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 Linear-equations/187407: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-8y=-18 32x+12y=-18 1 solutions Answer 140493 by solver91311(16872)   on 2009-03-19 18:10:51 (Show Source): You can put this solution on YOUR website! and So, calculate the slopes. Since both equations are in standard form, i.e. , you take the opposite of the coefficient on x, which would be -3 in the case of your first equation, and divide it by the coeffiecient on y, which would be -8 in the case of your first equation. Do the same thing for your second equation. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular. If there is any other relationship between the slopes, then the lines are neither parallel or perpendicular. John
 Miscellaneous_Word_Problems/187403: "Frozen (quater-pound) hamburger patties cost $5.80 for 12. How many can be purchased for$7.00?" I believe that this question has been asked before but the answer did not help me much because I really need someone to explain how to reach the answer. Please help if you can. Thank you1 solutions Answer 140476 by solver91311(16872)   on 2009-03-19 15:22:00 (Show Source): You can put this solution on YOUR website! If you can buy 12 of something for $5.80, then each one of them costs you 5.80 divided by 12. Once you have the cost of each one, divide that number into the amount you have (7.00 in this problem) to determine the number that you can buy for that much money. In this problem, following this procedure will result in an answer with a decimal fraction. Since no one is likely to sell you a fraction of a hamburger patty, your answer should just be the integer part of the results of your calculations. Yes, you have to do your own arithmetic. John  Money_Word_Problems/187406: A salesperson has two job offers. Company A offers a weekly salary of$200 plus commission of 10% of sales. Company B offers a weekly salary of $400 plus commission of 5% of sales. What is the amount of sales at which company A's offer is the same as company B's?1 solutions Answer 140475 by solver91311(16872) on 2009-03-19 15:09:20 (Show Source): You can put this solution on YOUR website! Let the amount of sales be x. Then amount of compensation from A would be: per week. Likewise B would pay: per week. You want to know the value of x that makes these two expressions equal, so set them equal to each other: Solve for x and you will have your answer. John  Travel_Word_Problems/187404: Hi I need help with 3 word problems. I don't even know where to begin. This is from my textbook. According to Kepler's third law of planetary motion, the average radius R of the orbit of a planet around the sun is determined R=T^2/3, where T is the number of years for one orbit and R is measured in astronomical units. a. It takes Mars 1,881 years to make one orbit of the sun. What is the average radius in AUs of the orbit of Mars? b.The average radius of the orbit of Saturn is 9.05 AU. How many number of years does it take for Saturn to make one orbit of the sun?1 solutions Answer 140474 by solver91311(16872) on 2009-03-19 15:04:27 (Show Source): You can put this solution on YOUR website! Remember that a fractional exponent means raise to the power of the numerator and take the root of the denominator Alternatively you could say: Same thing. Now all you need to do is substitute the given value for T and start punching buttons on the calculator: For the other problem, you need to solve: for T by cubing both sides, and then taking the square root: Now, just plug in the given value for R and get to work with your calculator. John  test/187401: please help. i need answers. i have school tommorow and i need these by tommorow.pleasee. copy each problem. use estimation to place the decimal point in each product. a.(0.18)(6.1)= 1098 b. (318.7)(0.09)=28683 c.(5.91)(0.328)= 193848 d. (612.3)(2.85)=1745055 write each fraction as a decimal rounded to the nearest hundreth a. 3/8 b. 1/6 c.7/9 d. 4/7 e. 2/9 f. 5/12 g. 1/3 h. 3/11 i. 5/6 j. 6/11 k. 5/7 l. 7/8 m. 11/12 n. 4/9 o. 8/11 thanks you for your inconvience for my help thanks you.. 1 solutions Answer 140472 by solver91311(16872) on 2009-03-19 14:48:02 (Show Source): You can put this solution on YOUR website! No one is going to do your entire homework assignment for you. For the estimation problems, a. 0.18 is a little less than 0.20 which is the same thing as 20%. 20% of 6 is a little more than 1. So put the decimal point so that the answer results in a number that is a little more than 1. d. Round off your factors. You are looking at approximately 600 times 3 which is 1800. Put the decimal point where it makes the answer as close as possible to 1800. Hint: 174.5055 is way too small while 17450.55 is way too large. For the rest of them, use your calculator to divide the numerator by the denominator, then round the answer to the nearest tenth: Rounded to the nearest tenth is 0.4. Do the rest of them the same way. John  Finance/187397: This question is from textbook Precalculus Hi, I'll write the problem word for word in case you can't find it: Toy manufacturing: After being in business for t years, a toy manufacturer is making x = 5000 + 50t + 10t^2 GI Jimmy toys per year. The sale price p in dollars per toy has risen according to the formula p = 10 + 0.5t. Write a formula for the manufacturer's yearly revenue as a. a function of time t. b. a function of price p. I've used the formula: (R)Revenue = (P)Price per item * (x)Number of items sold, and came up with: R(t)=(10+0.5t)*(5000+50t+10t^2) for part a. I'm not sure if this is right or not. Part b I'm not sure either. I had: R(p)=p(5000+50t+10t^2). Any help at this point would be really appreciated. Thank you, Lynn Scott 1 solutions Answer 140471 by solver91311(16872) on 2009-03-19 14:37:25 (Show Source): You can put this solution on YOUR website! You are almost there. Part a is technically correct, although you should finish it by multiplying the price binomial across the quantity trinomial: The problem with your answer to Part b is that what you are saying is a function of p is actually a function of p and t. What you need to do is take the price function of t: and solve it for t, , and then substitute this expression for t into your function for price, thus: Simplifying to a single polynomial expression is left as an exercise for the student. John  Polynomials-and-rational-expressions/187398: a mini-TV screen has a diagonal of 6.5 inches. the length of the screen is 3.5 inches longer than the width. what are the actual dimensions of the screen. now with this I thought I would try and use the Pothagorean therom. which would be a squared + b squared = c squared. so far i have gotten that 6.5 squared is 42.251 solutions Answer 140470 by solver91311(16872) on 2009-03-19 14:18:08 (Show Source): You can put this solution on YOUR website! Your thought about the Pythagorean Theorem was a very good thought indeed because that is the only way to solve this problem. Instead of a and b for the measures of the legs of your triangle, let's use l and w because we are talking about the sides of a rectangle after all. So: shows the relationship between the lengths of the sides of the rectangle with the rectangle's diagonal. By itself, that doesn't do much good because there are an infinite number of pairs of l and w values that would make this true. Fortunately, we are also given another relationship between the length and the width of the rectangle, namely that the length is 3.5 inches longer than the width, so: Knowing that, we can substitute w + 3.5 anywhere we see an l, so let's put it into the Pythagorean equation: Expand using FOIL: Collect terms and add to both sides: Notice that you have the difference of two squares on the right, so: Put into standard form by adding -30 to both sides: And finally, solve the quadratic which very conveniently factors: The Zero Product Rule gives us: or Notice that one of the roots of the quadratic is negative. Since it is absurd to have a negative value for the measure of length of something, we can exclude that root as being extraneous -- having been introduced by the act of squaring the variable in the process of solving the problem. The other root, the positive one, is the desired answer for the measure of the width. And the value of the measure of the length comes from simply adding 3.5 inches to the calculated width, or 2.5 + 3.5 = 6. Check the answer: Answer checks. John  Triangles/187308: If there is a right triangle that has two other angles of 30 and 60 which makes it a 30 60 90 triangle the base is 20ft what is the hight?1 solutions Answer 140427 by solver91311(16872) on 2009-03-19 00:17:08 (Show Source): You can put this solution on YOUR website! A 30-60-90 right triangle has sides in proportion: So if the base is the side opposite the 30 angle, then the height is the other leg and is: John  Systems-of-equations/187305: The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number reversed. Find the number.1 solutions Answer 140426 by solver91311(16872) on 2009-03-19 00:12:44 (Show Source): You can put this solution on YOUR website! 10s digit: x 1s digit: y So: Also the number is then: And the number with the digits reversed is: And we are given that: Substituting: And the number is 38. Note that 38 + 45 = 83 and 3 + 8 = 11, so the answer checks. John  Geometry_Word_Problems/187283: A trough is 2 m long, and its ends are triangles with sides of length 1 m, 1 m, and 1.2 m. a) Find the volume V of the water in the trough as a function of the water level h. b) If water is pumped into the empty trough at the rate of 6 L/min, find the water level h as a function of the time t after the pumping begins. (1 m^3 = 1000L) 1 solutions Answer 140425 by solver91311(16872) on 2009-03-18 23:51:44 (Show Source): You can put this solution on YOUR website! You don't say, but I have to presume that the sides of the trough are 1 meter and the measure across the top is 1.2 meters. Part a. Since the triangle is isoceles, the height segment is a perpendicular bisector of the base, forming two right triangles with sides 1, .6, and That means the base varies as the height in the proportion 1.2 to 0.8, or: Hence, the area of the triangle as a function of the height of the water is: And therefore the volume is just the area times the length of the trough: Part b. We need to find volume per unit time, or So: Solve for h: John  Finance/187310: The average of nine numbers is 40. If 1 is added to the first number, 2 is added to the second number, 3 is added to the third number and so on up to the ninth number, what is the new average?1 solutions Answer 140420 by solver91311(16872) on 2009-03-18 21:54:56 (Show Source): You can put this solution on YOUR website! If the average of 9 numbers is 40, then the sum of the nine numbers must be 9 times 40 or 360. If you add 1 to the first number, 2 to the second, and so on, then you must be adding: So the sum is 360 + 45 = 405, and the new average is 405 divided by 9 = 45. John  Equations/187326: I have a story problem!! Thank you. 223 yards of rope is to be cut into 3 parts. The second part is three more than three times the first part and the third part is 10 yards less than the first. What is the length of each part. I have this: Let x = length of the 1st part Let 3 + x * 3 = 2nd part Let x - 10 = 3rd part From there I cant figure out how to write in an equation. Gets all confusing from there. x + 3 + ( x * 3 ) + x - 10 = 223 3x * 3 - 10 = 223 3x * ( - 7) = 223 -7 3x = 216 --------- both by 3 x = 72 1 solutions Answer 140419 by solver91311(16872) on 2009-03-18 21:38:54 (Show Source): You can put this solution on YOUR website! Your analysis and equation setup were perfect. I don't quite follow how you went about solving the equation though. In the first place you might have had less confusion if you had written it this way: Now, collect like terms: Add 7 to both sides: Finally, multiply by : So one piece is 46 yards, the second piece is 46 X 3 + 3 = 141, and the third is 46 - 10 = 36. And 46 + 141 + 36 = 223. John  Miscellaneous_Word_Problems/187298: one integer is 6 less than another integer. the product of the lesser integer and -7 is 42 more than the greater integer. what are the integers?1 solutions Answer 140395 by solver91311(16872) on 2009-03-18 18:30:52 (Show Source): You can put this solution on YOUR website! One integer: x Another integer: y One integer is 6 less than another integer: x = y - 6 And the lesser integer must be x because it is some amount less than the other integer. The product of the lesser integer and -7: -7x Is 42 more than the greater integer: -7x = y + 42 Substitute: The greater integer is 0 and since 6 less than 0 is -6, the lesser integer is -6. Check: -7 X -6 = 42 which is 42 greater than 0. John  Linear-equations/187289: (-2,0) (4,0) what is the slope?1 solutions Answer 140392 by solver91311(16872) on 2009-03-18 18:16:52 (Show Source): You can put this solution on YOUR website! Use the formula for the slope: where and are the coordinates of your given points. Plug in the numbers and do the arithmetic. John  Square-cubic-other-roots/187260: Solve the equation x/2 + 1 = sqrt(3) for both the exact irrational root and its rational approximation to the nearest tenth. 1 solutions Answer 140389 by solver91311(16872) on 2009-03-18 17:46:34 (Show Source): You can put this solution on YOUR website! Add -1 then multiply by 2. That's your exact answer. You can work a calculator as well as I can to get the approximation. John  Numbers_Word_Problems/187252: This question is from textbook Algebra 1 Four less than five times a number is tweleve more than another number. Three times the first number less twice the second number is eight. Find the numbers1 solutions Answer 140361 by solver91311(16872) on 2009-03-18 14:49:43 (Show Source): You can put this solution on YOUR website! A number: x Five times a number: 5x Four less than five times a number: 5x - 4 Is: "=" Another number: y Twelve more than another number: y + 12 So: The first number: x Three times the first number: 3x The second number: y Twice the second number: 2y Three times the first number less the second number: 3x - 2y Is eight: = 8 So: Solve the two-variable, two-equation linear system: John  Sequences-and-series/187230: how do i find the sum of this series? 25 is on top of the ∑ symbol i=1 with (4i+1)1 solutions Answer 140342 by solver91311(16872) on 2009-03-18 12:39:49 (Show Source): You can put this solution on YOUR website! This means to replace i in 4i + 1 with the integers from 1 to 25 and add up the results. So the first term is: and the second term is: and so on until you get to the last term which is: Now you could do this the hard way, namely directly compute the sum: But that method is long, arduous, and prone to error. Fortunately, there is a formula for the sum of any series of numbers: Where a is the first element of the series, l is the last element of the series, and n is the number of elements. So for your problem: You can do your own arithmetic. John  Angles/187122: This question is from textbook Mathematics concepts and skills An Angle has a measure of 35 degrees. Find the measures of a complementary angle and a supplementary angle.1 solutions Answer 140267 by solver91311(16872) on 2009-03-17 20:10:32 (Show Source): You can put this solution on YOUR website! Complementary: 90 - 35 = Supplementary: 180 - 35 = You can do your own arithmetic. John  Rate-of-work-word-problems/187121: This question is from textbook It takes amy twice as longt to deliver papers ai it does nancy. How long would it take each girl to deliver the papers by herself if they can deliver the papers together in 40 minutes.1 solutions Answer 140262 by solver91311(16872) on 2009-03-17 20:03:38 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. Your problem is stated backwards, so you can say: But you also know that because one of them works twice as fast as the other, so: Solve for x to get the faster person's time, and then multiply that by 2 to get the slower person's time. John  Polynomials-and-rational-expressions/187119: if a^2+b^2= 11 and ab=3 what does (a-b)^2=? 1 solutions Answer 140261 by solver91311(16872) on 2009-03-17 19:52:40 (Show Source): You can put this solution on YOUR website! John  Radicals/187110: can you show me how to work problem 20 page 561 prob 28 page 5611 solutions Answer 140258 by solver91311(16872) on 2009-03-17 19:48:59 (Show Source): You can put this solution on YOUR website! We can't help you. We don't have your book. You have to type in the problem. John  Linear-equations/187111: please show me in detail what to do with fractions when dealing with linear equations write the equation of the line through(-3,4) AND (6,1) IN SLOPE INTERCEPT FORM THANK YOU!1 solutions Answer 140257 by solver91311(16872) on 2009-03-17 19:47:10 (Show Source): You can put this solution on YOUR website! Given two points, use the two-point form of the equation of a line: Substitute the values from your two points: Do the arithmetic and arrange it into the slope-intercept form, namely: John  Linear-equations/187114: confused on what to do with fractions please help in detail write an equatuin of line through (1,-5) and parallel to y=5/6x+ put in slope intercept form thank you!1 solutions Answer 140255 by solver91311(16872) on 2009-03-17 19:42:38 (Show Source): You can put this solution on YOUR website! The first thing to do is use the fact that: to determine that the slope of the line for which you must derive an equation is equal to the slope of your given line, . (I put the b in there because you left something off of your given equation. It won't make any difference to the solution of this problem, but I just like to be neat). Now you need to use the point-slope form of the equation of a line, the slope number that you get by inspection of your given equation, and the coordinates of your given point to derive your equation. Where and and Finally, all you need to do is rearrange this equation into form and you are done. John  Linear_Algebra/187108: This question is from textbook please help me. i need help i cant figure this out. if the roots of y = x2 + 10x + 24 are(x + 6)(x + 4) , what is the axis of symmetry? 1 solutions Answer 140251 by solver91311(16872) on 2009-03-17 19:25:02 (Show Source): You can put this solution on YOUR website! First of all, and are not the roots of They are the factors of the trinomial. x = -6 and x = -4 are the roots of: The axis of symmetry of any polynomial equation of the form: is the line where is the x coordinate of the vertex. The x coordinate of the vertex is given by either: or the average of the roots: Where and are the roots of In your case: or and the equation for the axis of symmetry is: John  Linear-equations/187097: Determine f(x) if f(x+2) – f(x-3)=20 and the point (-2, 6) lies on the line1 solutions Answer 140249 by solver91311(16872) on 2009-03-17 19:06:49 (Show Source): You can put this solution on YOUR website! The first thing to realize is that if f( x ) were non-linear, then: would be some function of x rather than a constant. Hence f( x ) is linear. Given that, we can use the point-slope form of the equation of a line to derive an equation for the line. So: And: And then: So: Now: Check the answer: and 22 - 2 = 20. John  Linear-equations/187095: I need help with finding the slope because in math class today my teacher went over it and about rise and run, but i mostly forgot!!!!! Please help me!!!! some examples are { Find the slope of the line that passess through each pair of points. A(-10,6), B(-5,8). I think tha i'm sussposed to put it into a fraction... but im not sure?!?!?!?!? If you understand what is Private tutoring?? Thank you soooooooooo much Liz {P.S. i'm a 6th grader}1 solutions Answer 140243 by solver91311(16872) on 2009-03-17 18:08:26 (Show Source): You can put this solution on YOUR website! Remember that your points are expressed as ordered pairs (x,y). Step 1: Subtract the second y value from the first y value: Step 2: Subtract the second x value from the first x value: Step 3: Divide the results of Step 1 by the results of Step 2: In general, given and the slope of line through and is given by: Note that it doesn't matter which of the two points you say is the 'first' and which the 'second' because, specifically for your problem: And in general: John  Miscellaneous_Word_Problems/187091: I have looked for this problem on this site but did not see it anyplace. Please help. Several of us cannot figure out how to work it. A man invests$8000 in savings for two years. At the start of the second year he adds $2500 to the$8000. At the end of the second year the account balance is $11,445. What is the annual interest rate? Please help, there are three of us and we cannot figure it out.1 solutions Answer 140239 by solver91311(16872) on 2009-03-17 17:38:17 (Show Source): You can put this solution on YOUR website! At the end of the first year, he will have: in his account. He adds$2500 at the beginnning of the second year: So at the end of the second year he will have: Which we are told is equal to 11,445, so: Solve the quadratic for r to get your desired annual interest rate. Note, the quadratic will have two roots. One of them will be negative and is an extraneous root introduced by squaring the variable during the process of solving the problem. Exlude the negative root, and your positive root will be the solution you seek. John
 Travel_Word_Problems/187080: A plane flies 420 miles with the wind and 340 miles against teh wind in same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in still air?1 solutions Answer 140237 by solver91311(16872)   on 2009-03-17 17:14:10 (Show Source): You can put this solution on YOUR website! This is the same problem as Problem 187089 (See link below). Change the numbers and solve it the same way. http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.187089.html John
 Travel_Word_Problems/187089: Fred bicycles 7km/h slower than samantha. In the time it takes fred to bicycle 40km, samantha travels 68km. How fast does fred bicycles?1 solutions Answer 140235 by solver91311(16872)   on 2009-03-17 16:58:54 (Show Source): You can put this solution on YOUR website! Use Fred's trip: d = 40 km, t unknown, but the same as Samantha's trip, r = Fred's rate of speed -- the answer we seek. Samantha's trip: d = 68 km, t unknown, but the same as Fred's trip, r = Fred's rate of speed so r + 7 = Samantha's rate of speed. For Fred: For Samantha: But t = t, so: Solve for r to get Fred's speed. Hint: First cross-multiply. John
 Parallelograms/186973: For A(-2,-4), B(-5,-1), and C(0,-4). find all locations of a fourth point, D, so that a paralleogram is formed using A, B, C, D in any order as vertices. Plot each point D on a coodinate grid and draw the parallelogram.1 solutions Answer 140167 by solver91311(16872)   on 2009-03-16 23:59:13 (Show Source): You can put this solution on YOUR website! Since you are given 3 points, you can select 3 pairs of points. Using the two-point form of the equation of a line, you can create three equations representing three lines. For and : For and : For and : Now, using: Create the equation of the parallel to each of the above lines through the given point not on that line using the point-slope form of the equation of a line: through through (Left as an exercise for the student) through Now that we have and we only need to find the point of intersection between and Since we know that from the equation for , we can just substitute into the equation for : Hence, Point D for the first parallelogram is (-3,-1). Now all you have to do is derive the equation for and find the points of intersection with the other two lines to get the other two coordinate pairs for the other two possibilities for Point D. John
 Angles/186979: Find the volume of a rectangular bread box that is 9 inches tall and has a base that is 18 inches by 12 inches. A) 1296 cubic inches B) 1944 cubic inches C) 2916 cubic inches D) 648 cubic inches E) 3888 cubic inches 1 solutions Answer 140148 by solver91311(16872)   on 2009-03-16 22:50:57 (Show Source): You can put this solution on YOUR website! Multiply 9 X 18 X 12 John