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 Parallelograms/466331: What is he most precise name for quadrilateral ABCD with vertices A(-5,2), B(-3,6), C(6,6) and D(4,2)? a) quadrilateral b) rectangle c) parallelogram d) rhombus1 solutions Answer 319665 by solver91311(16897)   on 2011-07-01 11:18:52 (Show Source): You can put this solution on YOUR website! Since vertices A and D have equal y-coordinates we can conclude that segment AD lies in a horizontal line. Likewise, since vertices B and C have equal y-coordinates, segment BC lies in a horizontal line. Since the y-coordinate of A is different than the y-coordinate of B, segments AD and BC lie in different horizontal lines and are therefore parallel to each other. Using the coordinates of points A and B, we can calculate the slope of the line containing segment AB. Similarly we can calculate the slope of the line containing segment CD. I leave it as an exercise for the student to show that the two described slopes are equal and therefore the two described segments are parallel. The slope of a horizontal line is zero, therefore the slope of a vertical line is undefined. One pair of sides is horizontal and the other pair has been shown to have a defined slope. Therefore, we have disabused ourselves of the notion that the angles at each of the vertices might possibly be right angles, and thereby have excluded rectangle as an appropriate description for ABCD. The measure of AD can clearly be seen to be 9 (square root of -9 squared plus 0 squared). The measure of AB is . I'll leave it to you to verifiy that this is not equal to 9, thereby excluding rhombus as a possible description of ABCD. That leaves quadrilateral or parallelogram. Since we have shown that there are two pairs of parallel sides, the answer should be obvious at this point. John My calculator said it, I believe it, that settles it
 Equations/466328: If x+15=19, evaluate x^3-x^-2+9x^-1 Thank you!1 solutions Answer 319662 by solver91311(16897)   on 2011-07-01 10:52:43 (Show Source): You can put this solution on YOUR website! If , then , so calculate: John My calculator said it, I believe it, that settles it
 Rectangles/466327: A rectangle has the length of 1.4 ft and a width of 1.2 ft . What is the effect on the perimeter if the length and width are doubled ?1 solutions Answer 319658 by solver91311(16897)   on 2011-07-01 10:47:06 (Show Source): You can put this solution on YOUR website! The perimeter of any rectangle is given by: If you multiply each of the length and width by some arbitrary number , then the perimeter of your resized but similar rectangle is: So multiplying each of the dimensions by results in the new perimeter being times the old perimeter. John My calculator said it, I believe it, that settles it
 Triangles/466326: if a right triangle has sides of length 2 and 4, what is the length of the other side?1 solutions Answer 319655 by solver91311(16897)   on 2011-07-01 10:39:51 (Show Source): You can put this solution on YOUR website! Depends on what you mean by "sides" when you say "sides of length 2 and 4." Do you mean that these are the two sides that include the right angle vertex of the triangle such that you want to calculate the measure of the hypotenuse, or is 4 the measure of the hypotenuse of the triangle and you want to calculate the unknown leg? The ambiguity arises because you rather carelessly referred to all three sides of your right triangle as "sides" rather than the more traditional and much more descriptive "short leg," "long leg," and "hypotenuse." Either: Case 1. Case 2. John My calculator said it, I believe it, that settles it
 Graphs/466324: What steps would I take to solve the equation 6y+7y = -251 solutions Answer 319654 by solver91311(16897)   on 2011-07-01 10:29:47 (Show Source): You can put this solution on YOUR website! Step 1: Collect like terms. Step 2: Multiply both sides by the reciprocal of the resulting coefficient on the variable. Step 3: If possible, reduce any fractions to lowest terms. (not possible in this particular problem) John My calculator said it, I believe it, that settles it
 Geometric_formulas/466319: Hi, If someone could please help me I would appreciate it.I have never done geometry before and I am a little lost any and all help is appreciated tremendously. Thank you :) Cost of Laminate Flooring The cost of Pergo Select Helsinki Birch laminate flooring is $5.89 per square foot if Nancy installs the flooring herself or$8.89 per square foot if she has the flooring installed by the flooring company. Determine the cost for the flooring in the living/dining room if a)Nancy installs it herself. b)Nancy has it installed by the flooring company. 1 solutions Answer 319653 by solver91311(16897)   on 2011-07-01 10:22:58 (Show Source): You can put this solution on YOUR website! Presuming the living room and dining room are two rectangular rooms each with length and width dimensions, find the area of each by multiplying the length in feet times the width in feet. Add the two areas. a) Multiply the total area by 5.89. b) Multiply the total area by 8.89. If the living/dining room is/are some other shape or configured so that you have to calculate dimensions, then all bets are off. No one can help you because you didn't bother to describe the shape and dimensions of the area you want to calculate. Nevertheless, once you are able to calculate the total area, the instructions for parts a) and b) above are still valid. John My calculator said it, I believe it, that settles it
 Money_Word_Problems/466266: This is a two part question; I have an idea on the second part which is graphing the equation but this first part I cannot solve. Media services charges $40 for a phone and$20/month for its econonmy plan. The equation c=20t + 40 describes the total cost, C of operating a Media Service phone for T months. The total cost for 8 months of service is $? My question is will I have to plug in the 8 were the t is like this: c=20(8) + 401 solutions Answer 319595 by solver91311(16897) on 2011-07-01 00:48:01 (Show Source): You can put this solution on YOUR website! Exactly. John My calculator said it, I believe it, that settles it  Average/466124: Rosa is on the school track team and ran the following distances during the past six days 5.6, 4.4, 3.6, 4.2, 5.3, 3.7 If she wantes to run at least a daily average of 4.7 miles over a 7-day period, what is the minimum number of miles she has to run on the seventh day? My answer was 1.4 but the book has a different answer.1 solutions Answer 319470 by solver91311(16897) on 2011-06-30 15:42:37 (Show Source): You can put this solution on YOUR website! The challenge for me on this one is trying to figure out the process you used to get to an answer of 1.4, and I confess to being utterly stumped. Except to say that you might have just reached around behind yourself and pulled a number out of your backside -- which would be one possible explaination of why your answer smells bad. Consider how you go about calculating the average. You add up all of your data elements and then divide by the number of data elements. In order to get an average of 4.7 over 7 days, the sum of the seven data elements must be 4.7 times 7 which is 32.9. So whatever the sum of your first six data points happens to be, subtracted from the required sum for 7 data points, namely 32.9, must be the required number of miles to be run on the last day to achieve the desired average. AH HA! I went back and found out what you did. You took the sum of the first six data points, 26.8, and then multiplied the required average, 4.7, by 6 to get 28.2, and then took the difference, 1.4. Close but no cigar. What you calculated was the average daily shortfall from a 4.7 average over the first 6 days. In order to achieve a 7 day average of 4.7, on the 7th day you would need to do the 4.7 PLUS that average daily shortfall of 1.4 for a total of 6.1. One way to get there, but the way I described in the previous paragraph is much easier and much less prone to error. John My calculator said it, I believe it, that settles it  Evaluation_Word_Problems/466052: Tracy's dog eats 8 ounces of dog food every day. How many pounds of dog food will her dog eat in 40 days? So my math teacher said 320 pounds but i know that 16 ounces equal a pound and my teacher said that if the dog eats 8 ounces everday then in 40 days he will eat 40 times the amount the dog eats every day (this is true) but once my teacher did 8 times 40 he got 320 ounces and in the answer space wrote 320 pounds. I was wondering why he never converted the 320 ounces to pounds which would be 320/16 (i think) please help... :)1 solutions Answer 319427 by solver91311(16897) on 2011-06-30 12:55:12 (Show Source): You can put this solution on YOUR website! Your math teacher probably got his tongue wrapped around his eye tooth and couldn't see what he was saying. The correct answer is 320 ounces which is 20 pounds. Put it to him this way: "So if you are feeding your dog 320 pounds of food every 40 days, then you are feeding your dog about 240 pounds every month since 30 is 3/4 of 40. Since even relatively inexpensive dog food runs nearly$1 per pound these days, that means you are spending $240 per month or nearly$3000 annually. I should eat so well. "Further, since you say you are feeding 8 ounces per day, you probably have a dog that weighs about 25 lbs. (c.f. Dog Breed Info Center), and that means, at 240 lbs/month of food, you are feeding your dog nearly 10 times his body weight each month. Hope they start "Biggest Loser for Dogs" soon. "Bottom line, Mr. Math Teacher, math HAS to make sense." John My calculator said it, I believe it, that settles it
 Surface-area/466044: Find the surface area of a square prism with a side measure of 6.1 solutions Answer 319419 by solver91311(16897)   on 2011-06-30 12:33:51 (Show Source): You can put this solution on YOUR website! I am going to presume that by "square prism" you mean "cube." The difference is that a cube has 6 identical square faces, where as a square prism is actually a rectangular prism that need only have two opposing faces (or sides) that are square. I make the presumption of a cube because you only provided a single dimension and the problem is not solvable with only a single dimension using the more general definition of a square prism. See Cuboids, Rectangular Prisms and Cubes for a comparison of definitions of rectangular prisim, square prism, and cube (about 2/3 down the page) The total surface area of a prism is the sum of the areas of the sides. A cube has six identical sides and the area of each is the square of the measure of an edge. I don't know if you mean that each side is 6 square units or you mistakenly used "side" to mean "edge" and that each edge measures 6 linear units, so you will have to take it from this point. John My calculator said it, I believe it, that settles it
 Travel_Word_Problems/466029: Last month, Jacob traveled from Miami to New Orleans by train and made two stops along the way. The average speed for the three legs of his trip is defined as v1, v2, v3 respectively. The average speed for the entire trip is given by 3 ____________ 1---1---1 __ + ___ + __ v1----v2----v3 a. Simplify the complex fraction. b. Find the average speed for the entire trip when v1 = 101mph, v2 = 71mph, v3 = 106mph. Round to the nearest mph. a. 3v1 v2 v3 ------------- v1v2+v1v3+v2v3; b. 91mph b. 3v1 v2 v3 ------------- v1+V2+v3-----; b. 93mph c. 3v1v2v3 ------------ v1+v2+v3----; b. 90mph d. 3v1v2v3 ------------ v1v3+v2v3---; b. 93mph e. 3v1v2v3 ------------ v1v2+v1v3+v2v3 ; b. 90mph1 solutions Answer 319393 by solver91311(16897)   on 2011-06-30 11:30:04 (Show Source): You can put this solution on YOUR website! So the answer is either a) or e). But which one? Looks like you have a little calculator work to do. John My calculator said it, I believe it, that settles it
 Triangles/466030: Find the perimeter of an isosceles triangle with a base of 15 and a side of 9. Find the perimeter of an equilateral triangle with a side measure of 39 Find the area of a regular hexagon with a base of 15 and an apothem of 20 Find the area of a regular hexagon with a base of 10 and an apothem of 12. Find the area of a regular heptagon with a side length of 12 and an apothem of 8. Find the perimeter of a regular pentagon with a side length of 11. Find the perimeter of a regular hexagon with a side length of 12. 1 solutions Answer 319390 by solver91311(16897)   on 2011-06-30 11:14:55 (Show Source): You can put this solution on YOUR website! Since the triangle (in your first problem) is isosceles and has a side that measures 9, it must also have a second side that measures 9. The third side is given as 15. The perimeter is the sum of the measures of the sides. Find the instructions for posting questions on this site. Read the instruction that says "One question per post" Repeat until you understand completely. John My calculator said it, I believe it, that settles it
 Triangles/466027: Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.1 solutions Answer 319389 by solver91311(16897)   on 2011-06-30 11:12:56 (Show Source): You can put this solution on YOUR website! Since XY is two times AB, XZ must be two times AC. Hence: Solve for John My calculator said it, I believe it, that settles it
 Trigonometry-basics/466025: what is the reference angle of -1.85radians??1 solutions Answer 319388 by solver91311(16897)   on 2011-06-30 11:03:55 (Show Source): You can put this solution on YOUR website! radians, exactly. radians, approximately. John My calculator said it, I believe it, that settles it
 Radicals/465887: I am supposed to solve this: 3+ root symbol (z-8) = root symbol(z+7) I am not sure what to do here, any help would be appreciated! With explanation if possible!1 solutions Answer 319270 by solver91311(16897)   on 2011-06-29 22:47:19 (Show Source): You can put this solution on YOUR website! Use sqrt(x) to indicate a radical. Everything inside the parentheses goes inside the radical. Square both sides, using FOIL in the LHS. Move all but the remaining radical to the RHS and collect like terms: Multiply both sides by Square both sides again: Substitute this value back into the original equation and do the arithmetic to check the work. John My calculator said it, I believe it, that settles it
 Unit_Conversion_Word_Problems/465835: 2.Sam had to pay Tony $238. He worked 2/3 of a day and makes$99 in a day at the Company. He had a yard sale and made $150, but he also had to pay Tina$78. He started out with $200 cash, so what was he left with after paying Tony and Tina? If he doesn’t have enough tell how much he will owe Tony because he pays Tina first?1 solutions Answer 319214 by solver91311(16897) on 2011-06-29 19:56:48 (Show Source): You can put this solution on YOUR website! Money in is plus, money out is minus. He had$200, so + 200 He made 2/3 of $99, so +66 He made$150, so + 150 He paid $78, so -78 He paid$238, so -238 Add all of the numbers. If the answer is positive, that's the amount left. If the answer is negative but greater than or equal to -238, then that's what he still owes Tony. If the answer is negative but less than -238, he owes Tony the entire 238 and the amount less than -238 is what he still owes Tina. John My calculator said it, I believe it, that settles it
 Finite-and-infinite-sets/465832: Let U = {x│x is an American} C = {x│x is a smoker} D = {x│x has a health problem} E = {x│x is a male} Describe in words a member of each of the following: (a) ¯C¯ (b) ¯C¯ ∩ ¯D¯ (c) C ∩ D (d) D - C (e) D U C NOTE: U denotes “union” , ∩ denotes “intersection” and ¯ ¯ denotes “negation”, for example, ¯ C¯ = is not a smoker Stumped unable to start.1 solutions Answer 319212 by solver91311(16897)   on 2011-06-29 19:49:58 (Show Source): You can put this solution on YOUR website! a) The set of all American non-smokers. b) The set of all American non-smokers who do not have any health problems. c) The set of all American smokers who do have at least one health problem. d) The set of all Americans who do have at least one health problem but do not smoke. This is a intersection of the complement of C with D. BTW, the correct notation for this is a backslash rather than a minus sign, thus which is equivalent to e) The set of all Americans who either have at least on health problem, smoke, or both. John My calculator said it, I believe it, that settles it
 Money_Word_Problems/465812: If you have 5,000 invested in a bank that pays 5.2 percent annually. How long will it take for your funds to triple?1 solutions Answer 319208 by solver91311(16897)   on 2011-06-29 19:31:12 (Show Source): You can put this solution on YOUR website! The formula for compound interest is: where is the future value, is the present value, is the annual interest rate expressed as a decimal, is the number of compounding periods per year, and is the number of years. In this case we really don't care what the present or future values are so long as the future value is three times the present value, so we can re-write the formula: We are given both and , so substitute the values: The only thing left is to take the logarithm of both sides (any base, it doesn't matter in the end) and solve for Write back and let me know what you get for an answer. John My calculator said it, I believe it, that settles it