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 Polynomials-and-rational-expressions/88205: PLease help! I tried to solve this, can't do it. Am I supposed to change the form of the problem befdore I solve it? The problem is I need to simplify as much as possible 6x^2-x-2 over 3x^2+x-2.1 solutions Answer 64044 by rapaljer(4667)   on 2007-07-12 15:16:07 (Show Source): You can put this solution on YOUR website!The first problem is to FACTOR the numerator and denominator. It's like in the last solution that I posted, but this time the factoring is a LOT harder. You may need some help with what I call "Advanced Trinomial Factoring" and I have a lesson on this if you are interested. Now, the (3x-2) factors divide out: The Lesson on Advanced Trinomial Factoring can be found in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Next, click on "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then in Chapter 2, look for the section about "Advanced Trinomial Factoring." While you are there, check out ALL the sections on Factoring. There are several sections devoted to this important skill. R^2
 Polynomials-and-rational-expressions/88206: Here's another problem like the first problem. X^2-4+4 over X62-4 1 solutions Answer 64042 by rapaljer(4667)   on 2007-07-12 15:08:02 (Show Source): You can put this solution on YOUR website! The first step is to FACTOR the numerator and denominator: Divide out the factors of (x-2): R^2
 Polynomials-and-rational-expressions/88199: Can someone help me please. Factor the polynomial by factoring out the negative of the GCF -24x4y3+30x2y31 solutions Answer 64041 by rapaljer(4667)   on 2007-07-12 15:03:55 (Show Source): You can put this solution on YOUR website!The GCF is the largest factor that divides into both terms in this expression. If variables are involved, it will be the LOWEST power of each variable. This would be . When you take out the NEGATIVE of this common factor, it changes all the signs. What is left is this: R^2
 Equations/88162: Rewrite the equation 4x – 6y = –30 as a function of x1 solutions Answer 64017 by rapaljer(4667)   on 2007-07-12 11:42:08 (Show Source): You can put this solution on YOUR website!4x – 6y = –30 Get the x term isolated by adding +6y to each side: 4x = 6y-30 Divide both sides by 4. There are two ways to write this: or or R^2
 Geometry_Word_Problems/88172: an angle is 14 degrees more than the measure of its complement. find the number of degrees in each angle 1 solutions Answer 64015 by rapaljer(4667)   on 2007-07-12 11:36:31 (Show Source): You can put this solution on YOUR website!Let x = first angle x+14= second angle x+x+14 = 90 2x +14= 90 2x=76 x= 38 degrees x+14= 52 degrees Check: 38+52 = 90 degrees R^2
 Geometry_Word_Problems/88176: two angles are complementary one contains 30 degrees more than the other . find both angles 1 solutions Answer 64013 by rapaljer(4667)   on 2007-07-12 11:34:11 (Show Source): You can put this solution on YOUR website!Let x= first angle x+30 = second angle x+ x+ 30= 180 2x= 150 x= 75 degrees x+30 = 105 degrees Check 75+105= 180 R^2
 Coordinate-system/88175: A satellite orbits the Earth on a path with equation x^2 + y^2 = 45 000 000. Another satellite, on the same plane, is currently located at (12 504, 16 050). Is the second satellite inside or outside the orbit of the first satellite? Explain. THNAK u1 solutions Answer 64012 by rapaljer(4667)   on 2007-07-12 11:31:54 (Show Source): You can put this solution on YOUR website!Assuming that the earth is located at the point (0,0), find the distance between (0.0) and the satellite at (12 504, 16 050). Find . Since this is greater than the of the orbit of the other satellite, I would say that it is OUTSIDE the orbit of this satellite. R^2
 Percentage-and-ratio-word-problems/88173: I had 14 Leases in June and 0 Leases for May. What is my percentage of increase for June over May? How do I figure this? Thank You1 solutions Answer 64011 by rapaljer(4667)   on 2007-07-12 11:21:46 (Show Source): You can put this solution on YOUR website!Percent of increase is always the amount of increase divided by the original amount. In this case you have an increase of 14, but the original amount is ZERO. You can't divide by zero, so the percent of increase is "undefined" or "infinity"!! R^2
 Geometry_Word_Problems/88170: two angles of a triangle have equal measures but the third angles measure is 36 degrees less than the sum of the other two . find the measure of each angle of the triangle1 solutions Answer 64010 by rapaljer(4667)   on 2007-07-12 11:19:03 (Show Source): You can put this solution on YOUR website!Let x = measure of one of the equal angles 2x-36 = third angle x + x + 2x-36 = 180 4x - 36= 180 4x -36+36= 180+36 4x = 216 x= 54 Degrees = Equal angles 2x-36 = 72 Degrees = Third angle Check: 54+54+72= 180 degrees R^2
 Quadratic_Equations/88166: Can someone show me how to do this problem with step by step instructions. Thank you The height h in feet of an object after t seconds is given by the function h=16t^2+90t+8. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.1 solutions Answer 64009 by rapaljer(4667)   on 2007-07-12 11:14:27 (Show Source): You can put this solution on YOUR website!Are you sure you copied this correctly? This particular equation NEVER hits the ground. Maybe you meant to say ?? R^2
 Linear-equations/88167: Find the slope of the graph of the linear function. f(2)=4, f(0)=61 solutions Answer 64008 by rapaljer(4667)   on 2007-07-12 11:11:55 (Show Source): You can put this solution on YOUR website!f(2)=4, f(0)=6 Slope = RISE = 6-4=2 RUN=0-2=-2 Slope = =. R^2
 Rectangles/88169: This question is from textbook Geometry:Seeing, Doing, Understanding In a quadrilateral with equal diagonals, why can't we conclude that it is a rectangle?1 solutions Answer 64007 by rapaljer(4667)   on 2007-07-12 11:08:52 (Show Source): You can put this solution on YOUR website!I apologize for my WRONG answer here!! It was pointed out to me that a trapezoid can have equal diagonals! I completely forgot about these. Diagonals of a quadrilateral being equal does NOT imply rectangularity!! I sincerely apologize for my error!! R^2
 Polynomials-and-rational-expressions/88164: Could someone help me please. This is a trinomial not a polynomial. Find the constant term that should be added to make the following expression a perfect square trinomial. x^2+18x1 solutions Answer 64006 by rapaljer(4667)   on 2007-07-12 11:04:00 (Show Source): You can put this solution on YOUR website!This is called "completing the square". Assuming that the coefficient of the x^2 term is 1, you take HALF of the x coefficient, and SQUARE it. In this case, take HALF of 18 (which is 9) and SQUARE (which is 81). Now you have The final answer is 81. R^2
 Complex_Numbers/88099: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form: [1/2(cos pi/10 + i sin pi/10)]^51 solutions Answer 64004 by rapaljer(4667)   on 2007-07-12 09:25:17 (Show Source): You can put this solution on YOUR website!According to DeMoive's Theorem = = Now, and = = = or R^2
 Geometry_Word_Problems/88133: find the length of the side of a square with the perimeter of 60 cm 1 solutions Answer 63973 by rapaljer(4667)   on 2007-07-12 00:35:31 (Show Source): You can put this solution on YOUR website!Let x = side of square 4x = 60 x= 15 cm R^2
 Polynomials-and-rational-expressions/88121: If there are 6 * 10^9 people on the Earth and there is enough freshwater to provide each person with 8.79 * 10^5 L, how much freshwater is on the Earth? 1 solutions Answer 63972 by rapaljer(4667)   on 2007-07-12 00:33:25 (Show Source): You can put this solution on YOUR website!Multiply the number of people times the number of liters of water per person: When you multiply numbers like , you add exponents! Now, change to scientific notation by converting 52.74 to . R^2
 Geometry_Word_Problems/88134: 1 solutions Answer 63971 by rapaljer(4667)   on 2007-07-12 00:24:39 (Show Source): You can put this solution on YOUR website!Perimeter of a triangle is just the sum of the three sides. So, add up the sides: x +3x +3x+2= 37 7x + 2 = 37 7x= 35 x= 5 3x = 15 3x+2 = 17 Check: 5 + 15+ 17 = 37 It checks! See my Lesson Plan in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for my MATH IN LIVING COLOR PAGES, then go to Basic Algebra, Chapter 1, then look for the section on Word Problems. FREE and in COLOR!! How is that!!! R^2
 Geometry_Word_Problems/88135: =22/the circumference of a circle is 132 yds find the radius using pie 71 solutions Answer 63969 by rapaljer(4667)   on 2007-07-12 00:19:07 (Show Source): You can put this solution on YOUR website!The formula for Circumference is or . Since you want the radius, take the second equation: To eliminate the fraction , multiply both sides by the reciprocal of the fraction which is . Did you notice that 44 divides into 132 exactly 3 times? That may make the calculation easier. Or just use a calculator. It comes out to an even 7*3= 21 yards. R^2
 Geometry_Word_Problems/88136: 1 solutions Answer 63967 by rapaljer(4667)   on 2007-07-12 00:09:54 (Show Source): You can put this solution on YOUR website!Let x = longer side (length) x-3 = shorter side (width) 2L + 2W = P 2(x) + 2(x-3) = 54 2x+2x-6=54 4x-6= 54 Add +6 to each side: 4x-6+6=54+6 4x= 60 x=15 Length x-3= 12 = Width Check: 2(15) + 2(12 ) = 54 30+ 24= 54 It checks! R^2
 Equations/88126: I know the answer is 5 and 12 but I can't get it to show as an equation (I must show my work and explann it in front of class tommorrow morning Help.1 solutions Answer 63963 by rapaljer(4667)   on 2007-07-12 00:04:15 (Show Source): You can put this solution on YOUR website!This is like working a problem backwards, starting from the answer and ending up with a quadratic equation. Start with x=5 and x= 12 Write each of these as mini-equations equal to zero. x-5=0 and x-12=0 Now, write the product of these factors equal to zero: (x-5)*(x-12)=0 Finally, multiply it all out: I hope you get this in time for your presentation!! R^2
 Polynomials-and-rational-expressions/87839: Simplify. square root of 7 over 1001 solutions Answer 63941 by rapaljer(4667)   on 2007-07-11 20:43:49 (Show Source): You can put this solution on YOUR website!The answer in simplest radical form is . It's always best, unless instructed to do otherwise, to rationalize the denominator. R^2
 test/88025: Find the slope of the line passing through the points (1, 4) and (7, 2).1 solutions Answer 63940 by rapaljer(4667)   on 2007-07-11 20:38:32 (Show Source): You can put this solution on YOUR website!The correct answer is -1/3. The other tutor made a small error. Sorry about that. R^2
 Numeric_Fractions/87969: Factor the trinomial. s2 + s + 141 solutions Answer 63939 by rapaljer(4667)   on 2007-07-11 20:36:06 (Show Source): You can put this solution on YOUR website!You asked to factor this trinomial! This trinomial CANNOT be factored! Moreover, this is NOT an equation, so you can't solve it by quadratic formula, as one of the other tutors tried to do. It is INCORRECT to solve something that is NOT an equation to begin with!! R^2
 Square-cubic-other-roots/88030: Use Property 2 to simplify each of the following radical expressions. square root of 10/49 The answer I got is square root of 10 over 71 solutions Answer 63937 by rapaljer(4667)   on 2007-07-11 20:32:48 (Show Source): You can put this solution on YOUR website!I just want you to know that I got your answer!! Your answer is in simplest radical form, no matter what anyone else may tell you!!! R^2
 Functions/88014: Explain the meaning of a function. Give an example.1 solutions Answer 63902 by rapaljer(4667)   on 2007-07-11 15:42:24 (Show Source): You can put this solution on YOUR website!A function is a set of points such that no two points have the same x coordinate. An example of a function is . R^2
 Polynomials-and-rational-expressions/88007: 4/x+4= 5/x-1 I have to solve this equation(i.e. x=4 or 6)1 solutions Answer 63901 by rapaljer(4667)   on 2007-07-11 15:40:46 (Show Source): You can put this solution on YOUR website!Remember that means that . Likewise, means that . This is easy to solve! Subtract 4x from each side: Subtract 20 from each side: Check the answer by substituting the value into the original equation: It checks!! R^2
 test/88013: What is the third term of a recursive sequence that follows the pattern x - 7 and has a first term x = 100?1 solutions Answer 63899 by rapaljer(4667)   on 2007-07-11 15:34:34 (Show Source): You can put this solution on YOUR website!If the first term is 100, the second term would be 93, and the third term would be 7 less than this which would be 86. Right??? R^2
 Functions/88008: find the function , quation of the line, that mathmatically models the data where the imput is the year (x) and the output is the cost of the war (y) 2007 and predict for 2008 2007 cost is 442 billion1 solutions Answer 63897 by rapaljer(4667)   on 2007-07-11 15:32:59 (Show Source): You can put this solution on YOUR website!You didn't give us enough information! R^2
 Polynomials-and-rational-expressions/88010: 2 8t +20t-12=0 That is supposed to read 8t squared. I need to solve the equation(i.e. x=4 or 6)1 solutions Answer 63896 by rapaljer(4667)   on 2007-07-11 15:31:10 (Show Source): You can put this solution on YOUR website! First factor the common factor of 4: Next, you have to factor the trinomial. By the way, this is a problem all in itself! Do you know how to factor these what I call "Advanced Trinomials"? I have a lesson on this if you are interested! Anyway, here is the factored form: Now, of the factors given above, the 4 factor cannot equal zero, so it does not give you any solutions. However, the other two factors do give solutions: or or R^2 Retired from SCC
 Polynomials-and-rational-expressions/88009: (2y-9)(y+4)(y-5)=0 I have to solve this equation(i.e. x=4 or 6)1 solutions Answer 63895 by rapaljer(4667)   on 2007-07-11 15:25:43 (Show Source): You can put this solution on YOUR website!When you have a product of factors equal to zero, then one of the factors must be zero. That is, (2y-9)(y+4)(y-5)=0 2y-9 = 0 or y+4= 0 or y-5=0 2y=9 or or R^2 Retired from SCC