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# Recent problems solved by 'rapaljer'

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 Quadratic_Equations/308022: what is the maximum or minimum value of the quardratic function ? f(x)=3x^2+12x+8 a. -28 b. -4 c. -2 d. 44 tthanks!1 solutions Answer 220265 by rapaljer(4667)   on 2010-05-24 14:50:12 (Show Source): You can put this solution on YOUR website!The maximum or minimum of a quadratic function occurs when x=-b/2a. In this case, a=3, b=12, so x=-12/6=-2. f(-2)=3(-2)^2+12(-2)+8 f(-2)=3*4+(-24)+8 f(-2)=12+(-16)=-4 = minimum value of f(x). Are graphing calculators allowed??? Dr. Robert J. Rapalje, Retired
 Numeric_Fractions/308016: 3x(x+2)and 6x(2x-3)1 solutions Answer 220262 by rapaljer(4667)   on 2010-05-24 14:44:47 (Show Source): You can put this solution on YOUR website!What should we do with these??? Multiply them out and get 3x^2+6x and 12x^2 -18x Dr. Robert J. Rapalje, Retired
 Polynomials-and-rational-expressions/308020: a number less 6% of that number equals = 450,000 How would I figure this out? is it? n-.06n=450000 ? if so, how would i figure it out from there?1 solutions Answer 220261 by rapaljer(4667)   on 2010-05-24 14:42:20 (Show Source): You can put this solution on YOUR website!n-.06n=450000 1.00n-.06n=450000 .94n=450000 Divide both sides by .94: Dr. Robert J. Rapalje, Retired
 Polynomials-and-rational-expressions/307969: i need to solve for x 3x^2+3x-126=01 solutions Answer 220258 by rapaljer(4667)   on 2010-05-24 14:37:11 (Show Source): You can put this solution on YOUR website!3x^2+3x-126=0 This is a quadratic equation that must be solved by factoring! The first step in factoring is to take out the common factor, in this case, 3. 3(x^2+x-42)=0 Next, factor the trinomial: 3(x+7)(x-6)=0 The 3 does not give any solutions to this problem. First solution: (x+7)=0 x=-7 Second solution: (x-6)=0 x=6 For additional help with solving quadratic equations by factoring, please see my own website. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. Then, look for the link on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", "Chapter 2", and look for "Section 2.09 Solving Quadratic Equations by Factoring." If you have trouble with the FACTORING, then these skills are also taught in Chapter 2. See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Exponential-and-logarithmic-functions/308011: solve the equation e^(2x)=20 for x .... a. x=10/e b. x=1n20/2 c. x=1n10 d. x=20-e/2 tthanks!1 solutions Answer 220254 by rapaljer(4667)   on 2010-05-24 14:24:00 (Show Source): You can put this solution on YOUR website!e^(2x) = 20 ln(e^(2x))= ln 20 2x= ln 20 . The correct answer is B). You may want to see my website for help with LOGARITHMS! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. For written explanations, look for "Basic, Intermediate, and College Algebra: One Step at a Time", choose "College Algebra" and look for "Chapter 4 Logarithms." See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR! For VIDEO explanations, on my Homepage look for "Rapalje Videos in Living Color". Choose "College Algebra" and select the topics of "Logarithms." These videos are from my own classroom a few years ago before I retired. I hope you find these helpful. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 logarithm/308012: which equation is equivalent to 3logx+log8-logy ? a. log 8x^3/y b. log (xy/8)^3 c. logx^3y /8 d. (logx^3y/8) tthanks!1 solutions Answer 220253 by rapaljer(4667)   on 2010-05-24 14:21:00 (Show Source): You can put this solution on YOUR website!3logx + log8 - log y The correct answer is A). You may want to see my website for help with LOGARITHMS! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. For written explanations, look for "Basic, Intermediate, and College Algebra: One Step at a Time", choose "College Algebra" and look for "Chapter 4 Logarithms." See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR! For VIDEO explanations, on my Homepage look for "Rapalje Videos in Living Color". Choose "College Algebra" and select the topics of "Logarithms." These videos are from my own classroom a few years ago before I retired. I hope you find these helpful. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Linear-equations/307998: How do I find the equation of the line given: 3x+2y=19 y=2x-81 solutions Answer 220252 by rapaljer(4667)   on 2010-05-24 14:16:26 (Show Source): You can put this solution on YOUR website!You are given the equations of lines. Maybe you wanted to find the point of intersection?? 3x+2y=19 y=2x-8 Substitute the 2x-8 into the first equation. 3x+2(2x-8) =19 3x+4x-16=19 7x-16=19 7x=35 x=5 y=2x-8 y=2(5)-8 y=10-8=2 Dr. Robert J. Rapalje, Retired
 Exponential-and-logarithmic-functions/308007: solve the equation e^(2x)=20 for x .... a. x=10/e b. x=1n20/2 c. x=1n10 d. x=20-e/2 tthanks!1 solutions Answer 220248 by rapaljer(4667)   on 2010-05-24 14:09:53 (Show Source): You can put this solution on YOUR website!Start by taking the ln of each side of the equation to "undo" the "e^": Divide by 2: You may want to see my website for help with LOGARITHMS! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. For written explanations, look for "Basic, Intermediate, and College Algebra: One Step at a Time", choose "College Algebra" and look for "Chapter 4 Logarithms." See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR! For VIDEO explanations, on my Homepage look for "Rapalje Videos in Living Color". Choose "College Algebra" and select the topics of "Logarithms." These videos are from my own classroom a few years ago before I retired. I hope you find these helpful. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 logarithm/308001: which equation is equivalent to 3log4+log6-log8 ? a. log 8x^3/y b. log (xy/8)^3 c. logx^3y /8 d. (logx^3y/8) tthanks!1 solutions Answer 220238 by rapaljer(4667)   on 2010-05-24 13:52:46 (Show Source): You can put this solution on YOUR website!Did you state this problem correctly?? Where did the x's and y's come from??? Maybe this is what you meant: 3logx+logy-log8 You may want to see my website for help with LOGARITHMS! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. For written explanations, look for "Basic, Intermediate, and College Algebra: One Step at a Time", choose "College Algebra" and look for "Chapter 4 Logarithms." See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR! For VIDEO explanations, on my Homepage look for "Rapalje Videos in Living Color". Choose "College Algebra" and select the topics of "Logarithms." These videos are from my own classroom a few years ago before I retired. I hope you find these helpful. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Mixture_Word_Problems/307995: In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture?1 solutions Answer 220235 by rapaljer(4667)   on 2010-05-24 13:39:48 (Show Source): You can put this solution on YOUR website!Let x = number of pounds of cashews. Set up a ratio of pounds of cashews to total pounds of nuts, realizing that there will be 2 pounds of cashews in a 7 pound mixture. Since means that , means that . or 1 1/7 pounds of cashews. Dr. Robert J. Rapalje, Retired
 Systems-of-equations/307992: if ax2+bx+c=0 Prove x=(-b+-SQROOT(b^2-4ac)/(2a)1 solutions Answer 220231 by rapaljer(4667)   on 2010-05-24 13:17:53 (Show Source): You can put this solution on YOUR website!The solution to this problem is posted on my website. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. From my Homepage, look for the link near the top of the page "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Intermediate Algebra", then "Chapter 4". Click on "Section 4.03 Quadratic Formula", and scroll to the last page before all the answers are given. This is the proof (derivation!) of the Quadratic Formula!! While you are there, from my Homepage, please check out my "Joke Page"--all safe for the little ears in your family!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Triangles/307973: the sum of two angles in a triangle totals 117 degrees, waht is the measure of the third angle?1 solutions Answer 220230 by rapaljer(4667)   on 2010-05-24 13:09:50 (Show Source): You can put this solution on YOUR website!The sum of all three angles of a triangle is 180 degrees. If you know two of the angles, then to find the third angle, just subtract the two that you know from 180 degrees. In this case, 180-117= 63 degrees. Dr. Robert J. Rapalje, Retired
 Rectangles/307974: find the perimeter and area of a square with side 9 inches.1 solutions Answer 220229 by rapaljer(4667)   on 2010-05-24 13:07:46 (Show Source): You can put this solution on YOUR website!P=4s P=4*9= 36 inches A=s^2 A=9^2=81 square inches. Dr. Robert J. Rapalje, Retired
 Rectangles/307976: Find the width of a rectangle when the area is 480 ft. to the second power and the length is 24 ft.1 solutions Answer 220228 by rapaljer(4667)   on 2010-05-24 13:05:13 (Show Source): You can put this solution on YOUR website!Area of a rectangle = L*W 480=24*W, you must solve for W. Divide both sides by 24: , so width is 20 feet. Dr. Robert J. Rapalje, Retired
 Triangles/307977: find the area of a triangle with base 21 inches and height 8 inches1 solutions Answer 220227 by rapaljer(4667)   on 2010-05-24 13:02:04 (Show Source): You can put this solution on YOUR website!Area of a Triangle = Area = Area = square inches. Dr. Robert J. Rapalje, Retired
 Square-cubic-other-roots/307981: the volume of a cube is given by V=s^3, where S is the length of a side. find the length of a side of a cube if the volume is 800cm^3. round the answer to three decimal places1 solutions Answer 220226 by rapaljer(4667)   on 2010-05-24 12:59:47 (Show Source): You can put this solution on YOUR website! By use of a calculator: cm, approximately Dr. Robert J. Rapalje, Retired
 Square-cubic-other-roots/307983: for the following function, C computes a value, where if u add millions of dollars to the value, the result is the cost of implementing a city recycling project when x as a percent (not its decimal equivalent) citizens participate. C(x)=1.5x/100-x1 solutions Answer 220225 by rapaljer(4667)   on 2010-05-24 12:55:29 (Show Source): You can put this solution on YOUR website!What was the question??? Dr. Robert J. Rapalje, Retired
 Rectangles/307978: find the perimeter and area of a rectangle with width 3 meters and length 11 meters1 solutions Answer 220224 by rapaljer(4667)   on 2010-05-24 12:49:43 (Show Source): You can put this solution on YOUR website!P = 2W + 2L P = 2*3 + 2*11 P = 6 +22 = 28 meters A= L*W A=11*3= 33 square meters Dr. Robert J. Rapalje, Retired
 Rectangles/307980: find the circunference and area of a circle with diameter 6 inches. use 3.14 1 solutions Answer 220223 by rapaljer(4667)   on 2010-05-24 12:45:15 (Show Source): You can put this solution on YOUR website!, where d= 6 inches inches , where r=3 inches square inches. Dr. Robert J. Rapalje, Retired
 Rectangles/307986: find the area of a parallelogram with height 6 inches and base 11 inches1 solutions Answer 220222 by rapaljer(4667)   on 2010-05-24 12:40:51 (Show Source): You can put this solution on YOUR website!Area of a parallelogram = b*h In this case, 6*11=66 square inches. Dr. Robert J. Rapalje, Retired
 Triangles/307982: if two angles of a triangle measure 40 degrees and 70 degrees, what is the measure of the third angle?1 solutions Answer 220221 by rapaljer(4667)   on 2010-05-24 12:39:30 (Show Source): You can put this solution on YOUR website!The sum of the angles of a triangle is 180 degrees. To find the third angle, add the first two together, and subtract this from 180. In this case, 40+70=110. Subtract 180-110= 70 degrees. As a check, add the three angles and see if it comes out to 180 degrees. 40+70+70= 180, so it checks. Dr. Robert J. Rapalje, Retired
 Quadratic_Equations/307795: factor completely 45x^4+50x^31 solutions Answer 220136 by rapaljer(4667)   on 2010-05-23 21:29:59 (Show Source): You can put this solution on YOUR website!The first step in factoring to take out the common factor, in this case, 5x^3. 5x^3(9x+10) Final answer. I have additional explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "Basic Algebra" (Chapter 2) for several sections on different types of Factoring. I also have a video from my own teaching in class before I retired a few years ago in Basic Algebra. To see the video, look for "Rapalje Videos in Living Color", and see Basic Algebra for the topic of Factoring. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE--even the VIDEO!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 test/307790: Your question goes here. Write clearly! We are not mind readers, so be sure to ask a question that we can understand.10a^ 3b^3/15ab^81 solutions Answer 220135 by rapaljer(4667)   on 2010-05-23 21:25:28 (Show Source): You can put this solution on YOUR website! Divide out the 3 and the b^3 by subtracting the exponents. Don't forget to leave a factor of 1 in the numerator! I have additional explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "Basic Algebra" (Chapter 3) or "Intermediate Algebra"(Chapter 2). I also have a video from my own teaching in class before I retired a few years ago in Intermediate Algebra. Parts of this video would also be helpful to students in lower levels of math. To see the video, look for "Rapalje Videos in Living Color", and see Intermediate Algebra for the topic of Fractions. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE--even the VIDEO!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Equations/307791: solve the equation 30x-15y=-45 jackiemomof3@gmail.com1 solutions Answer 220133 by rapaljer(4667)   on 2010-05-23 21:20:27 (Show Source): You can put this solution on YOUR website!Solve for y in terms of x??? Start by subtracting 30x from each side: 30x -15y =-45 -15y= -30x -45 Divide both sides by -15: Dr. Robert J. Rapalje, Retired
 Volume/307768: A storage tank is shaped like a cylinder. The cylinder is 8 ft tall, and the base has a diameter of 10 ft. Find the cost of the container if the material f which the cylinder is made costs \$5 per square foot.1 solutions Answer 220132 by rapaljer(4667)   on 2010-05-23 21:15:57 (Show Source): You can put this solution on YOUR website!The SURFACE AREA of a cylinder consists of the lateral (side) area plus two end pieces (circles!). Lateral Area = Distance around the circle (i.e., circumference) * Height Lateral Area = * height. Lateral Area = Circular Base = , where radius = 5 feet. Circular Base = Total Area = square feet. Total Cost = Total Area * \$5 = \$ or approximately \$2041. I have some additional explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look near the bottom of my Homepage for the link "Topics from Geometry". There are several topics that relate specifically to perimeters, areas, and volumes, with applications very similar to this problem. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 logarithm/307756: Solve log (5-2x) = 01 solutions Answer 220130 by rapaljer(4667)   on 2010-05-23 20:57:05 (Show Source): You can put this solution on YOUR website! which means that I have additional explanation in both written and video format with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "College Algebra" (Chapter 4). I also have a complete video from my own teaching in class before I retired a few years ago on Logarithms. To see the video, look for "Rapalje Videos in Living Color", and see College Algebra for the topic of Logarithms. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE--even the VIDEO!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Polynomials-and-rational-expressions/307764: I need help simplifying rational expressions the question is x^3-x^2-12x over x^3-9x1 solutions Answer 220128 by rapaljer(4667)   on 2010-05-23 20:50:50 (Show Source): You can put this solution on YOUR website! First, factor out the x: Now finish factoring the numerator and denominator completely: Divide out the factors x and (x+3): I have quite additional explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "Basic Algebra" (Chapter 3) or "Intermediate Algebra"(Chapter 2). I also have a video from my own teaching in class before I retired a few years ago in Intermediate Algebra. Parts of this video would also be helpful to students in lower levels of math. To see the video, look for "Rapalje Videos in Living Color", and see Intermediate Algebra for the topic of Fractions. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE--even the VIDEO!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 absolute-value/307762: 1 solutions Answer 220125 by rapaljer(4667)   on 2010-05-23 20:47:30 (Show Source): You can put this solution on YOUR website!State the problem???
 Linear_Algebra/307760: with a fixed cost of \$4000, 20 items cost a total of \$10,000, find a linear cost function1 solutions Answer 220124 by rapaljer(4667)   on 2010-05-23 20:46:44 (Show Source): You can put this solution on YOUR website!If 20 items cost \$10,000, then the cost of each item is \$500. There is a fixed cost of 4000. Since each item costs \$500 to produce, the cost of producing x times is \$500*x. The total cost is the sum of the actual production of the items \$500x PLUS the total fixed costs of \$4000. The cost function is f(x)= 500x+ 4000 Dr. Robert J. Rapalje, Retired
 test/307753: I need help with simplifying rational expressions and the question is X^3-X^2-12X over X^3-9X1 solutions Answer 220123 by rapaljer(4667)   on 2010-05-23 20:44:14 (Show Source): You can put this solution on YOUR website! First, factor out the x: Now finish factoring the numerator and denominator completely: Divide out the factors x and (x+3): I have quite additional explanation with examples solved in LIVING COLOR on my own website. Please go to "www2.seminolestate.edu/rrapalje". Look for the links on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time" and also "MATH IN LIVING COLOR", and look under "Basic Algebra" (Chapter 3) or "Intermediate Algebra"(Chapter 2). I also have a video from my own teaching in class before I retired a few years ago in Intermediate Algebra. Parts of this video would also be helpful to students in lower levels of math. To see the video, look for "Rapalje Videos in Living Color", and see Intermediate Algebra for the topic of Fractions. I think you will find the explanations, both written and video, much easier to understand than traditional textbooks. Best of all, it's all FREE--even the VIDEO!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 test/307739: How do you solve problems such as ln3=36?1 solutions Answer 220122 by rapaljer(4667)   on 2010-05-23 20:35:37 (Show Source): You can put this solution on YOUR website!Is there supposed to be a variable in this??? You can't really solve if you don't have an unknown??? Dr. Robert J. Rapalje, Retired