = 5.1 R^2 at SCC
 Rational-functions/37572: This question is from textbook college algebra f(x)=x^3+2 graph and solve 1 solutions Answer 24157 by rapaljer(4667)   on 2006-05-19 22:31:25 (Show Source): You can put this solution on YOUR website! R^2 at SCC
 Miscellaneous_Word_Problems/37893: A circle has an inscribed right triangle having an altitude of 4 and an area of 28. What are the circumference and area of circle? (Inscribes means inside with vertex's touching the edsge of the circle)1 solutions Answer 24156 by rapaljer(4667)   on 2006-05-19 22:27:02 (Show Source): You can put this solution on YOUR website!If a right triangle is inscribed in a circle, then the legs of that right triangle will be the base and altitude of the triangle, and the hypotenuse of the right triangle will be the diameter of the circle. To find the area and circumference of the circle, you need to find the diameter (and radius!) of the circle. If altitude = 4 and area = 28, then Next, Let d= diameter of the circle, which is also the hypotenuse of the right triangle. According to the Theorem of Pythagoras: Remember that the radius is HALF of the diameter, so if r= the radius, then and Area = square units. Circumference = units. R^2 at SCC
 Polynomials-and-rational-expressions/37751: 2x^2+11x-6/x+61 solutions Answer 24154 by rapaljer(4667)   on 2006-05-19 22:20:59 (Show Source): You can put this solution on YOUR website!The key is to factor the numerator! This is usually a tough factoring problem, but since the denominator has a factor of (x+6), you might just expect a factor of (x+6) in the numerator also. Otherwise, there won't be anything to do in this problem. I'd start with , and realize it has to start out . Expecting the factor of x+6 to show up here, I would next try: . Since the LAST term has to be a -6, this means that the blank space left in the previous step will have to be -1. Do you follow this? . Now, check the middle term: 12x - 1x = + 11x. Divide out the x+6 factors, and you have a final answer of . R^2 at SCC
 Miscellaneous_Word_Problems/37752: Five men were to share the treasure with Long John Silver. If the treasure were split in the following ratio 2:5:7:10:20:50, and the least amount any of the six pirates recieved was 14,000 pounds of gold, what is the total weight of the treasure?1 solutions Answer 24153 by rapaljer(4667)   on 2006-05-19 22:12:28 (Show Source): You can put this solution on YOUR website!First I would add up the numbers given in the ratio: 2+5+7+10+20+50 = 94 shares. The one who receives the least amount, therefore, received 2 shares out of a total of 94 shares of the total treasure, or th of the treasure. Let x = total treasure, then Multiply both sides by 47: pounds = total weight of gold. R^2 at SCC
 Coordinate-system/38197: Graph the following inequality and shade it - - include your coordinates in the spaces below. 4x + y > or = 4 ( , ) ( , ) I found one similar except it didn't have "or =" to in the equation just the greater than sign. Don't understand it. Thank you, 1 solutions Answer 24152 by rapaljer(4667)   on 2006-05-19 22:07:32 (Show Source): You can put this solution on YOUR website!The "or =" just means to make the graph with a SOLID line, which means that the line itself is included. In my opinion the easiest way to graph this is to use the intercepts method and graph the line with an "=" sign only. We can handle the ">" sign later: Let x = 0, then y=4. Let y = 0, then 4x = 4, so x = 1. Graph these two points, and remember that if you have a POSITIVE Y-coefficient, the ">" or ">+" means to shade ABOVE the line. If you have a "<" or "<=" then it means to shade BELOW the line. In this case you will have to graph with a SOLID line, and shade ABOVE the line. I don't know how to do this in algebra.com graphing so I'll graph the line, and YOU make it a SOLID LINE and SHADE ABOVE the line: R^2 at SCC
 Polynomials-and-rational-expressions/38120: Add x/x-2 + 1-5x/x^2 -8x+121 solutions Answer 24149 by rapaljer(4667)   on 2006-05-19 21:57:49 (Show Source): You can put this solution on YOUR website! Since this is addition of two fractions, you must first find a common denominator. Begin by factoring the second denominator: The LCD must have all factors of the denominators, and this will be (x-2)*(x-6). The second fraction already has the common denominator, but you will have to multiply the numerator and denominator of the first fraction by the missing factor (x-6). DON'T CANCEL ANYTHING --THESE ARE TERMS!!! Multiply the numerators out and add them together, and divide by the LCD: R^2 at SCC
 Polynomials-and-rational-expressions/38612: If the expression 4z + 1 over 4z - 6 is to make sense, the values that z can take must be restricted. State the restriction on z.1 solutions Answer 24148 by rapaljer(4667)   on 2006-05-19 21:46:56 (Show Source): You can put this solution on YOUR website!Denominators can NEVER be zero, so any value that makes a denominator equal zero is a restriction. In this case, the denominator is 4z-6. Therefore, the denominator 4z-6 must not be zero. Therefore, the forbidden value would be 4z-6=0 Add 6 to both sides: 4z=6 Divide both sides by 4: IS THE FORBIDDEN VALUE!! Therefore the restriction on z is that Z must NOT equal . R^2 at SCC
 Polynomials-and-rational-expressions/38613: Reduce the following expression to lowest terms: x^2 - 9x + 14/5x^2 - 201 solutions Answer 24147 by rapaljer(4667)   on 2006-05-19 21:41:40 (Show Source): You can put this solution on YOUR website!The critical step here is FACTORING, and I mean FACTOR COMPLETELY!! Divide out the x-2 factor in the numerator and denominator, and this should be what is left: R^2 at SCC
 Polynomials-and-rational-expressions/38618: OOPS...The last problem I submitted, 2/5w+10 - 3/2w-4 The correct answer is -11w-38/10(w+2)(w-2) Sorry!! Please help!1 solutions Answer 24146 by rapaljer(4667)   on 2006-05-19 21:36:31 (Show Source): You can put this solution on YOUR website! Because this is a fraction subtraction, your first step must be to find a common denominator. To do this, you'll have to factor each denominator, and take ALL the factors of all the denominators for the LCD. The LCD will have to have within it factors of . To set up each fraction so it has the common denominator, you will have to multiply numerator and denominator of the first fraction by the factors 2(w-2), and the second fraction by the factors 5(w+2). It should look like this: Now, the LCD becomes the denominator of the entire problem, and you subtract numerators: In this last step, DON'T be tempted to divide anything out! These are TERMS! NEVER DIVIDE OUT TERMS!! Instead, multiply out the numerators, and combine like terms. This should be the answer you are looking for: R^2 at SCC