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solver91311 answered: 17063 problems
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Quadratic_Equations/207069: write quadratic equation in the variable x having the given numbers as a solution. make sure its in the ax^2+bx+c=0 form. Solution is 10, only solution. 1 solutions Answer 156565 by solver91311(17077)   on 2009-08-17 03:09:52 (Show Source): You can put this solution on YOUR website! All quadratic equations have 2 solutions. So if you are only given one, the other one must be identical -- that is to say and That means the two factors of your trinomial must be: Apply FOIL and the result will be the desired trinomial. John

Polygons/207079: How would you find the area of a regular octagon whose side length is 4.7 in. and the apothem is 6.5 in. please help 1 solutions Answer 156564 by solver91311(17077)   on 2009-08-17 03:06:28 (Show Source): You can put this solution on YOUR website! The area of a regular polygon is given by: where is the number of sides, is the measure of one side, and is the measure of the apothem (i.e., the radius of the inscribed circle). Hint: An octagon has 8 sides. John

Circles/207080: Alright in a circle. a 90 degree sector has an area of 36pi ft square. what would the radius of the circle be? please help 1 solutions Answer 156563 by solver91311(17077)   on 2009-08-17 03:01:33 (Show Source): You can put this solution on YOUR website! The area of a sector of a circle where the central angle is expressed in degrees is given by: Substitute what you know: And solve for John

Rectangles/207082: the width of a rectangle is 3 meters less than the lenght. the perimeter is 14 meters. find the width. 1 solutions Answer 156562 by solver91311(17077)   on 2009-08-17 02:56:00 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle is found by adding 2 times the length to 2 times the width. Here, your width is 3m less than the length, so if is the width, then the length is , and the area is: Solve for and you have your answer. John

Rectangles/207084: the area of a square is 64 square inches. what is the lenght of each side? 1 solutions Answer 156561 by solver91311(17077)   on 2009-08-17 02:50:23 (Show Source): You can put this solution on YOUR website! The area of a square is found by multiplying the length of a side times itself. So what number when multiplied by itself equals 64? That's your answer. John

Exponents/207081: I don't know if this is the right section because I don't know the name of what I am trying to do!! We have to use the numbers 1, 9, 5 and 6 in basic equations and come up with answers from 0-30. For example, (9+1) divided by 5 x 6 = 12. I was wondering if there was an actual formula that I am supposed to be using? Also, can't use decimals, only whole numbers. HELP!!! 1 solutions Answer 156560 by solver91311(17077)   on 2009-08-17 02:48:10 (Show Source): You can put this solution on YOUR website! Nope, there is no 'formula' for this. You just have to use your imagination and come up with ways to put those 4 numbers together in thirty-one different ways so that you come up with the results from 0 through 30. and so on... Sorry, but you are just going to have to do some thinking. What a concept! John

Inequalities/206155: If you replace the equal sign of a equation with an inequality sign, is ther evert time when the value will be a solution to both the equation and the inequality. Write an inequality and provide a value that may or may not be a solution to the inequality. 1 solutions Answer 155715 by solver91311(17077)   on 2009-08-10 15:03:01 (Show Source): You can put this solution on YOUR website! If you replace the equals sign with or , then yes. Otherwise, no. , 7 is THE element of the solution set. , 7 is NOT an element of the solution set. , 7 is an element of the solution set. John

Probability-and-statistics/205657: This question is from textbook Algeba I: An Incremental Development Can You Please Help Me With This Probability Question: If two dice are rolled, what is the probability that their sum will be a number greater that 10? Thanks :D 1 solutions Answer 155277 by solver91311(17077)   on 2009-08-06 12:51:50 (Show Source): You can put this solution on YOUR website! The only two possibilities for a sum greater than 10 are 11 and 12. There is one way to make a 12 and two ways to make an 11 out of 36 total possibilities. So the probability of an 11 is: . And the probability of a 12 is . Finally, the probability of either an 11 or a 12 is the sum of these two probabilities: John

Linear-systems/205584: Please help me solve this equation! 2x+6y=17 and 5x+6y=29 1 solutions Answer 155202 by solver91311(17077)   on 2009-08-05 19:40:52 (Show Source): You can put this solution on YOUR website! Since you can't solve either one of them individually, except for one of the variables in terms of the other, I have to presume that you really meant to ask, "Please help me solve this system of equations." Multiply the second equation by -1: Add this new equation term by term to the original first equation: Substitute this calculated value for into either of the original equations (let's use the first one) Solution set is the ordered pair John

Polynomials-and-rational-expressions/205066: This question is from textbook intermediate algebra how do i solve polynomials 1 solutions Answer 155200 by solver91311(17077)   on 2009-08-05 19:22:50 (Show Source): You can put this solution on YOUR website! The simple answer is that you can't. Polynomials cannot be 'solved' in any meaningful sense of the word. You can do all sorts of things with them, i.e. factor them, collect like terms, and add, subtract, multiply, and divide them to or by other polynomials. Now, if you happen to have an equation that contains a polynomial, there is a possibility that you may be able to solve it. If it is a 4th degree (or less) polynomial equation then you certainly can solve it because there are general formulae to determine the roots for all polynomial equations of the 4th degree or less. Quintics and above, you are on your own. They all have solutions, but in many cases the roots can only be approximated by numerical means. I know this wasn't very helpful, but then again you weren't very specific. John

Systems-of-equations/205429: What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance in which a linear equation is not a function? Create an equation of a nonlinear functions. 1 solutions Answer 155079 by solver91311(17077)   on 2009-08-04 21:24:15 (Show Source): You can put this solution on YOUR website! All 2-variable linear equations that can be expressed in slope-intercept form, i.e. . This is all linear equations except those of the form that represent vertical lines. John

Signed-numbers/205215: Jill asks each of her classmates to choose a number, then multiply the number by –3, add 2 to the product, multiply the result by –2, and then subtract 14. Finally, each student is asked to divide the result by 6 and record the answer. When Jill gets an answer from a classmate, she just adds 3 to it in her head and announces the number each classmate originally chose. How did Jill know to add 3 to each answer. 1 solutions Answer 154957 by solver91311(17077)   on 2009-08-03 17:38:19 (Show Source): You can put this solution on YOUR website! Pick a number: Multiply by -3: Add 2: Multiply by -2: Subtract 14: Divide by 6: Add 3 and you are back where you started. John

Pythagorean-theorem/205229: PQR is an isosceles trianlge such that QP=QR=13 cm and the altitude PS=12 cm. Find the length PR. 1 solutions Answer 154952 by solver91311(17077)   on 2009-08-03 17:31:45 (Show Source): You can put this solution on YOUR website! If PS is an altitude, then you know two things. 1. S lies on the segment QR and 2. PS forms a right angle with QR. Therefore PQS is a right triangle with a hypotenuse (PQ) of 13 and a long leg (PS) of 12. Either recognizing two numbers from the Pythagorean Triple 13-12-5, or using the Pythagorean Theorem, you can calculate the measure of QS, which is 5. Knowing that QS = 5, we can determine that SR = QR - QS = 13 - 5 = 8. Now consider the right triangle PSR with legs PS = 12 and SR = 8. , so: John

Money_Word_Problems/204247: The marketing department of a company estimates that the demand for a product is given by dollars, where is the price per unit and is the number of units. The cost of producing units is given by dollars, and the profit for producing units is given by Skech the graph of the profit function and estimate the number of units that would produce a maximum profit. for maximum: 1 solutions Answer 154935 by solver91311(17077)   on 2009-08-03 14:20:44 (Show Source): You can put this solution on YOUR website! Can't help you unless you share the actual functions. John

Complex_Numbers/205256: Given z=5+3i and w=7-4i find zw 1 solutions Answer 154934 by solver91311(17077)   on 2009-08-03 14:17:27 (Show Source): You can put this solution on YOUR website! Use FOIL just like multiplying any other pair of binomials. Just remember that John

Volume/205226: what is the circumference of the circle whose equation is (x-9)^2+(y-3)^2=64? (^) means squared) 1 solutions Answer 154933 by solver91311(17077)   on 2009-08-03 14:10:10 (Show Source): You can put this solution on YOUR website! The equation of a circle centered at with radius is: So you have a circle centered at where . And the circumference of a circle is given by John

Divisibility_and_Prime_Numbers/205237: How many integers between 1 and 10 are multiples of either 3 or 5 but not multiples of both? 1 solutions Answer 154929 by solver91311(17077)   on 2009-08-03 13:25:47 (Show Source): You can put this solution on YOUR website! In the first place, none of the integers between 1 and 10 are multiples of both 3 and 5. In order for an integer to be a multiple of 3 and 5, it has to be at least 15, because 3 times 5 is 15. There are 3 integers between 1 and 10 that are multiples of 3, namely 3, 6, and 9. As to the number of multiples of 5 in that range, there are either 1 or 2. It depends on whether the given range is inclusive of the endpoints. The question here is: Does "between 1 and 10" mean 2 through 9 or 1 through 10. So your answer is either 4 or 5 depending on the actual definition of the range. John

Linear_Equations_And_Systems_Word_Problems/204444: 1. A rectangular field is to be enclosed by 600m of fence. What dimensions will give the maximum area? What is the maximum area? 2. The captain of a riverboat charges $36 per person including lunch. The cruise averages 300 customers a day. The captain is considering increasing the price. A survey of the customers indicates that for every $2 increase, there would be 10 fewer customers. What increase in price would maximize the revenue? 1 solutions Answer 154352 by solver91311(17077)   on 2009-07-27 18:50:15 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle is given by: which can be restated as: The area of a rectangle is given by: Substituting: This function has an extremum where the first derivative is equal to zero: Setting the first derivative equal to zero: This extremum is a maximum if the value of the 2nd derivative is negative. Which is negative for all values of the independent variable, hence the extremum is a maximum. In order for the width to be one fourth of the perimeter, the length must also be one-fourth of the perimeter. That is to say, the maximum area for a rectangle with a given perimeter is achieved when the rectangle is a square with side measure of one-fourth of the perimeter. ===================================================== Let represent the price of one fare. Then the revenue function is the number of passengers times the price of a fare. The price of one fare minus 36, quantity divided by 2 is the number of $2 increases to the price. So: Which simplifies to: First derivative: Set equal to zero: Second derivative: Hence extreme point is a maximum. John

Polynomials-and-rational-expressions/204445: Can you help me solve this word problem: 1) A piece of cardboard has a length of 60cm and a width of 40cm. In order to make the cardboard into an open box, a box with no lid), a piece of length x must be cut out of each corner. -Write an equation to represent each dimension of the box. -Using the dimensions from part a), find the S.A and Volume of the box. (Remember that it is an open box with no lid.) 1 solutions Answer 154350 by solver91311(17077)   on 2009-07-27 18:10:28 (Show Source): You can put this solution on YOUR website! Let represent the measure of the side of the cutout square, then is the length of the box, is the width of the box, and is the depth of the box. Surface area of an open-topped box is two times the length times the depth plus two times the width times the depth plus the length times the width. (it would be two times the length times the width if the box had a top). The volume is just the length times the width times the depth. John

Geometry_Word_Problems/204366: In a triangular cross-section of a lean-to for water fowl in an aviary, the second angle is 2 times as large as the first angle. And the measure of the third angle is 20 degrees greater than that of the first angle. How lare are the angles? 1 solutions Answer 154348 by solver91311(17077)   on 2009-07-27 18:05:12 (Show Source): You can put this solution on YOUR website! Let represent the measure of the first angle. Then the measure of the second angle must be and the measure of the third angle must be , all measures in degrees. Since the sum of the measures of the angles of any triangle is 180 degrees, you can say: Solve for to get the measure of the first angle and the others follow easily. John

Circles/204284: The circumference of a circle is 18 pie inches. Determine the area of the circle. 1 solutions Answer 154233 by solver91311(17077)   on 2009-07-26 16:46:51 (Show Source): You can put this solution on YOUR website! The circumference of a circle is , therefore the radius of a circle, given the circumference is . The area of a circle is . Substituting Substitute the given value of and then do the indicated arithmetic. John

Quadratic_Equations/204283: This question is from textbook Elementary & Intermediate Algebra Open-Top Box: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and foldiing up the ssides. If the area of the base is to be 80 square inches, then what size square should be cute from each corner 1 solutions Answer 154232 by solver91311(17077)   on 2009-07-26 16:41:41 (Show Source): You can put this solution on YOUR website! Let represent the measure of the side of one of the cut-out squares. Since each of the dimensions of the original piece of cardboard will be reduced by to form the base of the box, the dimensions of the base of the box will be and . Since the area of a rectangle is length times width and we know the area of the base must be 80 square inches, we can write: Multiply the binomials and collect like terms: This does not factor conveniently, so use the quadratic formula: Both roots are real and positive, but one of them is way too large, namely meaning that the cutout squares would overlap and you would have no box at all. So exclude this root as extraneous having been introduced by the act of squaring the variable. The other root, is the correct answer. John

Polynomials-and-rational-expressions/204277: i and -2i are two zeros of . Find the other zeros and write p(x)as a product of linear factors. 1 solutions Answer 154231 by solver91311(17077)   on 2009-07-26 16:29:19 (Show Source): You can put this solution on YOUR website! Complex roots always come in conjugate pairs, so if is a root then so is . Likewise, if is a root, then so is . Therefore, four of the factors you are looking for are: or The next step is to do two iterations of polynomial long division using each of the two 2nd degree factors above. Polynomial long division is too difficult to render on this site -- at least I haven't figured out a way to actually show it in under 45 minutes to an hour of work. So I'm just going to give you the result and if you need to see those steps, you can either send a thank-you note reply with your request, or you can go to: www.purplemath.com/modules/polydiv2.htm Where you can see an excellent explanation of the process Then Which is then easily factored to: Therefore your six linear factors are: John

Miscellaneous_Word_Problems/204217: How many different three-digit numbers can be formed from the digits 0 through 9 if the first digit must be odd and the last digit must be even? I have been staring at this problem all night and I still have no idea what it is asking... This question is so weird.. Please help... 1 solutions Answer 154184 by solver91311(17077)   on 2009-07-25 23:45:41 (Show Source): You can put this solution on YOUR website! Of the digits 0 through 9, 5 of them are odd, so there are 5 ways to select the first digit. There are no restrictions on the second digit so it can be any one of the 10 digits 0 through 9. Of the digits 0 through 9, 5 of them are even (0 is an even number by definition), so there are 5 ways to select the third digit. In all: You can do your own arithmetic. John

Permutations/204215: Here is the question: In how many ways can John, Todd, Lisa, and Marie line up so that they alternate gender? Here is the solution that I came up with (Choices for gender)*(Number of ways to arrange the genders) There two choices for gender: either a girl or a boy. For the first position you can choose two boys, in the second you can choose two girls, in the third you can choose one boy, and in the fourth you can choose one girl: Here it is: 2 * 2*1*2*1 = 8 ways of arranging them so that the genders are always alternated. Please let me know if my reasoning is correct. 1 solutions Answer 154183 by solver91311(17077)   on 2009-07-25 23:40:14 (Show Source): You can put this solution on YOUR website! You have the correct answer, but either your reasoning is a little skewed or I'm having trouble understanding what you are saying. Look at it my way and see if it makes sense to you: The first person in line can be any one of 4 people, so 4 ways to pick the first person. Once you have chosen the first person, the gender of the second person is fixed, and there are only 2 ways to pick the second person. There is then only 1 possibility left for the third person, and only 1 possibility for the fourth person. So: John

Quadratic_Equations/204107: Could someone please help me with this proble? Determine the number of solutions and classify the type of solutions for the following equation and justify the answer. x^2 + 3x - 15 = 0 my answer is that there are two solutions x = 2.65, -5.65 but I'm not sure how to classify the type of solution and justify it. 1 solutions Answer 154069 by solver91311(17077)   on 2009-07-24 16:06:32 (Show Source): You can put this solution on YOUR website! The Fundamental Theorem of Algebra says that any polynomial equation of the form: Has roots. So your equation must have two roots. The Discriminant, , is the portion of the quadratic equation under the radical in the quadratic equation, namely: , where the given equation is Classify the roots as follows. Two real and unequal roots. If is not a perfect square, then the two roots are a conjugate pair of irrational numbers of the form where and 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, your claim that the roots are and is not precisely correct. If you want to express the roots as decimals, the best you can do is express them as an approximation. So you should have said and . The only way to express the roots exactly is to leave the answers in radical form, namely John

Equations/204104: Could someone please help me out? I got this far and now am lost..... A rope is stretched from the ground to the top of a tower. The wire is 10 ft. long. The height is 2 ft greater than the distance from the towers base to the end of the wire. Find the distance &height. r(r+10)=2 r(r+10)-2=0 (r- )(r+ ) not sure??????? 1 solutions Answer 154049 by solver91311(17077)   on 2009-07-24 13:59:01 (Show Source): You can put this solution on YOUR website! You talk about a rope and then a wire. I'm going to go out on a limb and presume that they are the same object. What you have is a right triangle where the length of the rope, 10 feet, is the hypotenuse. Let represent the distance from the base of the tower to where the rope meets the ground. Then must be the height of the tower. So we can say: Thank you, Mr. Pythagoras. So: Just solve the quadratic and exclude the negative root. John

Word_Problems_With_Coins/203845: In a column of hard candies, there is a single red one. Above the red candy, there is one less candy than there is below it. In the entire column, there are twice as many candies as there are below the red one. How many candies are in the column? 1 solutions Answer 153978 by solver91311(17077)   on 2009-07-23 20:09:40 (Show Source): You can put this solution on YOUR website! The total number of candies can be any even number greater than 2. Let represent the number of candies below the red one. Then must represent the number of candies above the red one, and must be the total number of candies. But the total number of candies is also given by adding the number below the red one, the red one, and the number above the red one, so: Which, as should be obvious to the most casual observer, is true for all real . Since it is reasonable to presume that we are counting whole candies, we can restrict our investigation to the positive integers. Since we cannot have a negative number of candies above the red one, the smallest value can assume is 1 (making the number of candies above the red one be 0 which is 1 less than 1 and still fits the given conditions), hence the smallest total we can have is: There is no upper bound on , hence the total can be as large as we like by taking a sufficiently large . But we know that is divisible by 2, therefore the total must be an even integer. That's the best I can do unless you left something out of the problem statement. John

Volume/203836: If you were buying nuts, would you rather pay $9/Kg or $4/500g? Explain. I was unable to send a thank you to my last tutur(Stan)helper who took the time to solve my problems a couple of weeks ago because the application would not send it(it kept saying error), so just in case-Thank you so much whoever takes the time to help me out-I am drowning in geometry and I cannot tell you what a huge help this is. 1 solutions Answer 153897 by solver91311(17077)   on 2009-07-23 00:43:25 (Show Source): You can put this solution on YOUR website! $4 for 500 grams is $8 for 1 kg. John

Numeric_Fractions/203934: . State the main points of the Central Limit Theorem for a mean. 1 solutions Answer 153895 by solver91311(17077)   on 2009-07-23 00:24:36 (Show Source): You can put this solution on YOUR website! The Central Limit Theorem consists of three statements: [1] The mean of the sampling distribution of means is equal to the mean of the population from which the samples were drawn. [2] The variance of the sampling distribution of means is equal to the variance of the population from which the samples were drawn divided by the size of the samples. [3] If the original population is distributed normally (i.e. it is bell shaped), the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases. (i.e. when increasingly large samples are drawn) John

Travel_Word_Problems/203761: Please help me solve, Iam unsure how to set up the problem... it shows in the book also but I cannot understand the explanation #10. A student finishes the first half of an exam in 2/3 the time it takes to finish the second half . If the entire exam takes an hour, how many minutes does she spend on the first half of the exam? The back of the book sets up the problem like this... 5/3S = 60, then 3/5 * 5/3S = 3/5*60, then S=36.... I do not understand how they came up with the 5/3, then I figured 2/3 + 2/3 + 1hr = 5/3, but why did they multiply the recipricols and then place 3/5 on the other side *60? 1 solutions Answer 153739 by solver91311(17077)   on 2009-07-21 13:59:28 (Show Source): You can put this solution on YOUR website! Let represent the time, in minutes, it took to finish the second half of the exam. Then we are given that is the time, in minutes, it took to finish the first half of the exam. Add these two quantities for the total time, again in minutes, to finish the exam which is 60 because there are 60 minutes in 1 hour. So: But , so: So far, so good. There are two ways to go about solving from here. You can either multiply both sides by 3: And then multiply both sides by : Or, you can combine those two steps into one, as your book shows, but multiplying by the reciprocal of the fractional coefficient on the variable. (That is because we know that ) Achieving the same result, as one would expect. John