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 Miscellaneous_Word_Problems/256389: When 270 is divided by the odd number n, the quotient is a positive prime number and the remainder is zero. What is n?1 solutions Answer 188539 by solver91311(16868)   on 2010-01-13 11:13:38 (Show Source): You can put this solution on YOUR website! First look at the prime factorization of 270. The quick way is to realize that you have 27 times 10 or 3 times 3 times 3 times 5 times 2. If you are going to divide 270 by something and get a positive prime number, then that positive prime number must be one of the above prime numbers, namely 2, 3, or 5. Furthermore, the 'something' must be the product of all of the prime factors except for the one that is the desired quotient. In order for n to be odd, it cannot have 2 as a factor. Therefore, the quotient must be 2 and n must be the product of 27 times 5 = 135. John
 Quadratic_Equations/256432: divide 12 into two partssuch that sum of thier squares is > than twice thier product by 41 solutions Answer 188536 by solver91311(16868)   on 2010-01-13 11:02:38 (Show Source): You can put this solution on YOUR website! Let represent one of the parts. Then must be the other part. The sum of the squares of the parts: Twice the product plus 4: These quantities are equal, so: Collect like terms: Eliminate common factor of 4: Solve the easily factorable quadratic. One of the roots will be one of the parts and the other will be the other part. John
 Quadratic_Equations/256431: If you are looking at a graph of a quadratic equation how do you determine where the solutions are?1 solutions Answer 188532 by solver91311(16868)   on 2010-01-13 10:49:04 (Show Source): You can put this solution on YOUR website! Where the graph intersects the -axis. John
 Linear-equations/256190: This is linear equations in one variable and problem solving. A falcon,when diving, can travel five times as fast as apheasant's top speed. if the total speeds for these two birds is 222 miles per hour, find the fastest speed of the falcon and the fastes speed of the pheasant. I am unable to figure out how to write the problem out. 1 solutions Answer 188393 by solver91311(16868)   on 2010-01-12 19:14:12 (Show Source): You can put this solution on YOUR website! Let represent the pheasant's top speed. Then the falcon's top speed must be . The sum of these two speeds is 222, then: Just solve for John
 Linear-equations/256217: this question has a few parts. does this count as my four question limit? a) find the slope of the line 2x -3y = 7 by placing the equation on slope intercept form. show work b) johnny is to work the following problem. let x be the number of small doghouses to be bulit under the following constraints. let y be the number of large doghouses to be built under the following constraints. x < y; y < or = to 10. give a verbal statement about what y < or = 10 means about the doghouses being built. johnny also adds two other constraints x > or = to 0 and y > or = to 0. why would theses two constraints be logical and needed? johnny decides to graph his related x, y values (x,y) as points. he ended up with all of his graph being in one of the four quandrants. explain why he is correct using only one quandrant. 1 solutions Answer 188387 by solver91311(16868)   on 2010-01-12 19:05:31 (Show Source): You can put this solution on YOUR website! To put your equation into slope-intercept form, just solve it for . That is, perform whatever manipulations are required to get all by itself on the LHS and everything else in the RHS. Add -2x to both sides: Multiply both sides by b) means that for some reason no more than 10 large doghouses can be built in a given time period. It might mean that Market Research says you can't sell more than 10 large ones in that time period, or the factory never has orders for more than 10 in that time period. Both of the variables have to be greater than or equal to zero. The factory certainly can produce 0 or any positive number (as long as it isn't more than 10 large ones) of either size doghouse. But a negative number of doghouses of either sized doesn't make any sense -- what are they going to do, disassemble one they built yesterday? Since both of the variables must always be positive and Quadrant 1 is the only quadrant where both variables are positive, it makes perfectly good sense that the usable part of the graph is in Quadrant 1 only. John
 Polynomials-and-rational-expressions/256219: what is the degree of 5c to the third power1 solutions Answer 188382 by solver91311(16868)   on 2010-01-12 18:51:25 (Show Source): You can put this solution on YOUR website! Same as the sum of all exponents in the term. is a third degree term. is a seventh degree term. is a second degree term because it is really and 1 plus 1 is 2. John
 Geometry_Word_Problems/256212: A rectangle parcel of land is 50ft wide. The length of a diagonal between opposite corners is 10ft more than the length of the parcel. What is the length of the parcel? x= length in ft of the parcel area = length x width x^2 + 50^2 = (x + 100)^2 x^2 + 2500 = x^2 + 1001 solutions Answer 188380 by solver91311(16868)   on 2010-01-12 18:48:08 (Show Source): You can put this solution on YOUR website! I'm not sure why you introduced the idea of the area of the rectangle into this. You are dealing with a right triangle which has sides of 50 and and a hypotenuse of At that, you almost had it right. Using Pythagoras: I'm assuming that the first relationship you wrote just had a typo in it and that you meant what I just wrote above. Now here is where you really got off track. You tried to say that . No! No! No! 1000 times No! In general, (Remember FOIL?) So, your next step SHOULD have been: Which simplifies to: John
 Money_Word_Problems/256211: A $5 roll of dimes has how may more coins than$10 roll quarters? can yo please explain the method to solve the roll of coins problem?1 solutions Answer 188375 by solver91311(16868)   on 2010-01-12 18:32:26 (Show Source): You can put this solution on YOUR website! There are 10 dimes in $1, so there must be 10 times 5 = 50 dimes in$5. There are 4 quarters in $1, so there must be 4 times 10 = 40 quarters in$10. John
 Geometry_Word_Problems/256207: if the sum of nine angles of a decagon is 1350 degrees, how large is theh tenth angle?1 solutions Answer 188374 by solver91311(16868)   on 2010-01-12 18:29:53 (Show Source): You can put this solution on YOUR website! The sum of the interior angles of any n-gon is given by: degrees. Substitute 10 for n, do the arithmetic, then subtract 1350, the sum of 9 of the angles, from the sum of all ten to get the measure of the last one. John
 Parallelograms/256206: If there was a parallelogram and one of the angles were 65 degrees and there were three missing angles.What would be the answer for the three missing angles?1 solutions Answer 188372 by solver91311(16868)   on 2010-01-12 18:23:32 (Show Source): You can put this solution on YOUR website! In a parallelogram, like in any other quadrilateral, the sum of the measures of the interior angles is 360 degrees. Also in a parallelogram, if you have one angle that is 65 degrees, you must also have a second angle that is 65 degrees, so the sum of those two angles is 130 degrees. The sum of the other two angles, which are of identical measure, is then 360 minus 130 equals 230 degrees. Divide 230 by 2 to get the measure of the other two angles. John
 Probability-and-statistics/256202: what is 55 over 70 in simplest form?????1 solutions Answer 188371 by solver91311(16868)   on 2010-01-12 18:19:54 (Show Source): You can put this solution on YOUR website! I'm curious. Does the fact that you used five question marks mean that you believe your question is five times more urgent than a person who used only 1? It is interesting that you used five question marks because the number 5 is the key to your problem. Divide both numerator and denominator of your fraction by 5. The reduced form of 55/70 is the ratio of the quotients you obtain. John
 Finance/256177: In the Florida Lottery, 6 out of 53 numbers are selected by a player. Each chance costs $1.00 Disregarding taxes, aministrative fees, etc., how much would the state have to pay for a winning ticket so that there is no advantage to the state in the Lottery?1 solutions Answer 188369 by solver91311(16868) on 2010-01-12 18:15:06 (Show Source): You can put this solution on YOUR website! for the number of combinations possible: Calculate I'll leave the arithmetic to you. The practical answer is "All of the proceeds." There is also the possibility that only 1 ticket is sold and that ticket has the winning combination, in which case the winner gets$1. No advantage to the state implies no disadvantage either. It also allows for the possibility that more tickets are sold than the number of possible combinations, in which case if the payout of a buck for each of the winning combinations were used, then the state would profit by the number of tickets sold in excess of the number of possible combinations. John
 Distributive-associative-commutative-properties/256173: how can you use the communitive property to solve this problem 4*21 solutions Answer 188356 by solver91311(16868)   on 2010-01-12 17:52:36 (Show Source): You can put this solution on YOUR website! I don't know what a "communitive" property is. Now there is Community Property, which is that which is owned by both husband and wife in some states. But I don't think that is what you mean. Then there is the Commutative Property of Multiplication which says that the order of factors in a multiplication doesn't matter. You would not use the Commutative Property to solve a multiplication product such as . You would use the Commutative Property to assure yourself that the result is 8 regardless of whether you perform or John
 Numbers_Word_Problems/256169: Polynomial word problems help please! Find three consecutive odd integers if the product of the first and second integer is 7 less than 10 times the third integer.1 solutions Answer 188347 by solver91311(16868)   on 2010-01-12 17:43:49 (Show Source): You can put this solution on YOUR website! Let represent the smallest of the three consecutive odd integers. The next larger consecutive odd integer must then be , and the one after that . The product of the first and second must be: . 7 less than 10 times the third must be: So: Solve the easily factorable quadratic. Both roots are valid answers to the question. John
 Triangles/256168: what is long length of right triangle when a=20inches and b=48 inches then what is the length of c?1 solutions Answer 188343 by solver91311(16868)   on 2010-01-12 17:35:45 (Show Source): You can put this solution on YOUR website! Use Pythagoras to find the measure of the hypotenuse of a right triangle given the measures of the two legs. For your problem: The arithmetic, as usual, is yours to do. Of course, you could also recognize that 20 is 5 times 4 and 48 is 12 times 4, and recall that 5, 12, and 13 is a Pythagorean Triple hence the hypotenuse of your triangle must be 13 times 4. John
 Equations/256108: Write the equation of the line containing P(3, 0) and perpendicular to the x-axis.1 solutions Answer 188340 by solver91311(16868)   on 2010-01-12 17:29:49 (Show Source): You can put this solution on YOUR website! A line perpendicular to the -axis is a vertical line. A vertical line through a given point has the property that ALL ordered pairs that comprise the line have identical -coordinates, and the -coordinates comprise the set of real numbers. Therefore, the only restriction on any given pair in the line you wish to describe is that . That equation fully and uniquely describes the line you seek and is, in fact, the equation you want. John
 Linear_Equations_And_Systems_Word_Problems/256155: I don't understand how to get 2 formulas. My HW say to write a system of two inequalities that describe the situation and I am completely confused! Here is the question: In basketball you score 2 points for a field goal and 1 point for a free throw. Suppose that you have scored at least 3 points in every game this season, and have a high season score of 15 points in one game. How many field goals and free throws could you have made in any one game? I think I have one (2x+1y {greater than or equal to} 3) but i don't know. Thanx!1 solutions Answer 188335 by solver91311(16868)   on 2010-01-12 17:12:06 (Show Source): You can put this solution on YOUR website! Yes, describes the low end, presuming that you have defined to mean the number of field goals and to mean the number of free throws. But your best game was 15, so the values of and must also satisfy In addition, you must also make the restriction that your solution set consists of . After all, wouldn't make much sense as a number of basketball field goals, now would it? John
 Divisibility_and_Prime_Numbers/256147: what prime numbers go into 8751 solutions Answer 188330 by solver91311(16868)   on 2010-01-12 17:02:36 (Show Source): You can put this solution on YOUR website! 875 is not even, so 2 is not a factor. 8 + 7 + 5 = 20. 2 + 0 = 2. 2 is not divisible by 3, so 875 is not divisible by 3. 875 ends in 5, so it is divisible by 5. 875/5 = 175. 175 ends in 5, so it is divisible by 5. 175/5 = 35. 35/5 = 7 The complete prime factorization of 875 is thus , and to answer your question precisely, 5 and 7. John
 Polynomials-and-rational-expressions/256140: Can someone please help me explain a real life application of a parabola other than using a satellite dish? Thnk you!!1 solutions Answer 188323 by solver91311(16868)   on 2010-01-12 16:49:51 (Show Source): You can put this solution on YOUR website! What is wrong with the satellite dish application? In nature, approximations of parabolae and paraboloids are found in many diverse situations. The best-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a baseball flying through the air, neglecting air friction). The parabolic trajectory of projectiles was discovered experimentally by Galileo in the early 17th century, who performed experiments with balls rolling on inclined planes. He also later proved this mathematically in his book Dialogue Concerning Two New Sciences. For objects extended in space, such as a diver jumping from a diving board, the object itself follows a complex motion as it rotates, but the center of mass of the object nevertheless forms a parabola. As in all cases in the physical world, the trajectory is always an approximation of a parabola. The presence of air resistance, for example, always distorts the shape, although at low speeds, the shape is a good approximation of a parabola. At higher speeds, such as in ballistics, the shape is highly distorted and does not resemble a parabola. Another situation in which parabola may arise in nature is in two-body orbits, for example, of a small planetoid or other object under the influence of the gravitation of the sun. Such parabolic orbits are a special case that are rarely found in nature. Orbits that form a hyperbola or an ellipse are much more common. In fact, the parabolic orbit is the borderline case between those two types of orbit. An object following a parabolic orbit moves at the exact escape velocity of the object it is orbiting, while elliptical orbits are slower and hyperbolic orbits are faster. Hercilio Luz Bridge, Florianópolis, Brazil. Suspension bridge cables follow a parabolic, not catenary, curve. Parabolic bridge in Newcastle-on-Tyne. Approximations of parabolae are also found in the shape of the main cables on a typical suspension bridge. Freely hanging cables as seen on a simple suspension bridge do not describe parabolic curves, but rather hyperbolic catenary curves. Under the influence of a uniform load (such as a horizontal suspended deck), the otherwise hyperbolic cable is deformed toward a parabola. Unlike an inelastic chain, a freely-hanging spring of zero rest length takes the shape of a parabola. Paraboloids arise in several physical situations as well. The best-known instance is the parabolic reflector, which is a mirror or similar reflective device that concentrates light or other forms of electromagnetic radiation to a common focal point. The principle of the parabolic reflector may have been discovered in the 3rd century BC by the geometer Archimedes, who, according to a legend of debatable veracity,[3] constructed parabolic mirrors to defend Syracuse against the Roman fleet, by concentrating the sun's rays to set fire to the decks of the Roman ships. The principle was applied to telescopes in the 17th century. Today, paraboloid reflectors can be commonly observed throughout much of the world in microwave and satellite dish antennas. Parabolic shape formed by a liquid surface under rotation. Two liquids of different densities are contained in a narrow rectangular tank. The tank is rotated and the transition point from one liquid to the other describes a parabolic shape. Paraboloids are also observed in the surface of a liquid confined to a container and rotated around the central axis. In this case, the centrifugal force causes the liquid to climb the walls of the container, forming a parabolic surface. This is the principle behind the liquid mirror telescope. Aircraft used to create a weightless state for purposes of experimentation, such as NASA's “Vomit Comet,” follow a vertically parabolic trajectory for brief periods in order to trace the course of an object in free fall, which produces the same effect as zero gravity for most purposes. The internet is full of this stuff...just Google it. John
 Linear-equations/256118: how do i solve this .5x-2y=4 and 4y-x=-8 by graphing them?1 solutions Answer 188313 by solver91311(16868)   on 2010-01-12 16:34:59 (Show Source): You can put this solution on YOUR website! Start with either one of the equations. Step 1: Select a value for . It can be anything you want, but I suggest selecting a small integer. (in the case of your first equation, it will be convenient to select small multiples of 2) Step 2: Substitute the selected value for in the equation, and then do the arithmetic to solve the equation for Step 3: Create an ordered pair using the value of you selected in Step 1 and the value of you calculated in Step 2. Step 4: Plot the ordered pair from Step 3 on your coordinate plane. Step 5: Repeat Steps 1 through 4 once more using a different value for . Step 6: Draw a line through the two plotted points. Go back and repeat all 6 steps for the other equation but use the same set of coordinate axes to graph the second equation. Once you have graphed both lines, see where they intersect. That is, if they intersect. If you end up with two separate lines that do not intersect, then your solution set is the empty set. If you end up with two lines that do intersect in one point, your solution set is the ordered pair representing that point of intersection. If you end up with one line right on top of the other, then your solution set is the set of ordered pairs that satisfies either of the two equations. Such a set has in infinite number of elements. John
 Miscellaneous_Word_Problems/256133: What would the solution to the system of equations to the right (in terms of a)? Briefly explain how you know that your answer is correct. Please help and thank you1 solutions Answer 188308 by solver91311(16868)   on 2010-01-12 16:30:29 (Show Source): You can put this solution on YOUR website! Sorry, this is not the Clairvoyants and Psychics Hot Line. You actually have to tell us the problem in order for us to help you. John
 Polynomials-and-rational-expressions/256131: Describe a real life application of a parabola.1 solutions Answer 188296 by solver91311(16868)   on 2010-01-12 16:18:44 (Show Source): You can put this solution on YOUR website! The shape of a cross section of a satellite TV antenna is a parabola. The shape of the antenna is a paraboloid. The 'dish' part of the antenna is really just a reflective surface. The actual antenna is the object held up in the center by an arm that comes off the side of the dish. The antenna is positioned at the focus. Any energy that is parallel to the axis of the parabola will reflect back to the focus of the parabola regardless of where the energy strikes the surface. John
 percentage/256128: I have a budget of £2500 to spend on a holiday. I have done out a list of expenditures but am not sure how to make them into a percentage so that I can draw a pie chart to reflect the amounts. Can you help? Thanks1 solutions Answer 188285 by solver91311(16868)   on 2010-01-12 16:00:08 (Show Source): You can put this solution on YOUR website! First thing is to add up all of your individual expense category amounts. If the sum is larger than £2500, then you either have to increase your budget or decrease one or more of your expense amounts. If the sum is less than £2500, create another "Miscellaneous" category to account for the difference. Divide each of your amounts by the total budget amount, move the decimal point two places to the right and affix a percent sign (%). So if, for example, you have £900 budgeted for airfare, then And so on... John
 Complex_Numbers/256124: 7+3i ____ 3+9i how do you write this expression as a complex number in standard form?1 solutions Answer 188279 by solver91311(16868)   on 2010-01-12 15:42:10 (Show Source): You can put this solution on YOUR website! Multiply by the conjugate of the denominator divided by itself. If is a complex number, then is its conjugate. The denominator is now the difference of two squares. Remember that . John
 Quadratic_Equations/256080: a doctor places an overweight man on a strict diet to reduce his weight from 200 kg to 80 kg . if he loses 3% of his weight every week how long will it take him to reach his target weight.?1 solutions Answer 188260 by solver91311(16868)   on 2010-01-12 13:59:35 (Show Source): You can put this solution on YOUR website! Well, that depends. Do you mean that the patient is supposed to lose 3% of 200kg (i.e. 6kg) each week, or is he supposed to lose 3% of the current weight each week? weeks. Or weeks Except that neither answer is correct in practical terms. In order to lose 1kg per week, a person needs to have a caloric deficit of about 1100 calories PER DAY. So 6 kg per week means a 6600 calorie PER DAY deficit, i.e. a combination of eating less and exercising more. Even at 440 lbs, at a 6600 calorie per day deficit, the poor schmuck would probably die from malnourishment and dehydration within 2 or three weeks. 0.5% per week, at least at the outset, is more like what would be a safe rate of weight loss. John
 Numbers_Word_Problems/256083: TWICE THE SMALLEST OF THREE CONSECUTIVE ODD NUMBERS ADDED TO 3 TIMES THE LARGEST IS 367.FIND THE NUMBERS.1 solutions Answer 188248 by solver91311(16868)   on 2010-01-12 12:53:06 (Show Source): You can put this solution on YOUR website! Is there some reason that you feel the need to shout? Typing in all caps is the electronic equivalent of shouting and is therefore both rude and annoying. Let represent the smallest odd integer. Then the next higher odd integer must be . The next one after that is . Twice the smallest is . Three times the largest is . Solve for to find the smallest, count up by 2s to get the other two. John
 Functions/256075: Please help me with this Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB?1 solutions Answer 188243 by solver91311(16868)   on 2010-01-12 12:42:27 (Show Source): You can put this solution on YOUR website! is a vertical line. Therefore the line containing the segment AB must be a horizontal line. All points in any horizontal line have identical coordinates. Therefore, since the -coordinate of A(-4,1) is 1, the -coordinate of point B must also be 1. The -coordinate of all points in any given vertical line are identical. Therefore, the -coordinate of all points on the line is 2. That means that the midpoint of the segment AB must be (2,1). The midpoint formula for gives the -coordinate of the midpoint given the -coordinates of the endpoints: But here we know the -coordinate of one of the endpoints and the -coordinate of the midpoint. So solve the formula for Substitute the known values and do the arithmetic. Therefore B is the point (8, 1) John
 Linear-equations/256070: I need to graph : y=-2x+7 and y=1/3x-2 but have no I dea where to start. How do I step by step solve the question?1 solutions Answer 188238 by solver91311(16868)   on 2010-01-12 12:20:30 (Show Source): You can put this solution on YOUR website! Start with either one of the equations. Step 1: Select a value for . It can be anything you want, but I suggest selecting a small integer. (in the case of your second equation, it will be convenient to select small multiples of 3) Step 2: Substitute the selected value for in the equation, and then do the arithmetic to solve the equation for Step 3: Create an ordered pair using the value of you selected in Step 1 and the value of you calculated in Step 2. Step 4: Plot the ordered pair from Step 3 on your coordinate plane. Step 5: Repeat Steps 1 through 4 once more using a different value for . Step 6: Draw a line through the two plotted points. Go back and repeat all 6 steps for the other equation. If you are trying to graphically determine the solution set of the system of equations that you presented, make sure that you graph both equations on the same set of coordinate axes and then proceed as follows: Once you have graphed both lines, see where they intersect. That is, if they intersect. If you end up with two separate lines that do not intersect, then your solution set is the empty set. If you end up with two lines that do intersect in one point, your solution set is the ordered pair representing that point of intersection. If you end up with one line right on top of the other, then your solution set is the set of ordered pairs that satisfies either of the two equations. Such a set has in infinite number of elements. John
 real-numbers/256067: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a. Since a can be any number, wouldnt a- be the only real number? I'm confused. Please help.1 solutions Answer 188229 by solver91311(16868)   on 2010-01-12 11:58:04 (Show Source): You can put this solution on YOUR website! Let be any real number. Then the opposite of is and the reciprocal of is . We are interested in the value of when the opposite is equal to the reciprocal, so: Multiply both sides by : Multiply both sides by -1: Which has no real number solutions. Hence, the set of all real numbers such that the opposite is equal to the reciprocal is the empty set. Symbolically: John
 Points-lines-and-rays/255984: A zip line is a taut rope or cable that you can ride down on a pulley. The zip line at the right goes from a 9 foot tall tower to a 6 foot tall tower. The towers are 20 feet apart. What is the slope of the zip line?1 solutions Answer 188227 by solver91311(16868)   on 2010-01-12 11:46:05 (Show Source): You can put this solution on YOUR website! The same as the slope of a line that passes through the points (0,9) and (20,6) [Presuming the 9ft tower to the left of the 6ft tower, (0,6) and (20,9) otherwise]. Use the slope formula: John
 Equations/256058: I am not sure why, but I cannot solve this problem: 4 1/5 x 3/4 x 6 = ? Thank you in advance for any help you are able to provide!1 solutions Answer 188221 by solver91311(16868)   on 2010-01-12 11:27:58 (Show Source): You can put this solution on YOUR website! so John