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 Angles/207896: find aagles angle A=5x+8 angle B=x+4 1 solutions Answer 157276 by rapaljer(4667)   on 2009-08-22 15:45:37 (Show Source): You can put this solution on YOUR website!5x+8 +x+4 = 90 6x+12 =90 6x=78 x=13 Angle A = 5x +8 Angle A = 5*13 + 8 = 65+8=73 degrees Angle B = x+4 Angle B = 13+4 = 17 degrees Check: 73 + 17=90 R^2 Dr. Robert J. Rapalje Altamonte Campus Seminole State College Florida
 Equations/207886: My motor boat normally travels at 24 km/h in still water. One day I travelled 36 km against a constant current in a river and it took me the same time to travel 48 km with the current. How fast was the current?1 solutions Answer 157246 by rapaljer(4667)   on 2009-08-22 08:42:58 (Show Source): You can put this solution on YOUR website!The basic formula is d=rt, and since the equation is based upon the fact that time up stream is equal to time downstream, it will be helpful to solve for t. Let x = rate of current. 24 = rate in still water 24+x = rate downstream 24-x = rate upstream time downstream = time upstream = Solve the equation: Since means that , means that Get out your calculator: km/h R^2 Dr. Robert J. Rapalje Altamonte Springs Campus Seminole State University
 Mixture_Word_Problems/207890: this is the given problem: Solution X is 2% alcohol and solution Y is 6% alcohol. A drugstore owner wants to mix them in order to get a 60-L of solution that is 3.2% alcohol. How many liters of each should the owner use? Solution: Let x = the number of liters of X y = the number of liters of Y ----------------------------------------------------------------- + solution + solution + mixture + + X + Y + + ---------------------+-------------+------------+---------------+ amt. of solution(L) + x + y + 60 + ---------------------+-------------+------------+---------------+ percent of alcohol + 2% + 6% + 3.2% + ---------------------+-------------+------------+---------------+ amt. of alcohol in + 0.02% + 0.06% + 0.032(60)or + 0.02x + 0.06y the mixture(L) + + + 1.92 + = 1.9 ----------------------------------------------------------------+ note: to get the amount of a alcohol, we multiply the amount of solution by the percentages. equations: (1) x + y = 60 (2) 0.02x + 0.06y = 1.92 multiplying eq.(2) by 100, we now have this system: (1) x + y = 60 (2)2x +6y = 192 solving the system using elimination, we first multiply eq. by -2 and add the result to eq. (2) -2x-2y =-120 2x+6y = 192 ------------ 4y = 72 y = 18 solving for x, we substitute 18 in place of y in eq. (1) x + 18 = 60 x = 42 Please help me why it was multiplied by negative 2, and where this -2 came from? 1 solutions Answer 157244 by rapaljer(4667)   on 2009-08-22 08:09:02 (Show Source): You can put this solution on YOUR website!(1) x + y = 60 (2)2x +6y = 192 The second equation has a 2x, while the first equation has only x. You need to make the x terms subtract out, so in order to subtract out the 2x, you need a -2x. To get that, you have to multiply the first equation by -2. You could also have eliminated the y terms by multiplying the first equation by -6. We usually try to eliminate using the smaller number. R^2
 Miscellaneous_Word_Problems/207887: A rectangular deck has an area of (x2 + 6x + 8) square feet. If its width is (x + 2) feet then: a. Find its length in terms of ‘x’. b. If x = 3, what will be the area, length and width in feet. 1 solutions Answer 157243 by rapaljer(4667)   on 2009-08-22 07:47:25 (Show Source): You can put this solution on YOUR website!x^2 + 6x +8 just happens to factor into (x+2)(x+4) So, if x+2 is the width, then x+4 must be the length. If x=3, then the width is x+2, which is 5 feet, the length is x+4, which is 7 feet, and the area is the product 5*7 which is 35 square feet. R^2
 Unit_Conversion_Word_Problems/207845: A table tennis ball has a circumfrence of 4and a half inches. The volume of a baseball is 8 times that of a table tennis ball. What is the circumfrence of a baseball?1 solutions Answer 157216 by rapaljer(4667)   on 2009-08-21 21:20:30 (Show Source): You can put this solution on YOUR website!If the volume of a baseball is 8 times that of a table tennis ball, then the radius is 2 times as much. If the radius is twice as much, then the diameter is twice as much, and the circumference which is is also twice as much. Therefore the circumference is TWO times 4.5 inches or 9 inches. R^2
 Equations/207839: solve system using substution method 4x+y=5 5y=x+y solution (?,?)1 solutions Answer 157214 by rapaljer(4667)   on 2009-08-21 21:16:47 (Show Source): You can put this solution on YOUR website!Did you copy this one correctly? Should the second equation should be 5=x+y? Either one is somewhat ugly, so I'll go with your problem as stated. In the second equation, subtract y from each side. 5y=x+y 4y=x Substitute this into the first equation for x: 4x+y=5 4(4y)+ y = 5 16y + y=5 17y=5 y=5/17 To solve for x, go back to the equation x=4y x=4y x=4(5/17) x=20/17 The solution is (20/17,5/17) Check in the OTHER equation 4x+y =5 It checks!! R^2
 Linear-equations/207827: x+5y=101 solutions Answer 157212 by rapaljer(4667)   on 2009-08-21 21:09:13 (Show Source): You can put this solution on YOUR website!x+5y=10 Graph by plotting the x and y intercepts: If x = 0, then 5y=10 so y=2 If y=0, then x=10 It should look like this: R^2
 Square-cubic-other-roots/207818: simplify the following square roots of 3 sqrt9x^2 y^3 1 solutions Answer 157210 by rapaljer(4667)   on 2009-08-21 21:04:48 (Show Source): You can put this solution on YOUR website!Do you mean ??? Or do you mean ?? If it is the first, then the answer is . If it is the second, then it is R^2
 Linear_Equations_And_Systems_Word_Problems/207838: Solve: -2x > 1/91 solutions Answer 157207 by rapaljer(4667)   on 2009-08-21 20:58:40 (Show Source): You can put this solution on YOUR website!One of the most important rules of first level algebra is "WHEN YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE NUMBER, YOU MUST REVERSE THE DIRECTION OF THE INEQUALITY SIGN!" You have to do this here, when you multiply both sides by -1/2: R^2
 Equations/207841: solve system using addition method x+2y=32 9x-2y=28 solution (?,?)1 solutions Answer 157206 by rapaljer(4667)   on 2009-08-21 20:53:46 (Show Source): You can put this solution on YOUR website!x+2y=32 9x-2y=28 Add the equations together: 10x = 60 x=6 Substitute x=6 into the first equation: x+2y=32 6+2y=32 2y=32-6 2y=26 y=13 Check in the second equation: 9x-2y=28 9(6)-2(13)=28 54 - 26=28 It checks!! R^2
 Linear_Equations_And_Systems_Word_Problems/207804: kelly had 12 dollars and spent x dollars. ami had 6 dollars and collected x dollars. the two girls then had the same amount of money. form an equation and solve it to determine the value of x.1 solutions Answer 157191 by rapaljer(4667)   on 2009-08-21 17:16:18 (Show Source): You can put this solution on YOUR website!Kelly = 12-x Ami = 6 + x 12-x=6+x Add x to each side: 12-x +x = 6+x+x 12=6 + 2x Subtract 6 from each side: 12-6=6+2x-6 6=2x x=3 = ANSWER! Check: Kelly =12 - x Kelly = 12 - 3 = 9 Ami = 6 + x Ami = 6 + 3 = 9 R^2
 Finance/207811: what is a letter that is used to represent one or more number which are the values.1 solutions Answer 157190 by rapaljer(4667)   on 2009-08-21 17:06:27 (Show Source): You can put this solution on YOUR website!A variable! R^2
 Polynomials-and-rational-expressions/207802: what value can x not equal 3x/x-1 where x=21 solutions Answer 157187 by rapaljer(4667)   on 2009-08-21 16:11:53 (Show Source): You can put this solution on YOUR website!Denominators MUST NEVER EQUAL 0, so x-1 must not equal 0 x cannot equal 1. By the way, on my website, I now have two videos explaining Functions, Domain, and Range. If you click on my tutor name "Rapaljer" anywhere in algebra.com, look for the link on my homepage "Rapalje Videos", and select either "Intermediate Algebra" or "College Algebra". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs, FL
 Graphs/207800: The value, v, of a shopkeepers inventory software program is given by v = -1/3t +3, where t is the number of years sincew the shopkeeper bought the program. What is the program worth 6 years after it is first purchased? Plot the point with the given t-value,6.1 solutions Answer 157186 by rapaljer(4667)   on 2009-08-21 16:06:35 (Show Source): You can put this solution on YOUR website!v=-1/3t + 3 v= -1/3*6+3 v=-2+3 v=1 Of course, the horizontal variable x is actually time t, and the vertical variable y is actually value v. Plot the point (6,1) on the given graph. R^2 Dr. Robert J. Rapalje
 Numeric_Fractions/207779: 1 solutions Answer 157181 by rapaljer(4667)   on 2009-08-21 15:23:14 (Show Source): You can put this solution on YOUR website!Post a problem???
 Polynomials-and-rational-expressions/207784: Dear sir or mam: factoring trinomials completely 16w^2-112w+1961 solutions Answer 157170 by rapaljer(4667)   on 2009-08-21 14:26:20 (Show Source): You can put this solution on YOUR website!It's probably a perfect square trinomial. But first, take out the common factor of 4. ALWAYS TAKE OUT THE COMMON FACTOR FIRST!! 4(4w^2 - 28w + 49) Now, try this, using perfect squares 4w^2 and 49. 4(2w - 7)(2w-7) 4(2w-7)^2 One more time, please see my own website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Polynomials-and-rational-expressions/207786: I am having trouble factoring trianomials without a book. can you please help me? here is my problem 9x^2+18xy-7y^21 solutions Answer 157168 by rapaljer(4667)   on 2009-08-21 14:20:29 (Show Source): You can put this solution on YOUR website!The first step is to write it in descending order: 9x^2 +18xy - 7y^2 It starts out (3x____)(3x____). Next, look at the last term. You need to find two numbers whose product is -7y^2, that will give you the middle term which is 18xy. This is a harder problem than the last two that I posted for you, and I call this "Advanced Trinomial Factoring." The LAST times LAST will have to be either 7y times y or y times 7y. You just have to try them and see which one works for you. (3x__7y)(3x__y) The middle term is 3xy and 21xy, whose difference is 18xy. This is correct. Now the signs must be OPPOSITE in order to give you the -7y^2, and the middle term has to be a positive 18xy, so make the signs like this: (3x+7y)(3x -y). That should do it!! By all means, especially if you don't have a book, or if you don't understand YOUR book, then try MY BOOK, which is FREE on my website. If you are interested in seeing my explanation of this, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials", "Advanced Trinomial Factoring". See also my link "Rapalje Videos" for a complete two hour explanation (by me!) explaining the topic of "Factoring" from Basic Algebra. See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". I have a lot of resources for whatever book or curriculum you may be using, and they are all free on my website. R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Polynomials-and-rational-expressions/207787: I am having trouble factoring trianomials without a book. can you please help me? here is my problem. z^2+289-34z1 solutions Answer 157167 by rapaljer(4667)   on 2009-08-21 14:09:32 (Show Source): You can put this solution on YOUR website!The first step is to write it in descending order: z^2 -34z + 289 It starts out (Z____)(Z____). Next, look at the last term. You need to find two numbers whose product is +289, that will add to give you the middle term which is -34z. This would be 17 times 17. Because the last term is positive, the signs must be the same, but in order for this to add up to -34z, you need to use -17 times -17. (z-17)(z-17) (z-17)^2 For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials" and also "Difference of Squares and Perfect Square Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Polynomials-and-rational-expressions/207788: i don't know how to factor trianomials without a book. can you please help me? here is my problem -56-m+m^21 solutions Answer 157166 by rapaljer(4667)   on 2009-08-21 14:04:24 (Show Source): You can put this solution on YOUR website!The first step is to write it in descending order: m^2 -m - 56 It starts out (m____)(m____). Next, look at the last term. You need to find two numbers whose product is -56, that will add (or in this case subtract!) to give you the middle term which is -1m. This would be -8 and +7, so write it this way: (m-8)(m+7) For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Square-cubic-other-roots/207696: This question is from textbook beginning and intermediate algebra f(x)= the square root of 2x-4 h(x)= 3the square root of 5x+171 solutions Answer 157157 by rapaljer(4667)   on 2009-08-21 11:09:15 (Show Source): You can put this solution on YOUR website!What is the question? Why don't you restate the problem and resubmit it. R^2
 Polynomials-and-rational-expressions/207702: factor trinomial completely 16x^2-104x+1691 solutions Answer 157156 by rapaljer(4667)   on 2009-08-21 10:54:56 (Show Source): You can put this solution on YOUR website!You may not have recognized this, but it is a perfect square trinomial: (4x-13)(4x-13) (4x-13)^2 R^2
 Pythagorean-theorem/207771: This question is from textbook algebra 1 an integrated approach a triangle has a side of length x. the second side of the triangle is 2 inches longer than the first side. the third side is 4 inches longer than the first side. the square of the first side plus the square of the second side is equal to the square of the third side. what is the length of each side of the triangle? use the five step method.1 solutions Answer 157155 by rapaljer(4667)   on 2009-08-21 10:52:17 (Show Source): You can put this solution on YOUR website!I'm not exactly sure what your "5 step method" is, but MY "5 step method is this: STEP 1: Identify the variable. Let x = first side x+2 = second side x+4 = third side STEP 2: Write the equation. STEP 3: Solve the equation. Set the equation equal to zero: This factors into (x-6)(x+2)=0 x=6 or x= -2 STEP 4: Answer the question. Reject the negative value since x is a side of a triangle. x=6 x+2=8 x+4=10 STEP 5: Check. You can do this. Let me know if MY five step rule is the same as YOUR 5 step rule. R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Graphs/207736: This question is from textbook Holt Algrbra 2 4x+y=-41 solutions Answer 157153 by rapaljer(4667)   on 2009-08-21 10:34:06 (Show Source): You can put this solution on YOUR website!Because this equation is in STANDARD form, it is easiest to graph with the TWO INTERCEPT method. 4x+y=-4 Let x=0, then 4*0+y=-4 y=-4 4x+y--4 Let y=0, then 4x +0=-4 4x=-4 x=-1 Graph these two points, and you should have this graph: For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 4, and look for "Graphing and Slope of a Line". I also did a video of me teaching this lesson. Look on my home page for "Rapalje Videos" and select "Basic Algebra." R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Mixture_Word_Problems/207764: This question is from textbook Hello, Can someone please help me. I submitted this problem yesterday and it due in about an hour. I not sure if my answer is right. 1. When discussing arguments, truth and validity are two basic concerns. Is it possible for an argument to be valid if it is not truthful? Discuss these two concepts, using truth tables and/or examples. Answer: First I will start with a false premises. As long as my premises, no matter how false, add up to a logical argument. It’s valid. For example: All fish live in the ocean Sea otters are fish Therefore sea otters live in the ocean Clearly not all fish live in the ocean and certainly sea otters aren't fish and yet it's a valid argument. All cow fly Molly is a cow therefore, Molly flies Clearly cow do not fly this is another example of false premises leading to a valid, logical conclusion. Thank you in advance. M 1 solutions Answer 157151 by rapaljer(4667)   on 2009-08-21 10:13:35 (Show Source): You can put this solution on YOUR website!You are correct! Both of these are VALID, although INCORRECT conclusions. As you mentioned, when you incorrect hypotheses (premises!), you get incorrect conclusions. However, are VALID. R^2
 Problems-with-consecutive-odd-even-integers/207768: This question is from textbook algebra 1 an integrated approach solve by factoring. check each answer. 10x^2=-100x1 solutions Answer 157150 by rapaljer(4667)   on 2009-08-21 10:09:03 (Show Source): You can put this solution on YOUR website!First, you have to set this equation equal to zero: 10x^2 +100x = 0 Next factor the common factor which is 10x: 10x(x+10)=0 Solve this in TWO parts! 10x=0 x=0 x+10=0 x=-10 For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Solving Quadratic Equations". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 real-numbers/207766: identify the sets of nunbers to which each givin number belongs. -2.7 choices: rational munbers irrational numbers whole numbes, integers, rational numbers natural numbers, whole numbers, integers, rational numbers1 solutions Answer 157149 by rapaljer(4667)   on 2009-08-21 10:05:04 (Show Source): You can put this solution on YOUR website!-2.7 is a rational number, since it is expressed as a terminating decimal. It is NOT a natural number, whole number, integer. It is NOT an irrational number. It is also a REAL number, but that was not one of the choices. R^2 Dr. Robert J. Rapalje Seminole State College Florida
 Polynomials-and-rational-expressions/207704: factor trinomial completely 13n+4n^2-121 solutions Answer 157146 by rapaljer(4667)   on 2009-08-21 09:14:27 (Show Source): You can put this solution on YOUR website!First you have to place the terms in descending order: 4n^2 + 13n - 12 Since the middle term is 13n which is an ODD number, the factoring CANNOT be an EVEN times EVEN combination. It is necessary therefore to begin with 4n*n (4n_____)(n_____) Next, the LAST times LAST must be 12 with OPPOSITE signs. It CANNOT be 6*2 since these numbers are both EVEN. My best guess will be 3*4: (4n__3)(n__4), with opposite signs. Let's try (4n-3)(n+4), which checks out because the middle term is 16n-3n, which is 13n. This is a classic problem!! For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Advanced Trinomial Factoring". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Equations/207739: the produce of 6 and y increase by1 solutions Answer 157145 by rapaljer(4667)   on 2009-08-21 09:05:10 (Show Source): You can put this solution on YOUR website!Did you state this problem correctly? It doesn't sound right to me. R^2
 Rectangles/207741: The perimeter of a rectangle is 38 m. The length is four more than two times the width. What is the width?1 solutions Answer 157144 by rapaljer(4667)   on 2009-08-21 09:03:35 (Show Source): You can put this solution on YOUR website!Let x = width of the rectangle 2x+4= length of the rectangle 2W + 2L = P 2(x) + 2(2x+4) = 38 2x + 4x +8 = 30 6x + 8= 38 6x=30 x=5 Width 2x+4 = Length 2*5+4 = Length 10+4 = 14 Length Check: 2*5 + 2 * 14 = 10 + 28 = 38 Perimeter For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 1, and look for "Word Problems". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 1. There I have a lot of problems like this solved in "Living Color". R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs Campus Florida
 Equations/207747: 14x=x1 solutions Answer 157140 by rapaljer(4667)   on 2009-08-21 08:54:26 (Show Source): You can put this solution on YOUR website!Subtract x from each side: 14x-x = x-x 13x=0 Divide both sides by 13: R^2
 Linear-equations/206402: What is the basic method for graphing a linear equation1 solutions Answer 155965 by rapaljer(4667)   on 2009-08-12 03:16:14 (Show Source): You can put this solution on YOUR website!There are three basic methods of graphing a straight line: 1. Point plotting. Select two or three values of x, find the corresponding value of y, plot the points, and connect the dots! 2. Slope-intercept method. Recommended for equations written in the form y=mx+b. 3. Two intercept method. Recommended for equations written in the form ax+by=c. For additional explanation, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time", select "Basic Algebra" and look for Chapter 4. The entire explanation is available at this link and it's all free. For a video of me explaining this topic, on my homepage, look for "Rapalje Videos", select "Basic Algebra", and look for "Graphing and Slope of a Line." Again, it's all FREE!! Send me an Email if you need help finding anything. R^2 Dr. Robert J. Rapalje Seminole State College Altamonte Springs, FL 31714