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jim_thompson5910 answered: 28684 problems
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absolute-value/585612: What is the solution set for |2x – 3| = 13? 1 solutions Answer 373422 by jim_thompson5910(28696)   on 2012-03-11 20:39:03 (Show Source): You can put this solution on YOUR website! |2x – 3| = 13 2x – 3 = 13 or 2x – 3 = -13 2x = 13 + 3 or 2x = -13 + 3 2x = 16 or 2x = -10 x = 16/2 or x = -10/2 x = 8 or x = -5 So the solutions are x = 8 or x = -5

Functions/585611: Find the range given the domain: y= 6 over x + 1 Domain: {-2, 3, 6} 1 solutions Answer 373421 by jim_thompson5910(28696)   on 2012-03-11 20:38:04 (Show Source): You can put this solution on YOUR website! When x = -2, y = 6/(x+1) = 6/(-2+1) = 6/(-1) = -6 So when x = -2, y = -6 When x = 3, y = 6/(x+1) = 6/(3+1) = 6/(4) = 3/2 So when x = 3, y = 3/2 When x = 6, y = 6/(x+1) = 6/(6+1) = 6/7 So when x = 6, y = 6/7 So the range is {-6, 3/2, 6/7} -------------------------------------------------------------------------------------------------------------- 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/585607: 6(b-x) = 4b + ax solve for X 1 solutions Answer 373417 by jim_thompson5910(28696)   on 2012-03-11 20:34:37 (Show Source): You can put this solution on YOUR website! 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/585606: 6x-7 = x + 4, 1 solutions Answer 373412 by jim_thompson5910(28696)   on 2012-03-11 20:32:01 (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 --------------------------------------------------------------------------------------------------------------

percentage/585602: 57 is 20% of? 1 solutions Answer 373408 by jim_thompson5910(28696)   on 2012-03-11 20:27:30 (Show Source): You can put this solution on YOUR website! 57 = 0.2x 57/0.2 = x 285 = x x = 285 So 57 is 20% of 285. -------------------------------------------------------------------------------------------------------------- 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/585510: x^2-16x+60 by factoring completely? 1 solutions Answer 373374 by jim_thompson5910(28696)   on 2012-03-11 17:37:32 (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 : 1,2,3,4,5,6,10,12,15,20,30,60 -1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*60 = 60 2*30 = 60 3*20 = 60 4*15 = 60 5*12 = 60 6*10 = 60 (-1)*(-60) = 60 (-2)*(-30) = 60 (-3)*(-20) = 60 (-4)*(-15) = 60 (-5)*(-12) = 60 (-6)*(-10) = 60 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 60 1+60=61 2 30 2+30=32 3 20 3+20=23 4 15 4+15=19 5 12 5+12=17 6 10 6+10=16 -1 -60 -1+(-60)=-61 -2 -30 -2+(-30)=-32 -3 -20 -3+(-20)=-23 -4 -15 -4+(-15)=-19 -5 -12 -5+(-12)=-17 -6 -10 -6+(-10)=-16 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/585505: Find all numbers for which the rational expression is undefined 6x^2 / 4x+7 1 solutions Answer 373373 by jim_thompson5910(28696)   on 2012-03-11 17:35:25 (Show Source): You can put this solution on YOUR website! Hint: you cannot divide by zero. So find all the values of x which make the denominator 4x+7 equal to zero. These are the values that make the rational expression undefined.

Proofs/585493: 1. (E∨F)→~G 2. ~H 3. H∨K 4. (K∨L)→E ∴ ~G 1 solutions Answer 373370 by jim_thompson5910(28696)   on 2012-03-11 17:17:31 (Show Source): You can put this solution on YOUR website! 1. (E∨F) → ~G 2. ~H 3. H∨K 4. (K∨L)→E / ∴ ~G ------------------------------- 5. K 3,2 Disjunctive Syllogism 6. K∨L 5 Addition 7. E 4,6 Modus Ponens 8. E∨F 7 Addition 9. ~G 1,8 Modus Ponens

Rectangles/585490: Factor. The perimeter of a rectangle is represented by 2l + 2w. Express the perimeter as the product of two factors. 1 solutions Answer 373369 by jim_thompson5910(28696)   on 2012-03-11 17:14:58 (Show Source): You can put this solution on YOUR website! 2l + 2w = 2(l+w)

Linear-equations/585488: what is an equation of a line that passes through points (5,4) and (-2,0) 1 solutions Answer 373368 by jim_thompson5910(28696)   on 2012-03-11 17:14:23 (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 Distribute Multiply Add 4 to both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation 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 --------------------------------------------------------------------------------------------------------------

Money_Word_Problems/585474: I was wondering how would you find the percentage of decrease, Traditions Clothing Store is having a sale. Shirts that were regularly priced at $20 are on sale for $17. What is the percentage of decrease in the price of the shirts? 1 solutions Answer 373367 by jim_thompson5910(28696)   on 2012-03-11 16:46:35 (Show Source): You can put this solution on YOUR website! Percent Decrease = [(Old - New)/Old] * 100 Percent Decrease = [(20-17)/20] * 100 Percent Decrease = [3/20] * 100 Percent Decrease = 0.15 * 100 Percent Decrease = 15% -------------------------------------------------------------------------------------------------------------- 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/585473: how do you use the change the base formula to solve this problem? base is 125 log125 25? -please help 1 solutions Answer 373366 by jim_thompson5910(28696)   on 2012-03-11 16:44:08 (Show Source): You can put this solution on YOUR website! log125 (25) = (log(25))/(log(125)) = (1.39794000867203)/(2.09691001300806) = 0.66666666666667 Notice how 2/3 = 0.66666666666667 as well So log125 (25) = 2/3

Permutations/585468: You wish to select a committee of president, vice president and secretary from a pool of 55 people. In how many ways can this committee be chosen? 1 solutions Answer 373362 by jim_thompson5910(28696)   on 2012-03-11 16:33:35 (Show Source): You can put this solution on YOUR website! P(n,r) = (n!)/((n-r)!) P(55,3) = (55!)/((55-3)!) P(55,3) = (55!)/(52!) P(55,3) = (55*54*53*52!)/(52!) P(55,3) = 55*54*53 P(55,3) = 157410 So there are 157410 different ways. -------------------------------------------------------------------------------------------------------------- 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/585463: how do i turn this into a single log? base is 10. 3logx + 5logy? 1 solutions Answer 373357 by jim_thompson5910(28696)   on 2012-03-11 16:17:36 (Show Source): You can put this solution on YOUR website! 3*log(x) + 5*log(y) log(x^3) + log(y^5) log(x^3y^5) So 3*log(x) + 5*log(y) = log(x^3y^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 --------------------------------------------------------------------------------------------------------------

logarithm/585462: The population of fish in a lake is decreasing. There are currently 24,000 fish in the lake. The population is decreasing 6% each year. In how many years will there be 1/4 of the current number of the fish in the lake? Use formula T(n)=a(1+r)^n to solve problem? -please someone help. 1 solutions Answer 373356 by jim_thompson5910(28696)   on 2012-03-11 16:16:32 (Show Source): You can put this solution on YOUR website! T(n)=a(1+r)^n T(n)=24000(1+(-0.06))^n T(n)=24000(1-0.06)^n T(n)=24000(0.94)^n So the formula is T(n)=24000(0.94)^n Now plug in T(n) = 24000/4 = 6000 and solve for n ------------------------------- T(n)=24000(0.94)^n 6000=24000(0.94)^n 6000/24000=(0.94)^n 1/4=(0.94)^n ln(1/4) = ln((0.94)^n) ln(1/4) = n*ln(0.94) ln(1/4)/ln(0.94) = n n = ln(1/4)/ln(0.94) n = 22.4046 So in roughly 22.4046 years, the population will be 1/4 of the current population. -------------------------------------------------------------------------------------------------------------- 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_proofs/585406: Given: Trapezoid WXYZ with bases WX and ZY, Rectangle WXAB, WA perpendicular to ZY XB perpendicular ZY , ZA is congruent to YB Prove:Trapezoid WXYZ is isosceles 1 solutions Answer 373351 by jim_thompson5910(28696)   on 2012-03-11 16:00:51 (Show Source): You can put this solution on YOUR website! It helps to draw a picture, so let's do so Statement Reason 1. WA perpendicular to ZY Given 2. XB perpendicular ZY Given 3. ZA = YB Given 4. < ZAW = < YBX All perpendicular angles equal 90 degrees 5. WA = XB Opposite sides of a rectangle are equal 6. triangle ZAW = triangle YBX SAS property 7. ZW = YX CPCTC 8. trapezoid WXYZ is isosceles nonparallel sides are congruent

Rectangles/585449: The dimensions of a retangle are 5cm by 13m. what are the dimensions of a similar rectangle with exactly double the area? 1 solutions Answer 373350 by jim_thompson5910(28696)   on 2012-03-11 15:44:23 (Show Source): You can put this solution on YOUR website! A = LW A = 5*13 A = 65 Double the area to get 65*2 = 130 A = LW 130 = xy y = 130/x -------------- x/y = 13/5 y = 13x/5 ------------- y = 130/x 13x/5 = 130/x 13x^2 = 130*5 13x^2 = 650 x^2 = 650/13 x^2 = 50 x = sqrt(50) x = 5*sqrt(2) x = 7.0710678 --------------------- y = 130/x y = 130/7.0710678 y = 18.384776 So the dimensions are roughly 7.0710678 by 18.384776

Surface-area/585446: Calculate the area of a rectangle with length 5 centimeters and width 2.5 Centimeters. I got 12.5 is that correct? 1 solutions Answer 373349 by jim_thompson5910(28696)   on 2012-03-11 15:39:15 (Show Source): You can put this solution on YOUR website! A = LW A = 5*2.5 A = 12.5 So you are correct. The area is 12.5 square cm.

Graphs/585447: 6x -y =-8 2x + y =-16 im getting stuck the first step! try to solve by elimination method 1 solutions Answer 373348 by jim_thompson5910(28696)   on 2012-03-11 15:38:17 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green) -------------------------------------------------------------------------------------------------------------- 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/585445: -9x+ y=20 9x+16y=14 y=20+-9 9x + 16 (20+-9x)=14 9x+320=144x=14 153x+320=14 I understand up to here x= -2 dont understand how they got these answers could you show me step by step please? y= 2 1 solutions Answer 373347 by jim_thompson5910(28696)   on 2012-03-11 15:36:20 (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. Now that you have x = -2, use it in 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 --------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/585441: -2x2 + 3x + 20 1 solutions Answer 373343 by jim_thompson5910(28696)   on 2012-03-11 15:25:35 (Show Source): You can put this solution on YOUR website! I'm assuming you want to factor this. Start with the given expression. Factor out the GCF . Now let's try to factor the inner expression --------------------------------------------------------------- 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)=-39 2 -20 2+(-20)=-18 4 -10 4+(-10)=-6 5 -8 5+(-8)=-3 -1 40 -1+40=39 -2 20 -2+20=18 -4 10 -4+10=6 -5 8 -5+8=3 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 -------------------------------------------------- So then factors further to =============================================================== Answer: So completely 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/585439: add or subtract (5a^5-2a^3-9a^2)+(2a^5+a^3)+(-a^5-3a^2) 1 solutions Answer 373342 by jim_thompson5910(28696)   on 2012-03-11 15:23:36 (Show Source): You can put this solution on YOUR website! (5a^5-2a^3-9a^2)+(2a^5+a^3)+(-a^5-3a^2) 5a^5-2a^3-9a^2+2a^5+a^3+-a^5-3a^2 (5a^5+2a^5-a^5)+(-2a^3+a^3)+(-9a^2-3a^2) 6a^5-a^3-12a^2 So (5a^5-2a^3-9a^2)+(2a^5+a^3)+(-a^5-3a^2) completely simplifies to 6a^5-a^3-12a^2 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------

Inequalities/585417: Solve the inequality. Then describe the graph of the solution on a number line using the boxes below. x-1>10 1 solutions Answer 373336 by jim_thompson5910(28696)   on 2012-03-11 14:29:23 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on the number line Note: there is an open circle at the endpoint. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------

Finance/585415: PLZZ help!!!!!!!!!!!!!!!!!!!! A young couple that recently had their third child decide they need to purchase a new van. They make a down payment of $10,000 and finance the remaining $22,000 to purchase a 2010 Toyota Sienna. They arrange financing with their local financial institution and arrange an annual interest rate of 5.2% compounded monthly. They decide to make monthly payments of $400. What will be the outstanding balance on their loan after 24 months? 1 solutions Answer 373335 by jim_thompson5910(28696)   on 2012-03-11 14:27:51 (Show Source): You can put this solution on YOUR website! 400*12t = A 4800t = A A = P(1 + r/n)^(nt) A = 22000(1 + 0.052/12)^(12t) 4800t = 22000(1 + 0.052/12)^(12t) use a graphing calculator to solve for t to get roughly t = 6.382878 A = 22000(1 + 0.052/12)^(12t) A = 22000(1 + 0.052/12)^(12*6.382878) A = 30637.82 Since they make monthly payments of $400, after 24 months (or 2 years), they will have paid 24*400 = $9600 So after 24 months, the outstanding balance is 30637.82 - 9600 = 21037.82

Finance/585410: PLZZ HELP!! i did it but not sure if i am right? You sign a contract to borrow $20000 which states you must pay back $27,000 six years from now. What simple annual interest rate are you paying? my answer is 5.18% 1 solutions Answer 373333 by jim_thompson5910(28696)   on 2012-03-11 14:19:28 (Show Source): You can put this solution on YOUR website! The interest paid is $27000 - $20000 = $7000 Now plug this into the formula I = Prt along with P = 20000 and t = 6 and solve for r: I = Prt 7000 = 20000r(6) 7000 = 120000r 7000/120000 = r 0.05833333333333 = r r = 0.05833333333333 r = 0.05833 So the interest rate is roughly 5.8333% (which is 5 and 5/6%)

Finance/585409: PLZ HLEP!! i did it but not sure if i did it right Cynthia decides to buy some furniture for her new house. She doesn’t have the money so she borrows $6,000 from her father. She agrees to pay her father back after 60 months with 4.5% simple interest. How much will she pay back to her father in total? my answer is $7350 1 solutions Answer 373332 by jim_thompson5910(28696)   on 2012-03-11 14:14:55 (Show Source): You can put this solution on YOUR website! You are correct. She'll have to pay back the original $6000 loaned to her and an additional 6000(0.045)(5) = $1350 in interest, which means she'll pay back a total of 6000+1350 = $7350

Numeric_Fractions/585403: 8n+6=10 please write the answers as a fraction 1 solutions Answer 373330 by jim_thompson5910(28696)   on 2012-03-11 14:05:17 (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 -------------------------------------------------------------------------------------------------------------- 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/585400: 1 over -27= (-3) to the blank power. What is the blank power? 1 solutions Answer 373327 by jim_thompson5910(28696)   on 2012-03-11 13:48:06 (Show Source): You can put this solution on YOUR website! 1/(-27) = (-3)^x (-3)^(-3) = (-3)^x -3 = x x = -3 So the answer is -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 --------------------------------------------------------------------------------------------------------------

Geometry_proofs/585399: Given:ABCD is a rectangle Proofs:triangle ADC is congruent triangle CBA 1 solutions Answer 373326 by jim_thompson5910(28696)   on 2012-03-11 13:46:54 (Show Source): You can put this solution on YOUR website! Statement Reason 1. ABCD is a rectangle Given 2. AB = CD Opposite sides of rectangle are congruent 3. BC = AD Opposite sides of rectangle are congruent 4. AC = AC Reflexive Property of Equality 5. triangle ADC = triangle CBA SSS Property

Linear-equations/585394: Find the domain and range of 56.1 1 solutions Answer 373322 by jim_thompson5910(28696)   on 2012-03-11 13:13:58 (Show Source): You can put this solution on YOUR website! We need problem 56.1 as we do NOT have your book. Thanks.

Functions/585393: If f(x) = x + 4, find f(3). a. 1 b. 7 c. -1 d. 12 1 solutions Answer 373321 by jim_thompson5910(28696)   on 2012-03-11 13:11:03 (Show Source): You can put this solution on YOUR website! f(x) = x + 4 f(3) = 3 + 4 f(3) = 7 So the answer is f(3) = 7, which is choice B -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------