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# Recent problems solved by 'rapaljer'

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 Functions/83402: Find f^-1(x). f(x) = 3/4x - 6/71 solutions Answer 59907 by rapaljer(4667)   on 2007-05-25 08:33:04 (Show Source): You can put this solution on YOUR website!I like to use a two step method for finding the inverse of a function: Step 1: Interchange the x and y. Once you interchange the variables, this y becomes the y that represents Step 2: Solve for y. Begin by writing this f(x) in notation of y: Step 1: Step 2: Clear fractions: R^2 at SCC
 logarithm/83401: Solve the logarithmic equation and express irrational solutions in lowest radical form. log(x) + log(x+15) = 2 I just can't seem to grasp how to solve this.1 solutions Answer 59906 by rapaljer(4667)   on 2007-05-25 08:22:39 (Show Source): You can put this solution on YOUR website!log(x) + log(x+15) = 2 Use the first law of logarithms to form a single logarithm: Using the basic definition, convert to exponential form: Solve the quadratic formula by factoring if possible, otherwise the quadratic formula or completing the square: (Isn't it nice when these kinds of problems factor? ) or You must check these answers to make sure that none of the values of x make a log of a negative (logs of negatives are not allowed in the real numbers!!). Therefore, the answer must be rejected. The final answer is . R^2 at SCC
 Functions/83400: Find intervals on which the given function is increasing and the intervals on which it is decreasing. f(x) = x^2 +1 I've tried to solve this and I've looked for examples throughout my textbook. I just can't seem to understand how to do it.1 solutions Answer 59905 by rapaljer(4667)   on 2007-05-25 08:09:07 (Show Source): You can put this solution on YOUR website!The graph of y=x^2 is a parabola that opens upward. Therefore, is that same parabola that opens upward, but it is moved UP one unit. It looks like this: A graph is increasing if when you move along the graph from LEFT to RIGHT, the y value becomes larger, and it is decreasing if when you move from LEFT to RIGHT the y value becomes smaller. From looking at the graph, notice that the graph is DECREASING on the left side of the graph, and INCREASING on the right side of the graph. Therefore, it is DECREASING from -infinity to x=0, and it is INCREASING from x=0 to infinity. R^2 at SCC
 Numeric_Fractions/83395: a taxi company charges R8 up front plus R3 per kilometer travelled. If the fare is R83, what distance was travelled.1 solutions Answer 59904 by rapaljer(4667)   on 2007-05-25 07:58:42 (Show Source): You can put this solution on YOUR website!Let x= number of kilometers traveled Then the total cost of the taxi is 8+3x = 83 8+3x -8 = 83-8 3x=75 x= 25 kilometers By the way, I am from the USA where we use \$. What is an R??? R^2 at SCC Sanford, FL USA
 Circles/83019: how do i find the area of a cirlce on a pie-graph1 solutions Answer 59639 by rapaljer(4667)   on 2007-05-22 23:54:35 (Show Source): You can put this solution on YOUR website!Area of a circle = . Is that what you wanted??? R^2 at SCC
 Polynomials-and-rational-expressions/83088: how do you solve 7x over 3y^2 plus 4y over 6x^2. i have tried multiplying 3y^2 by 2x^2 so that i get the denominator the same as the second denominator and then i multiplied 6x^2 by y^2 to get it the same as 6x^2 y^21 solutions Answer 59637 by rapaljer(4667)   on 2007-05-22 23:51:22 (Show Source): You can put this solution on YOUR website! In order to add two fractions, you must first find the Least Common Denominator (LCD). In this case, the LCD = In order to get the LCD in the first fraction, you must multiply the numerator and denominator of this first fraction by all the missing factors, which would be . In the second fraction, the missing factors are only . It should look like this: I just noticed that we could have reduced the second fraction FIRST, which would have made this easier. However, you can reduce the answer now by factoring the numerator: Divide out the factors of 2: ------------------------------------------------------------------------------------ Here is what it looks like if you reduce the fraction FIRST: Now the LCD= I don't know!! It's very late in Central Florida, USA, and I may have made a errors on this problem. If you find any, please let me know!! If you need more help with LCD problems, click on my tutor name "rapaljer", go to "MATH IN LIVING COLOR" and look for Basic Algebra, Chapter 3. R^2 at SCC
 Linear-equations/83081: What is the equation of the line through (0,9) that is parallel to the line 3x+5y=15?1 solutions Answer 59636 by rapaljer(4667)   on 2007-05-22 23:26:58 (Show Source): You can put this solution on YOUR website!In order to find the equation of a line, you must know two things: 1) Slope 2) Y-intercept In this problem, the slope must be found by writing the given equation in "slope-intercept" form. That is, you must solve for y in terms of x. 3x+5y=15 5y = -3x + 15 Divide both sides by 5: The slope of the given line is m=-3/5, so the slope of any line PARALLEL to this line is also m=-3/5. Secondly, the given point (0,9) just happens to be the Y-intercept, so in the equation y=mx+b m=-3/5 and b=9 R^2 at SCC
 Expressions-with-variables/83021: This question is from textbook begining algebra its factoring i dont know how to do those 2 problems 1 solutions Answer 59634 by rapaljer(4667)   on 2007-05-22 23:20:23 (Show Source): You can put this solution on YOUR website!You will have to give us the problems, since we don't have your book. ---OR--- Check out MY book, portions of which are explained "IN LIVING COLOR". Click on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", then click on either Basic or Intermediate Algebra, Chapter 2. Look at all these factoring topics. You may find what you need there. R^2 at SCC
 Polynomials-and-rational-expressions/82814: Please help me with this problem, it said to factor the polynomial: 2xy - 4x + 3y - 61 solutions Answer 59400 by rapaljer(4667)   on 2007-05-21 04:11:59 (Show Source): You can put this solution on YOUR website!Anytime there are four terms in a factoring problem, first try grouping the first two and the last two terms together: 2xy - 4x + 3y - 6 From the first two terms take out a common factor of 2x, from the second two terms take out a 3 factor: 2xy - 4x + 3y - 6 2x(y - 2) + 3(y - 2) Notice the common factor of (y-2): (y-2)(2x-3) For additional help with factoring, see my Lesson Plans in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", then look in either Basic or Intermediate Algebra for "Chapter 2," then "Factoring the Common Factor." R^2 at SCC
 Geometry_Word_Problems/82817: This question is a mix between geometery and algebra. I have gotten past putting the values into a right angled triangle and then substituting it into the Pythagorean Theorem, but I don't know what to do next. "A sail is in the shape of a right-angled triangle. The longest side of the sail is √3 times longer than the shortest side. The third side is 3m longer than the shortest side. Find the length of each sail." Any help really appreciated. Daniel1 solutions Answer 59399 by rapaljer(4667)   on 2007-05-21 04:03:32 (Show Source): You can put this solution on YOUR website!Let x = shortest side (a leg of the right triangle) x+3 = longer side (a leg of the right triangle) = longest side (hypotenuse of right triangle) Set equal to zero, moving everything to the right side of the equation: This does NOT factor (does this have an ugly answer??), so you'll have to complete the square or use the quadratic formula. I will complete the square: Reject the negative answer, since a side of a triangle cannot be negative: meters (shortest side) meters (second leg of the right triangle) meters (hypotenuse) meters (hypotenuse) R^2 at SCC
 Age_Word_Problems/82784: PROBLEM A woman is 5 years older than her husband and 10 times as old as their daughter. In 14 years, the sum of their ages will be 100. How old is each one now? ________________________________________________________________________________ Woman= h+5 Husband= h Daughter=h+5/10(I think) +________ 100 (h+5)+(h)+(h+5/10)=100 2h+5+(h+5/10)=100 3h+10=1000 3h/3=990/3 h=330 My question is what did i do wrong I know that this is way too high of a number and I can't figure out where I went wrong. Thanks 1 solutions Answer 59378 by rapaljer(4667)   on 2007-05-20 21:10:15 (Show Source): You can put this solution on YOUR website!You are correct in your set up of the problem: Woman= h+5 Husband= h Daughter=(h+5)/10 However, the equation has to do with the sum of their ages in 14 years. These are the ages in 14 years: Woman= h+5 +14 Husband= h +14 Daughter=(h+5)/10 + 14 The equation should be: (h+5)+14 +(h)+14 +((h+5)/10)+14 =100 Subtract 14*3 = 42 from each side, and your equation will equal 58 instead of 100. Try that and see if it works. I think you may have had another error as well: (h+5) +(h) +((h+5)/10) =58 2h+5 + (h+5)/10 = 58 20h + 50 + h+5 = 580 21h + 55 = 580 21h = 525 h= 525/21 = 25 years old = Husband w = 30 years old = Wife d = 30/10= 3 years old = Daughter In 14 years: Husband will be 39 Wife will be 44 Daughter will be 17 Check: 39+44+17= 100 years young!! R^2 at SCC
 logarithm/82735: log25 5=x1 solutions Answer 59352 by rapaljer(4667)   on 2007-05-20 16:41:29 (Show Source): You can put this solution on YOUR website! Translated to exponential notation, this means Indeed, since , R^2 at SCC
 logarithm/82737: 2log4+2logx=log321 solutions Answer 59350 by rapaljer(4667)   on 2007-05-20 16:26:37 (Show Source): You can put this solution on YOUR website! (NOTE: is NOT a valid solution, since you can't have a log of a negative number!) Final answer: R^2 at SCC
 Equations/82738: if i =radical 1, evaluate (-15i)^21 solutions Answer 59348 by rapaljer(4667)   on 2007-05-20 16:15:15 (Show Source): You can put this solution on YOUR website!Don't you mean i = radical -1??? And therefore, Anyway, R^2 at SCC
 Equations/82734: N=F+d(n-1) Solve for N1 solutions Answer 59347 by rapaljer(4667)   on 2007-05-20 16:11:54 (Show Source): You can put this solution on YOUR website!N=F+d(n-1) Perhaps you mean to solve for lower case n! It is very important to realize that in math, when upper case and lower case letters are used in an equation, they represent DIFFERENT variables. If you really wanted to solve for capital N, then the given equation does that already. However, assuming that you want to solve for "n", first remove the parentheses by distributive property: N= F+ dn - d Next, get all the NON-"n" terms on the left side, and get the "n" term (that is, "dn") by itself. You can do this by subtracting F and adding d to each side: N= F+ dn - d N-F +d = F+dn-d -F +d N-F + d = dn Next, divide both sides by d, so as to "undo" the multiplication of d times n: Resist the temptation to reduce this expression by dividing out the d's! You NEVER DIVIDE OUT TERMS!!! R^2 at SCC
 Polynomials-and-rational-expressions/82733: how do I factor 81x^2-16w^21 solutions Answer 59343 by rapaljer(4667)   on 2007-05-20 15:44:01 (Show Source): You can put this solution on YOUR website!This is a difference of two squares, which factors like this: (First-Second)*(First + Second) If you need more help, please see my Lesson Plans in algebra.com on Factoring the Difference of Squares, or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", then go to Chapter 2 of either Basic Algebra or Intermediate Algebra. R^2 at SCC
 Polynomials-and-rational-expressions/82695: using the 5 properties of exponents simplify the following (y5)3is aboove(y3)2 is above ____________________________ (y4)4 is above I am very confused how to do this.1 solutions Answer 59342 by rapaljer(4667)   on 2007-05-20 15:40:12 (Show Source): You can put this solution on YOUR website!I was RIGHT!! This is the way the problem could have been stated: over When you raise a power to a power, you MULTIPLY exponents! (By the way, if you need help with the Laws of Exponents, please see my Lesson Plan on algebra.com, or go to my own website by clicking on my tutor name "rapaljer", then look for "MATH IN LIVING COLOR," then "Basic Algebra", then Chapter 2.) over When you divide, you must SUBTRACT exponents: over When you divide, again you SUBTRACT exponents: When you have a negative exponent, this means R^2 at SCC
 Radicals/82696: Find the length x. Express your answer in simplified radical form. The known dimensions are 20 cm and 15 cm. This is a 3-D shape. Thank you.1 solutions Answer 59341 by rapaljer(4667)   on 2007-05-20 15:31:35 (Show Source): You can put this solution on YOUR website!I can't tell from your description what x is. Maybe you should resubmit the question. R^2 at SCC
 Complex_Numbers/82729: Please sove 4x^2-6x+2=01 solutions Answer 59339 by rapaljer(4667)   on 2007-05-20 15:28:50 (Show Source): You can put this solution on YOUR website! You can start by factoring out the common factor of 2: This trinomial just happens to factor: There are two solutions: 2x-1=0 2x=1 x-1=0 x=1 If you need more help solving quadratic equations by factoring, see my Lesson Plans in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for "Math in Living Color", then look in Basic Algebra or Intermediate Algebra, Chapter 2 for the topic "Solving Quadratic Equations". R^2 at SCC
 Polynomials-and-rational-expressions/82705: if there are 6x10^9 people on earth and there is enough freshwater to provide each person with 8.78x10^5 L, how much freshwater is on the earth?1 solutions Answer 59336 by rapaljer(4667)   on 2007-05-20 15:23:54 (Show Source): You can put this solution on YOUR website!You just multiply the number of people times the amount of water per person: L L L L R^2 at SCC
 Polynomials-and-rational-expressions/82715: find each opf the following squares (7p+6q)^21 solutions Answer 59332 by rapaljer(4667)   on 2007-05-20 15:19:26 (Show Source): You can put this solution on YOUR website!Introductory note: On this problem, you really have to watch your p's and q's!!! R^2 at SCC
 Polynomials-and-rational-expressions/82712: The price of an item is given by p=2x^2-100. find the polynomial that represents the revenue generate from the sale of x items.1 solutions Answer 59331 by rapaljer(4667)   on 2007-05-20 15:16:31 (Show Source): You can put this solution on YOUR website!Revenue = (Selling Price per item) * (Number of items sold) Revenue = Revenue = R^2 at SCC
 Equations/82728: Which expression cannot be rewrittin using distributive property? f 3(2+8) h (18-9)7 g 5(2*33) i 9(14-6)1 solutions Answer 59329 by rapaljer(4667)   on 2007-05-20 15:13:18 (Show Source): You can put this solution on YOUR website!The Distributive Property is MULTIPLICATION OVER a SUM or DIFFERENCE! That is, there must be a multiplication and within parentheses, you MUST have either a sum or difference. In this case, the third answer does NOT meet these conditions: g) 5(2*33) is NOT distributive property! R^2 at SCC
 Polynomials-and-rational-expressions/82727: how do I factor this x^2+25x+241 solutions Answer 59324 by rapaljer(4667)   on 2007-05-20 15:10:15 (Show Source): You can put this solution on YOUR website! A trinomial like this usually factors into the product of two binomials. The trick is to find two numbers whose product is the last number (in this case 24!) and whose sum (or difference!) is the middle number (in this case 25!). The answer to these questions is 24 times 1, so the answer is For more help on this topic, see my Lesson Plans on Factoring Trinomials in algebra.com, or visit my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", then look for topics relating to "Factoring", which would be in Chapter 2 of Basic Algebra, or Chapter 2 of Intermediate Algebra. R^2 at SCC
 Rational-functions/82591: This question is from textbook Find value of a where f(x)=6x-10/2x-a1 solutions Answer 59227 by rapaljer(4667)   on 2007-05-19 10:28:57 (Show Source): You can put this solution on YOUR website!Was there more information given in this problem? Were you looking for the value of a where the function is undefined? Were you looking for the value of a that gives a particular value of f(x)? I don't think the question can be answered without more information. R^2 at SCC
 Linear-equations/81814: Can someone assit me with this problem? I am stuck. The volume of a cumbe is given by V=s3, where s is the length of a side. Find the length of a side fo a cube if the volume is 1000 cm3 Answer: Show work here: 1 solutions Answer 58633 by rapaljer(4667)   on 2007-05-13 06:56:08 (Show Source): You can put this solution on YOUR website!You are correct, . Now if volume is 1000 cm^3, then R^2 at SCC
 Quadratic_Equations/81806: Problem In 1981 Vladimir Poliakov set a world record of 19ft3/4in for the pole vault. To reach that height, Poliakov obtained a speed of approximately 36 ft per second on the runway. The formula h = -16t + 36t gives his height t seconds after leaving the ground. Use the formula to find the exact values of t for which his height is 18ft. This is what I have 18 = -16t + 36t 18 = 20t 20t/20 = 18/20 t = 9/10 Not sure if I did this right, would appreciate your input. Thank you1 solutions Answer 58631 by rapaljer(4667)   on 2007-05-12 23:02:52 (Show Source): You can put this solution on YOUR website!It looks right to me!!! R^2 at SCC
 Equations/81817: Graph the following: y <= –31 solutions Answer 58630 by rapaljer(4667)   on 2007-05-12 23:00:14 (Show Source): You can put this solution on YOUR website!First draw a horizontal line at y = -3. Make this a SOLID line. Then since this is y<= -3, shade everything BELOW the line: . You will have to shade the graph yourself, since I don't know how to do shade the region in algebra.com. R^2 at SCC
 Equations/81818: Graph the following: y <= –31 solutions Answer 58629 by rapaljer(4667)   on 2007-05-12 22:58:59 (Show Source): You can put this solution on YOUR website!First draw a horizontal line at y = -3. Make this a SOLID line. Then since this is y<= -3, shade everything BELOW the line: . You will have to shade the graph yourself, since I don't know how to do shade the region in algebra.com. R^2 at SCC
 Polynomials-and-rational-expressions/81832: This question is from textbook i need help on this equation: (5x^4-2x^2+1)(x^2-5x+3) 1 solutions Answer 58628 by rapaljer(4667)   on 2007-05-12 22:54:42 (Show Source): You can put this solution on YOUR website!I'm not sure exactly what you want to do with this. First, it is not an equation. Second, did you want to multiply the two trinomials? If so, then this is what you should do: (5x^4-2x^2+1)(x^2-5x+3) = 5x^4(x^2-5x+3) -2x^2(x^2-5x+3) +1(x^2-5x+3) = 5x^6 -25x^5 +15x^4 -2x^4 +10x^3 -6x^2 + x^2-5x+3 Finally, combine like terms: = 5x^6 -25x^5 +13x^4 +10x^3 -5x^2 -5x+3 R^2 at SCC
 Rational-functions/81836: Graph the function. f(x)=-2x+7 iff(x)=4x-3 find the following f(-1)1 solutions Answer 58627 by rapaljer(4667)   on 2007-05-12 22:45:45 (Show Source): You can put this solution on YOUR website!f(x)=-2x+7 This is the graph of a straight line whose y intercept is 7 and whose slope is -2. There are several ways to graph it, but it should look like this: For your second question: if f(x)=4x-3 find f(-1). This means that x=-1, so substitute this for x: f(-1) =4(-1) -3 f(-1)=-7 R^2 at SCC