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# Recent problems solved by 'Fombitz'

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 Age_Word_Problems/114792: A man lived a fourth of his life as a boy, a fifth as a young man and a third as an adult. He spent 13 years in his old age. How old was he when he died?1 solutions Answer 83521 by Fombitz(13828)   on 2007-12-05 14:56:20 (Show Source): You can put this solution on YOUR website!Life as a boy + Life as young man + Life as adult + Life in old age=Whole life Where O is the fraction of his life spent in old age. Multiply both sides by 60 (4*5*3) to remove fractions. The man spent 13/60 of his life in old age. His total years in old age equals 13 years. The man was 60 years old when he died.
 Equations/114791: This question is from textbook investments I was having some problems with this equation and know the answer is 57.14, but can't seem to get that answer. Could somebody please walk me through this? 100p - 4000 ------------ = .3 100p1 solutions Answer 83520 by Fombitz(13828)   on 2007-12-05 14:47:08 (Show Source): You can put this solution on YOUR website! Multiply both sides of the equation by 100p. Subtract 30p form both sides of the equation. Add 4000 to both sides of the equation. Divide both sides of the equation by 70.
 Functions/114782: Let f(x)=sqrt x+1 and g(x)= 1/x+1. Evaluate f(g(0)) 1 solutions Answer 83519 by Fombitz(13828)   on 2007-12-05 14:42:36 (Show Source):
 Equations/114789: How do I solve this problem? x(3x + 1) (x + 1) = 01 solutions Answer 83518 by Fombitz(13828)   on 2007-12-05 14:39:45 (Show Source): You can put this solution on YOUR website!x(3x + 1) (x + 1) = 0 You need to find x so that the equation equals zero. There are three cases when the equation will equal zero, that is, when the three individual expressions equal zero. 1.x=0 2.3x+1=0 3.x+1=0 The first solution is x=0. The second solution requires some manipulating. 3x+1=0 3x=-1 x=-1/3. The second solution is x=-1/3. The third solution is found similarly. x+1=0 x=-1 The third solution is x=-1.
 Average/114498: Calculate the standard deviation for the following data set: 16, 35, 25, 29, 26, 301 solutions Answer 83354 by Fombitz(13828)   on 2007-12-04 16:38:16 (Show Source): You can put this solution on YOUR website!First step, find the mean (average), Next find the deviation of each value from the mean, Then square the deviations, Sum the squares of deviation, Divide by the number of samples and take the square root,
 Polynomials-and-rational-expressions/114553: find the interval(s) for the equation f(x)=1/x^2-2x-8, where f(x)>01 solutions Answer 83352 by Fombitz(13828)   on 2007-12-04 16:28:25 (Show Source): You can put this solution on YOUR website!For f(x) to be positive, the denominator has to stay greater than zero. You can factor the denominator, The zeros are then x=-2 and x=4. Let's break up the problem into three parts 1. 2. 3. That then covers the entire number line. Let's look at each region, 1. Negative times a negative equals a positive. f(x) is positive when . 2. Positive times a positive equals a positive. f(x) is positive when . 3. Negative times a positive equals a negative. f(x) is negative when . The interval where f(x) is positive is () and ().
 decimal-numbers/114576: This question is from textbook prentice hall mathmatics algebra i am confused as to what it means be "Write each expression as a decimal" with problems like 57) 10 to the negative 5th power 58) 10 to the negative 8th power 59) 4 times 10 to the negative first power 60) 6 times 10 to the negative 4th power please help me to figure out what this means! cody- 9th grade Lake Howell High School!1 solutions Answer 83351 by Fombitz(13828)   on 2007-12-04 16:17:50 (Show Source): You can put this solution on YOUR website!Let's take them one at a time. 57) is the same as 58) is the same as 58) is the same as 59) is the same as
 Matrices-and-determiminant/114564: This question is from textbook Algebra for College Students I just need to solve the matrix-I do know the answer, however, I'm not sure of how to do the problem. 3x+4y=13 2x-3y=-14 the answer is (-1,4) Please help!1 solutions Answer 83348 by Fombitz(13828)   on 2007-12-04 16:10:06 (Show Source): You can put this solution on YOUR website!3x+4y=13 2x-3y=-14 In matrix form, it would look like, [][]=[] The solution is Where k,l,m,n are coefficients of the inverse matrix of []=[][] The inverse of a 2x2 matrix, A, where []= is given by []= Using your coefficients in the inverse matrix formula, []= []= []= The solution is therefore Let's carry out each calculation separately,
 Money_Word_Problems/114226: This question is from textbook Four hamburgers and three orders of french fries cost \$5.15. Three hamburgers and five orders of fries cost \$5.10. What would one hamburger and one order of fries cost?1 solutions Answer 83171 by Fombitz(13828)   on 2007-12-03 16:32:37 (Show Source): You can put this solution on YOUR website!Let's let H=cost of hamburger and F=cost of fries. 1. 2. Let me use equation 1 to solve for H in terms of F and then substitute into equation 2. 1. Now substitute into 2. 2. Now that you have F, you can substitute into either equation to find H. 2. Hamburgers cost \$0.95 and french fries cost \$0.45. One hamburger and one order of fries would cost \$1.40.
 Triangles/114241: Find the perimeter and area of a triangle measuring 5x3x4 I think the perimeter = 5x3x4=60 I think the area= 5+3+4=121 solutions Answer 83170 by Fombitz(13828)   on 2007-12-03 16:25:02 (Show Source): You can put this solution on YOUR website!No, that's not correct. The perimeter is the sum of the sides The area of a triangle is where b is the base and h is the height. You can find it by letting b=3 and h=4, or by letting b=4 and h=3. The answer will be the same.
 Linear-systems/114281: im having trouble understanding the systems of equations..... how do i solve by graphing?? for ex: y=x+2, y=-x+4?? i dont understand how to solve then graph it......!!!!1 solutions Answer 83167 by Fombitz(13828)   on 2007-12-03 16:20:33 (Show Source): You can put this solution on YOUR website!First you draw the two lines. Where the lines intersect, the (x,y)point is a solution to the system of equations. If the lines never intersect (that is, are parallel) then there is no solution. From the graph it looks like (1,3) is a solution to both equations. Verify by substituting into each equation. 1. True statement 2. True statement Your solution led to true statements from both equations. Therefore it is a good solution.
 Polynomials-and-rational-expressions/114249: Rewrite the middle term as the sum of two terms and then factor completely. 12w squared + 19w + 41 solutions Answer 83165 by Fombitz(13828)   on 2007-12-03 16:14:13 (Show Source): You can put this solution on YOUR website! Find a,b,c,d using the FOIL method (First, Outer, Inner, Last) and equating to the coefficients of your equation. Now to expand the equation you use the FOIL method (First, Outer, Inner, Last) First : Outer : Inner : Last : Comparing to your equation 1. 2. 3. From 1, since ac=12, you can choose 12 and 1, 6 and 2, 4 and 3, and also 3 and 4, 2 and 6, and 1 and 12 for possible a-c combinations. From 3, since bd=4, you can choose 4 and 1, 2 and 2, and 1 and 4 for possible b-d combinations. Let's start with a=6 and c=2 From 2, Notice the coefficients of b and d. This solution set cannot be a solution because 2 even numbers will never sum to an odd number. So 6 and 2 and 2 and 6 are out as possible a-c combinations. Start again, Let's choose a=12 and c=1, From 2, Now substitute possible b,d values. for b=4, d=1. for b=2, d=2. for b=1, d=4. No solutions for a=12 and c=1. Our last chance is 4 and 3. Let's start with a=4 and c=3. From 2, Again, substitute possible b,d values. for b=4, d=1 for b=2, d=2 for b=1, d=4 Looks like a winner. a=4,c=3,b=1,d=4
 Numbers_Word_Problems/113426: A=1/2(b+B) solve for B1 solutions Answer 82619 by Fombitz(13828)   on 2007-11-30 15:24:58 (Show Source): You can put this solution on YOUR website!Your equation is unclear. Do you mean or do you mean We'll do it both ways. Multiply both sides by 2. Subtract b from boths sides. and Multiply both sides by 2(b+B). Distribute 2A through. Subtract 2Ab from both sides. Divide both sides by 2A.
 Linear-equations/113421: Solve the system by graphing 3x + y = 6 3x – y = 01 solutions Answer 82617 by Fombitz(13828)   on 2007-11-30 15:13:59 (Show Source): You can put this solution on YOUR website! Looks like the solution is (1,3) Check your answer in both equations. The answer checks out for both equations. The intersection point is (1,3).
 Quadratic_Equations/113411: I have a problem that is not from the textbook. My teacher has assigned the following problem and we are to use applications of the quadratic formula. I don't see how to put the problem into a square in order to use the quadratic formula. Here is the problem: The rate of a bicyclist is 5mph faster than the rate of a runner. The bicyclist travels 12 miles in the same amount of time that it takes the runner to travel 8 miles. Find the rate of the runner. This is how far I got: 12/x+5 = 8/x then, 8x - 12x +40 = 0 I would really appreciate any help. Thank you in advance. Tynk 1 solutions Answer 82616 by Fombitz(13828)   on 2007-11-30 15:10:35 (Show Source): You can put this solution on YOUR website!You're on the right track. You do not need to use the quadratic formula to solve this linear problem. That is the correct two equation. The runner runs at 10 mph, the bicyclist bikes at 15 mph.
 Percentage-and-ratio-word-problems/113448: Please Help The ratio of key club members to student councel members is 7 to 9 or 7:9. there are 353 total members. How many key club members are there? I think 154 but not sure. I need the solution to figure this and other similiar problems. Thanks1 solutions Answer 82608 by Fombitz(13828)   on 2007-11-30 14:27:21 (Show Source): You can put this solution on YOUR website!If the ratio of key to student council is 7 to 9, then the ratio of key to total is 7 to 16 and the ratio of student council to total is 9 to 16. If the total is 353, then the ratio equation would be,, where X is the total number of key members in your total. We round that value down to 154 since we can only have integer values. X=154
 Functions/113498: Trying to find the domain and range for the function f(x)=eX Both needs to be expressed in interval notation. The X following the (E) above should be typed as a exponent. 1 solutions Answer 82603 by Fombitz(13828)   on 2007-11-30 14:14:31 (Show Source): You can put this solution on YOUR website!I assume you mean There are no restrictions on the value of x. The domain is (,) For the range since you are taking a positive number to a power, the result will always be greater than zero. Other than that there are no restrictions on f(x). The range is (,)
 Numbers_Word_Problems/113520: This question is from textbook Arithmetic and algebra again The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number. here is what I have done: original number 10x + y new number 10y + x x + y = 7 10x + y = 10y + x + 3 10x -x + y -y = 10y -y + x -x + 3 9x = 9y + 3 x = y + 3 x + y = 7 (y+3) + y = 7 2y + 3 = 7 2y +3 -3 = 7 -3 2y = 4 2y/2 = 4/2 y = 2 x + y = 7 2 + y = 7 2 -2 + y = 7 -2 y = 5 x = 2 I get an answer, but it don't check. Every time I do this problem this my answer or fractional. please help1 solutions Answer 82598 by Fombitz(13828)   on 2007-11-30 13:56:15 (Show Source): You can put this solution on YOUR website!Your analysis is correct and you're on the right track. You made a mistake at this point. The new number (digits reversed) increased by 3 equals 4 times the original number. You forgot the 4. Now together with should get you a quick answer. Good luck. Post another question if you get stuck.
 Radicals/113495: This question is from textbook Algebra 2 (6n-5)^(1/3)+3=-21 solutions Answer 82557 by Fombitz(13828)   on 2007-11-30 09:06:52 (Show Source): You can put this solution on YOUR website! Check your answer True statment. Good answer.
 Equations/113333: If x=3 and x=5, then form a quadratic equation1 solutions Answer 82477 by Fombitz(13828)   on 2007-11-29 16:46:01 (Show Source): You can put this solution on YOUR website!From x=3 and x=5 you can form a quadratic equation that says Since x=3 and x=5 are both solutions, True. True. Now to expand the equation you use the FOIL method (First, Outer, Inner, Last) First : Outer : Inner : Last : Then you sum all of the terms Therefore your quadratic equation with roots x=3 and x=5 is
 Triangles/113319: Find the number od degrees of each angle of a regular decagon.1 solutions Answer 82472 by Fombitz(13828)   on 2007-11-29 16:35:41 (Show Source): You can put this solution on YOUR website!Let's look at a regular decagon. Draw it out, it doesn't have to be perfect. You have 10 sides and 11 vertices where the sides intersect. Find the center of the decagon and draw lines from the vertices to the center point. You'll get 10 identical isoceles triangles shown here with angles A,B, and B. Only three of the ten triangles are shown here for simplicity. From the rules for triangles, you know that 1. 1. You also know from the diagram that 2. 2. since the sum of the A angles equals one revolution and there are 10 A angles(10 triangles total). The interior angle of a regular decagon is 2B. From 1, 1. 1. 1. The interior angle of a regular decagon is 144 degrees.
 Polynomials-and-rational-expressions/113317: I'm trying to factor polynomials; I'm doing word problems. However, I cannot understand how to find the factor of a number that will add up to the middle number. For example n^2+2n-112=0 - 2(n2+n-112)= 0 - (n )(n ) How do I find the multiples for 112. Is there an easy method? 1 solutions Answer 82463 by Fombitz(13828)   on 2007-11-29 16:01:05 (Show Source): You can put this solution on YOUR website!Any number that ends in 2 is divisible by 2. 112=2*56 I don't think that's what you want to do here. I think you want to complete the square. That is, there's a number,d, such that If you look at your equation and compare the "n" terms, you have In your case d=1, And then I can substitute in your original equation, The solutions are and
 Triangles/113318: This question is from textbook basic math, algebra and geometry with applications Find the coordinates of hte midpoint of the segment with endpoints (-3, 4) and (5, -9)1 solutions Answer 82462 by Fombitz(13828)   on 2007-11-29 15:50:08 (Show Source): You can put this solution on YOUR website!Take the average of the x coordinates to find the x midpoint. Take the average of the y coordinates to find the y midpoint. The coordinates of the midpoint are (1,-5/2)
 Sequences-and-series/112706: Find the sum of the infinite geometric series: .8+.08+.008 please help! thanks! <31 solutions Answer 82157 by Fombitz(13828)   on 2007-11-27 10:33:14 (Show Source): You can put this solution on YOUR website!If you look at the sum as it starts to accumulate, you'll notice a pattern. .8 .88 .888 .8888 .88888 .888888 .8888888 .88888888 Look for a fraction that has a repeating pattern. I know that 1/9=0.1111111.... So my sum looks like 8 times that much or 8/9.
 expressions/112458: How would I write the quotient of n and twelve?1 solutions Answer 82043 by Fombitz(13828)   on 2007-11-26 16:33:30 (Show Source): You can put this solution on YOUR website!The quotient is the result of a division. The quotient of n and 12 is .
 Geometric_formulas/112457: C=2(pie)r for r..i dont understand how to solve this. i would like some help exlaining how to do it!!! there's no way to put a pie symbol on here!!! Also there is a problem on here that you have to solve this, 6 days's : 3 weeks, and then it shows 6 - 3 and the answers turns out to be 2/7..HELP!!!1 solutions Answer 82042 by Fombitz(13828)   on 2007-11-26 16:32:07 (Show Source): You can put this solution on YOUR website! is the equation for the perimeter of a circle. The number, , is approximately equal to 3.14. The second half of the question is a little unclear. Could you please re-state the question?
 Reduction-of-unit-multipliers/112444: Change 2.6 km/day to m/week.1 solutions Answer 82041 by Fombitz(13828)   on 2007-11-26 16:22:39 (Show Source): You can put this solution on YOUR website!1000 m = 1 km 7 days = 1 week 2.6 km/day = 2.6 km/day x 1000 m/km x 7 days/week 2.6 km/day = 18,200 m/week
 Linear_Equations_And_Systems_Word_Problems/112455: Please help. Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x + 5y = 10 - 2x - 10y = - 20 Thanks JMS1 solutions Answer 82040 by Fombitz(13828)   on 2007-11-26 16:15:37 (Show Source): You can put this solution on YOUR website!1. 2. if you multiply both sides of equation 1 by -2, 1. you get equation 2. These are dependent equations (the same equation).