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 Travel_Word_Problems/246104: A plane flew for 576 miles directly into a strong wind and then flew back with the same wind. If the total flying time was 5 hours, and the plane's airspeed was 250 mph, what was the speed of the wind?1 solutions Answer 179746 by rapaljer(4667)   on 2009-12-05 12:33:16 (Show Source): You can put this solution on YOUR website!Let x = air speed 250+x = speed with the wind 250-x= speed against the wind Distance with the wind = Distance against the wind=576 TOTAL TIME = 5 Multiply both sides by (250-x)(250+x): (I'm on vacation, and I don't have my calculator. Use it if you have one!!) , which I can do even WITHOUT a calculator!!! mph--a pretty strong wind!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Quadratic_Equations/245316: Enter the quadratic equation in standard form. x^2 - 10 + 3x = (x - 2)^2 + 1 1 solutions Answer 179236 by rapaljer(4667)   on 2009-12-02 23:18:59 (Show Source): You can put this solution on YOUR website!x^2 -10+3x=x^2 -4x+4 + 1 Subtract x^2 from each side, and all the x^2 terms are gone. Therefore, this is NOT a quadratic equation after all. -10+3x= -4x+5 Add +4x to each side: -10+3x+4x=-4x+4x+5 -10+7x=5 Add +10 to each side: 7x= 15 Divide both sides by 7: x=15/7 Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 absolute-value/244950: why is blake a jerk???1 solutions Answer 179089 by rapaljer(4667)   on 2009-12-02 10:44:40 (Show Source): You can put this solution on YOUR website!Is Blake one of the algebra.com tutors? Somehow related to math? If so, try re-posting your question, and see if you can get a better solution. Good questions deserve good answers, and NO ONE should be a JERK about it!! Dr. Robert J. Rapalje, Retired
 Square-cubic-other-roots/244948: solve the eqaution. If the equation has no real solution, so state. square root of k + 9 = 81 solutions Answer 179088 by rapaljer(4667)   on 2009-12-02 10:41:21 (Show Source): You can put this solution on YOUR website! Square both sides of the equation: Check: It checks!! Dr. Robert J. Rapalje, Retired
 Square-cubic-other-roots/244942: simplify the expression 9 square root of 7x - 6 sqaure root 7x1 solutions Answer 179085 by rapaljer(4667)   on 2009-12-02 10:37:29 (Show Source): You can put this solution on YOUR website!9 square root of 7x - 6 square root 7x Just combine like radicals: 9 apples -6 apples = 3 apples Likewise 9 square root of 7x - 6 square root 7x= 3 square root 7x! You should see my own website for additional explanation on Square Roots, and especially to see a FREE hour and a half video of me teaching this lesson a few years ago. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. From my homepage, click on "Rapalje Videos in Color", choose "Basic Algebra", and look for the video "Radicals (Square Roots)". In addition to this video explanation, I have a written explanation that you will probably find easier to understand than your textbook. From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and then select "Chapter 5". The entire chapter is my own non-traditional explanation of Square Roots, which is also supported by my "MATH IN LIVING COLOR" pages. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Square-cubic-other-roots/244935: Indicate whether the statement is true or false. square root of 112 is a rational number.1 solutions Answer 179083 by rapaljer(4667)   on 2009-12-02 10:32:15 (Show Source): You can put this solution on YOUR website!False!! Any square root that is not of a perfect square is irrational.
 Square-cubic-other-roots/244937: Simplify square root of 281 solutions Answer 179081 by rapaljer(4667)   on 2009-12-02 10:30:49 (Show Source): You can put this solution on YOUR website! You should see my own website for additional explanation on Square Roots, and especially to see a FREE hour and a half video of me teaching this lesson a few years ago. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. From my homepage, click on "Rapalje Videos in Color", choose "Basic Algebra", and look for the video "Radicals (Square Roots)". In addition to this video explanation, I have a written explanation that you will probably find easier to understand than your textbook. From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and then select "Chapter 5". The entire chapter is my own non-traditional explanation of Square Roots, which is also supported by my "MATH IN LIVING COLOR" pages. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Square-cubic-other-roots/244934: classify the number as rational, irrational, or immaginary. sqauare root of - 251 solutions Answer 179077 by rapaljer(4667)   on 2009-12-02 10:23:05 (Show Source): You can put this solution on YOUR website!The square root of a negative number is an imaginary number.
 Exponential-and-logarithmic-functions/244851: I started with: then got: Logx=2*x don't know where to go from there1 solutions Answer 179021 by rapaljer(4667)   on 2009-12-01 23:54:12 (Show Source): You can put this solution on YOUR website! Take the log of each side: Subtract logx from each side: Factor out the logx: Divide both sides by (log2-1): Finally, raise both sides as a power of 10: . This comes out to approximately .137609. I checked this with a graphing calculator, and it is correct!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Functions/244850: find the domain and range of the following equation? y=3+5x+2y1 solutions Answer 179017 by rapaljer(4667)   on 2009-12-01 23:33:45 (Show Source): You can put this solution on YOUR website!Solve for y in this equation by subtracting 2y from each side. y=3+5x+2y y-2y=3+5x+2y-2y -y=3+5x Now divide both sides by -1, and you get y=-3 -5x This is a straight line graph with y intercept of -3 and slope of -5. Any value of x is allowed in this equation, since there are no denominators and no radicals in the equation. Therefore the domain is all real values of x. The graph goes all the way up and all the way down on a graph, so the range is also all real values. You may want to see my own website for my own explanation of Domain and Range, and also a FREE video (or TWO!) that I had recorded in my classes a few years ago. To see my website, click on my tutor name "Rapaljer" anywhere in algebra.com. On my Homepage, look for "Rapalje Videos in Living Color". There, you will find a video in "Intermediate Algebra" and also one in "College Algebra" called "Functions, Domain, and Range." These are different videos, the one from Intermediate Algebra being presented on a lower level with less depth of coverage. I call it "FDR Lite"!! The videos were taken of me teaching in my class a few years ago, but they might help you understand this concept. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Complex_Numbers/244791: -2z + 6z - 91 solutions Answer 179016 by rapaljer(4667)   on 2009-12-01 23:30:17 (Show Source): You can put this solution on YOUR website!Just combine like terms: 4z-9
 logarithm/244831: Use the change of base formula and a calculator to evaluate the logarithm. Round the answer to three decimal placesl. log1/6^71 solutions Answer 179015 by rapaljer(4667)   on 2009-12-01 23:25:24 (Show Source): You can put this solution on YOUR website!I'm not sure if you mean or ??? Can you clarify??? Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Linear-equations/244832: For what value of k does kx + 7 = 10 have a slope of 3?1 solutions Answer 179013 by rapaljer(4667)   on 2009-12-01 23:20:13 (Show Source): You can put this solution on YOUR website!Is there supposed to be a y somewhere in this equation?? Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Quadratic_Equations/244844: what kind of roots does x^2+2x+8=0 have?1 solutions Answer 179011 by rapaljer(4667)   on 2009-12-01 23:16:58 (Show Source): You can put this solution on YOUR website!x^2+2x+8=0 Calculate b^2-4ac 2^2 -4*1*8 4-32 , which is a negative. Since this is negative, this means that you have complex roots. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 absolute-value/244372: What is the value of n=21 solutions Answer 178782 by rapaljer(4667)   on 2009-12-01 00:52:47 (Show Source): You can put this solution on YOUR website!There is not enough information. What was the question? Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Equations/244386: What is -27+20w=731 solutions Answer 178781 by rapaljer(4667)   on 2009-12-01 00:50:24 (Show Source): You can put this solution on YOUR website!-27+20w=73 Start by adding +27 to each side to get all the number terms on the right side: -27+27+20w= 73+27 20w= 100 Next, divide both sides by 20: If you need additional help with the topic of Equation Solving, please see my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, which will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Alegebra: One Step at a Time". Choose "Basic Algebra", look in "Chapter 1" for "Section 1.08" for my complete nontraditional, explanation of Equation Solving. These lessons are supported by my MATH IN LIVING COLOR pages. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Complex_Numbers/244390: (-6-7i)-(1+3i)1 solutions Answer 178780 by rapaljer(4667)   on 2009-12-01 00:45:14 (Show Source): You can put this solution on YOUR website!Just combine like terms: (-6-7i)-(1+3i) -6-7i-1-3i -7-10i Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Rational-functions/244395: find the horizontal asympeote, if any, of the graph of the rational function. f(x)=17x/5x^2+8 type the equation of the horizontal asyptote. or if there is not one1 solutions Answer 178779 by rapaljer(4667)   on 2009-12-01 00:42:36 (Show Source): You can put this solution on YOUR website!Since the degree of the numerator (which is 1) is LESS than the degree of the denominator (which is 2), the horizontal asymptote is always y=0. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Proportions/244398: Write a model for the statement A is directly proportional to W1 solutions Answer 178778 by rapaljer(4667)   on 2009-12-01 00:40:19 (Show Source): You can put this solution on YOUR website!A=k*W, where k is a constant. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Triangles/244421: what does a right triangle look like1 solutions Answer 178776 by rapaljer(4667)   on 2009-12-01 00:38:07 (Show Source): You can put this solution on YOUR website!A right triangle is a triangle that has two sides mutually perpendicular to each other. One of the angles will be exactly 90 degrees--that is, a "RIGHT" angle. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 logarithm/244407: slove for x: log (x+2) - log (x-1)= log 4 3 3 3 please show work 1 solutions Answer 178775 by rapaljer(4667)   on 2009-12-01 00:35:53 (Show Source): You can put this solution on YOUR website! Therefore, Check: There are NO cases in which x=2 results in a log of a negative, so the answer checks! Actually, it really can be checked, by substituting x=2: If you need additional help with the topic of LOGARITHMS, please see my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, which will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Alegebra: One Step at a Time". Choose "College Algebra", look in "Chapter 4" for my complete nontraditional, explanation of Logarithms. This particular question actually comes from "Section 4.04 Exponential and Logarithmic Equations." These lessons are supported by my MATH IN LIVING COLOR pages. In addition, there are TWO two hour videos of me teaching the topic of Logarithms in my own classroom a few years aog. These are FREE. To see the videos, look on my Homepage for "Rapalje Vidoes in Living Color." Choose "College Algebra" and look for "Logarithms Part II." Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Angles/244408: what the complement of a 70 degree angle. A triangle has a 75 angle and a 40 find the measure of the third angle. what is the supplement of a 100.5 angle 1 solutions Answer 178772 by rapaljer(4667)   on 2009-12-01 00:19:55 (Show Source): You can put this solution on YOUR website!Is this three separate questions?? 1. Complement of 70 is 90-70= 20 degrees. 2. 75+40=115. Now, subtract 180-115= 65 degrees. 3. Supplement of 100.5 is 180-100.5 = 79.5 degrees. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Functions/244410: What is the domain of the given problem over 1 solutions Answer 178771 by rapaljer(4667)   on 2009-12-01 00:14:48 (Show Source): You can put this solution on YOUR website!In Domain, the denominator must NEVER be zero. So must not equal 0. You can have any value of x EXCEPT x(x+3) must NOT equal zero. x cannot equal 0, x cannot equal -3. Domain is all real values except 0 and -3. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Coordinate-system/244417: y2-12y+36=01 solutions Answer 178769 by rapaljer(4667)   on 2009-12-01 00:09:48 (Show Source): You can put this solution on YOUR website!y2-12y+36=0 (y-6)(y-6)=0 y=6 Since this seems to be a two-dimensional problem, in an xy coordinate system, you have a HORIZONTAL line that is 6 units above the x axis. It looks like this; Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 logarithm/243307: Find the value of the expression. Show your work. Do not use the Change of base formula. log base 6 1 a. 6 b. 0 c. 10 d. 1 I think the answer is b. Let me know1 solutions Answer 178333 by rapaljer(4667)   on 2009-11-28 23:34:44 (Show Source): You can put this solution on YOUR website!You got it!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 logarithm/243309: Covert to an exponential equation log base 6 36=t a. 6^36=t b.t^6=36 c.6^t=36 d.36^t=6 I think the answer is c. thanks1 solutions Answer 178332 by rapaljer(4667)   on 2009-11-28 23:33:41 (Show Source): You can put this solution on YOUR website!The basic definition of a logarithm is the BASE NUMBER raised to the power of, in this case t, equals 36. 6^t=36 Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Trigonometry-basics/243316: please help me: Find the phase shift of the function y=cos(x+pi/4) HERE ARE THE POSSIBLE ANSWERS: a)pi/4 left b)pi/4 right c)1/4 right1 solutions Answer 178330 by rapaljer(4667)   on 2009-11-28 23:31:38 (Show Source): You can put this solution on YOUR website!Set x+pi/4=0 You get x=-pi/4, so it is a phase shift of pi/4 to the LEFT, since the value is negative. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Trigonometry-basics/243320: please help me: Find the phase shift of the function y= 3 sin(2x-1): here are the possible answers: a)1 right b)1 left c)1/2 right1 solutions Answer 178329 by rapaljer(4667)   on 2009-11-28 23:30:12 (Show Source): You can put this solution on YOUR website!To find the phase shift, set the angle equal to zero. 2x-1=0 2x=1 x=1/2 If the value of x is positive, then the shift is to the right. If it is negative, then the phase shift is to the left. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Trigonometry-basics/243348: what is sin(theta)= -11 solutions Answer 178328 by rapaljer(4667)   on 2009-11-28 23:28:11 (Show Source): You can put this solution on YOUR website!Because the , the answer is theta = Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Travel_Word_Problems/243379: Leaving home traveling to work which is 10 miles away driving at 40 mile per hour how long will it take to get to work?1 solutions Answer 178327 by rapaljer(4667)   on 2009-11-28 23:25:33 (Show Source): You can put this solution on YOUR website!The basic formula is D=r*t. You are given that D=10 mi and r=40 mph, and time t is the unknown: 10=40t Divide both sides by 40, and you get t=10/40=1/4 hour. In other words 15 minutes. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus