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Graphs/585068: y=1/3x-4 1 solutions Answer 373086 by jim_thompson5910(28476)   on 2012-03-10 12:00:20 (Show Source): You can put this solution on YOUR website! I'm assuming you want to graph this equation. 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 1 and the run is 3. This means that to go from point to point, we can go up 1 and over 3 So starting at , go up 1 unit and to the right 3 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 --------------------------------------------------------------------------------------------------------------

Geometry_Word_Problems/585021: A flowerbed measures 40 inches across. Whats the distance around the edge of the flowerbed? 1 solutions Answer 373085 by jim_thompson5910(28476)   on 2012-03-10 11:56:43 (Show Source): You can put this solution on YOUR website! Assuming this is a square, the perimeter is then P = 4s = 4(40) = 160 inches. So the distance around the edge of the flowerbed is 160 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 --------------------------------------------------------------------------------------------------------------

Geometry_Word_Problems/585079: 2.5m plus what equals 5m 1 solutions Answer 373084 by jim_thompson5910(28476)   on 2012-03-10 11:53:51 (Show Source): You can put this solution on YOUR website! 2.5m + x = 5m x = 5m - 2.5m x = 2.5m So the answer is 2.5m

Equations/585019: How do you solve 4(x+2)=20 1 solutions Answer 373030 by jim_thompson5910(28476)   on 2012-03-10 00:37:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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 --------------------------------------------------------------------------------------------------------------

Quadratic_Equations/585018: c) Calculate the value of if the difference between the roots of x^2-6x+k=0 is 3. 1 solutions Answer 373029 by jim_thompson5910(28476)   on 2012-03-10 00:30:33 (Show Source): You can put this solution on YOUR website! p-q = 3 (x-p)(x-q) x^2-xp-xq+pq x^2-(p+q)x+pq -(p+q)=-6 p+q=6 p-q=3 2p=9 p = 9/2 p+q = 6 9/2+q = 6 q = 6-9/2 q = 3/2 ----------------------- (x-p)(x-q) x^2-xp-xq+pq x^2-(p+q)x+pq x^2-(9/2+3/2)x+(9/2)(3/2) x^2-6x+27/4 So the value of 'k' is

Polynomials-and-rational-expressions/585010: Simplify. Do not use negative exponents in the answer. x^−4 • x^−7 1 solutions Answer 373028 by jim_thompson5910(28476)   on 2012-03-10 00:09:21 (Show Source): You can put this solution on YOUR website! x^(-4)*x^(-7) = x^(-4+(-7)) = x^(-11) = 1/(x^11) So the answer is

Polynomials-and-rational-expressions/584994: Simplify. Do not use negative exponents in the answer. x−4 • x−7 1 solutions Answer 373027 by jim_thompson5910(28476)   on 2012-03-10 00:08:18 (Show Source): You can put this solution on YOUR website! x^(-4)*x^(-7) = x^(-4+(-7)) = x^(-11) = 1/(x^11) So the answer is 1/(x^11)

Linear-equations/584971: (-2,0),(0,4) 1 solutions Answer 373026 by jim_thompson5910(28476)   on 2012-03-10 00:07:34 (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 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

Quadratic_Equations/585004: In questions 6-9, use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions. The above is the instructions for the problems. Below I have worked out each math problem, but once again, I'm not sure whether or not the solutions I have are real or complex. I think I worked each problem out correctly. If I have not please let me know. If I have, I guess the only thing I need clarifying on is if the solution I have is real or complex. 6. x²+6x-7=0 Use the quadratic formula to find the solutions. X=-b±√b²-4ac ax²+bx+c=0 2a A=1, B=6, C=-7 b²-4ac The discriminant of a quadratic is the expression inside the radical of the quadratic formula. ((6)²-4(1)(-7)) Substitute in the values of a,b, and c. 36-4(1)(-7) Squared 6 36-4(-7) Multiplied 1 by -7 36+28 Multiplied -4 by each term inside the parenthesis. 64 Added 36+28 ANSWER: 64 Real or complex???? 7.z²+z+1=0 Use the quadratic formula to find the solutions. X=-b±√b²-4ac ax²+bx+c=0 2a A=1, B=1, C=1 b²-4ac The discriminant formula ((1)²-4(1)(1)) Substitute in the values of a,b, and c 1-4(1)(1) Expand the exponent 2 to the expression 1-4(1) Multiply 1*1 1-4 Multiply -4 by each term inside the parenthesis -3 Subtract 4 from 1 ANSWER: -3 Real or complex?? 8. (3)½y²-4y-7(3)^½=0 √(3)*y²-4y-7(3)^½=0 An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent √3*y²-4y-7(3)^½=0 Removed the parenthesis around the expression 3 √3*y²-4y+(-7*√(3))=0 Reduced √3*y²-4y+(-7*√3)=0 Removed the parenthesis around the expression 3 √3*y²-4y+(7√3)=0 Multiplied -7 by √ y²√3-4y-7√3=0 Multiplied √3 by y² Y=-b±√b²-4ac ay²+bx+c=0 2a A=√3, B=-4, C=-7√3 b²-4ac Discriminant formula ((-4)²-4(√3)(-7√3)) Substitute in the values of a,b,c (4)(-4)-4(√3)(-7√3) Squared 16-4(√3)(-7√3) Multiply to simplify the expression (-4)(-4) 16-4(-7√3²) Multiply -7W to get -7W² 16+28√3² Multiplied -4 by each term inside the parenthesis. 16+28(3) Squared 16+84 Multiplied 28 by each term inside the parenthesis. ANSWER: 100 Real or complex??? 9. 2x²-10x+25=0 X=-b±√b²-4ac ax²+bx+c=0 2a A=2, B=-10, C=25 b²-4ac ((-10)²-4(2)(25)) Substitute in the values of a,b, and c. (-10)(-10)-4(2)(25) Squared 100-4(2)(25) Multiplied to simplify the expression (-10)(-10) 100-4(50) Multiplied 2 by25 100-200 Multiplied -4 by each term inside the parenthesis. ANSWER: -100 real or complex?? 1 solutions Answer 373025 by jim_thompson5910(28476)   on 2012-03-09 23:23:48 (Show Source): You can put this solution on YOUR website! The quantity is the determinant. This determines whether your solutions are real or complex. If is positive, then you'll have two real solutions. In the first problem (#6), you found that . Since this is a positive number, this means that you have two real solutions. On the other hand, for problem #9, you got -100. This means that there are 2 complex solutions. Hope this clears things up a bit. If not, let me know.

Triangles/584949: How many triangles can a decagon be divided into ? Is it 8 or 10 ? Thank you 1 solutions Answer 373009 by jim_thompson5910(28476)   on 2012-03-09 20:44:55 (Show Source): You can put this solution on YOUR website! It can be divided into 10-2 = 8 triangles. So your first choice is correct.

Probability-and-statistics/584957: In a study of internet users, researchers discovered that 80% of users own at least one computer ans that 25% of users log onto the internet for more that 30 hrs per week. Suppose that 15% of users own at least one computer AND log onto the internet for more that 30 hrs per wk. Given that an internet user owns at least one computer, what is the probability that he\she logs onto the internet for more than 30hrs per week? I know that P(I and C) = P(I) X P(I|C) but I am having trouble figuring out the numbers. Thank you 1 solutions Answer 373001 by jim_thompson5910(28476)   on 2012-03-09 19:06:49 (Show Source): You can put this solution on YOUR website! P(I|C) = P(I and C)/P(C) P(I|C) = 0.15/0.8 P(I|C) = 0.1875 So the probability that the user logs on for more than 30 hrs a week, given that the internet user owns at least one computer, is 0.1875 (which is an 18.75% chance)

Money_Word_Problems/584952: My monthly disability went from $468.00 to $ 492.00. What is the percentage of the raise? I know it rose by $24, but I can't figure out the percentage. Thank you! 1 solutions Answer 372993 by jim_thompson5910(28476)   on 2012-03-09 18:44:28 (Show Source): You can put this solution on YOUR website! Percent Increase = [(New - Old)/(Old)]*100 Percent Increase = [(492-468)/468]*100 Percent Increase = [24/468]*100 Percent Increase = [0.05128]*100 Percent Increase = 5.128% So it rose roughly 5.128%.

Volume/584942: What is the volume of a right circular cylinder with a diameter of 20 ft and a height of 60 ft? 1 solutions Answer 372988 by jim_thompson5910(28476)   on 2012-03-09 17:43:05 (Show Source): You can put this solution on YOUR website! A = pi*r^2*h A = pi*(10)^2*(60) A = pi*100*60 A = 6000pi So the exact volume is 6000pi cubic feet which approximates to 18849.5559 cubic feet.

Expressions-with-variables/584933: 5 times a number ,x, decreased by y 1 solutions Answer 372987 by jim_thompson5910(28476)   on 2012-03-09 17:10:48 (Show Source): You can put this solution on YOUR website! "5 times a number ,x, decreased by y" translates to

Triangles/584932: One equilateral triangle has sides 5 ft long. Another equilateral triangle has sides 7 ft long. Find the ratio of the areas of the triangles. I think I need to start with the similarity ratio. But I'm not sure, and I don't know where to go from there! Thank you. (: 1 solutions Answer 372986 by jim_thompson5910(28476)   on 2012-03-09 17:10:31 (Show Source): You can put this solution on YOUR website! If the side length of an equilateral triangle is x units, then the height/altitude is (x/2)*sqrt(3) units. So the area is then A = (bh)/2 = (x*(x/2)*sqrt(3))/2 = ((x^2)/4)*sqrt(3) So in short, the area of the equilateral triangle with side length 'x' is ((x^2)/4)*sqrt(3) square units. So the triangle with sides 5 ft long has an area of ((5^2)/4)*sqrt(3) = (25/4)*sqrt(3) and the triangle with sides 7 feet long has an area of ((7^2)/4)*sqrt(3) = (49/4)*sqrt(3) Divide the two to get ( (25/4)*sqrt(3) )/( (49/4)*sqrt(3) ) = (25/4)(4/49) = 25/49 So the ratio between the two areas is 25:49

Graphs/584929: Describe what the graph of interval [-4,10] looks like. 1 solutions Answer 372985 by jim_thompson5910(28476)   on 2012-03-09 17:04:23 (Show Source): You can put this solution on YOUR website! It's the shaded region on the number line from -4 to 10 where there are closed circles at the endpoints -4 and 10. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------

Trigonometry-basics/584928: 4xsquared+36x+35 i need two numbers that multiply to 56 but add to 36 (x+?)(x+?) 1 solutions Answer 372984 by jim_thompson5910(28476)   on 2012-03-09 17:03:40 (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 : 1,2,4,5,7,10,14,20,28,35,70,140 -1,-2,-4,-5,-7,-10,-14,-20,-28,-35,-70,-140 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*140 = 140 2*70 = 140 4*35 = 140 5*28 = 140 7*20 = 140 10*14 = 140 (-1)*(-140) = 140 (-2)*(-70) = 140 (-4)*(-35) = 140 (-5)*(-28) = 140 (-7)*(-20) = 140 (-10)*(-14) = 140 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 140 1+140=141 2 70 2+70=72 4 35 4+35=39 5 28 5+28=33 7 20 7+20=27 10 14 10+14=24 -1 -140 -1+(-140)=-141 -2 -70 -2+(-70)=-72 -4 -35 -4+(-35)=-39 -5 -28 -5+(-28)=-33 -7 -20 -7+(-20)=-27 -10 -14 -10+(-14)=-24 From the table, we can see that there are no pairs of numbers which add to . So cannot be factored. =============================================================== Answer: So doesn't factor at all (over the rational numbers). So is prime.

Travel_Word_Problems/584927: While driving at 90km/hr, how far in meters can you travel in 1.0 seconds? 1 solutions Answer 372981 by jim_thompson5910(28476)   on 2012-03-09 16:33:04 (Show Source): You can put this solution on YOUR website! d = rt d = 90*(1/3600) ... Note: 1 second = 1/(60*60) = 1/3600 hours d = 90/3600 d = 1/40 d = 0.025 Now convert to meters: 0.025*1000 = 25 So the answer is 25 meters.

Travel_Word_Problems/584926: 3. Is the time it takes to drive to the ski resort a function of the speed you drive? Explain. 1 solutions Answer 372979 by jim_thompson5910(28476)   on 2012-03-09 16:30:46 (Show Source): You can put this solution on YOUR website! You can start with the formula d = rt and solve for t to get t = d/r If the distance is held constant and fixed, then the time will change as the speed changes. So the answer is yes.

Probability-and-statistics/584924: If one vase contains 3 red, 4 pink and 5 white roses and another vase has 2 red, 2 pink and 2 white roses, what is probability that one rose chosen from each vase will be the same color? Please explain how to come to the answer. Thank you. 1 solutions Answer 372977 by jim_thompson5910(28476)   on 2012-03-09 16:16:17 (Show Source): You can put this solution on YOUR website! There are 3 possible scenarios: Scenario 1) Both roses are red P(Both Red) = P(Red)*P(Red) = (3/12)*(2/6) = 6/72 = 1/12 ------------------------------------------------------- Scenario 2) Both roses are pink P(Both Pink) = P(Pink)*P(Pink) = (4/12)*(2/6) = 8/72 = 1/9 ------------------------------------------------------- Scenario 2) Both roses are white P(Both White) = P(White)*P(White) = (5/12)*(2/6) = 10/72 = 5/36 Now add up all the probabilities: 1/12 + 1/9 + 5/36 = 3/36 + 4/36 + 5/36 = (3+4+5)/36 = 12/36 = 1/3 So the probability that one rose chosen from each vase will be the same color is 1/3

Rectangles/584923: i must find the missing dimension of a rectangle. the width is 2 and the length is x 1 solutions Answer 372975 by jim_thompson5910(28476)   on 2012-03-09 16:06:52 (Show Source): You can put this solution on YOUR website! You either need to know the area or the perimeter to find the missing dimension.

Equations/584917: Please help me solve this equation: Solve for W V=1/3LWH 64=1/3(6)W(4) 64=8W W=8 ??? 1 solutions Answer 372970 by jim_thompson5910(28476)   on 2012-03-09 15:51:24 (Show Source): You can put this solution on YOUR website! I'm assuming you were given V = 64 (volume), L = 6 (length) and H = 4 (height) If so, then are you are 100% correct. Congratulations.

Polynomials-and-rational-expressions/584915: How many real and complex roots does the plynomial f(x)=x^3+9x have? 1 solutions Answer 372966 by jim_thompson5910(28476)   on 2012-03-09 15:34:56 (Show Source): You can put this solution on YOUR website! f(x)=x^3+9x 0=x^3+9x x^3+9x=0 x(x^2+9)=0 x=0 or x^2+9=0 x=0, x=3i or x=-3i So there is one real root and two complex roots. -------------------------------------------------------------------------------------------------------------- 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/584914: Multiply and simplify the following: 4 squared 4 x 4 squared -5 1 solutions Answer 372964 by jim_thompson5910(28476)   on 2012-03-09 15:31:38 (Show Source): You can put this solution on YOUR website! (4^2)^4 * (4^2)^(-5) 4^(2*4)*(4^(2*(-5))) 4^8*4^(-10) 4^(8+(-10)) 4^(-2) 1/4^2 1/16 So (4^2)^4 * (4^2)^(-5) = 1/16 -------------------------------------------------------------------------------------------------------------- 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/584904: m/9 - 7/18 =1 1 solutions Answer 372963 by jim_thompson5910(28476)   on 2012-03-09 15:27:10 (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. Add to both sides. 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 --------------------------------------------------------------------------------------------------------------

Sequences-and-series/584884: Given a term in a arithmetic sequence and the common difference find the explicit formula a12=30 d=6 1 solutions Answer 372936 by jim_thompson5910(28476)   on 2012-03-09 14:22:06 (Show Source): You can put this solution on YOUR website! a[n] = a[1] + (n-1)d a[12] = a[1] + (12-1)*6 30 = a[1] + (12-1)*6 30 = a[1] + 66 30-66 = a[1] -36 = a[1] a[1] = -36 ------------------------------------------------------- a[n] = a[1] + (n-1)d a[n] = -36 + (n-1)6 a[n] = -36 + 6n-6 a[n] = 6n-42 So the explicit formula for the sequence is

Sequences-and-series/584882: Find the common ratio 2 12 72 432 1 solutions Answer 372935 by jim_thompson5910(28476)   on 2012-03-09 14:14:40 (Show Source): You can put this solution on YOUR website! To find the common ratio, simply divide a selected term by its previous term. r = 12/2 = 6 r = 72/12 = 6 r = 432/72 = 6 So the common ratio is r = 6.

Geometry_Word_Problems/584877: For a convex 40-gon, what is the sum of the measures of the interior angles? 1 solutions Answer 372934 by jim_thompson5910(28476)   on 2012-03-09 14:13:08 (Show Source): You can put this solution on YOUR website! S = 180(n-2) S = 180(40-2) S = 180(38) S = 6840 So the sum of the measures of the interior angles is 6840

Probability-and-statistics/584876: Find the mean, variance,and binomial distribution with the given values of n and p. n=122,p=0.24 The mean is: _____ (round to the nearest tenth as needed) The variance is:_____(round to the nearest tenth as needed) The standard divination is: _____(round to the nearest tenth as needed) 1 solutions Answer 372932 by jim_thompson5910(28476)   on 2012-03-09 14:04:59 (Show Source): You can put this solution on YOUR website! Mean: mu = np = 122*0.24 = 29.28 So the mean is 29.3 (rounded to the nearest tenth) ------------------------------------------------------- Variance: sigma^2 = np(1-p) = 122*0.24(1-0.24) = 22.2528 So the variance is 22.3 (rounded to the nearest tenth) ------------------------------------------------------- Standard Deviation: sigma = sqrt(np(1-p)) = sqrt(122*0.24(1-0.24)) = 4.717287 So the standard deviation is 4.7 (rounded to the nearest tenth)

Probability-and-statistics/584875: Use the confidence interval to find the margin of error and the sample mean: (0.256,0.380) a.The margin of error is: _____ b.The sample mea is: _____ 1 solutions Answer 372931 by jim_thompson5910(28476)   on 2012-03-09 14:02:13 (Show Source): You can put this solution on YOUR website! a) The margin of error is equal to the radius of the confidence interval or half the width of the confidence interval. Margin of Error: ME = (b-a)/2, where the confidence interval is (a,b) ME = (0.380-0.256)/2 ME = 0.062 So the margin of error is 0.062 ------------------------------------------------------- b) The sample mean is the center of the confidence interval. Note: this is assuming that this is a confidence interval for the true population mean. Sample Mean: xbar = (a+b)/2, for some confidence interval (a,b) xbar = (0.256 + 0.380)/2 xbar = 0.318 So the sample mean is 0.318

Equations/584808: 10+x-(2-3x)=4 1 solutions Answer 372920 by jim_thompson5910(28476)   on 2012-03-09 12:52:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is