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# Recent problems solved by 'vleith'

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 Word_Problems_With_Coins/214061: Tabitha has \$3.20 in quarters and nickels. If she has 20 coins in all, how many quarters does she have?1 solutions Answer 161683 by vleith(2825)   on 2009-09-16 07:16:59 (Show Source): You can put this solution on YOUR website!Let q be the number of quaters and n be the number of nickles You are told that You are also told that You have two equations and 2 unknows, so you can solve this one. Check your answer Is there are 11 quarters, then there must be 9 nickels (11+9 = 20) Is ????
 Graphs/213221: This question is from textbook algebra1 {(-2,-4),(-1,-1),(0,0)(1,-1),(2,-4)} it ask to express each relation as a table, as a graph, and as a mapping diagram. I don't know how to do that like what exactly do you do1 solutions Answer 161080 by vleith(2825)   on 2009-09-13 15:09:55 (Show Source): You can put this solution on YOUR website!1)As a table, make a table with 2 columns and 5 rows. Label the first column "x" and the second column "y". Then use the coordinates of the given points to fill in the table. row 1 has -2 -4 row 2 has -1 -1 and so on 2) As a graph, lay down a standard Cartesian grid (like graph paper). Then plot the 5 given points. If you see a "curve" in thyat data, then sketch in the curve 3) As mapping diagram, draw an ellipse shaped like a "0", leave an inch of two of space and then draw a second one to the right of the first (same shape, same size). Put all of the x values in the left ellipse (see column one from the table in part 1). Put all the y values in the right ellipse (see column two from the table above). Now connect the x values in the left ellipse with the corresponding y values in the roght ellipse. Just draw a line from one to the other. That is the "map" See this URL for an example --> http://img.sparknotes.com/figures/4/4d7924c96427a340a0f1be4c7e650f7c/mapping.gif
 Functions/212978: given the function defined by y=-7x^2+3x-8 determine whether function opens upward or downward1 solutions Answer 160885 by vleith(2825)   on 2009-09-12 13:14:20 (Show Source): You can put this solution on YOUR website!downward, the high order coeefficient (-7 on the x^2 term) is negative. So it must open down. See this URL for a plot --> http://www.wolframalpha.com/input/?i=-7x^2%2B3x-8
Triangles/212968: The hypotenuse of a right triangle is twice as long as one of the legs and 4 inches longer than the other. What are the lengths of the sides of the triangle?
1 solutions

Answer 160883 by vleith(2825)   on 2009-09-12 13:12:47 (Show Source):
You can put this solution on YOUR website!
Let h be the length of the hypotenuse. Then one side is h/2 and the third side is h-4.
Since it is a right triangle, you know that

Use the quadratic equation to solve
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=768 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 29.856406460551, 2.14359353944898. Here's your graph:

Since one of the answer is too short to make that number -4 positive, the hypotenuse is ~29.85

 Graphs/212970: sketch the graph of the function y= x^2+12y-361 solutions Answer 160881 by vleith(2825)   on 2009-09-12 13:04:18 (Show Source): You can put this solution on YOUR website! Pick some values for x, and then solve for y. Plot those points and draw the curve. Use this URL to check your answer http://www.wolframalpha.com/input/?i=(36-x^2)%2F11
 Polynomials-and-rational-expressions/212967: find the domain s(x)=x-2/x+101 solutions Answer 160879 by vleith(2825)   on 2009-09-12 13:01:06 (Show Source): You can put this solution on YOUR website!The denominator of any "fraction" cannot be 0. So the only value of x that is not in the domain is x=-10, since it makes the denominator 0. domain - all x except x=-10 [infinity,-10) (-10, infinity]
 Expressions-with-variables/212860: How do I find the solution to this input output problem? E P 1 3 2 5 3 9 4 17 5 33 1 solutions Answer 160840 by vleith(2825)   on 2009-09-12 07:06:01 (Show Source): You can put this solution on YOUR website!Most of these type problems are practice. I like to start by looking at the series of numbers. You can see the difference in the inputs goes up by 1 one each entry. Now look and see if you can find a pattern in the output numbers. You can see they are getting larger by increasingly larger amounts. However, nothing obvious jumps out a bout their values. So, the first thing I like to try is to see if there are patterns in the series of outputs. For instance, perhaps every other number has an obvious pattern. One thing I always try is finding the difference between each successive output number. difference between 5 and 3 = 2 difference between 9 and 5 = 4 difference between 17 and 9 = 8 do you see the pattern yet difference between 33 and 17 = 16 So each output increases by a value that is power of 2. Now all that is left to figure out is what the 'starting' value is. A little trail and error will show you that value is 1. So, the function that fits the given data points is x>=1
 Permutations/212781: How many different ways can 9 letters be grouped without any letter being repeated?1 solutions Answer 160711 by vleith(2825)   on 2009-09-11 13:33:13 (Show Source): You can put this solution on YOUR website!Assuming english alphabet and lower case and upper case count as one, then you have 26 letters. So how many ways can you use 9 different letters? First letter can be anyone of the 26. The second one can't duplicate the first, so there are 25 you could choose then 24, 23, 22, 21 ...
 Equations/212729: The density of concentrated sulfuric acid is 1.85g/ml. What volume of the acid would weigh 74.0g?1 solutions Answer 160660 by vleith(2825)   on 2009-09-11 10:03:38 (Show Source):
 Linear-systems/212630: 6x=2x-11 dont understand how to solve!1 solutions Answer 160556 by vleith(2825)   on 2009-09-10 20:25:46 (Show Source): You can put this solution on YOUR website! you need to 'get the terms with x on one side and the constant on the other' So subtract 2x from both sides you know that 2x-2x = 0 divide both sides by 4 you know that 4/4 = 1
 Polynomials-and-rational-expressions/212640: I need help with the problem x^3+5x^2/2x^2+9x-5. I have to express the following rational expressions in lowest terms.1 solutions Answer 160553 by vleith(2825)   on 2009-09-10 20:22:26 (Show Source): You can put this solution on YOUR website!use this URL to check factoring work --. http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic
 Expressions-with-variables/212639: what's the expression for the pattern 10+1, 10+2, 10+3....1 solutions Answer 160552 by vleith(2825)   on 2009-09-10 20:19:55 (Show Source): You can put this solution on YOUR website!f(x) = 10 + x; where x is an natural number (an integer greater than 0)
 Linear-equations/212637: Could someone help me solve the problem 8y-(5y+2)=16?1 solutions Answer 160550 by vleith(2825)   on 2009-09-10 20:18:51 (Show Source): You can put this solution on YOUR website! distribute the (-1) across the term (5y+2) and remove the parens simplify add 2 to each side divide both sides by 3
 Equations/212636: 13-8v=5v+21 solutions Answer 160549 by vleith(2825)   on 2009-09-10 20:16:34 (Show Source): You can put this solution on YOUR website! collect like terms. subtract 2 from each side add 8v to each side divide both sides by 13
 Geometry_proofs/212632: This question is from textbook If ray AB and ray CD intersect, then segment AB and segment CD intersect. How is this statement false?1 solutions Answer 160547 by vleith(2825)   on 2009-09-10 20:14:28 (Show Source): You can put this solution on YOUR website!the two rays could intersect at a point that is not on segment AB or segment CD or both. Net, the rays 'go on forever', so there are lots of points where the two culd intersect and not be on the segments
 Proportions/212495: a 6-foot tall man is standing near a tree on level ground, and the mans shadow is 4feet long, how many feet tall is the tree.(the tree is 18 feet_1 solutions Answer 160462 by vleith(2825)   on 2009-09-10 14:41:35 (Show Source): You can put this solution on YOUR website!I assume the tree shadow is 18 feet. use ratios
 Triangles/212421: A certain triangle has area 6 cm^2. If you know that its base is one less than it height, what are the base and height of the triangle?1 solutions Answer 160415 by vleith(2825)   on 2009-09-10 09:38:53 (Show Source): You can put this solution on YOUR website! Let the height be represented by h. You are told the base, b, is So h is either 4 or -3 Since the height can't be negative, it must be 4 Which makes the base Check your answer, is the area of a triangle with a base of 3 and a height of 4 equal to 6???
 Vectors/212412: please could someone help me with this question? A tea connoisseur has a collection of teapots that are scaled versions of the same design. The one-cup teapot is 10cm high. Choose the TWO options that are true statements. A The two-cup teapot is 20cm high B The eight-cup teapot is 20cm high. C The nine-cup teapot is 30cm high. D The 25cm high teapot is appropriate to make 20 cups of tea. E The 16cm teapot is appropriate to make 4 cups of tea. Thank you very much Dawn1 solutions Answer 160411 by vleith(2825)   on 2009-09-10 09:15:32 (Show Source): You can put this solution on YOUR website!The amount of tea is a volume. So, in order to scale, each of three dimensions must scale in the same ratio as the single dimension you are given. All that ends up saying is "the change in volume is the cube of the change in a single dimension". For instance, if the pot is changed from 10cm to 20cm, then the scale has doubled. So you need to cube that to get the volume. Thus, a 20cm high pot will brew = cups. A 30cm high pot will brew cups Do that same type of conversion and you can find the two answers that "fit". If you can't get them, let me know.
 Numeric_Fractions/212109: This question is from textbook Elementary and Intermediate Algebra, Chapter According to Dr. Aaron R. Folsom of the University of Minnesota School of Public Health, your maximum ideal waist size is directly proportional to your hip size. For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips?1 solutions Answer 160193 by vleith(2825)   on 2009-09-09 08:59:02 (Show Source): You can put this solution on YOUR website! So, the equation is Substitute in a 35 inch hip and solve
 Human-and-algebraic-language/212113: YOU PAY A TOLL IN EITHER ALL QUARTERS OR ALL DIMES. THE TOLL IS 3 MORE DIMES THAN QUARTERS. WHAT IS THE TOLL?1 solutions Answer 160191 by vleith(2825)   on 2009-09-09 08:54:52 (Show Source): You can put this solution on YOUR website! Either 2 quarters of 5 dimes. Either way, the toll is \$0.50
 Polynomials-and-rational-expressions/212112: Please I need help with please! 1. √65+√21= 2.square root of 2 + square root of 18 = 3. sqrt(50) - sqrt(2)1 solutions Answer 160190 by vleith(2825)   on 2009-09-09 08:52:16 (Show Source): You can put this solution on YOUR website!1) since 65 is 5*13 and 21 is 3*7, you can't simplify this one without converting to estimates 2) 3)
 Triangles/212114: A segment is divided into two parts having lengths in the ratio of 5:3. If the difference between the length of the parts is 6," find the length of each part. x = Segment 1 = (5x) = inches Segment 2 = (3x) = inches 1 solutions Answer 160188 by vleith(2825)   on 2009-09-09 08:47:36 (Show Source): You can put this solution on YOUR website!The difference in their lengths is So Now that you know x, finding 5x and 3x is a dropkick.
 Travel_Word_Problems/211588: A man rides out into the country at a uniform rate of 30 miles per hour. He rests 2 hours and then rides back at 20 miles per hour. He is gone 5 hours. How far did he go? Please work me through this problem! Thanks!1 solutions Answer 159874 by vleith(2825)   on 2009-09-07 16:40:51 (Show Source): You can put this solution on YOUR website!First thing, let's get rid of the 2 rest hours. That says the the man is actually moving for 3 hours. You also know he goes as far at 30mph as he returns at 20mph. Let the distance he goes each way be represented by d Let the time at 30mph be given by t. Then the time at 20mph is so So the man travels at 30mph for 6/5 hour = miles Check your answer. Does
 Travel_Word_Problems/211587: This question is from textbook Can you please help me with this uniform motion problem? If the speed were increased by 10mph, a 420 mile trip would take 1 hr less time. How long will the trip take at the slower speed? Please show me all the steps and please get back to me before Tues. 10am. Thank you guys1 solutions Answer 159871 by vleith(2825)   on 2009-09-07 16:33:51 (Show Source): You can put this solution on YOUR website! You are told the distance is 420 miles. Let the slow speed be represented by s (in miles per hours) and the slow time be represented by t (in hours) So Thus You are told that at , the time will be So Now substitute in the value you found for s above factor this or use the quadratic equation For a product to equal 0, one or more of the terms multiplied must be 0. So either ot that means either or since the time cannot be negative, the time at the slow speed must be 7 hours. Now check your answers. If the time is 7 hours then the slow speed must be 60mph If the speed if 10mph faster, then the faster speed is 70mph. At 70mph, the time is 420/70 = 6 hours. Which is an hour faster. So there you have it. happy Labor day -- and still int time for 10am tomorrow
 Age_Word_Problems/211116: Carl is a years old. His sister Jenny is six more than twice his age. What is the average of their ages?1 solutions Answer 159500 by vleith(2825)   on 2009-09-05 12:46:06 (Show Source): You can put this solution on YOUR website!Carl is Jenny is To find an average, add all the elements and divde that total by the number of elements.
 Equations/210732: What does it mean, both algebraically and graphically, when an ordered pair (x,y) is a solution to a system of two linear equations? 1 solutions Answer 159196 by vleith(2825)   on 2009-09-03 12:38:40 (Show Source): You can put this solution on YOUR website!algebraically, it means that point is a solution to each equation graphically, the point is the intersection of the two lines (assuming the lines are not 'the same line' or parallel lines, then they only intersect at a single point)
 Equations/210735: After solving a system of equations in two variables you surmise a solution, (x,y). How can you determine if the solution is correct? 1 solutions Answer 159192 by vleith(2825)   on 2009-09-03 12:35:21 (Show Source): You can put this solution on YOUR website!Plug the x and y values into the original equation(s). If the result ends up being = (like 10=10 or 153=153) then the solution is correct