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Linear-equations/198824: Let A(-2,4), B(-7,1) and C(-1,-5) be the vertices of a triangle. a. Find an equation whose graph is a line that contains the median from A to the midpoint of line segment BC. b. Find the length of the median from A to line segment BC. c. Find the length of the altitude from A to line segment BC. d. Find the area of the traingle ABC. Thanks. 1 solutions Answer 149323 by solver91311(16868)   on 2009-06-03 15:50:55 (Show Source): You can put this solution on YOUR website! Let A(-2,4), B(-7,1) and C(-1,-5) be the vertices of a triangle. a. Find an equation whose graph is a line that contains the median from A to the midpoint of line segment BC. Use the midpoint formulas to find the midpoint of the segment BC. and where and are the coordinates of points B and C. (doesn't matter which is which) Then use the two-point form of the equation of a line to derive the desired equation: Where are the coordinates of point A and are the coordinates of the midpoint derived in the previous step. b. Find the length of the median from A to line segment BC. Use the distance formula: Where are the coordinates of point A and are the coordinates of the midpoint derived in the previous step. c. Find the length of the altitude from A to line segment BC. Step 1. Derive the equation of the line containing segment BC. Use the two-point form of the equation of a line: where and are the coordinates of points B and C. Put the equation into slope-intercept form ( Step 2. Determine the slope of the line that contains the altitude segment, namely a line perpendicular to segment BC passing through A. First you need the slope of the line containing BC which you can obtain by inspection of the slope-intercept form of the equation of the line containing BC derived in Step 1. The slope of the line containing the altitude segment is the negative reciprocal of the slope of the line containing BC because: Step 3. Derive the equation of the line containing the altitude segment. Use the point-slope form of the equation of a line: Where are the coordinates of point A and is the slope number calculated in step 2. Put this equation in slope-intercept form as well. Step 4. Solve the system of equations derived in steps 1 and 3 to determine the point of intersection between the altitude and segment BC. Since both equations are in slope intercept form, you can simply equate the two right-hand sides and solve for , then substitute back into either equation to calculate . This is where this problem gets really ugly -- for example the -coordinate of the point of intersection is -- like a mud fence. But persevere and you will be rewarded in the end. Step 5. Use the distance formula: Where and are the coordinates of point A and the point of intersection calculated in step 4. d. Find the area of the traingle ABC. Use the distance formula to calculate the measure of segment BC: Where and are the coordinates of points B and C. Call this the measure of the base of the triangle. Use the area of a triangle formula: where is the measure of the base and is the measure of the altitude calculated in part c of the question. John

Quadratic_Equations/198830: Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and number of nickels was decreaseed by 10, the value of the coins would be $9.85. how many dimes does he have? f(x) = ax^2 + bx + c = 0 using this formula I cannot figure the answer out. please help. 1 solutions Answer 149304 by solver91311(16868)   on 2009-06-03 14:18:42 (Show Source): You can put this solution on YOUR website! I already answered this question -- probably for you (and I say that because you are off on the same wrong tangent as before). is the standard form of the quadratic function. is the general form of the quadratic equation. Two different things that you combined into one thing for some unknown reason. Neither of them, nor the inappropriate combination that you provided, are of any value for finding the solution to the coin problem stated. You are trying to saw a board in two using a teaspoon. Go back and look at question 198744. Paste the following link into your browser: http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.198744.html John

Permutations/198820: What is the formula for combinatorics and permutations? 1 solutions Answer 149296 by solver91311(16868)   on 2009-06-03 13:29:47 (Show Source): You can put this solution on YOUR website! Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics. Aspects of combinatorics include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics). [Source: http://en.wikipedia.org/wiki/Combinatorics] So there is no "formula for combinatorics". There is, however, a formula for combinations. Don't you DARE roll your eyes and say "Whatever" either. Mathematics is a very precise science and therefore requires exquisite precision of language when describing it. The number of combinations of things taken at a time is: Also denoted or The number of permutations of things taken at a time is: Also denoted or Notice that the difference is the factor of in the denominator of the formula for combinations. That factor represents the number of ways that things can be ordered, hence use the formula for combinations when order DOES NOT matter, and permutations when order DOES matter. This fact also gives rise to what may become a handy relationship to know: John

Vectors/198819: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. a) x2 + 3x - 15 = 0 b) x2 + x + 4 = 0 c) x2 – 4x - 7 = 0 d) x2 – 8x + 16 = 0 e) 2x2 - 3x + 7 = 0 f) x2 – 4x - 77 = 0 g) 3x2 - 7x + 6 = 0 h) 4x2 + 16x + 16 = 0 1 solutions Answer 149291 by solver91311(16868)   on 2009-06-03 12:47:59 (Show Source): You can put this solution on YOUR website! Each of these problems is in the form: For each of them, calculate the discriminant (): Then evaluate the character of the roots based on the value of according to the following criteria (which presume rational coefficients on your quadratic): Two real and unequal roots. If is a perfect square, then both roots are rational. Otherwise the two roots are a conjugate pair of irrational roots of the form where is rational and is irrational. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by By the way, if you thought that you could just drop your entire homework assignment in here and get someone to do it for you, let me disabuse you of that notion right now. John

Probability-and-statistics/198807: two cards are drawn from a standard deck of cards. find the probability that a king or red card is drawn. 1 solutions Answer 149290 by solver91311(16868)   on 2009-06-03 12:37:28 (Show Source): You can put this solution on YOUR website! There are actually two different answers to this question depending on whether or not you put the first drawn card back in the deck before you draw the second one. The easiest way to calculate this probability is to calculate the probability of NOT drawing either a King or a red card in two draws and then subtracting that probability from 1. Without Replacement. There are 26 red cards in a deck of 52, two of which are Kings, and then there are 2 black Kings, for a total of 28 possible. That means that there are 24 cards remaining that are NOT either a King or a red card. So the probability that you do NOT draw a King or a red card on the first draw is Now, given that you were 'successful' -- that is you did not draw a King or a red card on the first draw, then there would remain 51 cards to choose from of which 23 would be not a King or red. So the probability, given non-replacement, is And the overall probability is the product of the probabilities of these two events: But since we actually want the probability of the opposite case, we have to subtract from 1: With replacement. If we put the first drawn card back into the deck before selecting the second one, then the probability of not getting a King or red card is identical for each of the draws, so our probability, for getting either a King or a red suit is: You get to do your own arithmetic. John

Linear-equations/198371: I am having trouble and need some help with this problem. Solve the system of linear inequalities by graphing. y 2x+y<-4 Thank you very much 1 solutions Answer 149289 by solver91311(16868)   on 2009-06-03 11:36:32 (Show Source): You can put this solution on YOUR website! For each of your equations, do the following: 1. Change the inequality sign to an equal sign and graph the resulting line. In both cases, use a dashed line because neither of the inequality signs is inclusive of equals. I.e., they are signs rather than signs. 2. Test the point (0,0) in the original inequality to determine if the origin is or is not an element of the solution set of the inequality. If substituting 0 for and 0 for results in a true statement, shade in the entire half-plane on the side of the line containing the origin. If it results in a false statement, shade in the side of the line that does not contain the origin. Once you have completed the above for both of your inequalities, you will have two shaded regions that overlap. The overlap region is your solution set. John

Equations/198516: Hi Good Day to all of you. Please help me derive this formula: ax^2 + bxy + cy^2 + dx + ey + f = 0 Thank you! 1 solutions Answer 149285 by solver91311(16868)   on 2009-06-03 02:25:23 (Show Source): You can put this solution on YOUR website! Your question makes no sense. In the first place, that isn't a formula; it is the general form of an equation of a conic section. And what do you mean by 'derive' it? John

Pythagorean-theorem/198781: I need to find out how to find the length of a diagonal of a square. If I knew the length and width of the square. such a length=40 ft. and width=60 ft. 1 solutions Answer 149284 by solver91311(16868)   on 2009-06-03 00:01:20 (Show Source): You can put this solution on YOUR website! The same way you find the length of the hypotenuse of a right triangle with those length legs. By the way, you don't have a square. A square has equal length sides. You have a rectangle. John

Percentage-and-ratio-word-problems/198772: Blake and Ned work for a home remodeling buisness. They are putting the final touches on a home they renovated. Working alone, Blake can paint one room in 8 hours. Ned can paint the smae room in 6 hours. How long will it take them to paint the room if they work together? 1 solutions Answer 149283 by solver91311(16868)   on 2009-06-02 23:55:32 (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. John

Quadratic_Equations/198711: The hypotenuse of a right triangle is 2cm more than the longer leg, while the longer leg is itself 2cm more than the shorter leg. Find the length of the hypotenuse. 1 solutions Answer 149280 by solver91311(16868)   on 2009-06-02 22:52:56 (Show Source): You can put this solution on YOUR website! Let represent the measure of the longer leg, then is the measure of the hypotenuse and is the measure of the short leg If we can believe our good friend Pythagoras, Square both binomials and collect like terms and then solve the very simple resulting quadratic. One of the roots won't make any sense, so toss it. The other root is the measure of the long side. Add 2 to get the hypotenuse. John

Rational-functions/198773: This question is from textbook A board of lenght 5/x+3 inches was cut into two pieces. If one pice is 4/x-3 inches, express the lenght od the other board as a rational expression. 1 solutions Answer 149279 by solver91311(16868)   on 2009-06-02 22:38:21 (Show Source): You can put this solution on YOUR website! It depends. Do you mean and or and Use parentheses next time so that your meaning is clear. Whichever it is, just subtract the second expression from the first and simplify the result. John

Circles/198771: Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumference of the two circles. Round to the nearest hundredth. Thanks. 1 solutions Answer 149278 by solver91311(16868)   on 2009-06-02 22:29:22 (Show Source): You can put this solution on YOUR website! The radius of the smaller circle is The radius of the larger circle is The circumference of the smaller circle is The circumference of the larger circle is So subtract John

Polygons/198770: Can you help me solve: Find the length of each side of a regular pentagon inscribed in a circle of radius 4 inches Thank you! 1 solutions Answer 149277 by solver91311(16868)   on 2009-06-02 22:16:59 (Show Source): You can put this solution on YOUR website! If the pentagon is inscribed in a circle, then a side of the pentagon is a chord of the circle. Since it is a regular pentagon, the angle subtended by such a chord is one-fifth of the circle, or radians. Knowing the radius and the subtended angle, you can calculate the chord length using: Where is the radius of the circle and is the subtended angle. All you need to do now is a little calculator work. John

Permutations/198768: Bob has 7 books he wants to put his bookshelf. 1. How many possible arrangements of books are there? 2. What if bob has room on the shelf for only 3 of vthe 7 books. In how many ways can he arrange the books now? 1 solutions Answer 149276 by solver91311(16868)   on 2009-06-02 21:57:29 (Show Source): You can put this solution on YOUR website! 7 ways to pick the first book, then 6 ways to pick the second book, and so on... So: For 3 of 7: So you want: You get to do your own arithmetic. John

Polygons/198762: a polygon has fifteen sides. how many vertices does the polygon have? 1 solutions Answer 149274 by solver91311(16868)   on 2009-06-02 21:50:14 (Show Source): You can put this solution on YOUR website! A triangle has three sides and three vertices, a square has four sides and four vertices, hmmmm... John

Points-lines-and-rays/198761: please help me solve. A diagram included five heptagons, ten circles, seven triangles, nine squares, and six line segments.how many polygons are in the diagram? 1 solutions Answer 149273 by solver91311(16868)   on 2009-06-02 21:48:39 (Show Source): You can put this solution on YOUR website! A heptagon is a polygon, a triangle is a polygon, and a square is a polygon. Circles and line segments are not polygons. John

Length-and-distance/198763: a box is 11 ft. wide, 20 ft. long, and 7 ft deep. what is the volume? 1 solutions Answer 149272 by solver91311(16868)   on 2009-06-02 21:44:14 (Show Source): You can put this solution on YOUR website! Multiply 11 times 20 times 7 John

test/198754: This question is from textbook Intro & Inter Algebra Sorry I forgot to include the problem: APPENDEX D 485/32 Section 8.1 at the back of the book. Find an equation of each line. Write the equation using function notation. Through (-4,8); perpendicular to 2x – 3y=1 1 solutions Answer 149262 by solver91311(16868)   on 2009-06-02 20:36:18 (Show Source): You can put this solution on YOUR website! Step 1: Solve the given equation for Now that the equation is in slope-intercept form you can see that the slope of the given line is . Step 2: Use the following rule to determine the slope of the desired line: In other words, find the negative reciprocal of the slope of the given line. Step 3: Use the given point and the slope you determined in step 2 to substitute values into the point-slope form of the equation of a line: Where are the coordinates of the given point and is the slope you derived in step 2. Since the problem only asks for 'an equation', you really don't have to do anything else, although typically you should either present the equation in slope-intercept () or standard () form. John

Geometric_formulas/198748: the side of a cube is 12 centiments. Find the surface-area-to-volume ratio, 1 solutions Answer 149254 by solver91311(16868)   on 2009-06-02 20:20:49 (Show Source): You can put this solution on YOUR website! I don't know what a 'centiment' is. I know what a centimeter is, perhaps that is what you meant. The surface area of a cube is given by: because there are six faces each having an area equal to the length of the side squared. The volume of a rectangular solid is the length times the width times the height, but for a cube the length, width, and height are all equal so the volume of a cube is: The ratio of the surface area to the volume is: Just divide 6 by the length of the side. John

Geometry_proofs/198553: How can i prove my triangle proofs? 1 solutions Answer 149250 by solver91311(16868)   on 2009-06-02 20:13:05 (Show Source): You can put this solution on YOUR website! You start with what is given, then progress logically step-by-step -- giving a definition, axiom, or previously proved theorem as a reason, until you reach the desired conclusion. That's all anyone can tell you given the paucity of information you provided in the question. Ask something specific, and you might get a specific answer in return. John

Pythagorean-theorem/198729: What is the perimeter of a square whose diagonal measures 12 inches? 1 solutions Answer 149245 by solver91311(16868)   on 2009-06-02 20:03:23 (Show Source): You can put this solution on YOUR website! The diagonal of a square is the hypotenuse of an isosceles right triangle. So, Which gives you one side. Since it is a square, multiply by 4 to get the perimeter. John

Polynomials-and-rational-expressions/198734: Please Help! The cost (C) of selling x calculators in a store is modeled by the equation: C= 3,200,000/x + 60,000. The store profit (P) for these sales is modeled by the equation: P = 500x. What is the minimum number of calculators that have to be sold for profit to be greater than cost? Thanks! 1 solutions Answer 149244 by solver91311(16868)   on 2009-06-02 19:58:16 (Show Source): You can put this solution on YOUR website! Set the profit function equal to the cost function and then solve for x. John

Equations/198746: This question is from textbook Intro & Inter Algebra The description described below is what I need to do for the problem on Page 485/32 it's the section at the back of the book SECTION 8.1 appendex. PLEASE HELP!!!! Find an equation of each line. Write the equation using function notation. 1 solutions Answer 149243 by solver91311(16868)   on 2009-06-02 19:56:27 (Show Source): You can put this solution on YOUR website! We don't have access to your book. There are more than 1000 Algebra, Trigonometry, Pre-Calculus, Calculus, and Statistics books out there, and they cost between $50 and $200 each. It is a bit much to expect that any of us would have your particular textbook at hand. John

Quadratic_Equations/198744: Word problem; Joe has a collection of nickles and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. how many dimes does he have? 10x2 + 6.05x + 9.85 = 0 using the formula I am not sure what numbers go to a,b, or c? 1 solutions Answer 149241 by solver91311(16868)   on 2009-06-02 19:53:41 (Show Source): You can put this solution on YOUR website! Whatever gave you the idea that you needed a quadratic equation for this problem? Read the problem carefully. Let d represent the number of dimes. Let n represent the number of nickels. It will be convenient to convert the amounts from dollars and cents to just cents, that is: $6.05 is 605 cents and $9.85 is 985 cents. Dimes are worth 10 cents each, so the value of the dimes that he has right now is 10d cents. His nickels, at 5 cents each, are worth 5n cents. Add them together: Likewise, if you double the amount of dimes, you have 2d dimes which are worth 20d cents. 10 fewer nickels is n - 10 which are worth 5(n - 10) cents. Add them together: which needs to be re-written as: Now you have two equations in two variables. Multiply the first one by -1 so that the coefficients on one of them become additive inverses: Then add this new equation to the other one we developed: So he has 43 dimes. Check: 43 dimes is $4.30, leaving $6.05 - $4.30 = $1.75 in nickels. $1.75 divided by .05 = 35, so 35 nickels. Twice the dimes, 86, is worth $8.60, 10 less nickels is 25, 25 nickels is worth $1.25. $8.60 plus $1.75 = $9.85. Answer checks. John

Exponential-and-logarithmic-functions/198742: Solve log x =5 I've tried putting this equation into my calculator but it doesn't come up with the answer my teacher gave me. This is from an exam review, not a book. 1 solutions Answer 149240 by solver91311(16868)   on 2009-06-02 19:36:17 (Show Source): You can put this solution on YOUR website! So, presuming that you intend the standard meaning for to be , then If you actually meant some other base, then raise that base to the 5th power for your answer. John

Trigonometry-basics/198738: Can anyone help please Given a cost function C(x)=600 square root symbol x^3+2 and a revenue function R(x)=500 square root symbol x^2+3, find the marginal profit function thanks 1 solutions Answer 149238 by solver91311(16868)   on 2009-06-02 19:23:49 (Show Source): You can put this solution on YOUR website! Just subtract the cost function from the revenue function. Profit is what you have in your hand after you pay to make or buy stuff (your cost) and then receive all the money from your customers (revenue) John

real-numbers/198737: Clarify as rational , irrational or complex (4)^1/2 + 2 My answers rational 6 + 0i complex 30007.413 irrational 3i complex 1 Rational 1 solutions Answer 149237 by solver91311(16868)   on 2009-06-02 19:16:38 (Show Source): You can put this solution on YOUR website! Everything is correct except your evaluation of 30007.413 exactly. Hence the number can be expressed as the quotient of two integers and is rational by definition. Here's a hint: You cannot express an irrational number exactly using a decimal fraction, therefore any decimal, regardless of the number of decimal places displayed, is not an exact representation of an irrational number and must therefore be rational. John

Geometry_proofs/198712: 3.(2 pts) Write the following compound statement in symbolic form Let p: Today is Friday. q: Tomorrow is not the day to go shopping. If tomorrow is not the day to go shopping, then today is not Friday. Sorry, for sounding dumb, but I am having trouble figuring this out. Can I please get help on this. Math I am not bright in. Thank you in advance!!!! 1 solutions Answer 149235 by solver91311(16868)   on 2009-06-02 19:07:39 (Show Source): You can put this solution on YOUR website! Let : Today is Friday. Which means that : Today is not Friday] Let : Tomorrow is not the day to go shopping. means If (whatever is in front of the arrow) then (whatever comes after the arrow) So: If tomorrow is not the day to go shopping (), then today is not Friday () John

Linear-systems/198730: I dont have a booklet I am stding witha final review 1 solutions Answer 149233 by solver91311(16868)   on 2009-06-02 18:58:32 (Show Source): You can put this solution on YOUR website! And just what would you like us to do about that? And what does "stding" mean? John

Equations/198735: This question is from textbook Math Find the next two numbers in the sequence 243,81,27,9 ..... 1 solutions Answer 149232 by solver91311(16868)   on 2009-06-02 18:56:30 (Show Source): You can put this solution on YOUR website! So, followed by John

Functions/198715: Hi! Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. g(x)=1/4x^x (x>0) thanks for your help! 1 solutions Answer 149230 by solver91311(16868)   on 2009-06-02 18:44:40 (Show Source): You can put this solution on YOUR website! Obtain the first derivitive: First take the natural log of both sides: Differentiate with the chain rule on the left and the product rule on the right: Set the first derivative equal to zero: Since , if and only if Hence Therefore is a local extreme point. The calculator tells us that but , and , so we can be assured that this is a minimum. John