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# Recent problems solved by 'jim_thompson5910'

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 test/632532: What is the simplified form of sin(x+pi)? A. cos x B. sin x C. -sin x D. -cos x1 solutions Answer 398732 by jim_thompson5910(28476)   on 2012-07-30 14:44:50 (Show Source): You can put this solution on YOUR website!sin(x+pi) sin(x)cos(pi)+cos(x)sin(pi) sin(x)(-1)+cos(x)(0) -sin(x)
 test/632818: How many terms has 3x^2y+7y1 solutions Answer 398730 by jim_thompson5910(28476)   on 2012-07-30 14:43:06 (Show Source): You can put this solution on YOUR website!3x^2y+7y has two terms
 test/632925: 4+6-4-231 solutions Answer 398729 by jim_thompson5910(28476)   on 2012-07-30 14:42:36 (Show Source): You can put this solution on YOUR website!4+6-4-23 = -17 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 test/632931: What's the equivalent to 3a+4b-(-6a-3b)?1 solutions Answer 398728 by jim_thompson5910(28476)   on 2012-07-30 14:41:42 (Show Source): You can put this solution on YOUR website!3a+4b-(-6a-3b) 3a+4b+6a+3b 9a+7b -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 test/633182: 1 solutions Answer 398726 by jim_thompson5910(28476)   on 2012-07-30 14:40:58 (Show Source): You can put this solution on YOUR website!Problem missing.
 Inequalities/633203: -6-6(5x-6)>-6(5+3x)1 solutions Answer 398725 by jim_thompson5910(28476)   on 2012-07-30 14:40:35 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left side. Subtract from 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. 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 --------------------------------------------------------------------------------------------------------------
 Expressions-with-variables/632728: 3 - 4x = 10x + 101 solutions Answer 398438 by jim_thompson5910(28476)   on 2012-07-28 17:32:41 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from 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 --------------------------------------------------------------------------------------------------------------
 Linear-equations/632687: Solve the system of equations by graphing 2y=5x+11 x=y+51 solutions Answer 398432 by jim_thompson5910(28476)   on 2012-07-28 16:18:40 (Show Source): You can put this solution on YOUR website!Graph the two equations to get Note: the first equation is the green line and the second equation is the blue line From the graph, we see that the two lines intersect at the point (-7,-12) So the solutions are x = -7 and y = -12 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Exponential-and-logarithmic-functions/632635: Graph y=10(3)x1 solutions Answer 398430 by jim_thompson5910(28476)   on 2012-07-28 16:11:08 (Show Source): You can put this solution on YOUR website!Use a graphing calculator to get -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Quadratic_Equations/632707: Can you compute the discriminant of the equation x^2+12x+36=01 solutions Answer 398424 by jim_thompson5910(28476)   on 2012-07-28 15:25:44 (Show Source): You can put this solution on YOUR website!From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Subtract from to get So the discriminant is Since the discriminant is equal to zero, this means that there is one real solution. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 test/632698: 1 solutions Answer 398421 by jim_thompson5910(28476)   on 2012-07-28 15:01:04 (Show Source): You can put this solution on YOUR website!Problem missing.
 Proportions/632690: 741/31 solutions Answer 398418 by jim_thompson5910(28476)   on 2012-07-28 14:36:46 (Show Source): You can put this solution on YOUR website!741 = 720 + 21 720 = 90*8 = 3*30*8 = 3*240 21 = 3*7 -------------------------------- 741 = 720 + 21 741 = 3*240 + 3*7 = 3(240+7) = 3*247 So 741 = 3*247 ------------------------------- 741/3 (3*247)/3 247 So 741/3 = 247 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 real-numbers/632685: 4x⁴ - 7x³ - 12x⁴ + 6x³1 solutions Answer 398415 by jim_thompson5910(28476)   on 2012-07-28 14:15:45 (Show Source): You can put this solution on YOUR website! So 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 --------------------------------------------------------------------------------------------------------------
 real-numbers/632675: (10-2(5))/(4-5)1 solutions Answer 398409 by jim_thompson5910(28476)   on 2012-07-28 13:43:16 (Show Source): You can put this solution on YOUR website!(10-2(5))/(4-5) (10-10)/(4-5) 0/(-1) 0 So (10-2(5))/(4-5) = 0 -------------------------------------------------------------------------------------------------------------- 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/632677: Given a binomial distribution with n = 21 and p = 0.77, would the normal distribution provide a reasonable approximation? Hi, I feel like I've missed a class. Everything I'm reading says that to do this I need np and n(1-p) = nq and I have no idea what this means!! can someone help please? I don't want the answer I want to know how to get the answer. Thanks.1 solutions Answer 398407 by jim_thompson5910(28476)   on 2012-07-28 13:39:11 (Show Source): You can put this solution on YOUR website!np = 21*0.77 = 16.17 So np = 16.17 ----------------------- n(1-p) = 21*(1-0.77) = 4.83 So n(1-p) = 4.83 or nq = 4.83 since q = (1-p) ------------------------ Since nq = 4.83 is NOT greater than 5, this means that the normal distribution would NOT provide a reasonable approximation It would only provide a reasonable approximation if BOTH np AND nq are greater than 5. -------------------------------------------------------------------------------------------------------------- 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/632514: What is the equation of a line that passes through points (-1, 2) and (5, 2)? 1 solutions Answer 398335 by jim_thompson5910(28476)   on 2012-07-27 20:17:18 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and 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 Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 2 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. 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 --------------------------------------------------------------------------------------------------------------
 Age_Word_Problems/632383: If Heather makes $2,000 a month and pays$750 for rent, what fraction of her income is spent on rent?1 solutions Answer 398330 by jim_thompson5910(28476)   on 2012-07-27 19:14:09 (Show Source): You can put this solution on YOUR website!750/2000 = (250*3)/(250*8) = 3/8 So of her income is spent on rent. -------------------------------------------------------------------------------------------------------------- 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/632495: Find the volume of a cube 4 inches on each side 1 solutions Answer 398325 by jim_thompson5910(28476)   on 2012-07-27 18:43:26 (Show Source): You can put this solution on YOUR website!V = s^3 V = 4^3 V = 64 cubic inches -------------------------------------------------------------------------------------------------------------- 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_And_Systems_Word_Problems/632476: Can a linear equation and a linear inequality be solved in the same way? Explain why. What makes them different? 1 solutions Answer 398307 by jim_thompson5910(28476)   on 2012-07-27 17:49:48 (Show Source): You can put this solution on YOUR website!They can be solved in the same way. The only difference is that when you multiply or divide both sides by a negative number, then the inequality sign will flip. Note: you can think of the equation sign flipping as well if you want (to stay consistent) since flipping the equation sign goes from = to = (and it doesn't change) -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 expressions/632467: -77+2xy+3x+7(-2xy+4x)+(-2y)+100-(-4y)1 solutions Answer 398293 by jim_thompson5910(28476)   on 2012-07-27 16:37:51 (Show Source): You can put this solution on YOUR website! So 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 --------------------------------------------------------------------------------------------------------------
 Linear-equations/632456: Write your solution using set builder notation -2(10x-9)-17x<12(6-x)1 solutions Answer 398277 by jim_thompson5910(28476)   on 2012-07-27 15:49:49 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left side. Subtract from 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in set-builder notation 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 --------------------------------------------------------------------------------------------------------------
 logarithm/632448: Write the expression in terms of common logarithms, and then give a calculator approximation. log9(77) 1 solutions Answer 398272 by jim_thompson5910(28476)   on 2012-07-27 14:57:18 (Show Source): You can put this solution on YOUR website!$\LARGE \log_{9}(77) = \frac{\log(77)}{\log(9)}$ (using the change of base formula) $\LARGE \log_{9}(77) \approx \frac{1.88649072517249}{0.95424250943932}$ $\LARGE \log_{9}(77) \approx 1.9769510439028$ $\LARGE \log_{9}(77) \approx 1.97695$ (rounded to 5 places) -------------------------------------------------------------------------------------------------------------- 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/632444: Determine whether the ordered pair (1,7) is a soultion of the equation: y=2x+5 I'm assuming that the answer is yes because I can can add 5+2 to get 7, but I don't have a clue how I would show my work on something like this...I would appreciate any help or explanation. Thanks, Michelle Lunde (Linear equations and graphs)1 solutions Answer 398270 by jim_thompson5910(28476)   on 2012-07-27 14:39:43 (Show Source): You can put this solution on YOUR website!y = 2x + 5 ... Start with the given equation 7 = 2(1) + 5 ... Plug in x = 1 and y = 7 7 = 2(1) + 5 7 = 2 + 5 ... Multiply 7 = 7 ... Add Since that last equation is true, this means that is true when and Therefore, (1,7) is indeed a solution 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 --------------------------------------------------------------------------------------------------------------
 Linear-equations/632382: Write the slope-intercept form of the equation of the line containing the points (-3,4) and (3,-2).1 solutions Answer 398269 by jim_thompson5910(28476)   on 2012-07-27 14:36:06 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and 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 Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 4 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. 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 --------------------------------------------------------------------------------------------------------------
 Miscellaneous_Word_Problems/632439: 14-9(4-3q)=5(q+6)-7q1 solutions Answer 398267 by jim_thompson5910(28476)   on 2012-07-27 14:33:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. 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 . ---------------------------------------------------------------------- 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/632254: 15y^2-10y=5y( ) Complete the factoring. Thank you! oh gosh thank you jim! you're a genius!1 solutions Answer 398158 by jim_thompson5910(28476)   on 2012-07-26 20:32:31 (Show Source): You can put this solution on YOUR website!15y^2-10y=5y(3y - 2) Notice how 5y*3y = 15y^2 and 5y*(-2) = -10y. So this confirms the answer. -------------------------------------------------------------------------------------------------------------- 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/632231: What is (4^7)^14?!1 solutions Answer 398142 by jim_thompson5910(28476)   on 2012-07-26 18:45:27 (Show Source): You can put this solution on YOUR website! So -------------------------------------------------------------------------------------------------------------- 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/632182: Slope of the line that passes through the points (0,0) & (-11,-10) is: Select one: 11/10 10/11 11 101 solutions Answer 398077 by jim_thompson5910(28476)   on 2012-07-26 15:31:54 (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 --------------------------------------------------------------------------------------------------------------
 Volume/632170: I have a spray tank that is 72" long and 36" in diameter how many gallons of water are in my tank if it is full? thank you very much!!1 solutions Answer 398068 by jim_thompson5910(28476)   on 2012-07-26 15:07:16 (Show Source): You can put this solution on YOUR website!V = pi*r^2*h V = pi*(18)^2*(72) V = 23328pi <<< --- Exact Volume V = 23328(3.14159) V = 73287.01152 <<< --- Approximate Volume So the approximate volume is 73287.01152 cubic inches. Now convert this to gallons (73287.01152 cubic inches)*(1 gallon/231 cubic inches) = 73287.01152/231 = 317.25979012987 and round it to get 317.2598 So the tank can hold approximately 317.2598 gallons. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 real-numbers/632152: is the squre root of 42 a rational or irrational number?1 solutions Answer 398045 by jim_thompson5910(28476)   on 2012-07-26 13:47:13 (Show Source): You can put this solution on YOUR website!$\LARGE \sqrt{42} \approx 6.48074069840787...$ So $\LARGE \sqrt{42}$ is irrational (since the decimal portion doesn't terminate or repeat) -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------