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Coordinate-system/717248: Find the equation of the line tangent to the given circle and passing through the given point 1. x^2+y^2= 26 (4,6) 1 solutions Answer 440201 by solver91311(16897)   on 2013-02-21 17:41:23 (Show Source): You can put this solution on YOUR website! Step 1: Recognize that a tangent to a circle makes a right angle with the radius at the point of tangency (hereinafter referred to as point T). Hence, the line segment between the center of the circle and the point (4,6) (hereinafter referred to as point A) is the hypotenuse of a right triangle where the legs are the radius at point T and the segement between point T and point A. Also note that your circle is centered at the origin, point O. Step 2: Determine the length of segment TA. Use the distance formula to calculate the measure of OA. Determine the radius of the given circle by inspection of the equation. Use these values for the hypotenuse and one leg of the right triangle described in Step 1 to calculate the measure of TA. Step 3: Notice that the segment TA is the radius of a circle centered at A that intersects the given circle at T. It is here that we realize that this problem will have two solutions because this new circle does, in fact, intersect the original circle at two points. Step 4: Having the radius and center of this new circle, write the equation of this new circle. Step 5: Solve the 2X2 quadratic system consisting of the equations of the two circles. It will be convenient to write both equations as functions of using the positive square root on the original circle equation and the negative square root on the new circle equation. The two roots of the resulting quadratic will be the -coordinates of points and . Finding the -coordinates is then trivial arithmetic. Step 6: Using the two-point form of an equation of a line, derive the two desired equations -- one containing the segment and the other containing the segment As you can see from the description of the solution, this is a complex problem with a labor intensive and difficult solution, and not something I care to do for free. Please write back for a quotation for a complete solution including a full explanation and graphical illustration, if desired. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Linear-equations/717265: i need help on inequality x+2>-2 i really dont know that one 1 solutions Answer 440182 by solver91311(16897)   on 2013-02-21 16:24:45 (Show Source): You can put this solution on YOUR website! Add -2 to both sides. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Numbers_Word_Problems/717262: The second of three numbers is five times the first. The third is three more than the second. If the second is decreased by twice the third, the answer is -21. Find the three numbers. 1 solutions Answer 440181 by solver91311(16897)   on 2013-02-21 16:24:14 (Show Source): You can put this solution on YOUR website! First number: Second number: Third number: The second decreased by twice the third: Set the expression equal to -21 and then solve for . Then calculate , and John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/717261: The amount P of pollution varies directly with the population N of people. City A has a population of 442,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that its population is 344,000? 1 solutions Answer 440179 by solver91311(16897)   on 2013-02-21 16:16:09 (Show Source): You can put this solution on YOUR website! Since it is direct variation you can write: Substitute the values given for P and N, then calculate the value of k. Then substitute the the calculated value of k and the new value of N to calculate the resulting value of P. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Triangles/717250: if one side of a triangle is 6cm and the other is 8cm what is the last lines measurement? 1 solutions Answer 440178 by solver91311(16897)   on 2013-02-21 16:12:45 (Show Source): You can put this solution on YOUR website! No way to tell exactly since you didn't bother to mention whether this is a right triangle or not, and if it is a right triangle whether the side that measures 8 cm is the hypotenuse or one of the legs. The only thing that you can say for sure is that the measure of the missing side is in the interval John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Travel_Word_Problems/717242: If it takes 7 minutes to go from point A to point B at a constant speed of 70 miles per hour, how many minutes does it take to travel the same route from point A to point B at a constant speed of 50 miles per hour? 1 solutions Answer 440177 by solver91311(16897)   on 2013-02-21 15:49:14 (Show Source): You can put this solution on YOUR website! The distance from A to B is miles. The time to travel miles at miles per hour is given by minutes. You can do your own arithmetic. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Numeric_Fractions/717243: what is 7/5x=70 1 solutions Answer 440176 by solver91311(16897)   on 2013-02-21 15:40:57 (Show Source): You can put this solution on YOUR website! It is either a linear equation or a rational function depending on whether the variable is in the denominator or not. Use parentheses so that we don't have to guess what you mean. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Trigonometry-basics/717244: The expression below is the factorization of what trinomial? enter the trinomial in descending order. enter exponents using the caret (^). For example , you would enter x^2 as x^2 -1(x+5)(x+6) 1 solutions Answer 440174 by solver91311(16897)   on 2013-02-21 15:39:50 (Show Source): You can put this solution on YOUR website! Just FOIL the two binomials and then change all of the signs -- including the lead coefficient. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Geometry_proofs/717236: I was given a triangle, Labeled ABC, which is bisected by line BD, to create two smaller triangles, ABD and DBC. Given: BD is the perpendicular bisector of AC. Prove: Line DB bisects Angle ABC What am I missing? I think it falls apart the last two reasons. :( Statements / Reasons Step 1 Line BD is the perpendicular bisector of Line AC / Given Step 2 Angle ADB and Angle BDC are right angles / Def. of perpendicular lines Step 3 Angle ADB is congruent to Angle BDC / Rt angles are congruent Step 4 Line AD is congruent to Line DC / Def. of bisector Step 5 Line DB is congruent to Line DB / Reflexive ppty of congruence Step 6 Triangle ABD is congruent to Triangle DBC / SAS Step 7 Angle ABD is congruent to Angle DBC / CPCTC Step 8 Line DB bisects Angle ABC / CPCTC 1 solutions Answer 440173 by solver91311(16897)   on 2013-02-21 15:38:27 (Show Source): You can put this solution on YOUR website! Everything is good except for the reason for the last step. Should be: " bisects by definition of Angle Bisector". The definition of an angle bisector is that the bisector divides the angle into two equal parts. You just showed in the previous step that the two parts are equal. Therefore the segment dividing the angle is a bisector by definition. Q.E.D. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/717234: The following project uses the game of Guess Your Card. This is a game in which each player draws (without looking) three (3) cards. Each card has a number between 1 and 9 on it. The players then place their cards on their heads so that everyone but the players can see the cards. The object of the game is to guess what cards you have. The first person to do this correctly wins. During the play, each player, in turn, draws a question at random from a stack of questions. The player then answers the question based on the cards that he /she sees (not the player’s cards, which the player cannot see). An Example Andy has the cards 6, 6, and 7 Belle has the cards 3, 6, and 7 Carol has the cards 1, 1, and 9 Dan has the cards 3, 4, and 8 Andy draws the question card, “How many 7’s do you see?” He answers, “One,” because he cannot see the 7 on his own head; he sees only the 7 on Belle's head. Next, Belle draws the question card, “Of the four even numbers, how many different even numbers do you see?” She answers, “Three,” because she sees the 4, 6, and 8 on Andy and Dan's head. From this, Dan can conclude he has two even cards, since he can only see a 6 and Belle sees two (2) more. Situation You are playing Guess Your Card with three (3) other players. Here is what you see: Andy has the cards 1, 5, and 7 Belle has the cards 5, 4, and 7 Carol has the cards 2, 4, and 6 Andy draws the question card, “Do you see two (2) or more players whose cards sum to the same value?” He answers, “Yes.” Next Belle draws the question card, “Of the five (5) odd numbers, how many different odd numbers do you see?” She answers, “All of them.” Andy suddenly speaks up. "I know what I have," he says. "I have a 1, a 5, and a 7." I need help understanding what it is that they are looking for? Am I looking for my numbers and which equation needs to be used. 1 solutions Answer 440164 by solver91311(16897)   on 2013-02-21 15:22:07 (Show Source): You can put this solution on YOUR website! Since Belle sees 1, 3, 5, 7, and 9 and you cannot see 3 and 9, you must have 3 and 9. You also know that your total matches either Belle (16) or Carol (12). Since you know that you have a 3 and a 9 and there are no cards with 0, it is not possible for you to have a total of 12, hence you must have a total of 16. 3 plus 9 is 12 plus 4 is 16, so your cards are 3, 4, and 9. Too bad you didn't figure this out before Andy spoke up and won the game. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

test/717230: 1. You roll two dice. What is the probability that you roll (a) doubles? (b) a sum greater than 9? (c) doubles or a sum greater than 9? 1 solutions Answer 440160 by solver91311(16897)   on 2013-02-21 15:13:13 (Show Source): You can put this solution on YOUR website! There are 36 possible outcomes when rolling a pair of standard 6-sided dice. There are 6 different doubles. There is 1 way to make 12, 2 ways to make 11, and 3 ways to make 10. There are 6 ways to make doubles and 6 ways to make greater than 9 as we have seen, but two of the ways to make doubles are already counted in the 6 ways to make greater than 9. So 4 plus 6 equals 10 possible successes. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/717227: in the men's shot put event, the shot weighs 7.26 kilograms and has a diameter of 120 millimeters. Consider a cylinder made of the same material as the shot. If it has a diameter of 60 millimeters, how thick will it have to be to weigh the same as a men's shot? 1 solutions Answer 440159 by solver91311(16897)   on 2013-02-21 15:08:48 (Show Source): You can put this solution on YOUR website! No idea. You didn't bother to mention the height of the cylinder. A cylinder that is 4 km high is going to have considerably less thickess than on that only measures half a meter. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Probability-and-statistics/717217: At a HOA meeting, a board member can vote ye, no, or abstain on a motion. There are two motions on which each board member must vote. Determine the number of piint in this sample space Determine th probability that a board member votes yes on both of the motions Deetermin e the probabilty that board member votes yea on at least one motion. 1 solutions Answer 440158 by solver91311(16897)   on 2013-02-21 15:05:25 (Show Source): You can put this solution on YOUR website! There are 4 points in the sample space: No on both No on the first, yes on the second Yes on the first, no on the second Yes on both Probability of yes on both, 1 possible success out of 4 possible results. Probability of at least one yes, 3 possible successes out of 4 possible results. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/717221: I do not know how to factor this. Can you help me? 4x^2-4x-8 1 solutions Answer 440156 by solver91311(16897)   on 2013-02-21 15:00:25 (Show Source): You can put this solution on YOUR website! Factor out a 4, then factor . Hint: -2 plus 1 is -1 and -2 times 1 is -2. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Trigonometry-basics/717197: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ. sec θ = 9/7 sin θ= cos θ= tan θ= csc θ= cot θ= 1 solutions Answer 440155 by solver91311(16897)   on 2013-02-21 14:58:15 (Show Source): You can put this solution on YOUR website! If the secant is , then the hypotenuse is proportional to 9, and the adjacent leg is proportional to 7. Hence the opposite leg is proportional to Now that you have the measures of the three sides, the remaining trigonometric functions are trival. Don't forget to rationalize the denominators in the case of the cosecant and the cotangent. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Square-cubic-other-roots/717214: what is the cube root of 8x cubed 1 solutions Answer 440150 by solver91311(16897)   on 2013-02-21 14:43:37 (Show Source): You can put this solution on YOUR website! Depends. Do you mean or ? John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Percentage-and-ratio-word-problems/717211: 10.8 out of every 50 employees at a company were women. If there are 40,377 total company employees, estimate the number of women. 1 solutions Answer 440148 by solver91311(16897)   on 2013-02-21 14:41:46 (Show Source): You can put this solution on YOUR website! Divide 10.8 by 50. Multiply the result times 40377. Round off to the nearest whole number since it is highly unlikely that the company has a fractional part of a woman in its employ. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Linear_Equations_And_Systems_Word_Problems/717173: Consider the following linear programming problem: Max. 3a + 3b s.t. 2a + 4b is less than or equal to 12 6a + 4b is less than or equal to 24 a.Find the optimal solution using the graphical solution procedure b. If the objective function is changed to 2a + 6b, what will the optimal solution be? c. How many extreme points are there? What are the values of a and b at each extreme point? 1 solutions Answer 440129 by solver91311(16897)   on 2013-02-21 13:21:51 (Show Source): You can put this solution on YOUR website! Step 1: Graph the constraint inequalities. From the looks of the objective function, the values have to both be non-negative to achieve a maximum, so also graph and as additional constraints. Hint: When graphing constraints for a graphical solution to linear programming problems, it is often convenient to shade each inequality graph in the opposite sense than would ordinarily be done. That is to say shade the side of the line that is NOT the solution set. The result is that the feasibility area will be more visually obvious because it will be the only area of the graph with no shading at all. Step 2: The feasibility area is where the solution sets overlap. Step 3: Determine the critical points. These will be the vertices of the feasibility polygon (a quadrilateral in the case of the given problem). Step 4: Test the objective function at the values of the coordinates of each of the critical points defined in Step 3. The optimum solution, if one exists, will be the set of vertex coordinates that make the objective function the maximum value. It is possible that two adjacent vertices give the same objective function result. In such case, there is no unique optimum. Rather, any point on the line segment that joins those two vertices gives an optimum result. Laying out one of these problems is a significant amount of work; enough that I don't care to do it for free. Write back if you would care to negotiate a price for a complete solution to the posted problem. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Inverses/717175: I need help finding the inverse for f(x)= 2x-1/3 1 solutions Answer 440128 by solver91311(16897)   on 2013-02-21 12:58:56 (Show Source): You can put this solution on YOUR website! Replace with Solve for in terms of Verification of the steps required is left as an exercise for the student. Swap the variables: Replace with John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/717115: We have a rectangular flower bed it is 3m longer than it is wide the flower bed will have an area of (108m with exponent of 2) what will the dimension be 1 solutions Answer 440127 by solver91311(16897)   on 2013-02-21 12:52:01 (Show Source): You can put this solution on YOUR website! The width is , the length is , and the area is the length times the width: , and since the area is 108 m², Solve the factorable quadratic for . Discard the negative root as an absurdity. Then calcualate John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Rectangles/717134: the ratio of the width and the length of a rectangular garden is 2.3. which of the following could be the width and the length of the garden? A) width=12 feet, length=13 feet B) width=18 feet, length=12 feet C) width= 24 feet,length= 39 feet D) width=12 feet, length= 18 feet 1 solutions Answer 440118 by solver91311(16897)   on 2013-02-21 11:26:59 (Show Source): You can put this solution on YOUR website! For each of the given answers, multiply the given length by 2 and the given width by 3. If you get the same answer, that choice is a possible set of values. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Numbers_Word_Problems/717135: three numbers add up to 60. all the numbers are even. each number is less than 20. 1 solutions Answer 440117 by solver91311(16897)   on 2013-02-21 11:23:40 (Show Source): You can put this solution on YOUR website! No solution. The largest even number less than 20 is 18. If all three numbers were 18, the sum would only be 54. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

absolute-value/717136: in this equation 135+X=-23 is X positive ,negative or zero ? 1 solutions Answer 440116 by solver91311(16897)   on 2013-02-21 11:22:11 (Show Source): You can put this solution on YOUR website! If you were standing on the number line at 135, would you have to go right, left, or not move to get to -23? John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Functions/717137: Given f(x)=square root of x and g(x)=2x squared+1. find f circle g(x) and g cicle f(x). 1 solutions Answer 440115 by solver91311(16897)   on 2013-02-21 11:19:39 (Show Source): You can put this solution on YOUR website! means the same thing as Replace the in the definition of with the definition of , then simplify. works the same way except that you are going to evaluate g at f(x) instead of the other way around. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Pythagorean-theorem/717127: Please help me solve this equation. i can not solve this question for my homework it said: The sides of the right-angle triangle are x,[x+2]and[2x-2]. The hypotenuse is lenght[2x-2]. Find the actual dimensions of the triangle. My math teacher told me to use Pythagoras Theorem c^2 = a^2+b^2 but i not sure about that. Thank you for your help. 1 solutions Answer 440114 by solver91311(16897)   on 2013-02-21 11:15:16 (Show Source): You can put this solution on YOUR website! Do exactly what your teacher told you to do. If the hypotenuse is , then we can say . The designation as to the other two sides is arbitrary because of the commutativity of addition, so we can assign and . Now plug these values into the Pythagorean relationship: Now all you have to do is expand the squared binomials and collect like terms in the LHS. That will leave you with a quadratic expression equal to zero, which is simply a quadratic equation. Given correct arithmetic you will have an easily factorable quadratic equation. Discard the zero root because that is clearly absurd, leaving you with a positive integer value for that you can use to calculate the measures of your three triangle sides. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Travel_Word_Problems/717133: an object is thrown vertically upwards with a velocity of 100m/s; at same time another object is dropped from a height of 150m. at what time will they pass each other? 1 solutions Answer 440113 by solver91311(16897)   on 2013-02-21 11:03:06 (Show Source): You can put this solution on YOUR website! Please seek help for your Physics homework on a Physics help site. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Permutations/717130: A test consists of 20 questions and students are to answer 16 of them. In how many different ways are the students able to choose the 16 questions? 1 solutions Answer 440109 by solver91311(16897)   on 2013-02-21 10:58:14 (Show Source): You can put this solution on YOUR website! Which is the number of ways to choose 16 things from 20 things. The number of ways to choose things from things is calculated with the formula: Congratulations! You have been randomly selected to be able to do your OWN arithmetic. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Quadratic-relations-and-conic-sections/717120: Find the equation of the ellipse with the following properties. The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3). 1 solutions Answer 440105 by solver91311(16897)   on 2013-02-21 10:53:11 (Show Source): You can put this solution on YOUR website! The foci are on the axis and symmetrical to the origin, hence the center of the ellipse is at . The foci of an ellipse centered at the origin with a horizontal major axis are at . The -intercepts of such an ellipse are at the endpoints of the minor axis, . We need to find the -coordinates of the endpoints of the major axis, . Fortunately we know that , , and are related by: Plugging in the values we know: Solve for then use the values of and to derive the equation of an ellipse centered at the orgin with a horizontal major axis: John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Triangles/717126: can a triangle have sides with the given lengths 4 in. and 7 in.? 1 solutions Answer 440100 by solver91311(16897)   on 2013-02-21 10:38:08 (Show Source): You can put this solution on YOUR website! As long as the third side is strictly less than 11 inches. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Permutations/717123: The test consists of 15 questions. 10 are true/false questions and 5 are multiple choice questions that have 4 choices each. A student must select and answer for each question. In how many way can this be done? 1 solutions Answer 440098 by solver91311(16897)   on 2013-02-21 10:37:19 (Show Source): You can put this solution on YOUR website! John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it

Triangles/716880: a right triangle that has legs of 2n and n. and a hypotenuse of n sqrt3. what would be n? 1 solutions Answer 440012 by solver91311(16897)   on 2013-02-20 19:09:46 (Show Source): You can put this solution on YOUR website! No such triangle exists for any real number . Now if you happened to have stated the problem incorrectly such that the hypotenuse is and the legs are and , then can be any positive real number you like. If the triangle you specified were to exist then: Then Then But... John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it