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# Recent problems solved by 'josmiceli'

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 Polynomials-and-rational-expressions/186809: There is a sales tax of \$12 on an item that costs \$147 before tax. A second item costs \$134.75 before tax. What is the sales tax on the second item?1 solutions Answer 140035 by josmiceli(9698)   on 2009-03-15 19:28:13 (Show Source): You can put this solution on YOUR website!What is needed is the rate at which items are taxed tax/before tax price = rate The tax is \$11
 Square-cubic-other-roots/186788: Ok I got another question; why doesnt sqrt(5)+1 over sqrt(5)-1= 2+sqrt(5) over 2??1 solutions Answer 140012 by josmiceli(9698)   on 2009-03-15 15:48:51 (Show Source): You can put this solution on YOUR website!Your answer is close Multiply top and bottom by answer You can check the answer by setting it equal to the original expression and do the algebra to see if it's true
 Sequences-and-series/186780: Deanna received an e-mail asking her to forward it to 10 other people. Assume that no one breaks the chain and that there are no duplicate recipients. How many e-mails will have been sent after 8 generations, including Deanna's? Could you do this problem? Thank you for your help.1 solutions Answer 140003 by josmiceli(9698)   on 2009-03-15 15:16:14 (Show Source): You can put this solution on YOUR website!The problem says that the 1st generation of e-mail senders is Deanna, who receives one sends emails to 10 other people So far I have: generation# --- emails sent --- 1 --------------1 --- 2 --------------10 So far, 11 people have gotten emails Now each of the 10 people send 10 emails and So far I have: generation# --- emails sent --- 1 --------------1 --- 2 --------------10 --- 3 --------------100 So far 111 people have gotten emails Now, there are 100 people who are going to send emails to 10 other people. So far I have: generation# --- emails sent --- 1 --------------1 --- 2 --------------10 --- 3 --------------100 --- 4 --------------1000 So far, 1111 people have gotten emails If I carry this process to 8 generations, the 8th is: generation# --- emails sent --- 8 --------------10000000 and the total number of people who have gotten emails is 11,111,111
 Equations/186634: This question is from textbook mathematical analysis a new television depreciates \$120 per year, and it is worth \$340 after four years. find a function that describes the value of this television, if x is the age of the television in years. In full details please, thank you1 solutions Answer 139924 by josmiceli(9698)   on 2009-03-14 17:30:55 (Show Source): You can put this solution on YOUR website!Let = the original value of the TV given: = depreciation/1 year You have to understand that depreciation is what the TV loses in value each year, so every year it's worth less, and then it gets depreciated again ------------------------------------------ is the value of the TV after 1 year is the value of the TV after 2 years is the value of the TV after 3 years is the value of the TV after 4 years The problem says the TV is worth \$340 after 4 years, so So, the TV was originally worth \$820 ------------------------------------ Now I need to write a function that tells me the value of the TV for any given year If is the year after purchase, and is the value of the TV that year A quick check is: What is the TV worth after 4 years? That's what it should be
 Distributive-associative-commutative-properties/186662: This question is from textbook Algebra 1 I need help understanding how to find the greatest common factor and factoring it out of a equation. e.x. 6y^4 + 14y^3 - 10y^21 solutions Answer 139923 by josmiceli(9698)   on 2009-03-14 17:07:48 (Show Source): You can put this solution on YOUR website!The limitation on picking out a common factor is lowest power of a symbol (x,y z, etc), or it must be the greatest common divisor of the numbers that are common to each term The common symbols are: , , and The lowest power is , so I can factor out For the numbers, the greatest common divisor is so I can factor out a
 Geometry_Word_Problems/186614: How many different triangles can have sides of length 8 and 11 if the third side must have a length which is an integer?1 solutions Answer 139888 by josmiceli(9698)   on 2009-03-14 07:47:37 (Show Source): You can put this solution on YOUR website!If I lay the side down flat, I see that sides equal to and will add up to the side, and will not be a triangle, So I must go higher than for the 3rd side I can have: and and and and (this is isosceles) and and . . . and The next one, and is like the and , because it lays down flat on top of the side, because so, the possible integer sides for the 3rd side are: 4 through 18.
 Equations/186625: This question is from textbook mathematical analysis passing through (-7,-5) and parallel to the line 3x+3y+6=0 please with full steps, thank you 1 solutions Answer 139886 by josmiceli(9698)   on 2009-03-14 07:32:34 (Show Source): You can put this solution on YOUR website!First, I'll find the slope of This is in the form where = slope, and Any line parallel to this one will also have The point-slope formula is I'm given (-7,-5), so Multiply both sides by Add to both sides answer check answer Does it go through (-7,-5)? OK
 Age_Word_Problems/186598: This question is from textbook Algebra Structure and Method Book I A man is three times as old as his son was at the time when the father was twice as old as the son will be in two years from now. Find the present age of each person if the sum of their ages is fifty-five years.1 solutions Answer 139880 by josmiceli(9698)   on 2009-03-14 00:27:19 (Show Source): You can put this solution on YOUR website!Let = Father's age now Let = Son's age now given: The Son's age in 2 years is When the Father was twice as old as the Son will be in two years is How old was the Son then? The difference in their ages is a constant The Father's present age is three time the Son's at that time (1) also, (2) (3) Substitute (3) in (1) (1) (1) (1) Multiply both sides of (2) by and subtract (1) from (2) (2) (1) (3) (3) and, since (2) (2) (2) The father is 39 now, and the Son is 16 ---------------------------------------- check answer: The Son's age in 2 years is When the Father was twice as old as the Son will be in two years is How old was the Son then? The difference in their ages is a constant The Father's present age is three time the Son's at that time (1) (1) (1) (1) (1) (1) and (3) (3) OK
 logarithm/186597: Hi guys, im stumped with this one: 2ln2 - ln(x-1) = ln(2x) solve for 'x'. cheers =)1 solutions Answer 139860 by josmiceli(9698)   on 2009-03-13 20:10:52 (Show Source): You can put this solution on YOUR website!In general: and check: OK The negative root doesn't work since raising to a power can't result in a negative
 Length-and-distance/186465: Two perpendicular lines intersect at point (9,2). If the x-intercept of one line is double the x-intercept of the other, find the possible sum(s) of these x- intercepts. 1 solutions Answer 139827 by josmiceli(9698)   on 2009-03-13 15:25:01 (Show Source): You can put this solution on YOUR website!One line would be The other line would be and are the y-intercepts ------------------------ Let the x-intercepts be and at the x-intercepts, so and and and Substituting: this is the answer Suppose the slopes of the lines are and the solution is (9,2) the equations are: 1st equation and 2nd equation Setting in both will find the x-intercepts and and Multiply both sides by OK
 Exponential-and-logarithmic-functions/186562: This question is from textbook The problem directions state: Solve the equation. Check for extraneous solutions. 49.) 2ln(-x)+7= 14 I understand you remove 7 from both sides, but I am wondering how I change this particular problem into exponential form and what is the set-up for exponential form! Thanks!1 solutions Answer 139818 by josmiceli(9698)   on 2009-03-13 12:05:56 (Show Source): You can put this solution on YOUR website! Subtract from both sides First of all, any number raised to any power cannot be negative, so By my calculator,
 Length-and-distance/186467: A straight line is drawn through the point (3,4). the line cuts the axes at the points A and B such that the area of the triangle OAB is 24. Find the x-intercepts of all such lines1 solutions Answer 139784 by josmiceli(9698)   on 2009-03-13 04:51:04 (Show Source): You can put this solution on YOUR website!Call the x-intercept Call the y-intercept Call the slope and The general equation is and goes through (3,4) and is the y-intercept The x-intercept is answer and check: The general equation is: does it go through (3,4)? OK
 Quadratic_Equations/186482: What is the answer to f(x) = -3x21 solutions Answer 139783 by josmiceli(9698)   on 2009-03-13 04:09:26 (Show Source): You can put this solution on YOUR website!What is the question?
 Equations/186495: Hello. I'm needing some help with checking what I did wrong on this problem: Perform the indicated operation and simplify (s+t)(s^2-st+t^2) thanks!1 solutions Answer 139779 by josmiceli(9698)   on 2009-03-13 00:47:56 (Show Source): You can put this solution on YOUR website! answer
 Quadratic_Equations/186469: A fraternity charters a bus for a ski trip at a cost of \$360. When 6 more students join the trip, each person's cost decreases by \$2. How many students were in the original group of ravelers?1 solutions Answer 139741 by josmiceli(9698)   on 2009-03-12 17:44:45 (Show Source): You can put this solution on YOUR website!Let = number of student in original group Let = the original cost per person given: (1) (2) (2) Substitute (1) in (2) (2) (2) (2) Substitute this in (1) (1) (1) (1) Use quadratic formula There were 30 students in the original group check: (1) (1) (1) and (2) (2) (2) (2) OK
 Exponents/186458: Could someone help me with this problem: (2/3)^-2(4/5)^-1 I am suppose to write it in simplest form without negative exponents. I am usually good in algebra but since I got a new math teacher I feel I dont grasp anything anymore :( 1 solutions Answer 139740 by josmiceli(9698)   on 2009-03-12 17:23:52 (Show Source): You can put this solution on YOUR website! If you don't get negative exponents, just think of them like this: 10^4 = 10000 10^3 = 1000 10^2 = 100 10^1 = 10 10^0 = 1 10^-1 = .1 10^-2 = .01 10^-3 = .001 10^-4 = .0001 In general, Now you just invert each fraction answer
 Systems-of-equations/186409: y=3x and x + y=2 answer: 1/2, 3/2 wanted to know how my book got these fractions as answer need full break down 1 solutions Answer 139711 by josmiceli(9698)   on 2009-03-12 11:28:03 (Show Source): You can put this solution on YOUR website!(1) and (2) There are 2 equations and 2 unknowns. Whenever the number of unknowns matches the number of equations, then a solution is possible. First, subtract from both sides of (1) (1) (1) Now simply add (1) and (2) (1) (2) (3) (3) To find , substitute in (1) (1) (1) (1) The solution is and
 Travel_Word_Problems/186407: From a point on a straight road, john and fred ride bicycles in opposite directions. john rides 5 miles per hour and fred rides 14 miles per hour. in how many hours will they be 57 miles apart?1 solutions Answer 139709 by josmiceli(9698)   on 2009-03-12 11:18:21 (Show Source): You can put this solution on YOUR website!They are driving away from eachother at a combined speed of mi/hr They will be 57 mi from eachother in 3 hrs
 Linear-systems/186418: An Airplane flew for 4 hours against headwind of 40 km/h. On the return flight the same wind was now a tail wind, and the flight took 3 hours. Find the speed of the airplane in still air1 solutions Answer 139708 by josmiceli(9698)   on 2009-03-12 11:12:19 (Show Source): You can put this solution on YOUR website!Let = speed of plane in still air Let = distance travelled one way given: (against wind) (with wind) Since both are equal to , set them equal to eachother The speed of plane in still air is 280 mi/hr check: ------------------- OK
 Mixture_Word_Problems/186415: a merchant has coffee worth \$20 a pound that she wishes to mix with 80 pounds of coffee worth \$90 a pound to get a mixture that can be sold for \$60 a pound. how many pounds of the \$20 coffee should be used?1 solutions Answer 139706 by josmiceli(9698)   on 2009-03-12 11:01:40 (Show Source): You can put this solution on YOUR website!Let = pounds of \$20 coffee used given: = cost in dollars of \$20 coffee used = cost in dollars of \$90 coffee used = pounds of coffee in final mixture = cost in dollars of final mixture ------------------- 60 pounds of \$20 coffee must be used check: OK
 Evaluation_Word_Problems/186343: Please help me quickly, I am trying to help my daughter with her homework. Problem: At a concert, main floor seats sell for \$25.00 and Upper Level seats sell for \$12.00. There were 50,000 people in attendance and the concert total ticket sales is \$1,112,000. How many main floor seats and upper level seats were sold?1 solutions Answer 139675 by josmiceli(9698)   on 2009-03-11 23:02:20 (Show Source): You can put this solution on YOUR website!Let = number of main floor tickets sold Let = number of upper level tickets sold given: (1) (2) There are 2 equations and 2 unknowns. When the number of equations matches the number of unknowns, it is solvable. Multiply both sides of (1) by and subtract from (2) (2) (1) (3) (3) (rounded off) and (1) (1) (1) (rounded off) 39,385 mainfloor seats were sold and 10615 upper level seats were sold check answer: (2) (2) (2) (2) (close enough) and (1) (1) (1) OK
 Polynomials-and-rational-expressions/186269: i just need help in trying to solve this division of polynomials: (24x2-19x+6)/(8x-1)1 solutions Answer 139629 by josmiceli(9698)   on 2009-03-11 18:31:08 (Show Source): You can put this solution on YOUR website!The 1st partial answer is Subtract from getting The 2nd partial answer is Subtract from getting The answer is (4 is the remainder) If you multiply by , you get
 Equations/186255: This question is from textbook Beginning Algebra Could you please help me solve this problem? Find three consecutive integers whose sum is -114.1 solutions Answer 139618 by josmiceli(9698)   on 2009-03-11 17:55:51 (Show Source): You can put this solution on YOUR website!Let be the smallest integer Then is the next larger And is the next larger given: The consecutive integers are -37, -38, and -39 check: OK
 Mixture_Word_Problems/186265: a tea shop sells grea tea for \$4.00 a pound and a white tea for \$2.75 per pound. the manager decides to combine the two types of teas to make a mix that sells for \$3.50 per pound. the mis should not cause any change in revenue. how much of each tea should combine to make a 10 pound mixture1 solutions Answer 139616 by josmiceli(9698)   on 2009-03-11 17:45:53 (Show Source): You can put this solution on YOUR website!Let = pounds of green tea needed Let = pounds of white tea needed given: (1) lb dollars (2) Multiply both sides of (1) by and subtract (2) from (1) (1) (2) (3) (3) and (1) (1) (1) 4 pounds of white tea and 6 pounds of green tea are needed
 Linear-systems/186085: This question is from textbook Algebra 1 How do you solve this linear system with substitution? 8x+3y=0 -x-9y=92 All I have got to is... x=-9y-92 3y(-9y-92)=0 -6y-92=0 -6y=92 I dont think I did it right??1 solutions Answer 139526 by josmiceli(9698)   on 2009-03-10 19:46:08 (Show Source): You can put this solution on YOUR website!(1) (2) Subtract from both sides of (1) (1) Divide both sides by (1) Multiply the right side by (1) Substitute this in (2) (2) (2) (2) (2) (2) And, from (1) (1) (1) (1) check answers: (1) (1) OK (2) (2) (2) OK
 Age_Word_Problems/186089: There are four children in a family. There were all born two years apart. The sum of their ages is 84. How old are the children?1 solutions Answer 139525 by josmiceli(9698)   on 2009-03-10 19:30:40 (Show Source): You can put this solution on YOUR website!Let the youngest child's age be Their ages are then: , , ,and Their ages are 18,20,22,and 24
 Numbers_Word_Problems/186080: This question is from textbook Holt Algebra 1 The sum of Anji's age and Carol's age is 66. Carol's age is 2 more than 3 times Anji's age. How old are Carol and Anji?1 solutions Answer 139524 by josmiceli(9698)   on 2009-03-10 18:49:14 (Show Source): You can put this solution on YOUR website!Let = Anji's age Let = Carol's age given: (1) (2) Subtract from both sides of (2) (2) Subtract (2) from (1) (1) (2) (3) (3) and, since (1) (1) (1) Anji's age is 16, and Carol's age is 50 check: (2) (2) (2) (2) OK
 Miscellaneous_Word_Problems/186070: Pietro's Pizza and Sandwiches delivered lots of sandwiches one rainy Saturday. They took orders for 30 sandwiches with cheese, 25 with tomatoes, and 18 with pepperoni. there were 18 with cheese and tomato, 14 with tomato and pepperoni, and 10 with all three toppings. there were 8 with only cheese. how many sandwiches did they deliver? i have worked with the numbers and the pizzas don't add up. i don't know if it is extra info.1 solutions Answer 139523 by josmiceli(9698)   on 2009-03-10 18:32:23 (Show Source): You can put this solution on YOUR website!I come up with sandwiches I drew 3 interlocking circles with an area in the middle common to all three Here's the breakdowns: c only ---t only ---p only --- c&t --- t&p --- c&p ----------------------------------------------------- ----8--------3-------0--------18--------14------14 I add up: 8 c only 8 c&t only 3 t only 4 t&p only 0 p only 4 p&c only 10 All 3 toppings ----- 37
 Polynomials-and-rational-expressions/186066: please help me with this polynomial. z^2+9z+20 thank you and please show work so i know how to complete it on my own.1 solutions Answer 139522 by josmiceli(9698)   on 2009-03-10 17:56:38 (Show Source): You can put this solution on YOUR website!This can be done by the method known as -completing the square- Take of the coefficient of the term, square it, then add the results to both sides ------------------------------- But first, I have to get the constant term on the other side. Subtract from both sides Now complete the square With this method, the left side always ends up being a perfect square. In this problem, both sides are a perfect square Now take the square root of both sides, both the (+) and (-) square root and and are the roots of the polynomial To factor , and The factoring is:
 Length-and-distance/186064: This question is from textbook Pre-Algebra brandon hikes 7 miles south and 4 west. How far is he from the starting point of his hike?1 solutions Answer 139521 by josmiceli(9698)   on 2009-03-10 17:35:09 (Show Source): You can put this solution on YOUR website!Call the distance from his starting point By the pythagorean theorem for a right triangle: mi
 Graphs/185934: Soybean meal in 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 10% protein?1 solutions Answer 139446 by josmiceli(9698)   on 2009-03-10 00:02:58 (Show Source): You can put this solution on YOUR website!Let = pounds of soybean meal needed Let = pounds of cornmeal needed given: = pounds of protein in soybean meal needed = pounds of protein in cornmeal needed = pounds of final mixture -------------- (1) (2) Multiply both sides of (1) by (1) (1) Multiply both sides of (2) by (2) Subtract (2) from (1) (1) (2) (3) (3) and (2) (2) (2) 80 pounds of soybean meal and 240 pounds of cornmeal are needed check: (1) (1) (1) (1) OK