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# Recent problems solved by 'rapaljer'

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 Linear-equations/142305: Is there an instance when a linear equation is not a function? 1 solutions Answer 103602 by rapaljer(4667)   on 2008-05-19 21:19:56 (Show Source): You can put this solution on YOUR website!YES!! When the line is VERTICAL it is NOT a function!! R^2
 Radicals/142279: I would really appreciate help on this problem. It is multiplying radicals. the square root of 3x^3 divided by the sqaure root of 4y^2 times the sqaure root of 9x^2 divided by the square root of 2y^4. I thought that you multiplied the top and bottom by the bottom, which gets rid of the radical on the bottom, but it just isnt working out.1 solutions Answer 103589 by rapaljer(4667)   on 2008-05-19 20:09:44 (Show Source): You can put this solution on YOUR website!Do you mean like this??? I would put it together into one square root: Simplify: Put all the perfect square factors in the first square root, and leftover factors in the second square root: Rationalize the denominator of the second fraction by multiplying inside the radical by . Simplify: For more help on square roots, please see my own user-friendly explanation by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." You may need to see Basic Algebra in Chapter 5, or click on Intermediate Algebra and choose Chapter 3. Explanation varies in level of difficulty between these two. If you want College Algebra, go to the MATH IN LIVING COLOR pages, and Choose College Algebra, Chapter 1. R^2
 logarithm/142274: Translate each verbal expression into an algebraic expression a. Five subtracted from a number. b. The ratio of a number and six1 solutions Answer 103585 by rapaljer(4667)   on 2008-05-19 19:52:56 (Show Source): You can put this solution on YOUR website!a. Five subtracted from a number. Let x = the number. Now, this is NOT 5-x, It has to be 5 subtracted FROM x, which is x-5. b. The ratio of a number and six. Ratio means a quotient, so you divide. Let x = the number. See my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and take the second link on my home page which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, choose Chapter 1, and look for Section 1.09 for an explanation of word problems that is probably a LOT easier to understand than your own traditional textbook. R^2
 Linear-equations/142271: what is the slope-intercept equation form of the line with the x-intercept=-3, y-intercept=2? thank you!1 solutions Answer 103581 by rapaljer(4667)   on 2008-05-19 19:47:13 (Show Source): You can put this solution on YOUR website!Xintercept = (-3,0) Yintercept = (0,2) First find the slope. Can you do that? If not, check out my website!! Send me an Email, and I'll tell you where to look!! Therefore the equation is y=mx+b, where m = slope and b= yintercept. FINAL ANSWER For more on this, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Choose Basic Algebra, and look for Chapter 4. The first three sections explain graphing and slope of a line. The slope of a line is in Section 4.02. The equation of a line is in Section 4.06. R^2
 logarithm/142269: Identify the variable and write an inequality. A. Tony is taller than 6 feet B. The miminum speed of teh freeway is 45 mph.1 solutions Answer 103576 by rapaljer(4667)   on 2008-05-19 19:38:36 (Show Source): You can put this solution on YOUR website!A) Let T= height of Tony in feet. B) Let S = freeway speed. R^2
 Unit_Conversion_Word_Problems/142250: I have 46 pounds of apples, each one weighs 4 ounces, How many apples do I have?1 solutions Answer 103574 by rapaljer(4667)   on 2008-05-19 19:35:38 (Show Source): You can put this solution on YOUR website! Each pound equals 16 ounces. If the apples are 4 ounces each, then this is 4 apples per pound. Multiply the number of pounds times 4, and you should get 4*46 = 184 apples. R^2
 Surface-area/141916: I have tried to solve this equation, but so far, I have been unsuccessful. I keep getting different answers because I don't know if I am reading the problem correctly. Any help will be greatly appreciated. The problem given is: A rectangular field has an unknown width. The length is 2 more yards than the width and the total is area is 120 yards with an exponent of 2 above and to the right the "s" in yards. I am not sure if this means yards squared or square yards. I have tried either squaring the 120 yds. or finding the square root of 120. In either scenario can I get the numbers to total 120 when plugging the values in for "x".1 solutions Answer 103370 by rapaljer(4667)   on 2008-05-17 16:18:31 (Show Source): You can put this solution on YOUR website!Let x= width of the rectangular field x+2 = length of the field. Area = Width * Length 120 = x(x+2) 120 = x^2 +2x This is a quadratic equation so set it equal to zero: 0=x^2 + 2x - 120 Let's hope it factors: 0=(x-10)(x+12) x=10 or x=-12 Reject the x=-12, since you can't have a negative width. x=10 yds = Width x+2= 12 yds = Length R^2
 percentage/141941: This question is from textbook PREALGEBRA A pound is equal to 16oz. What fractional part of a pound is 6 oz?1 solutions Answer 103368 by rapaljer(4667)   on 2008-05-17 16:07:18 (Show Source): You can put this solution on YOUR website!6/16=3/8 R^2
 Quadratic_Equations/141870: Solve. Then Graph. 7x >_ 63 (The _ is supposed to be under the >) Would the solution be {xlx<9} ?? AND the graph be a hollow circle on the 9 and and arrow towards the numbers higher than 9? Am I even close? 1 solutions Answer 103360 by rapaljer(4667)   on 2008-05-17 00:37:41 (Show Source): You can put this solution on YOUR website!When you solve an inequality by dividing both sides by a POSITIVE number, the inequality sign remains the same. When you divide by a NEGATIVE number, the inequality sign must be reversed. In this case, you divided by a POSITIVE number, so the inequality sign stays the same. This means go to 9 on the right side of the numberline, and from 9, shade the number line from 9 to the RIGHT, with an arrow pointing to the right towards number larger than 9. Use a SOLID circle on the point at the 9. The solution will be { x| }. For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 1. Problems like this one will be found in Section 1.11 Inequalities. Students tell me that my explanations are easier to understand than expensive, traditional textbooks. R^2
 Quadratic_Equations/141872: Graph the equation using the slope and y-intercept. y = 9/4x + 7 (the 9/4 is a fraction) HELP PLEASE1 solutions Answer 103359 by rapaljer(4667)   on 2008-05-17 00:20:33 (Show Source): You can put this solution on YOUR website!The y-intercept is where the graph crosses the x-axis. It is the point where x=0. If x=0, then y=7. It turns out that the number term in this type of equation is always the y-intercept. Next, find the slope, which, in this type of equation, is always the coefficient of x. The slope is 9/4. Slope is the . So the RISE =9, and the RUN=4. Start by plotting the y-intercept by going UP 7 units on the y-axis, and put the FIRST point. Next, start with your pencil ON the y-intercept, and measure from this point UP a distance of 9 units (that would be a total of 16 units!), then go from there OVER 4 units to the RIGHT, and put the SECOND point. Connect the two points with a straight line, and you have the graph, which should look like this: For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 4. Problems like this one will be found in Section 4.02 Slope Intercept Method. You may find my explanations easier to understand than traditional textbooks. R^2
 Quadratic_Equations/141873: Translate to an algebraic expression. The product of 16% and some number. I do not understand this one at all will someone help please.?1 solutions Answer 103358 by rapaljer(4667)   on 2008-05-17 00:09:26 (Show Source): You can put this solution on YOUR website!Let x = the unknown number (or whatever letter you would like to use!) You realize (I hope!) that 16% can be written as a decimal, 16%=.16, so take the "product" of these, which is .16x. R^2
 Quadratic_Equations/141874: Solve the following system of equations. x+2y=7 (1) x=8-2y (2) How do I do this one???1 solutions Answer 103357 by rapaljer(4667)   on 2008-05-17 00:06:50 (Show Source): You can put this solution on YOUR website!Since the second equation is stated in the form "x= ____", I would recommend the substitution method. Substitute what x= in the second equation, back into the first equation: x+2y=7 (1) x=8-2y (2) (_____) +2y = 7 (8-2y) +2y=7 A funny thing happens here!! All the variables subtract out, and you are left with 8=7. This is NOT POSSIBLE, so there is NO SOLUTION. Actually, the two given straight lines are PARALLEL LINES. For a more detailed explanation, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and choose Chapter 4. Problems like this one will be found in Section 4.07 Systems of Equations. You may find my explanations easier to understand than traditional textbooks. R^2
 Equations/141875: Solve for the indicated letter. d=7e, for e The solution of e is? How the heck do I go about doing this one, can someone please help??1 solutions Answer 103356 by rapaljer(4667)   on 2008-05-16 23:59:24 (Show Source): You can put this solution on YOUR website!To solve for e, you must get the "e" by itself. You have to eliminate the 7. Since the 7 is multiplied times the e, in order to UNDO this, you have to DIVIDE both sides by 7. This would be: For additional help in an easier to understand format, see my website, by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, and look for Chapter 1, Section 1.08 Equation Solving. R^2
 Inequalities/141817: -3w+3greater than or equal to 181 solutions Answer 103297 by rapaljer(4667)   on 2008-05-16 12:22:10 (Show Source): You can put this solution on YOUR website! Subtract 3 from each side: Here is the tricky step! When you muliply or divide both sides of an inequality by a negative number, you must REVERSE the inequality sign! For a simpler explanataion of this than the one you have in traditional textbooks, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for about the second link on my home page, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on "Basic Algebra", "Chapter 1", and look for "Section 1.11 Inequalities." My own students and students who discover my website tell me that I have a "user-friendly" explanation. I hope you will find it helpful. R^2
 Inequalities/141441: How do I solve this problem? y-5>-15 What does the horizontal line mean that is between the y? {y|y>?}1 solutions Answer 103083 by rapaljer(4667)   on 2008-05-14 10:59:26 (Show Source): You can put this solution on YOUR website!Do you mean the VERTICAL line?? It means "such that". The set of all values of y, SUCH THAT, y> what value. Of course the answer, if you add +5 to each side, is y>-10. R^2
 Polynomials-and-rational-expressions/141387: FIND THE ZEROS OF THE POLYNOMIAL FUNCTION AND STATE THE MULTIPLICITY IF EACH. f(x)=x cubed+7x squared-x-7 A)-7, multiplicity 1; -1 multiplicity 2 B)-7, multiplicity 2; 1, multiplicity 1 C)-1 multiplicity 1; 1, multiplicity 1; 7, multiplicity 1 D)-7, multiplicity 1; -1 multiplicity 1; 1, multiplicity 1 I'm thinking the answer is D, but I would like to know for sure. Thanks!1 solutions Answer 103064 by rapaljer(4667)   on 2008-05-13 22:01:09 (Show Source): You can put this solution on YOUR website! Factor by grouping: Zeros are at x=-7,x=1, and x=-1, each of multiplicity 1. D is correct! R^2
 Exponents/141431: How do you solve this rational expression? (5X^3)(16X^2)/80X^3. I have tried doing it on my own, but my teacher did not explain how to do it...1 solutions Answer 103063 by rapaljer(4667)   on 2008-05-13 21:53:31 (Show Source): You can put this solution on YOUR website! First multiply 5 times 16 =80. Secondly, when you multiply with the same base number, you must ADD the exponents! Next, divide out the 80s, and when you divide, you must SUBTRACT the exponents! You probably need additional explanation! I have a complete explanation that is designed for folks who have trouble with math. See my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Click on Basic Algebra, then click on Chapter 2, and look for Section 2.12 Positive Exponents. At least I think it is Section 2.12. See if this helps. R^2
 Geometric_formulas/141430: what is geometry?1 solutions Answer 103061 by rapaljer(4667)   on 2008-05-13 21:44:23 (Show Source): You can put this solution on YOUR website!It's what the acorn said after it grew up!! R^2 In case you didn't get this one, "Gee! I'm a tree!"
 Functions/141388: Find the domain of the function. g(x)= 4/4-9x (this is a fraction) Will someone please help me on this? I do not no how to do it at all.1 solutions Answer 103060 by rapaljer(4667)   on 2008-05-13 21:41:33 (Show Source): You can put this solution on YOUR website!To find the domain, you must make sure the denominator does NOT equal zero. In this case, make sure that 4-9x does NOT equal zero. To solve this, solve 4-9x=0 and the domain will be all values of x EXCEPT this value! 4=9x x=4/9 Domain is all values of x EXCEPT 4/9. For additional explanation, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for MATH IN LIVING COLOR, which is about the third link on my homepage. Choose College Algebra, then Chapter 2, the section called "Functions, Domain, and Range". R^2
 Numeric_Fractions/141418: -3/2 - -2/31 solutions Answer 103032 by rapaljer(4667)   on 2008-05-13 20:10:06 (Show Source): You can put this solution on YOUR website! Find the LCD= 6. R^2
 Complex_Numbers/141419: i don't get them?1 solutions Answer 103031 by rapaljer(4667)   on 2008-05-13 20:05:25 (Show Source): You can put this solution on YOUR website!Do you have a particular problem or two to post? We don't have your textbooks!! R^2
 test/141420: Evaluate (-4x)small 2 and -4x small2 when x = 4 I did not know how to put the small 2 next to the number sorry1 solutions Answer 103029 by rapaljer(4667)   on 2008-05-13 20:03:23 (Show Source): You can put this solution on YOUR website!Is the small 2 written as a superscript (an exponent?) or a subscript??? My guess is that these are exponents! R^2
 Linear-equations/141409: (2,5)and (2,-9) Find the slope if it exists of the line containing the pair of points. Help me with this one please. 1 solutions Answer 103027 by rapaljer(4667)   on 2008-05-13 20:01:00 (Show Source): You can put this solution on YOUR website!These points form a vertical line, so the slope is UNDEFINED! R^2
 Equations/141421: A line intercepts the y-axis at the point (0,8). From there the line moves up four units for every one unit it moves to the right. What is the equation of the line in slope-intercept form. here is my work Y=mx+b y=1/4x+81 solutions Answer 103026 by rapaljer(4667)   on 2008-05-13 19:58:24 (Show Source): You can put this solution on YOUR website!RISE = 4, RUN = 1 Slope m= = y=mx+b y=4x+8 R^2
 Finance/141105: Please work this out set by set so I can understand how to get from a-z please. 1/5 x+2=1/2 x+11 solutions Answer 102794 by rapaljer(4667)   on 2008-05-12 00:52:33 (Show Source): You can put this solution on YOUR website!Multiply both sides of the equation by the LCD which is 10: R^2
 Polynomials-and-rational-expressions/141125: Can someone help me* my problem is to find a polynomial function of degree 3 with the given numbers as zeros. 2, i, -i1 solutions Answer 102792 by rapaljer(4667)   on 2008-05-12 00:34:41 (Show Source): You can put this solution on YOUR website! R^2
 Polynomials-and-rational-expressions/141127: Could I havehelp with this problem please* Find an equation of variation for the given situation. y varies inversely as the square of x, and y=6 when x=31 solutions Answer 102791 by rapaljer(4667)   on 2008-05-12 00:26:29 (Show Source): You can put this solution on YOUR website! R^2
 Volume/141129: what is the formula to calculate the inside volume of a rectangular container with width 10cm,length 10cm and height 21 cm? 1 solutions Answer 102790 by rapaljer(4667)   on 2008-05-12 00:23:07 (Show Source): You can put this solution on YOUR website!Volume =L*W*H V=10*10*21=2100 cu cm R^2
 Finance/141102: Plaese answer this in detail for me its due May 12 at mid night 3= 5/11 x-21 solutions Answer 102788 by rapaljer(4667)   on 2008-05-11 23:48:05 (Show Source): You can put this solution on YOUR website!Start by adding +2 to each side: 3= 5/11 x-2 5=5/11 x Next, you must "undo" the multiplication by the fraction 5/11. The best way to do this is to multiply both sides of the equation by the "reciprocal" of 5/11, which is 11/5. Did we make it by 12:00 May 12??? R^2
 Equations/141118: How do you know when an equation has an infinitely number of solutions or when an equation has no solution?1 solutions Answer 102787 by rapaljer(4667)   on 2008-05-11 23:32:48 (Show Source): You can put this solution on YOUR website!An equation has infinitely many solutions when, in the process of solving for the variable, you come down to a statement (for example, 0=0) that is ALWAYS TRUE. In math, this is called an IDENTITY. An equation has NO SOLUTIONS when, in the process of solving for the variable, all of the variables subtract out, and you get a statement (for example, 0=3)that is NEVER TRUE. This is called a CONTRADICTION. R^2
 Quadratic-relations-and-conic-sections/141095: I need to Identify the conic section, then place in standard form. The equation is: 4x^2+y^2+8x-4y-28=0 This is as far as i have been able to solve it. (4x^2+8x)+(y^2-4y)=28 [4(x+1)^2-1]+(y-2)^2-4=28 +4 +4 4(x+1)^2+(y-2)^2-1=32 +1 +1 4(x+1)^2/33+(y-4)^2/33=1 any help you can give would be wonderful. Thank you. 1 solutions Answer 102775 by rapaljer(4667)   on 2008-05-11 20:39:54 (Show Source): You can put this solution on YOUR website!4x^2+y^2+8x-4y-28=0 Sort it out and factor the coefficient of x^2. Leave spaces in order to complete the square in the next steps: To complete the square, you must take half of the x coefficient (Half of 2 is 1, and square which is 1. On the right side, however, you must add 4*1 which is 4. It should look like this: Divide both sides by 36 to write this in standard form for an ellipse: This is an ellipse, with center at (-1,2), with a "radius" of 3 in the x direction, and a "radius" of 6 in the y direction. R^2