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 Linear-equations/320774: what would the equation be with these characteristics slope=-3 point=(3,5)1 solutions Answer 229739 by solver91311(17074)   on 2010-07-08 17:06:36 (Show Source): You can put this solution on YOUR website! Use the point-slope form: where is the given slope and are the coordinates of the given point. to get AN equation with the given characteristics. You cannot find THE equation , because there are an infinite number of ways to represent any given line. John
 Word_Problems_With_Coins/320797: what is 35 quarters 13 dimes 10 nickels and 11 pennies? 1 solutions Answer 229738 by solver91311(17074)   on 2010-07-08 17:02:51 (Show Source): You can put this solution on YOUR website! A big handful of change. John
 Linear-equations/320824: Find the slope of the graph of the linear function "f" if f(3)=6 and f(-2)=-41 solutions Answer 229737 by solver91311(17074)   on 2010-07-08 17:01:32 (Show Source): You can put this solution on YOUR website! This is exactly the same as problem #320825. Copy and paste the following link: http://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.320825.html John
 Linear-equations/320825: Find the slope of the graph of the linear function "g" if g(-2)=4 and g(2)=5. Thank you! :D1 solutions Answer 229736 by solver91311(17074)   on 2010-07-08 16:58:53 (Show Source): You can put this solution on YOUR website! If then the graph of the function must contain the point If then the graph of the function must contain the point That is because the notation actually means "the value of the function at ". Since the function is linear, you can calculate the slope from the coordinates of two points using the slope formula: where and are the coordinates of the given points. John
 Inequalities/320803: In what ways do the graphs of the inequalities 2x-y>3 and 2x-y3 differ1 solutions Answer 229735 by solver91311(17074)   on 2010-07-08 16:53:11 (Show Source): You can put this solution on YOUR website! You only have one inequality. is an inequality. isn't really much of anything. John
 Graphs/320810: How would you graph the inequality on a plane with the inquality being x+y=2?1 solutions Answer 229730 by solver91311(17074)   on 2010-07-08 16:15:50 (Show Source): You can put this solution on YOUR website! Your first difficulty is that you don't have an inequality. is an equation, NOT an inequality. But assuming you do come up with an actual inequality, proceed as follows. Step 1: Change the relationship symbol to "=". Graph the resulting line. If the original relationship symbol was or , do it with a dashed or broken line. If your symbol was or , graph the equation with a solid line. Step 2: Pick any point on the coordinate plane that does not lie on the line you just graphed. If the line does not pass through the origin, then the origin is an excellent choice for this step. If the line does pass through the origin, select a point other than the origin -- I recommend a point that has small integer coordinates. Step 3: Substitute the values of the coordinates of the point chosen in Step 2 for the corresponding variables in the inequality you started with in Step 1. Step 4: Do the appropriate arithmetic to determine whether the substitution created a true statement or not. If you created a true statement, shade in the side of the line containing the point selected in Step 2. If you created a false statement, shade in the side of the line that does not contain the selected point. John
 Travel_Word_Problems/320814: If Paul drives at 60 mph to work and arrives 1 hour early. But when he drives at 40 mph he arrives 1 hour late. What is the appropriate speed Paul should go at? i know the answer is 48mph i just dont get how which is what i need help on1 solutions Answer 229727 by solver91311(17074)   on 2010-07-08 16:11:26 (Show Source): You can put this solution on YOUR website! Start with the basics: Distance equals Rate times Time Let represent the actual distance to work. Let be the amount of time it would take him to get to work if he arrives on time. That means that the amount of time required to go distance at 60 miles per hour must be -- that's because he gets there an hour early. And the amount of time to go that same distance at 40 miles per hour must be , one extra hour, meaning one hour late. So, since we know , we can write: and we can also write: But the distance to work doesn't vary just because he travels at a different speed, so since , we can write: Solve for So now we know that it should take him 5 hours to get to work IF he drove at a speed that would get him there right on time. So if he gets there one hour early at 60 miles per hour, then at 60 it takes him 4 hours, 60 times 4 is 240. And now we know the distance to work is 240 miles. miles per hour. Now THAT is a killer commute. The guy drives 10 hours a day in order to work for 8 hours a day. Why don't math teachers consider the real world when they concoct word problems? John
 Exponential-and-logarithmic-functions/320812: Please help me solve this equation: find the inverse of f(x)=5^x+6 -71 solutions Answer 229726 by solver91311(17074)   on 2010-07-08 15:57:14 (Show Source): You can put this solution on YOUR website! Replace with . Solve for the independent variable in terms of the dependent variable. Swap positions of the variables and set the resulting expression equal to John
 Exponential-and-logarithmic-functions/320816: Please help me solve this equation: 5^x= (7)(3^x)1 solutions Answer 229722 by solver91311(17074)   on 2010-07-08 15:43:45 (Show Source): You can put this solution on YOUR website! Take the natural log of both sides (actually, it can be the log to any base as it won't matter in the end). The log of the product is the sum of the logs: Add to both sides: Then use: so: Factor: The difference of the logs is the log of the quotient: Finally, multiply by Use the calculator for a numerical approximation if necessary. John
 Probability-and-statistics/320800: You roll a single die 10 times: a. probability that at least one resut will be divisible by three. b. probability of getting exactly 2 sixes. Thank you in advance1 solutions Answer 229717 by solver91311(17074)   on 2010-07-08 15:30:08 (Show Source): You can put this solution on YOUR website! In order for the result of rolling one die to be divisible by 3, the result of rolling the die must be either a 3 or a 6. Since there are six possible results and only two of them are considered a success, the probability of success on any one trial is The probability of successes in trials where is the probability of success on any given trial is given by: Where is the number of combinations of things taken at a time and is calculated by The probability of at least successes in trials is equal to 1 minus the probability of at most successes in trials, or: So for part a) you need: Or in the common vernacular, highly likely. For part b) you need: And you can do your own arithmetic. John
 Circles/320791: When the radius of a circle is multipled by 4, the area of the new circle is 40 in3. What was the area of the original circle?1 solutions Answer 229715 by solver91311(17074)   on 2010-07-08 14:56:04 (Show Source): You can put this solution on YOUR website! The areas of two circles are in proportion as the square of the ratio of their radii. Hence your new circle is times larger than the old circle. By the way, area is measured in square units, not cubic units. John
 Equations/320806: 6 over sigma 3k k=31 solutions Answer 229713 by solver91311(17074)   on 2010-07-08 14:52:22 (Show Source): You can put this solution on YOUR website! Are you trying to say that you want to determine the sum: ? John
 Trigonometry-basics/320808: find the exact value of cos theta/2 if sec theta=4 and theta lies in quadrant 11 solutions Answer 229711 by solver91311(17074)   on 2010-07-08 14:50:09 (Show Source): You can put this solution on YOUR website! Hard tellin' I can't figure out whether you want the value of or John
 Geometry_Word_Problems/320790: When a hexagon has 2-inch sides, its area is about 10.4in2. What will be the approximate area of a hexagon whose sides are 10 inches long??1 solutions Answer 229694 by solver91311(17074)   on 2010-07-08 13:54:51 (Show Source): You can put this solution on YOUR website! The formula for the area of a regular hexagon as a function of the measure of one of the sides, denoted , is: Therefore, the ratio of the areas of two regular hexagons is the square of the ratio of the measures of their sides. 10 divided by 2 is 5. 5 squared is 25. Your bigger hexagon is about 259 square inches. John
 Average/320796: Before she took her last exam, the average of Tara’s exam scores was 89. She figures that if she scores 97 on the last exam, her average for all the exams will be 90. If she scores a 73, her average for all the exams will be 87. How many exams, including the last one, are given in the class? 1 solutions Answer 229692 by solver91311(17074)   on 2010-07-08 13:42:11 (Show Source): You can put this solution on YOUR website! This is a problem where you have an embarrassment of riches as far as given information goes. Actually it is sufficient to know that the current average is 89 and a 97 on the last exam will result in an overall average of 90 to answer the question "How many exams...?" Let represent the total number of exams, including the last one. That means that up until now, exams have been given. Hence, if the average for the exams already given is 89, then the sum of the scores of the exams already given must be . The average of all the exams is then the sum of the first exams plus 97 all divided by and that is equal to 90. Multiply by Therefore 8 total exams. Check. Seven times 89 is 623. 623 plus 97 is 720. 720 divided by 8 is 90. Further check. Seven times 89 is 623. 623 plus 73 is 696. 696 divided by 8 is 87. John
 Age_Word_Problems/320793: Mary is 20 and Betty is 53, at what age would Betty be when she is three times older than Mary.1 solutions Answer 229691 by solver91311(17074)   on 2010-07-08 13:24:32 (Show Source): You can put this solution on YOUR website! Your question is grammatically incorrect. It should read, "Mary is 20 and Betty is 53. At what age was Betty when she was three times older than Mary?" Let represent the number of years that have elapsed since the time Betty was three times older than Mary. Check: John
 Linear-equations/320767: Find the slope of the line through the points (3,2) and (7,11). Show all steps. Thanks 1 solutions Answer 229690 by solver91311(17074)   on 2010-07-08 13:12:46 (Show Source): You can put this solution on YOUR website! Use the formula for the slope: where and are the coordinates of the given points. John
 Quadratic_Equations/320763: Find the vertex, line of symmetry, and the maximum or minimum value of the quadratic function. Problem: f(x) = -2x^2 + 2x + 9 Type in a simplified fraction Thank you!!!1 solutions Answer 229689 by solver91311(17074)   on 2010-07-08 13:06:23 (Show Source): You can put this solution on YOUR website! Put your function into standard, namely , form. The -coordinate of the vertex is given by The -coordinate of the vertex is the value of the function at the -coordinate of the vertex, to wit: The line of symmetry is the equation The maximum or minimum value of the function is . It is a minimum if the lead coefficient (the in ) is positive and a maximum if it is negative. John
 Quadratic_Equations/320764: Find the vertex (ordered pair), the line of symmetry, and the maximum or minimum value of the quadratic function. Problem: f(x) = 5 - x^2 Thank you!!1 solutions Answer 229677 by solver91311(17074)   on 2010-07-08 12:01:38 (Show Source): You can put this solution on YOUR website! Put your function into standard, namely , form. The -coordinate of the vertex is given by The -coordinate of the vertex is the value of the function at the -coordinate of the vertex, to wit: The line of symmetry is the equation The maximum or minimum value of the function is . It is a minimum if the lead coefficient (the in ) is positive and a maximum if it is negative. John
 Quadratic_Equations/320766: Find the x and y intercepts. Use a comma to separate answers or type N is there is no intercept. Problem: f(x) = -x^2 + 5x + 14 Thanks a lot!1 solutions Answer 229676 by solver91311(17074)   on 2010-07-08 11:55:09 (Show Source): You can put this solution on YOUR website! The -intercept is the point where , in other words, the value of the constant term. The -intercepts are the points and where is a root of the equation . Factor your quadratic and solve for the two roots. John
 Quadratic_Equations/320754: Find the vertex and type in an ordered pair. Problem: f(x) = x^2 - 8x - 1 Thanks in Advance!!1 solutions Answer 229675 by solver91311(17074)   on 2010-07-08 11:45:33 (Show Source): You can put this solution on YOUR website! The -coordinate of the vertex of a parabola expressed in the form is given by: The -coordinate of the vertex is the value of the function at that point, i.e.: John
 Linear-equations/320637: In a rectangle, the perimter is 94 inches. The length of the rectangle is 5 inches less than three times the width. What is the length and width?1 solutions Answer 229633 by solver91311(17074)   on 2010-07-08 00:32:31 (Show Source): You can put this solution on YOUR website! Let represent the width. Then the length must be: . The perimeter is two times the length plus two times the width. Solve for John
 Linear-equations/320634: y2 + y- 240 y-15 y- 15 Find the slope if it exist of the line containing the pair of points. undefined (3,7) and (4-,7) The slope m = Type an integer or a fraction, type N if the slope is 1 solutions Answer 229630 by solver91311(17074)   on 2010-07-08 00:28:32 (Show Source): You can put this solution on YOUR website! The slope is given by: If the denominator is zero, the slope is undefined. John
 Miscellaneous_Word_Problems/320608: Jeanna wants to buy a new boat for her family. she has two payment options. the first option is to pay a cash payment of $7,200. the second option is to finance the boat with a three-year installment loan. the loan requires a 10% down payment and 36 equal monthly payments of$205. according to this information, what would be the finance charge on the loan? 1 solutions Answer 229628 by solver91311(17074)   on 2010-07-08 00:26:28 (Show Source): You can put this solution on YOUR website! The down payment plus the total of the payments minus the sales price: You can do your own arithmetic. John
 Polynomials-and-rational-expressions/320624: how to factor out 8x^3+641 solutions Answer 229617 by solver91311(17074)   on 2010-07-07 23:07:04 (Show Source): You can put this solution on YOUR website! This is the sum of two cubes. Memorize the pattern for the sum and difference of two cubes: Then recognize that and You should be able to take it from here. John
 Quadratic_Equations/320619: Two negative intergers have the sum of -13 and a product of 42. What are the interges?1 solutions Answer 229615 by solver91311(17074)   on 2010-07-07 23:01:51 (Show Source): You can put this solution on YOUR website! I don't know what intergers or interges are. If you have two negative integers that have the sum of -13 and a product of 42, then I can show you how to determine the value of the two integers. In the first place, you should be able to quickly see that the answer is -6 and -7, just because you are that intimately familiar with the 12 by 12 multiplication tables. (if that is not true, go back and study your multiplication facts until it is true and you exude products of integers from 1 to 12 from your pores). Let represent one of the integers. Let represent the other one. Which is to say: Then Substituting: Putting it into standard form: Now all you need to do is factor and solve. The two roots will be the two integers you seek. John
 Linear-equations/320620: Write an equation of the line containing the given point and perpendicular to the given line using the formula y=mx+b form 1. (8,9) x + 7y + 4 2. (-9,7) 3x= 2y + 9 3. (5,8) 3x + y = 2 4. (6,-6) 3x + 5y = 81 solutions Answer 229611 by solver91311(17074)   on 2010-07-07 22:48:58 (Show Source): You can put this solution on YOUR website! One question per post please. First find the slope of the given line. Since your given equations are in standard form, , the slope is equal to Perpendicular lines have negative reciprocal slopes, that is: So take the negative reciprocal of the slope of the given line to determine the slope of the desired line. Armed with the slope of the desired line and the given point, use the point slope form of the equation of a line: where is the slope of the desired line and is the given point. Once you have substituted the given values, you can rearrange: Where is the slope and is the -intercept. John
 Linear-systems/320609: 1.Without graphing, determine whether each system has one solution, no solutions, or an infinite number of solutions. Show your work. (2 marks each) ( a ) 4 x – y = 5 y = 4 x + 6 ( b )3x + 2y = 5 15x + 10y = 25 2. How can you tell by looking at an equation whether it has one, none or infinite solutions? 1 solutions Answer 229609 by solver91311(17074)   on 2010-07-07 22:37:38 (Show Source): You can put this solution on YOUR website! One question per post, please. If you have a system: and the coefficients are such that: and but then you have a system that is inconsistent, i.e., has no solutions. (parallel lines) If the coefficients are such that: and and then you have a system that is consistent and dependent, i.e. there are infinite solutions (the same line) If the coefficients are such that: but , then you have a consistent and independent system, i.e. exactly one solution (intersecting lines) John
 Linear-systems/320615: Solve the following systems of equations using any method. ( a ) x + 4 y = - 5 2 y + 3 x = 5 ( b ) 2x-1/3y=1/3 3(x+1)-2(y-3)=11 ( c ) 2.4 x = 2.2 y – 3.2 1.6 x + 1.2 y = 3.2 1 solutions Answer 229607 by solver91311(17074)   on 2010-07-07 22:24:47 (Show Source): You can put this solution on YOUR website! Sorry, one question per post. Multiply the second equation by -2 and then add the two equations. Substitute into either of the original equations: Hence the solution set is John
 expressions/320553: multiply (2x+7y)(2x-7y)1 solutions Answer 229561 by solver91311(17074)   on 2010-07-07 18:18:07 (Show Source): You can put this solution on YOUR website! This is the product of two conjugates. The product is the difference of two squares. Follow the pattern: John
 Polynomials-and-rational-expressions/320533: Factor the trinomial x2 - 2x - 8. Write each factor as a polynomial in descending order.1 solutions Answer 229560 by solver91311(17074)   on 2010-07-07 18:16:31 (Show Source): You can put this solution on YOUR website! Hint: -4 times 2 equals -8. -4 plus 2 equals -2. John