Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'rapaljer'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679, >>Next

 Problems-with-consecutive-odd-even-integers/307510: If p and r are positive integers and 2p + r -1 = 2r + p + 1, which of the following must be true? I. p and r are consecutive integers. II. p is even. III. r is odd. (A) None (B) I only (C) II only (D) III only (E) I, II, and III 1 solutions Answer 219995 by rapaljer(4667)   on 2010-05-23 08:30:09 (Show Source): You can put this solution on YOUR website!2p+r-1=2r+p+1 can be simplified by subtracting p and r from each side. 2p+r-1-p-r=2r+p+1-p-r p-1=r+1 Now, add +1 to each side: p=r+2 This means that p and r are NOT consecutive integers. It does indicated that if r is even, then p is also even. If r is odd, then p is also odd. The numbers are either BOTH even or BOTH odd. However, you can't say that p is necessarily even or odd, and you can't say that r is necessarily even or odd. The correct answer is A) NONE. Dr. Robert J. Rapalje, Retired
 Divisibility_and_Prime_Numbers/307512: What is the smallest positive integer p for which 2^2p + 1 is not a prime number?1 solutions Answer 219994 by rapaljer(4667)   on 2010-05-23 08:20:15 (Show Source): You can put this solution on YOUR website!Let p=1, 2^2+1= 5 which is prime. Let p=2, 2^4+1=17 which is prime. Let p=3, 2^6+1=65 which is NOT prime. The smallest positive integer p is 3. Dr. Robert J. Rapalje, Retired
 Percentage-and-ratio-word-problems/307511: If each of the fractions 3/k, 4/k, 5/k is in lowest terms, which of the following could be the value of k? (A) 48 (B) 49 (C) 50 (D) 51 (E) 52 1 solutions Answer 219993 by rapaljer(4667)   on 2010-05-23 08:15:32 (Show Source): You can put this solution on YOUR website!Using 49 as a denominator, the fractions 3/49, 4/49, and 5/49 do NOT reduce. The answer is B) 49. Dr. Robert J. Rapalje, Retired
 Quadratic_Equations/307265: Find all numbers for which the rational expression is undefined. p^3 - 9p/p^2 -811 solutions Answer 219981 by rapaljer(4667)   on 2010-05-23 00:03:51 (Show Source): You can put this solution on YOUR website!A rational expression will be undefined if the denominator is zero!! The problem here is to find all values for which the denominator is zero. (The numerator is actually irrelevant!) This means that or Dr. Robert J. Rapalje, Retired
 Functions/307293: find the domain of the function g(x)=sqrt(5x+5) what is the domain of g? type answers in interval notation.1 solutions Answer 219980 by rapaljer(4667)   on 2010-05-22 23:57:01 (Show Source): You can put this solution on YOUR website! The restriction here is due to the fact that there is a square root in the function. The RADICAND must be greater than or equal to zero. That is, In interval notation, this is [-1,inf). Please see my own website at "www2.seminolestate.edu/rrapalje". Look for the link on my Homepage "MATH IN LIVING COLOR", and look under either Intermediate (Chapter 5) OR College Algebra (Chapter 2). I also have a video of my own teaching in class a few years ago. To see the videos, look for "Rapalje Videos in Living Color", and see either Intermediate or College Algebra for the topic "Functions, Domain, and Range". Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Functions/307292: find the domain of the function f(x)=sqrt (x+8) what is the domain of f?1 solutions Answer 219979 by rapaljer(4667)   on 2010-05-22 23:51:27 (Show Source): You can put this solution on YOUR website!In this function , you have a SQUARE ROOT. The RADICAND (that is, whatever is INSIDE the square root) must NEVER be negative. The RADICAND must be GREATER than or EQUAL TO 0. In this case, the domain is , so . Please see my explanation of this topic on my own website. Go to "www2.seminolestate.edu/rrapalje". Look for the link on my Homepage "MATH IN LIVING COLOR", and look under either Intermediate (Chapter 5) OR College Algebra (Chapter 2). I also have a video of my own teaching in class a few years ago. To see the videos, look for "Rapalje Videos in Living Color", and see either Intermediate or College Algebra for the topic "Functions, Domain, and Range". I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. My own students did!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Functions/307290: find the domain of the function f(x)=12/x-15 what is the domain of f?1 solutions Answer 219978 by rapaljer(4667)   on 2010-05-22 23:44:44 (Show Source): You can put this solution on YOUR website!f(x)=12/x-15 In the real numbers, DENOMINATORS must NOT equal zero. Since there is a denominator in this function, there is a restriction that x-15 must NOT equal zero. The forbidden value is x=15. All other values are permitted. The domain is all values EXCEPT x=15. You really should see my explanation of this topic on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the link on my Homepage "MATH IN LIVING COLOR", and look under either Intermediate (Chapter 5) OR College Algebra (Chapter 2). I also have a video of my own teaching in class a few years ago. To see the videos, look for "Rapalje Videos in Living Color", and see either Intermediate or College Algebra for the topic "Functions, Domain, and Range". I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. My own students did!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Functions/307291: find the domain of the function f(x)=x^2-9x-11 what is the domain of f?1 solutions Answer 219977 by rapaljer(4667)   on 2010-05-22 23:40:00 (Show Source): You can put this solution on YOUR website!The domain is all real numbers, since there are NO restrictions (i.e., no denominators, no square roots!) in the equation. You really should see my explanation of this topic on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the link on my Homepage "MATH IN LIVING COLOR", and look under either Intermediate (Chapter 5) OR College Algebra (Chapter 2). I also have a video of my own teaching in class a few years ago. To see the videos, look for "Rapalje Videos in Living Color", and see either Intermediate or College Algebra for the topic "Functions, Domain, and Range". I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. My own students did!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Unit_Conversion_Word_Problems/307470: how do I convert 110 kilometers per hour to miles per minute. I can't remember how to correctly do the procedure-conversion, fractions and cancellation of units1 solutions Answer 219976 by rapaljer(4667)   on 2010-05-22 23:30:56 (Show Source): You can put this solution on YOUR website! * * = 1.1 I had to look up the conversion numbers on my own website! By the way, for additional explanation on Metric System conversions, please visit my website at "www2.seminolestate.edu/rrapalje". Near the bottom of my Homepage, look for "Topics from Geometry", then click on "Metric System." For all the algebra in my teaching and on this website, strangely enough, this Metric System page (that I seldom make use of myself!) is my most frequently visited page!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Equations/307471: what is an equation of a vertical line that passes through the point (5,-6)1 solutions Answer 219974 by rapaljer(4667)   on 2010-05-22 23:05:10 (Show Source): You can put this solution on YOUR website!A vertical line is always in the form x = a number. In this case it is x=5. Dr. Robert J. Rapalje, Retired
 Polynomials-and-rational-expressions/307466: I have tried this problem, but I keep getting a remainder. Can you help please? (3x^2-7x+1)/(3x-1)1 solutions Answer 219972 by rapaljer(4667)   on 2010-05-22 22:59:34 (Show Source): You can put this solution on YOUR website!I get a remainder also! Are you sure you copied the problem correctly? If the problem had been (3x^2-7x+2)/(3x-1), then the remainder is zero. Actually, the numerator would have factored, and the fraction would have reduced. Dr. Robert J. Rapalje, Retired Seminole State College of Florida P.S. Check out my website at "www2.seminolestate.edu/rrapalje". It has a lot of algebra help and great joke page!!
 logarithm/307342: find the value of the given expression 2 log 11 solutions Answer 219970 by rapaljer(4667)   on 2010-05-22 22:53:24 (Show Source): You can put this solution on YOUR website!log 1 = 0, since 10^0=1. Therefore, 2 log 1=2*0=0. Dr. Robert J. Rapalje, Retired
 Miscellaneous_Word_Problems/307463: The cardinal number of the set {triangle, rectangle, square, trapezoid, octagon, rhombus, circle, ellipse, pentagon} is _________.1 solutions Answer 219969 by rapaljer(4667)   on 2010-05-22 22:50:42 (Show Source):
 Rational-functions/307297: find the vertical asymptotes, if any, of the graph of the rational function f(x)=x/x-6 type the equation(s) of the vertical asymptote(s)1 solutions Answer 219968 by rapaljer(4667)   on 2010-05-22 22:49:39 (Show Source): You can put this solution on YOUR website!The vertical asymptote is where the denominator equals zero! In this case, the denominator equals zero at x=6. This is the vertical asymptote. Dr. Robert J. Rapalje, Retired
 expressions/307459: Simplify the expression. Answer without using negative exponents. (-2*y)^41 solutions Answer 219964 by rapaljer(4667)   on 2010-05-22 22:08:08 (Show Source): You can put this solution on YOUR website!(-2*y)^4 (-2)^4*y^4 16y^4 Dr. Robert J. Rapalje, Retired P.S. If you need more help with the Laws of Exponents, I have a pretty good explanation on my website at "www2.seminolestate.edu/rrapalje". If you find this page, then choose the link from my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 2 for Sections 2.12 and 2.13 on the Laws of Exponents. I think you will find it "user-friendly" and MUCH easier to read than traditional textbooks. It's all FREE.
 Evaluation_Word_Problems/307458: The Perimeter of a rectangle is 6x+6 yds. If the width is x yards, find a binomial that represents the length. 1 solutions Answer 219963 by rapaljer(4667)   on 2010-05-22 22:02:17 (Show Source): You can put this solution on YOUR website!Let x = width Let L = Length P = 6x+6 2x+2L= P 2x+2L= 6x+6, you must solve for L. Subtract 2x from each side. 2x-2x+2L = 6x+6-2x 2L= 4x+6 Divide both sides by 2. L= 2x+3 Dr. Robert J. Rapalje P.S. Please visit my website at "www2.seminolestate.edu/rrapalje". It's a pretty good website with lots of good math materials and a nice JOKE page!! I need the hits!!
 Miscellaneous_Word_Problems/307448: If the area of square PQRS is 500 square feet, the length of each side is in between which two numbers?1 solutions Answer 219962 by rapaljer(4667)   on 2010-05-22 21:51:49 (Show Source): You can put this solution on YOUR website!Area = x= 22.36 approximately Therefore, the length of each side is between 22 and 23. Dr. Robert J. Rapalje, Retired
 Polynomials-and-rational-expressions/307454: 6x-42/x^2-5x-14 /(devide)2x-12/x^2-4x-121 solutions Answer 219961 by rapaljer(4667)   on 2010-05-22 21:39:52 (Show Source): You can put this solution on YOUR website!Divided By Factor, Factor, Factor, and INVERT the second fraction and MULTIPLY! * Divide out the factors (x-7),(x+2), and (x-6). Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Linear_Algebra/307453: what do points on the parallel to x-axis 5 units above it have in common?1 solutions Answer 219959 by rapaljer(4667)   on 2010-05-22 21:31:12 (Show Source): You can put this solution on YOUR website!They are points on the line whose equation is y = 5 .
 Polynomials-and-rational-expressions/307419: how do i simplify the following expression: sqrt6 times sqrt36/sqrt21 solutions Answer 219958 by rapaljer(4667)   on 2010-05-22 21:21:50 (Show Source): You can put this solution on YOUR website!Is this what you mean? If so, Dr. Robert J. Rapalje, Retired
 Square-cubic-other-roots/307418: how do i simplify the expression: 2square root of 42 times square root of 91 solutions Answer 219956 by rapaljer(4667)   on 2010-05-22 21:16:43 (Show Source): You can put this solution on YOUR website! The square root of 42 does NOT simplify, since no perfect squares divide evenly into it. The only simplification that can be done is That's it!! Dr. Robert J. Rapalje P.S. I have a GREAT website with a LOT of different help with square roots. Go to "www2.seminolestate.edu/rrapalje". To see my FREE video, look for the link that says "Rapalje Videos in Living Color" and choose "Basic Algebra". Select the topic "Radicals". For written explanation, look at the link on my Homepage called "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look at Chapter 5 on Radicals. There are a LOT of problems solved in LIVING COLOR.
 Linear_Algebra/307444: what can be said of points with equal abscissa? with equal ordinates?1 solutions Answer 219955 by rapaljer(4667)   on 2010-05-22 21:07:59 (Show Source): You can put this solution on YOUR website!The "abscissa" refers to the x-axis. The "ordinate" refers to the y-axis. If these are "equal", then you have a line whose equation is y=x. Dr. Robert J. Rapalje, Retired
 Coordinate-system/307442: how do I solve 2x + 3 -7x is greater than or equal to 12?1 solutions Answer 219954 by rapaljer(4667)   on 2010-05-22 21:05:28 (Show Source): You can put this solution on YOUR website! Divide both sides by -5, but remember that when you divide both sides by a NEGATIVE number, you REVERSE the inequality!! Dr. Robert J. Rapalje, Retired
 Rectangles/307446: how do you find the perimeter of the rectangle with the length 4x-1 and the width 2x+1? Then Simplify the expression.1 solutions Answer 219953 by rapaljer(4667)   on 2010-05-22 21:00:55 (Show Source): You can put this solution on YOUR website!Perimeter = 2W + 2L P= 2(2x+1)+2(4x-1) P=4x+2+8x-2 P=12x Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Exponential-and-logarithmic-functions/307443: What approaches can be used to solve equations and inequalities involving logarithms?1 solutions Answer 219951 by rapaljer(4667)   on 2010-05-22 20:58:42 (Show Source): You can put this solution on YOUR website!For the answer to this, you really need to see my website at www2.seminolestate.edu/rrapalje. If you can find this website, look for the link called "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", "Chapter 4", and look at Section 4.04 Equation Solving. In addition to this, I have a complete explanation of Logarithms on Video that you can see for FREE from the website. On the Homepage, look for "Rapalje Videos in Living Color." Choose "College Algebra," and then look for "Logarithms." Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Travel_Word_Problems/307439: A jet plane flying with the wind flew 2400 miles in 4 hours. Against the wind, the plane flew only 2000 miles in 4 hours. Find the rate of the plane in calm air and the rate of the wind.1 solutions Answer 219948 by rapaljer(4667)   on 2010-05-22 20:27:45 (Show Source): You can put this solution on YOUR website!Let x = rate of the plane in still air. Let y = rate of the wind. Rate WITH the wind = Rate AGAINST the wind = x+y=600 x-y=500 Add the equations together: 2x=1100 x=550 mph = speed of the plane in still air. Now, x+y=600, where x=550 550+y=600 y=50 mph = speed of the wind. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Problems-with-consecutive-odd-even-integers/307440: This one has me stumped: "If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less than the sum of the first and twice the sum of the second of the integers. Find the integers." My thought process: 1st Int. x 2nd int. x+1 3rd int. x+3 (x-23)+ 2(x+1)+ x+3-6= 2x or x + 2(x+1)+ x+3-6= 2x-23 Nothing seems to pan out with this and a few other runs.1 solutions Answer 219947 by rapaljer(4667)   on 2010-05-22 20:18:07 (Show Source): You can put this solution on YOUR website!I'm not quite sure about the wording of the last part of this, but I can tell you that for three consecutive ODD integers, you should use x= first x+2= second x+4= third The equation will be 2(x+4-6)= x+2(x+2) - 23 See how that works for you. Dr. Robert J. Rapalje, Retired Seminole State College of Florida P.S. If you want to check the wording of the last part and have me finish this for you, then send an Email to Email address at rapaljer@seminolestate.edu. For some reason, the "Thank You" notes apparently are going into the spam filter tonight.
 Coordinate-system/307433: Consider the line 3x+2y=18 A. what is the x-intercept? B. what is the y-intercept? C. is the point (3,-2) in the line?1 solutions Answer 219945 by rapaljer(4667)   on 2010-05-22 20:09:30 (Show Source): You can put this solution on YOUR website!3x+2y=18 The x intercept is where y=0. If y=0, then 3x=18, so x=6. The y intercept is where x=0. If x=0, then 2y=18, so y=9. The point (3,-2) means that x=3 and y=-2. If x=3 and y=-2, 3x+2y 3(3)+2(-2) does NOT equal 18, so NO it is NOT a point on the line. Please see my own website for additional explanation on Graphing. Do a Google search for my name "dr robert j rapalje," and look for "Rapalje Homepage" near the top of the list. Then find the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra," and look in Chapter 4. You will find a complete explanation with examples and exercises, with many of the exercises solved in the MATH IN LIVING COLOR pages that are attached. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Surface-area/307436: What is the surface area of this cylinder that has a radius of 6 inches and a height of 8 inches?1 solutions Answer 219943 by rapaljer(4667)   on 2010-05-22 20:01:31 (Show Source): You can put this solution on YOUR website!The total surface area consists of the lateral (side) area and two end pieces (circles). Lateral area is actually the distance around the base (circumference) which is times the height which is h. Lateral area = Lateral area = Each end piece is a circle whose area is The grand total = Total Area = Please see my own website for additional explanation on Geometric problems. Do a Google search for my name "dr robert j rapalje," and look for "Rapalje Homepage" near the top of the list. Then look for the link called "Topics from Geometry" near the bottom of the page. Several sections might be helpful to you, and it's all FREE!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Miscellaneous_Word_Problems/307435: Write and solve two mathmatical sentences for the following problem: The length of a crayon box base is 2 more than 3 times its width. If the perimeter of the base of the crayon box is 14 centimeters, find the length and width.1 solutions Answer 219939 by rapaljer(4667)   on 2010-05-22 19:39:19 (Show Source): You can put this solution on YOUR website!Let x= width 3x+2 = length The formula for Perimeter is 2W + 2L = P 2(x)+2(3x+2)=14 2x+6x+4=14 8x+4=14 8x=10 x=10/8=5/4 cm Length = 3x+2 Length = 3(5/4)+2 Length = 15/4 +2 =15/4 + 8/4=23/4 cm Check: 2W + 2L 2(5/4) + 2(23/4)=10/4 + 46/4= 56/4= 14 cm. It checks!! Please see my own website for additional explanation on perimeter problems. Do a Google search for my name "dr robert j rapalje," and look for "Rapalje Homepage" near the top of the list. Then find the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra," and look in Chapter 1 for Section 1.11. You will find a complete explanation with examples and exercises, with many of the exercises solved in the MATH IN LIVING COLOR pages that are attached. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Square-cubic-other-roots/307426: how do i simplify: 8sqrt27 times sqrt721 solutions Answer 219935 by rapaljer(4667)   on 2010-05-22 19:07:15 (Show Source): You can put this solution on YOUR website! Break it down instead of multiplying it out. Multiply the numbers that are OUTSIDE the square root and keep them OUTSIDE the square root. Multiply the numbers that are INSIDE the square root and keep them INSIDE the square root, as follows: For additional explanation on square roots, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 5 for an entire chapter on Square Roots. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!! In addition, there is a FREE video of me teaching this topic a few years ago. To see the video, from my Homepage, look for "Rapalje Videos in Living Color." Choose Basic Algebra, and look for the video called "Radicals." I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus