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Geometry_Word_Problems/244512: The area of a rectangular garden is 54 square meters. The Width is 7 meters longer than one-third of the length. Find the length and the width of the garden. 1 solutions Answer 178825 by solver91311(16868)   on 2009-12-01 11:34:44 (Show Source): You can put this solution on YOUR website! Let represent the length. The width is then . The area is the length times the width, so: A little manipulation results in: Solve the quadratic for . Hint: It factors. Exclude the negative root because you are looking for a positive measure of length. The positive root is the length, from which you should be able to easily calculate the width. Multiply your results for length and width to make sure that you obtain a result of 54. John

Expressions-with-variables/244494: Ax+By=C how do u solve this 1 solutions Answer 178820 by solver91311(16868)   on 2009-12-01 11:11:56 (Show Source): You can put this solution on YOUR website! I don't solve . Nobody does. That is because you cannot "solve" it. It is nothing more than a pattern, or a recipe if you will, for an equation of a straight line in . It is called the standard form of the equation of a line. Some texts require that , , and be integers for proper standard form -- check with your instructor. John

Equations/244226: 180 (n-2) ________ = 135 n 1 solutions Answer 178723 by solver91311(16868)   on 2009-11-30 18:52:26 (Show Source): You can put this solution on YOUR website! Multiply by and remove parentheses Add to both sides: It's an octagon. John

Radicals/244206: how do you simplified 6radical2divide by 3 1 solutions Answer 178719 by solver91311(16868)   on 2009-11-30 18:46:05 (Show Source): You can put this solution on YOUR website! Depends. Do you mean: (6*sqrt(2))/3 or do you mean: 6*sqrt(2/3) Use more parentheses so it is clear what you want. John

Parallelograms/244194: The points A(0,0), B(2,4)and D(7,O) are three of the four vertices of a parallelogram. What are the coordinates of the fourth? The coordinates of three vertices of a square are A(2,-3), B(-2,-1) and C(0,3). What are coordinates of the fourth vertex 1 solutions Answer 178715 by solver91311(16868)   on 2009-11-30 18:30:17 (Show Source): You can put this solution on YOUR website! Presuming that the sides of the parallelogram are the segments AB, BC, CD, and DA, proceed thusly: Compute the slope of the line containing the segment AB using the slope formula: Where and are the coordinates of the endpoints of the segment. Write an equation of the line that passes through point D with a slope equal to the slope of the line that contains the segment AB using the point-slope form of the equation of a line: Where is the slope you just calculated and are the coordinates of D. Call this equation 1. Repeat the above steps with respect to line segment BC and point D. Call this equation 2. Solve the system of equations formed by equations 1 and 2. The solution set will be the desired coordinates of the fourth vertex. Do your other problem the same way. John

Angles/244186: What is the complementary angle of an angle that is 118 degrees? 1 solutions Answer 178711 by solver91311(16868)   on 2009-11-30 18:20:54 (Show Source): You can put this solution on YOUR website! No such thing. The measure of an angle in degrees plus the measure of its complement in degrees is 90 degrees. The complement of an angle which measures more than 90 degrees makes no sense -- sort of like saying you have 14 inches of string and want to know how much you have to add so that you have a foot of string. Now, if you just made a mistake and really meant "supplement" instead of complement, then your question does make sense. An angle and its supplement sum to 180 degrees, so just subtract the angle measure from 180 to get the measure of the supplement. John

Graphs/244160: Okay don't get confused this is suppost to be a data table but I don't know how to do it on this program!!! Directions: Does the data in the table below show direct variation? Explain. x_-2_-1_0_1_2 y_-5_-2_1_4_7 Hope that makes sence!!!! 1 solutions Answer 178704 by solver91311(16868)   on 2009-11-30 18:05:55 (Show Source): You can put this solution on YOUR website! I don't know whether or not it makes "sence." I've never seen anything that makes "sence" and I don't even know what "sence" is. Your question does make sense, however. And yes, spelling does count, even in mathematics. If gets bigger when gets bigger, then the variation is direct. If gets smaller when gets bigger, then the variation is indirect. John

Numbers_Word_Problems/244134: peter made a letter L from six squares. The side of each square is 1cm in length. Find the perimeter of the letter he made. 1 solutions Answer 178690 by solver91311(16868)   on 2009-11-30 17:29:35 (Show Source): You can put this solution on YOUR website! The perimeter of each of the 1 cm by 1 cm squares is 4 cm. Since there are 6 of these little squares, the total perimeter is 6 times 4 equals 24 cm. BUT!!! When you arrange the squares into the shape of an L, no matter what configuration you make (how tall or squatty the L is), there are 5 places where the squares meet and each of these places subtracts two sides, or 2 cm from the total. 24 - 10 = 14 cm for the perimeter of the L. John

Percentage-and-ratio-word-problems/244123: Here is the problem that I am having trouble explaining to my son. Scott and Dan are traveling together. First Scott drives one fifth of the way. Then Dan drives one third of the remaining distance. Next Scott drives one half of the remaining distance, and finally Dan drives the last 80 miles. What is the total distance traveled? How far does each person drive. I know the answer is 300 miles total drive. Scott drove 140 and Dan drove 160. I don't know how to explain the answer. Can you help? 1 solutions Answer 178687 by solver91311(16868)   on 2009-11-30 17:22:28 (Show Source): You can put this solution on YOUR website! The first thing I have to say is that there is absolutely nothing wrong with the way Alan did this problem. I'm going to look at it from a slightly different direction, then you can choose the one you understand the best. If Dan drove the final 80 miles, and that was what was left over after Scott had driven half of the remaining distance, then Scott must have driven 80 miles. Score: Dan 80, Scott 80, Total 160. If Dan drove one-third of the remaining distance and left 160 miles to go, 160 must have been two-thirds of what remained when Dan started, so if 160 is two-thirds, 80 must be one-third, which is the amount Dan drove that leg. Score: Dan 160, Scott 80, Total 240. Next, if Scott drove one-fifth of the total trip and left 240 miles to go, then 240 miles must be four-fifths of the total trip. Dividing 240 by 4 gives 60 which is then one-fifth of the total trip and is what Scott drove at the start. Final Score: Dan 160, Scott 140, Total 300. John

Trigonometry-basics/244126: please help me to solve this quadratic equation: Give the propeties for the equation x^2+y^2+8x-2y+15=0, center: here are the possible answers: a)(4,1) b)(-4,1) c)(-8,2) 1 solutions Answer 178683 by solver91311(16868)   on 2009-11-30 17:07:56 (Show Source): You can put this solution on YOUR website! You need to complete the square on both and , then factor the perfect squares. First, move the constant to the RHS: Rearrange: Divide the coefficient on the -term by 2, then square the result. Add this result to both sides of the equation. Do the same thing for the -term: Factor and and then replace these two trinomials in your equation with the squared binomial representation. You can then determine the center by inspection since a circle centered at with radius is defined by: Pay careful attention to the signs on your center coordinates. John

Linear-equations/244117: in algebra 1 how do you find the slope? 1 solutions Answer 178680 by solver91311(16868)   on 2009-11-30 16:55:36 (Show Source): You can put this solution on YOUR website! Depends on what you know. If you are given two points, then use the slope formula: Where and are the coordinates of two given points. If you are given an equation of the line, solve the equation for to put the equation into slope intercept form, looking like this: Then the slope is just the coefficient on If you are given the slope of a line that is either parallel or perpendicular to the line whose slope you wish to determine, then use one of the following rules: John

Graphs/244092: Find the equation for each of the following items below: a. A line that passes through (6,2) and has a slope of 2. b. A line that passes though the points (2,4) and (8,16) c. A line that passes through (7,3) and has a slope of -1. d. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12. e. A circle with a radius of 9 and a midpoint at (3,3) 1 solutions Answer 178671 by solver91311(16868)   on 2009-11-30 16:45:04 (Show Source): You can put this solution on YOUR website! First thing: You cannot find (or write) "the" equation of a line. There are an infinity of equivalent representations of any line, hence the best you can do is find "an" equation of a line. If you are given a point and the slope, then use the point-slope form of a line: Where is the given slope and is the given point. If you are not given the slope directly, but are given that the desired line is either parallel or perpendicular to a given line, use one of the following to determine the slope: If you are given two points, you can either compute the slope using the slope formula, Where and are the coordinates of the given points And then use the point-slope form as above, or you can use the two-point form of a line: Which is really nothing more than a combination of computing the slope and writing the equation. In all cases, you should determine, either from the instructions in your text or from your instructor's guidance, what form your answers should take. Generally, it is one of two forms that are specified, if any: 1. Slope-intercept form: where is the slope and is the point of intersection of the line with the -axis. 2. Standard form: Some text require , , and to be integers for proper standard form. A circle centered at and with radius is described by: Since you were given the center and a point on the circle, you will have to calculate the radius by using the distance formula to determine the distance from the center to the given point. Again where and are the coordinates of the given points. John

Rational-functions/244097: solve each question by factoring ? x^2=-8x 1 solutions Answer 178665 by solver91311(16868)   on 2009-11-30 16:14:27 (Show Source): You can put this solution on YOUR website! Both sides of your equation have at least one factor of . Eliminate it. John

Quadratic_Equations/244090: how do u solve 2x squared-13x+6=0 in completing the square 1 solutions Answer 178664 by solver91311(16868)   on 2009-11-30 16:12:44 (Show Source): You can put this solution on YOUR website! I'll do you one better. Here is how to complete the square on any quadratic: Step 1: Make sure the equation is in standard form. This one is, so go on. Step 2: Add the additive inverse of the constant term to both sides. Step 3: Divide both sides of the equation by the coefficient on Step 4: Divide the coefficient on the first degree term by 2, square the result, then add that result to both sides of the equation. Step 5: You will have created a perfect square trinomial in the LHS of the equation. Factor it. Step 6: Take the square root of both sides remembering to consider both the positive and negative root. Step 7: Add the additive inverse of the constant term on the left to both sides. Step 8: Simplify, remembering to remove pairs of factors of the radicand from under the radical. John

Linear-systems/244084: graph the linear inequality x > -3 1 solutions Answer 178663 by solver91311(16868)   on 2009-11-30 16:04:14 (Show Source): You can put this solution on YOUR website! Graph the line except that you need to draw a dashed line instead of a solid line. That's because the inequality is greater than, , only instead of greater than or equal . Then select a point on the plane that is NOT on the line you just graphed. Since this line does not pass through the origin, the origin, (0, 0), is an outstanding choice for this step. Substitute the values of the coordinates from the point you selected into the original inequality. If the result is a true statement, shade in the half-plane on the side of the line containing the point you selected. If the result is a false statement, shade in the other side of the line. John

Radicals/244077: Trying to assist 13 yr old son.. Just when I think there wont be a problem helping him cause he says it's LCD'S mom. I look at the problem and it involves fractions and LCD'S, these I do not know how to do. Any help much appreciated.. What I am looking for is the LCD between the two fractions on questions 1 and 2 1. 5/x-6,7/x^2-12x+36 2.5/7ab^5,2/7a^3b^3 Can anyone help me with these problems? Ihad previously posted this but did not clarify what it was I was looking to find. Sorry 1 solutions Answer 178662 by solver91311(16868)   on 2009-11-30 15:57:51 (Show Source): You can put this solution on YOUR website! Problem 1: Factor the denominator in the right hand rational expression: So the left hand fraction has one factor of and the right hand fraction has 2 such factors. The LCD is the product of all the factors with duplicates removed. Hence, the LCD is just: If I had to continue to manipulate these rational expressions, I would leave the LCD expressed as the squared binomial. Problem 2: The first denominator has one factor of 7, one factor of , and five factors of The second denominator has one factor of 7, three factors of , and three factors of . At most you have: one factor of 7, three factors of , and five factors of . Hence, your LCD is: John

Miscellaneous_Word_Problems/244070: The total number of votes cast for class president was 352. If Chet received 50 fewer votes than Marcella, how many did each receive? 1 solutions Answer 178661 by solver91311(16868)   on 2009-11-30 15:46:33 (Show Source): You can put this solution on YOUR website! Let represent the number of votes Marcella received. Then is the number of votes cast for Chet. The sum is 352, so: Just solve for to get the number for Marcella. 50 less than that is the number for Chet. John

Polynomials-and-rational-expressions/244071: Solve the formula for the specified letter. I=kE/R for R 1 solutions Answer 178659 by solver91311(16868)   on 2009-11-30 15:28:17 (Show Source): You can put this solution on YOUR website! Multiply both sides by Multiply both sides by John

Travel_Word_Problems/244059: I hope you can help A car travels 180 miles. A second car, traveling 15 m/h faster than the first car, makes the same trip in 1 hour less time. Find the speed of each car. 1 solutions Answer 178658 by solver91311(16868)   on 2009-11-30 15:26:40 (Show Source): You can put this solution on YOUR website! Let represent the distance traveled by the first car. Let represent the speed of the first car Let represent the travel time of the first car Then represents the distance traveled by the second car also. And represents the speed of the second car And represents the travel time for the second car. Since we know that distance is equal to rate times time, we can say with respect to the trip taken by the first car: And with respect to the trip taken by the second car: Multiply the second equation by Add 1 to both sides: Multiply the first equation by Set the two expressions that are equal to Let equal to each other: Simplify and then solve the resulting quadratic for . Exclude the negative root. The positive root will be the speed of the first car. Add 15 to find the speed of the second car. John

Numbers_Word_Problems/244060: The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 and the remainder is 1. Find the numbers. 1 solutions Answer 178655 by solver91311(16868)   on 2009-11-30 15:06:24 (Show Source): You can put this solution on YOUR website! Multiply the second equation by Substitute back into the first equation: Solve for and then calculate using the first equation. John

Travel_Word_Problems/244061: A man has eight minutes to catch a train. The train station is 4 miles away. If he travels the first two miles at 20 mph, how fast will he have to drive for the remaining distance? 1 solutions Answer 178654 by solver91311(16868)   on 2009-11-30 14:59:44 (Show Source): You can put this solution on YOUR website! 60 miles per hour is a mile per minute, so 20 miles per hour has to be a mile every 3 minutes. That means 20 miles per hour for 2 miles is going to take 6 minutes. That leaves 2 minutes left out of the 8 minutes he had to start with. Now he has to travel the last 2 miles in 2 minutes -- one mile per minute, or 60 miles per hour. Except that will get him to the train station parking lot just as the train is leaving with 0 time to park the car, walk into the station, buy his ticket, and board the train. John

Problems-with-consecutive-odd-even-integers/244003: Find three consecutive integers whose sum is the square of 6. 1 solutions Answer 178620 by solver91311(16868)   on 2009-11-30 12:09:20 (Show Source): You can put this solution on YOUR website! Let represent the first integer. Then is the next integer, and is the one after that. Also, the square of 6 is 36. So: Solve for . Then count. John

real-numbers/243988: prove cube root 6 is irrational 1 solutions Answer 178619 by solver91311(16868)   on 2009-11-30 12:03:24 (Show Source): You can put this solution on YOUR website! Prove is irrational. Assume is rational. That means where is reduced to lowest terms, that is and have no common integer factors. It follows then that: Since at least one factor of the RHS is even, the entire RHS must be even. Since the RHS is even, the LHS must therefore also be even. Since the product of two odd numbers is always odd, it follows that: Since is even, it follows that So: Now, since at least one factor of the LHS is even, the LHS must be even. Therefore the RHS must be even and must be even. But if is even, then must be even. Since the the original assumption leads to the conclusion that both and are even, contradicting the part of the original assumption that and have no common integer factors, the assumption that is rational must be false. Therefore is irrational. QED. John

Angles/243985: In any triangle, the sum of the measures of the angles is 180° . In ΔABC, ∢ A is three times as large as ∢ B and also 16° larger than ∢ C. Find the measure of each angle. 1 solutions Answer 178613 by solver91311(16868)   on 2009-11-30 11:34:13 (Show Source): You can put this solution on YOUR website! Let represent the measure of angle B. Then is the measure of angle A, and is the measure of angle C. So: Solve for to get angle B. Multiply the measure of B by 3 to get angle A. Subtract 16 from the measure of A to get C. Or, you could let represent angle A. Then is the measure of angle B, and is the measure of angle C. So: Or, you could let represent angle C. Then is the measure of angle A and is the measure of angle B. So: Personally, I like the first way the best, but they all give the same answer in the end. John

Quadratic_Equations/243867: I am suppose to find out if this equations S= -0.0643t^2 + 3.2152t + 23.9801 is a good equation to base off a companies salary. I figured it wasn't because it happens to be a parabole that goes down after 25 years of experience. I thought of tbe possibility of people staying at a job for 25 years is highly unlikely but possible... so I figured 18yrs + 25yrs = 43 years of age. So I figured lowering a employees salary at the age of 44 and on was unethical. Plus the pay rate increase beforehand was just way to fast and high... What would you suggest would be a good solution for this company to pay salaries in a equation. It doesn't have to be a quadratic equation but I must be able to graph it. 1 solutions Answer 178593 by solver91311(16868)   on 2009-11-30 03:07:12 (Show Source): You can put this solution on YOUR website! In general, I agree with your analysis. Actually, lowering people's salary based solely on their age is more than unethical, it is illegal. My personal experience has been that I've seen about a 5% increase per year since 1988 -- but that is not necessarily typical. If you had to write a formula for a company, you would first have to define job categories and pick a base starting salary for each, call that . Then you would have to select a percentage rate, , of increase for each one. Then for job class number 1 current salary, , you could write: Where is the number of years of employment. So if the starting salary were say $50K and the rate of increase were 4%, then a graph of: Would look like the red line and Would look like the green line John

Square-cubic-other-roots/243866: square root of 27 simplify by factoring 1 solutions Answer 178591 by solver91311(16868)   on 2009-11-30 02:38:03 (Show Source): You can put this solution on YOUR website! Hint: 3 times 9 = 27 John

Numbers_Word_Problems/242724: The denominator of a fraction is 3 less than 4 times the numerator. If 5 is added to both terms the resulting fraction has the value 1/2. What is the original fraction? 1 solutions Answer 177736 by solver91311(16868)   on 2009-11-25 16:57:05 (Show Source): You can put this solution on YOUR website! Let represent the numerator. Then the denominator must be . Hence the fraction is: If you add 5 to both terms (I presume that means add 5 to both numerator and denominator) you get: And this is equal to one-half, so: Now all you have to do is cross-multiply and solve for John

logarithm/242767: just wanna see how these problems are worked out. 1.logc 3sq root y^3 z^2/x^4. sorry could make the sq root sign. 2.1/2loga-log2 3.ln2x-3(lnx-lny) 1 solutions Answer 177732 by solver91311(16868)   on 2009-11-25 16:40:31 (Show Source): You can put this solution on YOUR website! Sorry, but #1 is confusing. What part goes inside of the radical? The way to represent square root with the keyboard is: sqrt(x) which means . Everything you put inside of the parentheses is under the radical. The way you wrote your problem, I can't tell if you meant: or or And you don't actually say what it is you want to do with this logarithm. #2. Always put your log arguments in parentheses. I presume you meant: I can only presume, because you didn't take the time to say, that you want to express this as a single logarithm. First: So The difference of the logs is the log of the quotient, that is: So: Use the same rules for solving 3 as I showed you for 2 with the addition of the rule: The sum of the logs is the log of the product: John

Mixture_Word_Problems/242727: Babbitt metal is an alloy made up of 90% tin, 7% antimony, 3% copper. How many pounds of pure copper must be added to 150 pounds of the alloy so that it will contain 17% copper? 1 solutions Answer 177724 by solver91311(16868)   on 2009-11-25 16:10:51 (Show Source): You can put this solution on YOUR website! The amount of pure copper in 150 lbs. of Babbitt is: lbs. The amount of pure copper in lbs. of pure copper is lbs. The sum of the two quantities above is the amount of pure copper in the 17% alloy which can be represented by: So we can say: Just solve for John

Triangles/242755: Given triangle ABC with the measure of angle A = 30o, the length of BC = 9, and the length of AC = 11. How many solutions are there for the measure of angle B? 1 solutions Answer 177722 by solver91311(16868)   on 2009-11-25 16:04:42 (Show Source): You can put this solution on YOUR website! Two. Since for a 30° angle, BC would have to be one-half of AC if the triangle were a right triangle, and 9 is not one-half of 11, we know this is not a right triangle. Hence there is a possible obtuse angle solution for B and a possible acute angle solution for B. John

Miscellaneous_Word_Problems/242766: THE NUMBER OF TAXI ACCIDENTS IS APPROXIMATED BY: y = -143.3x^2+1823.3x+6820 and the number of injuries is approximated by: y = -416.72x^2+4416.7x+8500 ACCORDING TO THE EQUATION FOR THE NUMBER OF ACCIDENTS, IF THE TREND CONTINUED, HOW MANY TAXI ACCIDENTS OCCURRED IN 1998? USE EQUATION FOR THE NUMBER OF INJURIES TO APPROXIMATE THE NUMBER OF PEOPLE INJURED IN 1998. X=0 REPRESENTS 1990 X=1 REPRESENTS 1991 AND SO ON. 1990 = 6820 1993 = 11,000 1996 = 12,601 1 solutions Answer 177721 by solver91311(16868)   on 2009-11-25 15:59:28 (Show Source): You can put this solution on YOUR website! Stop typing in all caps. It is both rude and annoying.