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# Recent problems solved by 'solver91311'

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 Graphs/251287: Is this true or false? To graph a line using its slope and intercept, it must be in slope intercept form.1 solutions Answer 183691 by solver91311(16885)   on 2009-12-21 19:15:58 (Show Source): You can put this solution on YOUR website! False. First of all, I presume by "it" you mean the equation which solution set is the set of ordered pairs comprising the line in question. While it is convenient to have the equation in slope-intercept form, the slope and intercept can be determined from the standard form coefficients thus: Given The slope is given by: And the -intercept is given by: John
 Graphs/251954: I need to find the midpoint of the line segment joining (4, 8) and (-2, -6)1 solutions Answer 183687 by solver91311(16885)   on 2009-12-21 18:56:16 (Show Source): You can put this solution on YOUR website! Use the midpoint formulas: and where and are the coordinates of the given points. Then your midpoint will be described by John
 Graphs/251955: I need to find the slope of the line joining the points A (-3, 2) and B (0, 4)1 solutions Answer 183683 by solver91311(16885)   on 2009-12-21 18:54:25 (Show Source): You can put this solution on YOUR website! Use the slope formula: where and are the coordinates of the given points. John
 Graphs/251951: Find the equation of the line perpendicular to the line x = 4 and passing through the point (4, 2)1 solutions Answer 183680 by solver91311(16885)   on 2009-12-21 18:53:30 (Show Source): You can put this solution on YOUR website! The line is a vertical line. Any line perpendicular to that line must be a horizontal line with an equation where is some constant. In order for the line to pass through a given point, must be equal to the -coordinate of the given point. John
 Graphs/251950: Find the slope of the line determined by the equation 6x -3y = 181 solutions Answer 183679 by solver91311(16885)   on 2009-12-21 18:50:23 (Show Source): You can put this solution on YOUR website! Solve the equation for , that is, manipulate the equation until is all by itself on one side of the equation and everything else is on the other side. The slope will then be the coefficient on John
 Graphs/251949: Find the slope of the line that passes through the points (-3, -6) and (1, 6)1 solutions Answer 183678 by solver91311(16885)   on 2009-12-21 18:48:25 (Show Source): You can put this solution on YOUR website! Use the slope formula: where and are the coordinates of the given points. John
 Geometry_proofs/251946: I really need help. i haven't done math in 13 years. I must do a proof. There are 2 triangles. one on top of the other only the top one is upside down. My given is segment AB is parallel to segment CD. those being the bases of each triangle. I must prove the top triangle APB is similar to the lower triangle DPC. the 2 triangles are sitting tip to tip not covering each other at all. face to face if u want to call it that thanks for your help1 solutions Answer 183676 by solver91311(16885)   on 2009-12-21 18:45:52 (Show Source): You can put this solution on YOUR website! AD is a transversal of the two given parallel segments, so angle A is congruent to angle D because of the congruence of opposite interior angles. BC is a transversal of the two given parallel segments, so angle B is congruent to angle C -- same reason. Angle APB is congruent to angle CPD because they are vertical angles (formed by the intersection of two straight lines) The two triangles are similar by Angle-Angle-Angle. John
 Linear-equations/251738: Maximize z = 2x + 4y subject to the constraints x ≥ 0, y ≥ 0, x + y ≥ 1, 3x + 2y <(underlined) 6 1 solutions Answer 183673 by solver91311(16885)   on 2009-12-21 18:40:36 (Show Source): You can put this solution on YOUR website! This is just a simpler version of Question number 251879 that I did earlier today. The process is the same. http://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.251879.html John
 Graphs/251704: Determine if the following maximum linear programming problem is in standard form. Do NOT solve. Maximize P = 2x1 + 3x2 + 8x3 Subject to the constraints: 0 <= x1 <= 4 x2 ≥ 0 x3 ≥ 0 x4 ≥ 0 x2 + x3 + x4 <= 8 1 solutions Answer 183648 by solver91311(16885)   on 2009-12-21 17:18:41 (Show Source): You can put this solution on YOUR website! Nope. This is augmented form. Notice the variable in the final constraint inequality? That is a slack variable that would not be found in standard form. John
 Triangles/251927: Ivan who is 1.96m tall, wishes to find the height of a tree. He walks 18.43m from the base of the tree along the shadow of the tree until his head is in a position where the tip of his shadow overlaps the end of the tree tops shadow. He is now 7.44m from the end of the shadows. How tall is the tree, round to the nearest hundredth.1 solutions Answer 183640 by solver91311(16885)   on 2009-12-21 16:44:17 (Show Source): You can put this solution on YOUR website! Similar right triangles. Big triangle has a leg that is the total length of the shadow (the distance he walked plus the length of his shadow) and another leg that is the tree itself. Small triangle is Ivan's shadow and Ivan. Corresponding sides of similar triangles are in proportion, so: Solve for to the nearest one-hundredth meter. John
 real-numbers/251916: a+b+c A =_____ 3 To solve for b in this formula, the first step is to:1 solutions Answer 183624 by solver91311(16885)   on 2009-12-21 16:04:06 (Show Source): You can put this solution on YOUR website! Multiply both sides of the equation by 3. John
 Numbers_Word_Problems/251902: How many integers, 1 to 1000, inclusive, are divisible by neither 2 nor 5?1 solutions Answer 183623 by solver91311(16885)   on 2009-12-21 16:00:56 (Show Source): You can put this solution on YOUR website! Even numbers are divisible by 2, odd numbers are not. Of the numbers 1 to 1000, half of them are odd, so half of them are not divisible by 2. Numbers that end in either 5 or 0 are divisible by 5. Of the 500 odd numbers in the range 1 to 1000, none of them end in 0 because any number that ends in 0 is even. All 500 of those odd numbers end in 1, 3, 5, 7, or 9, evenly distributed, so one-fifth of them end in 5. That means that 4/5 of the 500 odd numbers is not divisible by either 2 or 5. John
 real-numbers/251915: In the equation D = r * t, to solve for "r" what should I do. 1 solutions Answer 183619 by solver91311(16885)   on 2009-12-21 15:47:58 (Show Source): You can put this solution on YOUR website! Divide both sides of the equation by John
 Geometry_Word_Problems/251904: A triangular region is enclosed by the lines y=x, y= -x, and y=7. How many lattice points are strictly inside the triangular region?1 solutions Answer 183617 by solver91311(16885)   on 2009-12-21 15:44:29 (Show Source): You can put this solution on YOUR website! That would depend a great deal on the granularity and type of lattice. Presuming a square lattice with a granularity of one unit, there are 0 points on the x-axis, one on the line y = 1, 3 on y = 2, and so on. The sum of the first six odd integers is 6 squared or 36. John
 Triangles/251908: The measures of two supplementary angles are in the ratio of 4:5. Find the number of degrees in the measure of the smaller angle. a. 20 b. 80 c. 100 d. 1801 solutions Answer 183611 by solver91311(16885)   on 2009-12-21 15:09:13 (Show Source): You can put this solution on YOUR website! The sum of the measures of two supplementary angles is 180 degrees. Now use the idea from the previous problem I solved for you, namely question number 251906, to solve this problem. http://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.251906.html John
 Triangles/251906: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is... a. 10 b. 20 c. 60 d. 180 pllz help me!!1 solutions Answer 183610 by solver91311(16885)   on 2009-12-21 15:06:31 (Show Source): You can put this solution on YOUR website! I have no idea why I should help someone who is too lazy to spell out the word 'please,' but here goes anyway. If the ratio of the three angles is 1:3:5, then the smallest angle is 1 part, the next larger angle is 3 parts, and the largest angle is 5 parts for a total of 1 plus 3 plus 5 equals 9 parts. The sum of the angles of a triangle is always 180 degrees. Dividing 180 by 9 means that 1 part is 20 degrees. Since the smallest angle is 1 part, the smallest angle must be 20 degrees. To check the answer, consider that the middle-sized angle is 3 parts, or 3 times 20 = 60 degrees, and the largest angle is 5 parts or 5 times 20 = 100 degrees, and then 20 + 60 + 100 = 180 -- so the answer checks. John
 Geometry_Word_Problems/251905: A regular tetrahedron is glued to each face of a regular octahedron so that the faces are perfectly aligned. The faces of the tetrahedrons are congruent to the faces of the octahedron. How many vertices does the resulting solid have?1 solutions Answer 183608 by solver91311(16885)   on 2009-12-21 14:58:33 (Show Source): You can put this solution on YOUR website! The original octahedron has 6 vertices which are still there after the tetrahedrons are attached. Each tetrahedron has 4 vertices, 3 of which each correspond to an existing vertex on the octahedron, so each of the eight tetrahedrons only adds one new vertex. So, the original 6 plus 8 new equals 14. John
 Equations/251892: The sum of the integers from 1 to n is n(n+1) over 2. The sum of the squares of the integers from 1 through n is n(n+1)(2n+1) over 6 . The sum of the cubes of the integers from 1 through n is n^2(n+1)^2 over 4 . Use the appropriate expressions to find the following values. B. The sum of the squares from 1 through 30. C. The sum of the cubes of the integers from 1 through 30. D. The square of the sum of the integers from 1 through 30. e. The cube of the sum of the integers from 1 through 30. my answers B. 620.16 c.216,225 D. not really sure how to get started e. not really sure how to get started1 solutions Answer 183605 by solver91311(16885)   on 2009-12-21 14:50:36 (Show Source): You can put this solution on YOUR website! Don't know where you went wrong with part B, but if you think about it for a second, you know that the answer cannot have a decimal fraction. You are adding a series of integers, and the integers are closed for addition. That means any time you add two integers, you get another integer. Part B: Try that arithmetic one more time. Part C: You have the correct answer. Part D and E First calculate the sum of the integers from 1 to 30: Square the result for part D and cube the result for part E. That is: and John
 Travel_Word_Problems/251893: 1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number? A. ZY - V B. Z/V - 3 - Y C. Z/3 - V - Y D. 3V- Z - Y E. V- Z - Y 2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? A. 2 hours B. 4 ½ hours C. 5 ¾ hours D. 6 hours E. 7 ½ hours 3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? A. 12 minutes B. 15 minutes C. 21 minutes D. 23 minutes E. 28 minutes 4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it? A. 2x + 5 (x-1) = 9, x = 2 B. p - 3(p-5) = 10, p = 2.5 C. 4 y + 3 y = 28, y = 4 D. 5 w + 6 w - 3w = 64, w = 8 E. t - 2t - 3t = 32, t = 8 5. What simple interest rate will Susan need to secure to make $2,500 in interest on a$10,000 principal over 5 years? A. 4% B. 5% C. 6% D. 7% E. 8% 6. Which of the following is not a rational number? A. -4 B. 1/5 C. 0.8333333... D. 0.45 E. 7. A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times? A. 55 B. 150 C. 200 D. 400 E. 600 8. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? A. 25 mph B. 37 mph C. 41 mph D. 49 mph E. 56 mph 9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? A. 2 minutes and 44 seconds B. 2 minutes and 58 seconds C. 3 minutes and 10 seconds D. 3 minutes and 26 seconds E. 4 minutes and 15 seconds 10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? A. 0.8 days B. 1.09 days C. 1.23 days D. 1.65 days E. 1.97 days 11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best? A. 3 feet B. 3 ¾ feet C. 3 ½ feet D. 3 ¼ feet E. 2 ½ feet 12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month? A. 58% B. 119% C. 158% D. 175% E. 200% 13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph? A. 50 miles B. 100 miles C. 500 miles D. 700 miles E. 1,000 miles 14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday? A. 345 B. 1,035 C. 1,725 D. 3,105 E. 9,315 1 solutions Answer 183597 by solver91311(16885)   on 2009-12-21 13:58:04 (Show Source): You can put this solution on YOUR website! Well, look at that! A 14-question multiple choice test that you want someone to take for you. Sorry -- not happening. John
 Graphs/251879: Maximize z = 3x + 5y subject to the constraints x ≥ 0, y ≥ 0, y <= 8, x + y ≥ 2, 4x + y <= 121 solutions Answer 183596 by solver91311(16885)   on 2009-12-21 13:56:22 (Show Source): You can put this solution on YOUR website! Graph the five constraint inequalities. The area where the five solution sets overlap is the area of feasibility. For this problem, that area is an irregular pentagon. Each of the five vertices of the area of feasibility is a potential maximum, and the maximum can only exist at a vertex. Plot the five vertices and test the coordinates in the objective function. The coordinates of the vertex that provides the maximum value of the objective function are the solution set of your problem. John
 Square-cubic-other-roots/251889: Rationalize the denominator: 2-√(7) divided by √(3) - √(2) In the examples I have I believe I am supposed to multiply the numberator and denominator by the denominator....is this the correct way to start this equation or am I missing something. I have read through the lessons and I am still very confused. If someone could show me the steps I would greatly appreciate it as maybe then I could wrap my brain around this. 1 solutions Answer 183593 by solver91311(16885)   on 2009-12-21 13:42:29 (Show Source): You can put this solution on YOUR website! You cannot simply multiply by the denominator because that would square the denominator. If you square the denominator, you would still have radicals in the denominator. Let's say that either or (or both) are the square root of an integer. Then, in general would still be irrational because while the the two 2nd power terms would be rational, the 2ab term in the middle would still be irrational -- and squaring it again would just make things worse. However, recall the difference of two squares factorization: So, given a binomial expression in the denominator where at least one of the factors of the binomial is an irrational square root, you need to multiply the entire fraction by 1 in the form of the CONJUGATE of the denominator divided by itself. Form the conjugate of a binomial by simply changing the sign in the middle, that is: is the conjugate of (and vice versa, of course). John
 Finance/251881: If the interest is zero, the future value interest factor equals a. -1 b. 0 c. 1 d. 2 I choose b.; because according to the future value interest factor table interest starts at 1%. Can you tell me if this is correct? Also if the answer is different can you show solution step by step?1 solutions Answer 183587 by solver91311(16885)   on 2009-12-21 13:24:52 (Show Source): You can put this solution on YOUR website! Think about it this way. Let's say you are my REALLY good friend and you are going to loan me $1000 at zero interest for a year. What do I owe you at the end of the year? 1000 times -1 = -1000, meaning you owe me ANOTHER$1000 1000 times 0 = 0, meaning I owe you nothing 1000 times 1 = 1000, meaning I've got to give you your original 1000 back or 1000 times 2 = 2000, meaning you actually charged me 100% interest John
 Square-cubic-other-roots/251887: Did I do this equation right? 3 sqrt of 12 + 2 sqrt of 3 3 sqrt (4*3) + 2 sqrt 3 3+2+2 sqrt 3 7 sqrt 3 Is this correct?? thanks :) 1 solutions Answer 183585 by solver91311(16885)   on 2009-12-21 13:19:09 (Show Source): You can put this solution on YOUR website! First thing, you do NOT have an equation. An equation has an equals sign in it somewhere. You have an expression that needs to be simplified. And, no you did not do it correctly. So far, so good, but I cannot fathom your thought process to get you to what you say is the next step, hence here is where I have to depart from your path. John
 Square-cubic-other-roots/251882: Please help me solve this problem: (squareroot)x^2/18 both the numerator and denominator are under one square root sign. the instructions say to rationalize the denominator. Becasue 18's square root is 4.24 I am unsure this is the right answer (x/4.24) I believe I may be missing something. Should I factor out the denominator? 1 solutions Answer 183582 by solver91311(16885)   on 2009-12-21 13:09:49 (Show Source): You can put this solution on YOUR website! In the first place 18's square root is NOT 4.24. 4.24 is only an approximation of the square root of 18. You cannot exactly represent the square root of 18 with a decimal fraction. If you could exactly represent the square root of 18 with some decimal fraction, then the square root of 18 would have to be rational -- that is because any decimal fraction with a finite number of decimal places can be represented exactly by the quotient of two integers. But we can prove that 18 is not rational... The first thing to do is to find the prime factorization of 18, namely 2 times 3 times 3. Take two factors of 3 out of the radical and leave one of them on the outside, hence: Now your problem looks like: So far, so good, but we still have a radical (irrational number) in the denominator. It would be tidy if we were able to multiply the denominator by , but that would change the value of the fraction. However, we can multiply the entire fraction by 1 and not change its value. So let's multiply by 1 in the form of , thus: Now you have an equivalent representation of the original expression with a rational number denominator. See my lesson on Rationalizing Denominators: http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson John
 Travel_Word_Problems/251883: The thrust SSC is the worlds fastest land vehicle. Suppose the driver of a car whose top speed is 200 miles per hour requests a race against the SSC. The car gets a head start of one-half hour. If there is unlimited spaces to race, at what distance will the SSC pass the car1 solutions Answer 183577 by solver91311(16885)   on 2009-12-21 12:44:06 (Show Source): You can put this solution on YOUR website! 200 mph car has one-half hour head start, so is 100 miles ahead when faster car starts. Subtract 200 from the speed of the faster car (which you didn't bother to share). How long would it take a vehicle traveling at the speed difference to go 100 miles? John
 Probability-and-statistics/251395: a box contains 15 keys. Three of them open the main door. Two keys are selected randomly without replacement. What is the probablity that the first key does not open the main dorr and the second key does open the main door?1 solutions Answer 183068 by solver91311(16885)   on 2009-12-18 16:41:39 (Show Source): You can put this solution on YOUR website! The probability that the first key selected will not open the door is the number of keys in the bag that won't open the door (15 - 3 = 12) divided by the number of keys in the bag altogether, so 12/15 = 4/5 = 80%. The probability that the second key selected WILL open the door is the number of keys in the bag that will open the door, which is still 3 because the first key we picked didn't open the door, divided by the number of keys in the the bag altogether, which is now 14 because we didn't replace the first key selected, so: 3/14. If you are calculating the probability that this happens OR that happens (either thing happening is a success), then you add the probabilities. On the other hand, if you are calculating the probability that this happens AND that happens (both have to happen to be a success), then you multiply the probabilities. The arithmetic is all yours. John
 Graphs/251290: The following linear equation can be used to determine the salvage value S, in dollars, of a color photocopier t years after its purchase. (0 < or equal to t < or equal to 5) S= -400t + 2000 (a)Identify and interpret the meaning of both the slope and the y-intercept. 1 solutions Answer 183060 by solver91311(16885)   on 2009-12-18 16:02:17 (Show Source): You can put this solution on YOUR website! The slope is the coefficient on the independent variable (Salvage value "depends" on time). The -intercept is the value of the constant term. The -intercept is the value of the item at time 0, the slope is the amount that it loses in value each year. John
 Travel_Word_Problems/251389: Kwan hiked up a hillat 4km/hr and backat 6km/hr. his total hiking time was 3hours. how long did the trip up the hill take him?1 solutions Answer 183059 by solver91311(16885)   on 2009-12-18 16:00:12 (Show Source): You can put this solution on YOUR website! Trip up the hill: Trip down the hill. We can use the same distance because we can assume that the mountain did not grow or shrink noticeably during the hike. And we use for the time because if was the time up the hill and the total trip was 3 hours, then is what is left for going down the hill. Set these two expressions equal to equal to each other: Solve this little equation in and you have your answer. John
 Length-and-distance/251374: 4. In navigational terms, a bearing is defined as the number of degrees a direction is from due north clockwise. If a plane flying 120 mph has flown 1 hour at a bearing of 32°, how far has it flown in a horizontal direction?1 solutions Answer 183058 by solver91311(16885)   on 2009-12-18 15:42:10 (Show Source): You can put this solution on YOUR website! If you truly mean "a horizontal" direction, meaning parallel to the horizon, then the answer is simply 120 mph times 1 hour = 120 miles. On the other hand, given the discussion of the meaning of bearing, you mean "an East-West" direction, then you want the magnitude of the East-West velocity vector times 1 hour. For North-South Where is the magnitude of the velocity vector in the direction of travel and is the bearing angle. And for East-West: Just whip out the calculator and make sure you are in Degrees mode. John
 logarithm/251341: Find the logarithm using the change-of-base formula. Round to the nearest ten-thousandth. log π 1500 the n should be lower than the g. thanks1 solutions Answer 183054 by solver91311(16885)   on 2009-12-18 15:31:42 (Show Source): You can put this solution on YOUR website! I did this same problem yesterday -- for the same guy. John