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# Recent problems solved by 'Fombitz'

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 Matrices-and-determiminant/166212: Can someone help with this problem please: Solve the matrix equation for X. A = 2 0 0 -1 2 0 -2 4 1 B = 4 10 11 AX = B CHOOSE FROM: a. 0 8 -9 b. 2 6 -9 c. 3 7 -8 d. 3 6 -101 solutions Answer 122506 by Fombitz(13828)   on 2008-11-06 16:37:38 (Show Source): You can put this solution on YOUR website! Find the inverse of A. Multiply rows of the inverse matrix by the column matrix to get the product. . . . . . . b.)
 Matrices-and-determiminant/166219: can someone please help: Determine whether the two matrices are inverses of each other by computing their product. 1. 2, -1, 0 -1, 1, -2 1, 0, -1 2. 1, -1, 2 -3, -2, 4 -1, 1, 1 yes or no1 solutions Answer 122505 by Fombitz(13828)   on 2008-11-06 16:22:50 (Show Source): You can put this solution on YOUR website!Multiply rows of the first matrix by columns of the second matrix to get the product. Example: First entry of the product matrix, , . . .
 absolute-value/166117: Solve (|3x-1|) / (x²+4) ‹ 0. Give a written explanation along with algebraic support. PLEASE HELP ME!!!1 solutions Answer 122478 by Fombitz(13828)   on 2008-11-06 12:56:11 (Show Source): You can put this solution on YOUR website! The denominator is always positive. The numerator is always positive or zero. Therefore, there is no value of x such that the left hand side would be less than zero. No solution. By definition, for all Y. . . . Graphical verification.
 Money_Word_Problems/166173: Would you rather have a kilometer of quarters or a kilometer of dimes? (in a straight line, with the heads up). How much better is your choice? THANK YOU SO MUCH!1 solutions Answer 122467 by Fombitz(13828)   on 2008-11-06 11:30:20 (Show Source): You can put this solution on YOUR website!Well I guess we have to count how many of each are in a kilometer. From a GOOGLE search, I found the following information, dime:1.35 mm thickness quarter:1.75 mm thickness Let's assume it's correct. So 1 km, which equals (1000)(1000)mm, there are this many dimes, Each dime is \$0.10, so the total in 1 km is, Similarly for the quarters, Fewer of them, but what about the total value, Wow, it's almost double. The exact difference is \$68,783 difference between the two coin kilometers. That's a lot of coin wrappers!
 Polynomials-and-rational-expressions/166197: (1/2x^3)^5(x^2)^3 I have worked on this and not sure if the answer I have is right.... (1/32x^15)(x^6)=1/32x^211 solutions Answer 122464 by Fombitz(13828)   on 2008-11-06 11:21:12 (Show Source): You can put this solution on YOUR website!That's correct!
 Quadratic-relations-and-conic-sections/166194: I submitted this question a couple of weeks ago, but I never received a response. Can anybody help me out? What is the equation of a parabola with vertex (0,0) and focus (0,4)? THanks alot!1 solutions Answer 122463 by Fombitz(13828)   on 2008-11-06 11:18:52 (Show Source): You can put this solution on YOUR website!The general equation for a parabola is, where (h,k) is the vertex of the parabola and p is the distance from vertex to focus. In your case, (h,k)=(0,0) p=4
 Sequences-and-series/166155: How to derive Nth term of the following series? 1,3,6,10,15,21.........upto n terms 25!!!!!!!!!!!!!!!!!!!!!!!!!1 solutions Answer 122459 by Fombitz(13828)   on 2008-11-06 10:19:10 (Show Source): You can put this solution on YOUR website!Look at the difference between terms, 1,3=2 3,6=3 6,10=4 10,15=5 15,21=6 . . . First term=1 Second term=First term +2=1+2 Third term=Second term+3=1+2+3 Fourth term=Third term+4=1+2+3+4 Starting to see a pattern here... Nth term=(N-1)term+N=1+2+3+...+(N-1)+N Look like the terms follow,
 Complex_Numbers/166180: I'm not sure if this is the right section, but I will still ask. 1. Use synthetic division to find f(-3) for f(x)2x^3-6x^2-5x+7. 2. One factor of f(x)=x^3+x^2-22x-40 is x+4. Find the other factors. I must show my work and have no textbook to explain. Will you PLEASE HELP!!!! Thanks1 solutions Answer 122454 by Fombitz(13828)   on 2008-11-06 09:55:09 (Show Source): You can put this solution on YOUR website!1. You don't need synthetic division to find f(-3). Just substitute. . . . 2. Here you need the synthetic division. Showing synthetic division is a little difficult. The first part will show the factor (left hand column), then the factor times the divisor, then the next line will show the subtraction. Repeat. Hopefully it makes sense. . . . ..........._______________ (x+4)|x^3+x^2-22x-40 x^2:...x^3+4x^2 ..................-3x^2-22x-40 -3x:..........-3x^2-12x .............................-10x-40 -10:......................-10x-40 Now you can factor the quadratic, and substitute back,
 Quadratic_Equations/166183: Please check my answers for in quadratic formula: solve: v^2 = 12v - 24 v^2 12v + 24 = 0 v = 12 =/- sqr. rt. of 12^2 - 4(24)/2 = 12 +/- sqr. rt of 144 - 96/2 = 12 sqr. rt of 48/2 = 12 sqr. rt. of 4*4*3/2 = 12 +/- 4 sqr. rt. of 3/2 answer: 6 - 4 sqrt rt. of 3, 6 + 4 sqr. rt. of 3 1 solutions Answer 122451 by Fombitz(13828)   on 2008-11-06 09:45:53 (Show Source): You can put this solution on YOUR website! You missed a division by 2 in front of the square root.
 Polynomials-and-rational-expressions/166175: PLEASE HELP!!! Solve -x^4+200=102x^2. I have to show my work and I don't understand how to do this. It is from a worksheet. Thanks1 solutions Answer 122447 by Fombitz(13828)   on 2008-11-06 09:02:13 (Show Source): You can put this solution on YOUR website! Looks kind of like a quadratic equation. Use a substitution. Now solve using the quadratic formula, Let's look at both solutions separately, . . .
 Quadratic-relations-and-conic-sections/166176: Can anybody tell me if I have identified these correctly? I'm not sure. Thanks!!! a) (x-3)^2/9 + (y-2)^2/4 = 1 ellipse b) (x+2)^2/25 - (y-1)^2/9 = 1 hyperbola c) x^2 + 4x = y - 4 parabola d) (x + 2)^2 + (y-3)^2 = 49 circle e) (x + 1)^2/25 + (y - 2)^2/25=1 circle ???? f) xy = 3 line or point ??????1 solutions Answer 122446 by Fombitz(13828)   on 2008-11-06 08:49:52 (Show Source): You can put this solution on YOUR website!a-e are correct. f is neither a line nor point, it's a function. Best description may be a discontinuous rational function?
 Rational-functions/166029: can someone please help me with this problem: Graph the rational funciton. Pf(x) = x+4 / x-11 solutions Answer 122346 by Fombitz(13828)   on 2008-11-05 16:29:54 (Show Source): You can put this solution on YOUR website!Let's look at the function first. It is undefined at x=1 (because of division by zero). . . . As you approach x=1 from the left, the numerator is positive, the denominator is negative, f(x) goes to negative infinity. . . . As you approach x=1 from the right, the numerator is positive, the denominator is positive, f(x) goes to positive infinity. . . . As x grow large (negative or positive), the function looks like, So there is a horizontal asymptote at y=1. . . . f(x) crosses the x-axis when f(x)=0 f(x) cross the x-axis when x=-4. . . . f(x) crosses the y-axis when x=0 f(x) crosses the y-axis when y=-4. . . .
 Rational-functions/166034: can someone please help with this: Give the equation of the horizontal asymptote of the rational function. g(x) = x-5 / x-1 a. x = 1 b. y = 0 c. y = 1 d. y = 51 solutions Answer 122343 by Fombitz(13828)   on 2008-11-05 16:16:17 (Show Source): You can put this solution on YOUR website!As x becomes very large (positive or negative), the function looks like, . . . Graphical proof of the asymptote, showing the discontinuity at x=1.
 Rational-functions/165803: what is the slope and the y intercept of 3y+3x+1=01 solutions Answer 122217 by Fombitz(13828)   on 2008-11-04 16:50:20 (Show Source): You can put this solution on YOUR website!Convert to slope-intercept form, Slope = -1 Y-intercept=-1/3
 Rational-functions/165790: what is the slope and the y intercept of 6y=3x+41 solutions Answer 122214 by Fombitz(13828)   on 2008-11-04 16:22:52 (Show Source): You can put this solution on YOUR website!Convert to slope-intercept form, Slope=(1/2) Intercept=(2/3)
 Numbers_Word_Problems/165797: The population of Gondor is 3020 and is dropping by 12 people per year. The population of Shire is 824 and is increasing by 5 hobbits per year. How long until Gondor and Shire have the same population?1 solutions Answer 122213 by Fombitz(13828)   on 2008-11-04 16:21:01 (Show Source): You can put this solution on YOUR website!"Gondor is 3020 and is dropping by 12 people per year" "Shire is 824 and is increasing by 5 hobbits per year" Set the two populations equal to each other and solve for Y. . . . It's not an exact year, around the second month in the 129th year. Around then, each village will have 1470 inhabitants.
 Evaluation_Word_Problems/165788: Hello, I'm trying to help my 5th grader with a word problem, it's below, will much appreciate it , if you would help, got your site from google. This problem is due tom. morning.Thank you Ivan, Zoe, Denys and Ethan wanted to divided up a big old pickle 30 feet long. Denys wants twice as much as Ivan does. Zoe wants twice as much as Denys does, but half as much as Ethan does. How should they divide the pickle? 1 solutions Answer 122212 by Fombitz(13828)   on 2008-11-04 16:08:53 (Show Source): You can put this solution on YOUR website!Let's name everyone's cut length after the first letter of their name. All their lengths together equal 30. 1. "Denys wants twice as much as Ivan does" 2. "Zoe wants twice as much as Denys does" 3. "Zoe wants half as much as Ethan does" 4. . . . Since 3 and 4 both equal Z, set them equal to each other, 5. . . . Now you can form an equation with only "I" as the variable, using substitutions from equations 2,3,and 5. 1. . . . Now go back and substitute this value in each of the equations, 2. 3. 5. . . . Ivan gets 2 feet, Zoe gets 8 feet, Denys gets 4 feet and Ethan gets 16 feet.
 Quadratic-relations-and-conic-sections/165719: This question is from textbook College Algebra What are the steps to the following problem, Instructions: "Write an equation for each ellipse" Problem: minor axis with length 4: foci at (-5,0),(5,0) Please Help I cannot seem to figure this one out. Thank You 1 solutions Answer 122167 by Fombitz(13828)   on 2008-11-04 10:25:21 (Show Source): You can put this solution on YOUR website!We have to work backwards from given information to find the major axis length (a) using minor axis length (b) and foci (c). The general equation for an ellipse centered at (h,k) is given by, . . . Foci for an ellipse are located at where . The length of the minor axis is Since the foci are symmetric about the y-axis, the ellipse is centered at (0,0). The equation then becomes,
 Expressions-with-variables/164667: Can someone help with this: Use synthetic division to find the quotient and remainder(4x^3-6x+5)/(x-3)? Thank you.1 solutions Answer 122165 by Fombitz(13828)   on 2008-11-04 10:13:17 (Show Source): You can put this solution on YOUR website!Showing synthetic division is a little difficult. The first part will show the factor (left hand column), then the factor times the divisor, then the next line will show the subtraction. Repeat. Hopefully it makes sense. . . . ..........._______________ (x-3)|4x^3+0x^2-6x+5 4x^2:.4x^3-12x^2 .......................12x^2-6x+5 12x:...............12x^2-36x ...................................30x+5 30:.............................30x-90 ............................................95
 Expressions-with-variables/165680: x2+5x+4 -------- x2+x1 solutions Answer 122159 by Fombitz(13828)   on 2008-11-04 09:49:27 (Show Source): You can put this solution on YOUR website! or
 Age_Word_Problems/146358: Write an equation which models how old, in years, you will be when you are 3 times as old as the younger person. Age now (mother) = 35 Younger person (daughter) age now = 14 age difference = 21 years mother = X + 21 daughter = X I was thinking it should be 3x + 21 = 3X. It's not coming out right. Please help.1 solutions Answer 122158 by Fombitz(13828)   on 2008-11-04 09:38:54 (Show Source): You can put this solution on YOUR website!Mother = M = 35 Daughter = D = 14 In x years, the mother will be, In x years, the daughter will be, When will the mother be 3 times the daughters age? 3 1/2 years ago, the mother was 3 times the daughter's age. The mother was 31 1/2 years old. The daughter was 10 1/2 years old. Are you sure the mother and daughter ages are correct??
 Age_Word_Problems/165703: A man is now 42 years old and his friend is 33 years old. How many years ago was the man twice as old as his friend was then?1 solutions Answer 122157 by Fombitz(13828)   on 2008-11-04 09:24:09 (Show Source): You can put this solution on YOUR website!Today, Find X such that, Twenty four years ago the man was while his friend was and
 Distributive-associative-commutative-properties/165710: Is there any reason why my question is going ignored. I am trying to figure out how to solve this problem and have submitted it three times, still no answer 1/2 divided by 3/8+5*(1/3) so, i am assuming the problem should written out like this: 1/2/3/8+5+(1/3)1 solutions Answer 122155 by Fombitz(13828)   on 2008-11-04 09:19:07 (Show Source): You can put this solution on YOUR website! Need a common denominator to add fractions. Division by a fraction is equivalent to multiplication by its reciprocal.
 Exponents/165534: (3x^2)^3(2x)^41 solutions Answer 122052 by Fombitz(13828)   on 2008-11-03 16:40:14 (Show Source):
 Quadratic_Equations/165538: how do i factor a quadratic equation and apply the zero product rule to find the solution set?1 solutions Answer 122051 by Fombitz(13828)   on 2008-11-03 16:36:59 (Show Source): You can put this solution on YOUR website!Here's an example. You can factor the quadratic equation. Zero product rule says either the first factor or the second factor could equal zero so solve for both. . . . First factor: Second factor: . . . The solution set (zeros) for the equation are x=-1,-2. You can check the answers by plugging into the equation or you could graph the equation to verify. . . .
 Vectors/165567: find a unit vector along each of the following vectors; (i) r=3i^+4j^ (ii)r=12i^-5j^ (iii)r=-2i^-2j^-5k^ (iv)r=i^+2j^+3k^1 solutions Answer 122049 by Fombitz(13828)   on 2008-11-03 16:26:45 (Show Source): You can put this solution on YOUR website!To find the unit vector in the direction of the given vector, divide the vector by its magnitude,M. This way it has the same direction and magnitude of 1. . . . i) . . . ii) . . . iii) . . . iv)
 Problems-with-consecutive-odd-even-integers/165493: the sum of the square of the two consecutive odd intergers is equal to 290 find the two intergers1 solutions Answer 121986 by Fombitz(13828)   on 2008-11-03 09:39:32 (Show Source): You can put this solution on YOUR website!Let n be the first integer, (n+2) would be the next consecutive odd integer. You can factor this quadratic equation. . . . First solution: The two integers are then -13 and -11. . . . Second solution: The two integers are then 11 and 13.
 Probability-and-statistics/165391: find the percent of the total area under the standard curve between the given z-scores. z = 2.18 and z = 3.451 solutions Answer 121984 by Fombitz(13828)   on 2008-11-03 09:29:44 (Show Source): You can put this solution on YOUR website!We can find the area under the curve from to and also from to , subtract them and that will give us the area between and . We then multiply by 100 to get the percentage. I used EXCEL's NORMSDIST function with the given z scores to calculate areas. . . . . . . 1.43% of the curve's area is between z=2.18 and z=3.45.
 Rational-functions/165465: what is the difference between Y= IxI and y= I-XI? does it mean that the second one reflected over y aixs? 1 solutions Answer 121982 by Fombitz(13828)   on 2008-11-03 09:19:46 (Show Source): You can put this solution on YOUR website!I'm assuming those are absolute value symbols? In that case, the graphs are identical. Take x=1,
 Linear_Algebra/165494: the problem: Prove that (1,0,0,1) and (0,1,1,0) are linearly independent. I think they are dependent, am i missing something?1 solutions Answer 121980 by Fombitz(13828)   on 2008-11-03 09:15:46 (Show Source): You can put this solution on YOUR website!The previous discussion regarding dot product was not correct. I mixed up orthogonality and linear independence. . . . For these two vectors to be linearly independent, then a combination of these two vectors with two scalar multipliers can only be zero when the multipliers are zero. (1,0,0,1)A+(0,1,1,0)B=(0,0,0,0) only if A=B=0. . . . Look at each individual component of the vectors. 1.(1)A+(0)B=0 2.(0)A+(1)B=0 3.(0)A+(1)B=0 4.(1)A+(0)B=0 . . . From 1 and 4, A=0 From 2 and 3, B=0 . . . Therefore, you proved that they are linearly independent because the combination of the two vectors can only equal the zero vector when A=B=0. Sorry for the confusion.