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# Recent problems solved by 'vleith'

vleith answered: 2822 problems
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 Quadratic_Equations/135067: What is the difference between domain and range? Describe a real-life situation that could be modeled by a function. Can someone explain this so I can understand it?1 solutions Answer 98893 by vleith(2825)   on 2008-04-03 13:05:09 (Show Source): You can put this solution on YOUR website!The domain is the set of all valid value for the 'independent' variable. The range is the set of the resulting 'dependent' variable. So, let's say you had a function like Then the domain is the set of all valid values for x and the range is the values you would get for all the 'y' when you subbed in all the 'x's. As far a a function goes, let's say you want to go to a local theme park. Tickets are \$25 and parking is \$10. The total price for a family is given by where a is the number of people in the family. For that function the domain is all values of 'a' that are positive (no family has 0 or negative number of members). The range is (35, 60, 85, 110, etc... like that)
 Equations/135065: I do not know how to solve this. Find three consecutive even intergers such that four times the middle interger is equal to two less than the sum of the first and third intgers. Equation:? Set up 1st no. = n 2nd no. = n+2 3rd no n+4 I have no clue how to solve this. 1 solutions Answer 98892 by vleith(2825)   on 2008-04-03 12:36:18 (Show Source): You can put this solution on YOUR website!You have more than a clue. Don't fret, You are part way there already. Your solution uses the number n. But there is nothing that ensures that 'n' is even. So let's use a different set of numbers. Let's assume n is even, if so, then n/2 is still an integer. Our three numbers will be n/2, (n+4)/2 and (n+8)/2 Add in one more given " four times the middle integer is equal to two less than the sum of the first and third integers." so Left left side is four times the middle number. The right side is the (sum of the first and third) minus 2 Now solve n = -6 Check : is 4(-4) = (-6 + -2) - 2? Nope, so I think there is not a solution to this one
 Numeric_Fractions/135064: What would be the radious of a circle with a diameter of 8 inches?1 solutions Answer 98890 by vleith(2825)   on 2008-04-03 12:17:34 (Show Source): You can put this solution on YOUR website!What does radius mean? The distance from the center of a circle to every point on the circle. What does diameter mean? A line segment that connects two points on a circle and passes through the center of the circle. So, the end points of a diameter are both on the circle and they are on the opposite each other on the circle. (directly across the circle). Thus d = 2r
 logarithm/135059: express the following as a single logarithm: 1/4loga(x) – 3loga(y) – 2loga(z) Note: the a's are subscripts I am homeschooling my 9th grade son; this problem is on a test, and we are questioning the solution given. Thanks, Beth.1 solutions Answer 98889 by vleith(2825)   on 2008-04-03 12:14:05 (Show Source): You can put this solution on YOUR website!Beth, i don' claim to be a guru at logs, but here is what I get. Compare that to your book and please let me know what it says . Does that agree with your book?
 Miscellaneous_Word_Problems/135060: The value in the table are generated by a rule of the form a = bc + d where b and d are constant. Find a when c = 19. c --->1 2 3 . . .19 a ---> 8 11 14 . . . Any help you can provide would be great. Thanks.1 solutions Answer 98886 by vleith(2825)   on 2008-04-03 12:03:46 (Show Source): You can put this solution on YOUR website!There a several ways to do this one. The form "" a = bc + d where b and d are constant" is just a line (the familiar y = mx + b). So you could figure out a slope and then do some math to get to the intercept. But let's look at this as a logic problem and find some patterns. Every increase of 'c' by 1, results in an increase of 'a' by 3. You can see that by finding the difference between each successive value in the series of 'c' and 'a' numbers. So that means . Now instead of moving up the 'a' and 'c' series, move back one. Decrease 'c' by 1 (1-1) and get 0. Decrease 'a' by 3 (8-3) and get 5. So when c = 0, a = 5. = Which means Now plug in b and d What is 'a' when 'c' = 19? I leave that to you :-D
 Inequalities/135058: what are the rules for solving inequalities? Please tell me.1 solutions Answer 98884 by vleith(2825)   on 2008-04-03 11:53:20 (Show Source): You can put this solution on YOUR website!The 'rules' are the same as solving equalities with a couple extras. 1)The main difference is that whenever you multiply or divide by a negative number, then the sign of the equality 'flips'. That is, a 'less than' becomes a 'greater than' and vice-versa. 2)Another thing that you need to look out for is: If the inequality is 'absolute' (that is, greater or less, not greater/equal to or less/equal to), then when you plot your answers, make sure to use a dashed line instead of a solid one. Then shade the portion of the graph that is your solution set.
 Miscellaneous_Word_Problems/135054: My question is: If 2 cats can catch 2 mice in 2 days, how many mice can 20 cats catch in 10 days? Thanks for your help.1 solutions Answer 98883 by vleith(2825)   on 2008-04-03 11:29:53 (Show Source): You can put this solution on YOUR website!2 cat, 2 mice, 2 days yields one mouse/cat/per day If you have 20 cats, and 10 days, then you'll get = mice in that period. That's a lot of mice. yikes!
 Linear-systems/135052: This question is from textbook Algebra 1 workbook How do I translate to a system of equations and solve? A collection of nickels and dimes is worth \$16.05. There are 218 coins in all. How many are nickels and how many are dimes? 1 solutions Answer 98882 by vleith(2825)   on 2008-04-03 11:25:27 (Show Source): You can put this solution on YOUR website!Let d be the number of dimes. Let n be the number of nickels. Given: total number of coins = 218 = number of dimes + number of nickels => total value of coins = 16.05 = 0.10d + 0.05n (multiply the value of each coin by the number and then add the totla for both types of coins) --> lets convert from dollars to pennies to make things easier (we just multiplied the eqaution above by 10) You now have 2 equations and 2 unknowns, so you can solve this. You have 115 nickles. 218-115 = 103 dimes Check your answer 10.30 in dimes + 5.75 in nickels = \$16.05. check!
 Coordinate-system/135053: solve graphicaly each of the following systems x-y=4 x+y=161 solutions Answer 98881 by vleith(2825)   on 2008-04-03 11:16:10 (Show Source):
 Linear_Equations_And_Systems_Word_Problems/135044: This question is from textbook Essentials of Elementary Algebra I am hoping you could help me with a problem I have with solving application problems using two variables with linear systems. A whale swimming against an ocean current traveled 60 miles in 2 hours. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 1.5 hours. Find the speed of the whale in calm water and the rate of the ocean current. I know the answer is the rate of the whale in calm water is 35mph. The rate of the current is 5mph. (From out of the book.) However, I not sure how to do the equations in order to get those answers. I think its something like: 2=60+x 1.5=60-x Thank you so much for trying to help me!1 solutions Answer 98876 by vleith(2825)   on 2008-04-03 10:51:43 (Show Source): You can put this solution on YOUR website!You're on the right track. But you need to establish the relationship between distance, time and speed. The distance the whale swims is the same going both directions. The rate changes based on swimming with or against the current Let the calmspeed = x and the current =y RateWith = calmSpeed+Current = x+y RateAgainst = calmSpeed-Current = x-y So with current against current So remember this for later use the value for x we found above to get x = 30+5 = 35
 Exponential-and-logarithmic-functions/135047: Solve the equation. 3^x=101 solutions Answer 98875 by vleith(2825)   on 2008-04-03 10:36:33 (Show Source): You can put this solution on YOUR website!Given : Check your answer. Does 3^2.0964 = 10???
 Polynomials-and-rational-expressions/135040: Find the LCD: x^3 over x^2+8x+16 times 3x-10 over x^2+x-121 solutions Answer 98874 by vleith(2825)   on 2008-04-03 10:25:48 (Show Source): You can put this solution on YOUR website!Given: So the LCD will be
 Quadratic_Equations/135036: Hello, tutors my homework assignment question is for college algebra. Response to the following: Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer? Why?) Thanks inadvance for your great work and assitance. Roosevelt1 solutions Answer 98873 by vleith(2825)   on 2008-04-03 10:15:12 (Show Source): You can put this solution on YOUR website!Great question. Some folks are more 'visual' than others. Folks that need to see things do well with graphical representations. Also, students with a bent toward geometry like graph. Graph are also a great way to link algebra with geometry. The quadratic equation will 'always get you an answer if there is one'. But it requires more arithmetic and, IMHO, presupposes that the user understands complex numbers -- since the question of 'what happens when the determinant is negative' is almost certain to be raised. On the other hand, the quadratic equation is easily programmed, so it is a great tool for computer solutions (and also more sophisticated calculators). Completing the square is an 'OK tool'. But fact is, once one uses it to prove the quadratic equation, I have found few places (outside of problems that specifically state one must use completing the square) where I actually used that method. Factoring is handy when the the equation are 'fairly simple'. Factoring is very important when polynomial division/multiplication is part of the problem. Plus, factoring is fun and helps students connect algebra to the underlying properties that also apply to arithmetic and also, later on, to more sophisticated algebras. If you get other responses, can you do me the favor of compiling them and sending the merged ideas to me? I am interested in what others might think.
 decimal-numbers/135027: Tutor I am trying to learn how to do scientific notations: Could you help me please? (4.2*10^-2) (3.5*10^8) would this be 4,200,000,000 times 3,500,000, how would I compute this and write it in scientific notation? also 4.2*10^-6/7*10^8 4.2.10^-6/7.10^8 I don't know how to do this one or where do I start? Karen thank you for your help!!!1 solutions Answer 98872 by vleith(2825)   on 2008-04-03 09:27:33 (Show Source): You can put this solution on YOUR website!Given : (4.2*10^-2) (3.5*10^8) = Think of it this way. = 1 10^1 = 10 10^2 = 100 10^-1 = 0.1 10^-2 = 0.01 You can see that each number has the decimal point moved. For positive numbers, the decimal point moves one place to the right with each increase of 1. With negative numbers, the decimal moves one place to left with each decrease of 1. For scientific notation, the "number part" is always between 1 and 10. So is already in scientific notation. So is Use the same technique to solve the second one. Ping me if you can't get it The value of is 0.042 (decimal moved two place to the left. The value for is 350,000,000 (deicmal 8 place to the right) To multiply the numbers, use the scientific notation form. You are almost there now. The only thing left to do is make the 'number part' be between 1 and 10. Use the same technique for the second one. Just remember that when you divide, that is the same as subtracting exponents. Ping me by email if you can't get it.
 Average/135028: you are deciding between two cars with different engines and want the bigger of the two. One engine displaces 350 cubic inches. The other displaces 5,500 cubic centimeters. By how many cubic centimeters is the bigger engine larger than the smaller one?1 solutions Answer 98871 by vleith(2825)   on 2008-04-03 09:12:12 (Show Source): You can put this solution on YOUR website!2.54cm = 1 inch = To convert 350 inch^3 into cm^3
 Unit_Conversion_Word_Problems/134972: you are riding home from a party and the driver has been drinking. The car is traveling at 60 miles per hour. suddenly a child steps into the road ahead. because the driver has been drinking his reaction time has been slowed by one second. how far towards the impending accident will the car travel before the driver begins to stops? (note: This is equal the extra distance it will take to stop the car becuase the driver has been drinking1 solutions Answer 98834 by vleith(2825)   on 2008-04-02 20:57:12 (Show Source): You can put this solution on YOUR website!Let's get the answer in feet Thats a long way. So don't EVER drink and drive or ride in a car with someone who has been drinking. Also notice how the "units" in the problem canceled out. Many times, units (feet, hour, miles, etc) can help you validate if an answer is correct or not. If the units endup being something that doesn't "make sense", then it is likely you did something wrong along the way.
 Circles/134978: A circle has a radius of 20cm and two chords measuring 15cm each, how far apart are the chords? I think the answer is 37.1cm:)1 solutions Answer 98831 by vleith(2825)   on 2008-04-02 20:50:42 (Show Source): You can put this solution on YOUR website!I get 37.08 - so you are correct
 Circles/134976: On a coordinate plane P(0,4a) and Q(3a,0) are the endpoints of a diameter of a circle. What is the radius of the circle?1 solutions Answer 98830 by vleith(2825)   on 2008-04-02 20:48:03 (Show Source): You can put this solution on YOUR website!You are given two points. The distance between two points is given as: distance = 5a
 Quadratic_Equations/134974: Given A(-4,6), B(-1,2),C(x,14) and D(5,10). If AB is parallel to CD, find the value of x.1 solutions Answer 98828 by vleith(2825)   on 2008-04-02 20:41:06 (Show Source): You can put this solution on YOUR website!Parallel lines have the same slope. The slope of AB = = The slope of CD = =
 Circles/134971: A circle has a diameter of 20cm.A chord is 6cm from the center of the circle. How long is the chord?1 solutions Answer 98826 by vleith(2825)   on 2008-04-02 20:38:07 (Show Source): You can put this solution on YOUR website!Use the Pythagorean theorem in this case, c=10 (the radius), a = 6 so solve for b You can see this is a 3:4:5 triangle. So b = 8 The chord will be 8+8 = 16
 Polynomials-and-rational-expressions/134968: We are having trouble factoring on this problem: 12y^2-24y-72 We took out the 12 and got 12(y^2-2y-6) We can't think of any factors of -6 that would give a -2. Is there a solution, or do you think it was typed incorrectly on the worksheet? Thank you! PS. This didn't come from a textbook, but from a teacher-created worksheet.1 solutions Answer 98824 by vleith(2825)   on 2008-04-02 20:34:12 (Show Source): You can put this solution on YOUR website!Use the quadratic formula. a =1, b = -2, c =-6
 Linear-systems/134936: This question is from textbook algebra 2 Could you please help with the following problem. It needs to be solved using the elimination method. The answer that I calculated is not what the book shows. Thanks. x^2+y^2=16 4x^2-9y^2=36 The answer must be in square root format (different form what the book asks for)1 solutions Answer 98796 by vleith(2825)   on 2008-04-02 19:11:13 (Show Source): You can put this solution on YOUR website!Given : Add these two
 Systems-of-equations/134935: This question is from textbook algebra 2 I need help with the following question. The problem needs to be solved using subsitution. The answer that I got does not agree with the answer in the book. y=x^2 x^2+y^2=1 1 solutions Answer 98794 by vleith(2825)   on 2008-04-02 18:58:37 (Show Source): You can put this solution on YOUR website!Given : Use the quadratic equation
 Polynomials-and-rational-expressions/134931: Under what situation would one or more solutions of a rational equation be unacceptable?1 solutions Answer 98792 by vleith(2825)   on 2008-04-02 18:49:01 (Show Source): You can put this solution on YOUR website!This applies often to problems in physics -- and in real life. So let's say an expression is given as the model for something based in time. Example, the trajectory of a batted ball. If the question asked "when will the ball hit the ground?" and one of the answer is -5 seconds. An answer that happens 'before the ball is hit', is a solution that is unacceptable.
 Linear-systems/134930: Are all linear equation functions? Is there an instance when a linear equation is not a function? Can you give an example of and nonlinear equation?1 solutions Answer 98791 by vleith(2825)   on 2008-04-02 18:36:52 (Show Source): You can put this solution on YOUR website!Use the "vertical line" rule to help decide if an expression is a function. If a vertical line intersects the graph of an expression in more than one point, then that expression is NOT a function. Now to your questions ; Are all linear equation functions? No. Is there an instance when a linear equation is not a function? Yes, a vertical line is linear, but fails the vertical line test. Can you give an example of and nonlinear equation? A parabola is an example of a non linear equation y = x^2
 Average/134928: Find the sum of the measures of the interior angles of a convex polygon with the given number of sides. Number of sides --> 6 Help with this equation would be appreciated.1 solutions Answer 98788 by vleith(2825)   on 2008-04-02 18:25:02 (Show Source): You can put this solution on YOUR website!The sum of interior angles of a polynomial is given by See http://www.geom.uiuc.edu/~dwiggins/conj07.html for a nice description and an example using 6 sides polynomial
 Quadratic_Equations/134922: Graph the equation y=8 Help please.1 solutions Answer 98784 by vleith(2825)   on 2008-04-02 18:02:31 (Show Source): You can put this solution on YOUR website!This is a line where every point on the line has a y coordinate of 8. x can be anything, but y is always 8. So it is a horizontal line that goes through point (0,8)
 Polynomials-and-rational-expressions/134919: factor this problem 2ax+bx-6ay-3by-bz-2az1 solutions Answer 98781 by vleith(2825)   on 2008-04-02 17:59:52 (Show Source): You can put this solution on YOUR website!Given :
 Miscellaneous_Word_Problems/134918: I have been given this problem for extra credit could someone please help with the solution. There are 100 open lockers. There are 100 students. (Note definition- Status change: If a locker is closed it becomes open or if the locker is open it becomes closed). The first student changes the status of all the lockers (Student closes 100 lockers). The second student changes the status of every two lockers (lockers 2,4,6,8...100 are opened). The third studen changes the status to every third locker (the status of lockers 3,6,9,12....99 are changed). This process is repeated until all 100 students have had their turn at changing the status of their locker(s). Question: What lockers are left closed? 1 solutions Answer 98778 by vleith(2825)   on 2008-04-02 17:53:01 (Show Source): You can put this solution on YOUR website!For problems like these, it is often helpful to scale small and look for patterns I suggest you work the problem with only 10 lockers and 10 students, and then with 20 and 20. Pay attention to the pattern you see. If you still can't figure it out, send me an email and I'll give you a hint.
 Polynomials-and-rational-expressions/134915: Last one. I love this to check my anwsers. Divide and express in standard form. 6-5i/8+4i Thank you all so much1 solutions Answer 98775 by vleith(2825)   on 2008-04-02 17:45:26 (Show Source): You can put this solution on YOUR website!Given:
 Polynomials-and-rational-expressions/134910: Need Help Factoring This Trinomial. a^2+2ab-3b^21 solutions Answer 98770 by vleith(2825)   on 2008-04-02 17:37:35 (Show Source): You can put this solution on YOUR website!given : On this type of problem, since the coefficient for the a^2 term is 1, you are looking for factors of 3 that sum to 2. The factors of 3 are 1 and 3. 3-1 equal 2. Make sense?