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jim_thompson5910 answered: 28583 problems
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Equations/591228: A equilateral triangle has sides of length (3x-2),(2x+3) and 13. Find x 1 solutions Answer 375549 by jim_thompson5910(28595)   on 2012-03-25 12:28:01 (Show Source): You can put this solution on YOUR website! Hint: An equilateral triangle has equal sides. So 3x-2 = 2x+3. Solve this equation for x.

Equations/591240: x+9/11 = 8/11 1 solutions Answer 375548 by jim_thompson5910(28595)   on 2012-03-25 12:27:14 (Show Source): You can put this solution on YOUR website! x+9/11 = 8/11 x+9/11-9/11 = 8/11 - 9/11 x = -1/11

Equations/591239: 4b = 76 1 solutions Answer 375547 by jim_thompson5910(28595)   on 2012-03-25 12:26:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Equations/591241: 8x + 3 + x = 5x + 3 + 4x 1 solutions Answer 375546 by jim_thompson5910(28595)   on 2012-03-25 12:25:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Simplify. Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.

Equations/591244: - 14a + 3 = 10 1 solutions Answer 375545 by jim_thompson5910(28595)   on 2012-03-25 12:25:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Equations/591238: x+1=7 1 solutions Answer 375544 by jim_thompson5910(28595)   on 2012-03-25 12:24:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is

Exponents-negative-and-fractional/588858: okay so can you help me solve this question? 5(5 x 10^4) 1 solutions Answer 375543 by jim_thompson5910(28595)   on 2012-03-25 12:23:54 (Show Source): You can put this solution on YOUR website! 5(5 x 10^4) = 5(5) x 10^4 = 25 x 10^4 = 2.5 x 10^5 So 5(5 x 10^4) = 2.5 x 10^5

Exponents-negative-and-fractional/591255: -5 to the -3 power 1 solutions Answer 375542 by jim_thompson5910(28595)   on 2012-03-25 12:22:27 (Show Source): You can put this solution on YOUR website! (-5)^(-3) = 1/((-5)^3) = 1/(-125) = -1/125 So (-5)^(-3) = -1/125

Exponential-and-logarithmic-functions/591071: How do you tell whether the function shows growth or decay? f(x)= 0.5(1.25)^x 1 solutions Answer 375475 by jim_thompson5910(28595)   on 2012-03-24 17:42:24 (Show Source): You can put this solution on YOUR website! Any equation in the form where 'b' is greater than 1 represents an exponential function with exponential growth. Graphing it confirms this

Trigonometry-basics/591060: Evaluate limit as x approaches 0 of (cos3x-cos4x)/x^2 I have tried using L'Hopital's but differentiating the function using the quotient rule keeps squaring the denominator. 1 solutions Answer 375473 by jim_thompson5910(28595)   on 2012-03-24 17:29:43 (Show Source): You can put this solution on YOUR website! When you use L'Hopital's rule, you differentiate the numerator and denominator SEPARATELY. Let me know what you get when you do this.

Equations/591061: Can you please help me solve this equation? the equation is: 3x-6x-2=2x-x+3 1 solutions Answer 375472 by jim_thompson5910(28595)   on 2012-03-24 17:28:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Geometry_Word_Problems/591070: Find the surface area of a sphere with a great circle that has an area of 49 π square miles. a.225π mi^2 b.126 π mi^2 c.196 π mi^2 d.343 π mi^2 1 solutions Answer 375471 by jim_thompson5910(28595)   on 2012-03-24 17:26:59 (Show Source): You can put this solution on YOUR website! A = pi*r^2 49*pi = pi*r^2 49 = r^2 r = 7 ---------------------------- SA = 4pi*r^2 SA = 4pi*(7)^2 SA = 4*49*pi SA = 196pi So the answer is choice C)

Numeric_Fractions/591054: What is 24/1300 simplified 1 solutions Answer 375462 by jim_thompson5910(28595)   on 2012-03-24 16:35:31 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Reducing Fractions Calculator In order to reduce , the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal. In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of and is (note: click here if you need help with finding the GCF). So divide both the numerator and denominator by In other words, to reduce the fraction you do this Plug in the numerator, denominator, and the GCF Now divide 24 by 4 to get 6. This is now the new numerator. Now divide 1300 by 4 to get 325. This is now the new denominator. So This means that reduces to In other words,

Equations/590560: 6z-7=2z-2 would the answer be z=6 1 solutions Answer 375450 by jim_thompson5910(28595)   on 2012-03-24 14:42:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Equations/590565: 9x-7=-7 1 solutions Answer 375449 by jim_thompson5910(28595)   on 2012-03-24 14:41:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Equations/590567: 3c-15=17-c 1 solutions Answer 375448 by jim_thompson5910(28595)   on 2012-03-24 14:41:14 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Equations/590599: 2/5x+7=9 1 solutions Answer 375447 by jim_thompson5910(28595)   on 2012-03-24 14:40:30 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Equations/590955: need help : add the following(2b^4-3b^3+4b^2+13b-7)+(b^5+9b^3+4b^2-4b+3)+(-5b^4+b^2-5b-7), simplify your answer 1 solutions Answer 375446 by jim_thompson5910(28595)   on 2012-03-24 14:39:53 (Show Source): You can put this solution on YOUR website! (2b^4-3b^3+4b^2+13b-7)+(b^5+9b^3+4b^2-4b+3)+(-5b^4+b^2-5b-7) 2b^4-3b^3+4b^2+13b-7+b^5+9b^3+4b^2-4b+3-5b^4+b^2-5b-7 b^5+(2b^4-5b^4)+(-3b^3+9b^3)+(4b^2+4b^2+b^2)+(13b-4b-5b)+(-7+3-7) b^5-3b^4+6b^3+9b^2+4b-11 So (2b^4-3b^3+4b^2+13b-7)+(b^5+9b^3+4b^2-4b+3)+(-5b^4+b^2-5b-7) completely simplifies to b^5-3b^4+6b^3+9b^2+4b-11 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Graphs/590949: Graph the equation id the Y y=3/4x-5 1 solutions Answer 375444 by jim_thompson5910(28595)   on 2012-03-24 14:36:37 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 4. This means that to go from point to point, we can go up 3 and over 4 So starting at , go up 3 units and to the right 4 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Linear-equations/590999: create an expression whose value will be 14 when x = -3 1 solutions Answer 375443 by jim_thompson5910(28595)   on 2012-03-24 14:34:49 (Show Source): You can put this solution on YOUR website! One such expression is 2x + 20 and here's why... 2x + 20 2(-3) + 20 -6 + 20 14 So 2x + 20 = 14 when x = -3 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Functions/591023: 1. domanin and range and function { (-8, -3), (7, -3), (3, 7), (4, 3), (-5, 3)} 13. domanin and range and function( {147, 180), (170, -200), (113, -200)} 1 solutions Answer 375440 by jim_thompson5910(28595)   on 2012-03-24 14:32:43 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started. # 1 Recall that the domain is the set of all allowable inputs. So the domain is the set of allowed 'x' values. The range is the set of possible outputs, so it's the set of possible 'y' values. So the domain and range are... Domain: {-8, -5, 3, 4, 7} Range: {-3, 3, 7} Note: duplicates are tossed out -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Probability-and-statistics/590929: I Roll a six-sided Dye one time. What is the probability that I'll get any number other than 4? 1 solutions Answer 375370 by jim_thompson5910(28595)   on 2012-03-24 03:09:02 (Show Source): You can put this solution on YOUR website! P(Not 4) = 1 - P(4) P(Not 4) = 1 - 1/6 P(Not 4) = 5/6

Polynomials-and-rational-expressions/590924: trial and error answer for 2x^2-5x-7 1 solutions Answer 375365 by jim_thompson5910(28595)   on 2012-03-24 01:09:49 (Show Source): You can put this solution on YOUR website! Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,2,7,14 -1,-2,-7,-14 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*(-14) = -14 2*(-7) = -14 (-1)*(14) = -14 (-2)*(7) = -14 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 -14 1+(-14)=-13 2 -7 2+(-7)=-5 -1 14 -1+14=13 -2 7 -2+7=5 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term =============================================================== Answer: So factors to . In other words, . Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical). -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Equations/590925: 8x-7=15+19x solve please 1 solutions Answer 375364 by jim_thompson5910(28595)   on 2012-03-24 01:09:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Exponents/590901: -√(7c)2) 1 solutions Answer 375360 by jim_thompson5910(28595)   on 2012-03-24 00:07:37 (Show Source): You can put this solution on YOUR website! So for all values of 'c' where

Graphs/590906: What is the slope of the line that contains the points (3, 4) and (1, 2)? 1 solutions Answer 375359 by jim_thompson5910(28595)   on 2012-03-24 00:05:34 (Show Source): You can put this solution on YOUR website! Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/590912: This is another problem I am struggling with. Would someone please show me how to go about solving it? Divide and check 16x^7 - 24x^6 + 20x _________________ 4x 1 solutions Answer 375355 by jim_thompson5910(28595)   on 2012-03-24 00:01:33 (Show Source): You can put this solution on YOUR website! So completely simplifies to In other words, for all values of x where . -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

absolute-value/590920: What is the solution to: -2|x|<6 ? 1 solutions Answer 375353 by jim_thompson5910(28595)   on 2012-03-23 23:57:51 (Show Source): You can put this solution on YOUR website! -2|x|<6 |x| > 6/(-2) |x| > -3 Since the absolute value of any number is ALWAYS nonnegative, this means that |x| will either be 0 or some positive number. So |x| is ALWAYS larger/greater than -3 for any value of x. So there are an infinite number of solutions. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/590916: Is there an easy way to understand how to work these? Would someone please show me? FACTOR BY GROUPING 5x^3 - 15x^2 - 4x + 12 1 solutions Answer 375352 by jim_thompson5910(28595)   on 2012-03-23 23:55:21 (Show Source): You can put this solution on YOUR website! Start with the given expression Group the terms in two pairs Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to In other words, for all values of x. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/590911: Would someone show me how to do this step by step? Factor completely 5s^2 - 22s + 8 1 solutions Answer 375350 by jim_thompson5910(28595)   on 2012-03-23 23:54:29 (Show Source): You can put this solution on YOUR website! Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is . Now multiply the first coefficient by the last term to get . Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ? To find these two numbers, we need to list all of the factors of (the previous product). Factors of : 1,2,4,5,8,10,20,40 -1,-2,-4,-5,-8,-10,-20,-40 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*40 = 40 2*20 = 40 4*10 = 40 5*8 = 40 (-1)*(-40) = 40 (-2)*(-20) = 40 (-4)*(-10) = 40 (-5)*(-8) = 40 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 40 1+40=41 2 20 2+20=22 4 10 4+10=14 5 8 5+8=13 -1 -40 -1+(-40)=-41 -2 -20 -2+(-20)=-22 -4 -10 -4+(-10)=-14 -5 -8 -5+(-8)=-13 From the table, we can see that the two numbers and add to (the middle coefficient). So the two numbers and both multiply to and add to Now replace the middle term with . Remember, and add to . So this shows us that . Replace the second term with . Group the terms into two pairs. Factor out the GCF from the first group. Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis. Combine like terms. Or factor out the common term =============================================================== Answer: So factors to . In other words, . Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical). -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/590909: Can someone please explain to me how to do this problem? (9x^2-xy+y^2)+ (-x^2-8xy+9y^2) 1 solutions Answer 375348 by jim_thompson5910(28595)   on 2012-03-23 23:53:53 (Show Source): You can put this solution on YOUR website! Remove unneeded parenthesis Group like terms Combine like terms So fully simplifies to -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------