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# Recent problems solved by 'scott8148'

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 Functions/81604: This question is from textbook beginners algebra I would like to ask a business and finance applcation involving functions. The inventor of a new product believes that the cost of producing the prodict is given by the function, example; C(x)=1.75+7000 How much does it cost to produce 2000 units of her invention? If the inventor in exercise 53 charges \$4 per unit, then her profit for producing and selling x units is given by the function. P(x)=2.25x-7000 a.) What is her profit isf she sells 2000 units? b.) What is her profit if she selss 5000 units? C.)What is the break-even point for sales? Please help 1 solutions Answer 58544 by scott8148(6628)   on 2007-05-11 21:46:42 (Show Source): You can put this solution on YOUR website!the cost to produce 2000 units is found by setting x equal to 2000 in the cost function C(2000)=1.75(2000)+7000 ... C=3500+7000 ... C=10500 the profit on x units is found by substituting the value of x into the profit function a.) P(2000)=2.25(2000)-7000 ... P=4500-7000 ... P=-2500 b.) P(5000)=2.25(5000)-7000 ... P=11250-7000 ... P=4250 C.) the break even point is where there is no profit or loss ... find by setting P(x) equal to zero and solving for x 0=2.25(x)-7000 ... 7000=2.25x ... x=28000/9 ... this is not an integer value, so the break even point is between 3111 and 3112
 Linear-equations/81659: At what points does the line 4x + 12 = 3y cross the x and y axes?1 solutions Answer 58539 by scott8148(6628)   on 2007-05-11 21:17:14 (Show Source): You can put this solution on YOUR website!when the line crosses the x axis, y=0; and vice versa 4(0)+12=3y ... 12=3y ... 4=y ... so y-intercept is (0,4) 4x+12=3(0) ...4x+12=0 ... 4x=-12 ... x=-3 ... so x-intercept is (-3,0)
 Equations/81690: I am so lost on this one, how do I solve? 10x – 4 – 5x = 6 + 3x – 81 solutions Answer 58534 by scott8148(6628)   on 2007-05-11 21:06:02 (Show Source): You can put this solution on YOUR website!the goal is to get the unknown on one side by itself start by combining like terms on both sides ... 10x-5x-4=3x-8+6 ... 5x-4=3x-2 now, subtract 3x from both sides ... 2x-4=-2 ... add 4 to both sides ... 2x=2 finally divide both sides by 2 ... x=1
 Linear-equations/81693: How do I write the equation of the line with slope -1/2 and y-intercept (0, 3)?1 solutions Answer 58529 by scott8148(6628)   on 2007-05-11 20:55:44 (Show Source): You can put this solution on YOUR website!the general form of the slope-intercept equation is y=mx+b, where m is the slope and b is the y-intercept in this case
 Equations/81694: How do I solve the system by addition? 5x – 3y = 13 4x – 3y = 11 1 solutions Answer 58526 by scott8148(6628)   on 2007-05-11 20:51:31 (Show Source): You can put this solution on YOUR website!the goal is to eliminate one of the variables ... since y has the same coefficient in both equations, you can multiply one of the equations by -1 and then add them together multiplying the second equation by -1 gives -4x+3y=-11 ... adding the first equation gives 5x-3y-4x+3y=13-11 combining terms gives x=2 ... so, using first equation, 5(2)-3y=13 ... 10-3y=13 ... -3y=3 ... so y=-1
 Exponents/81658: Hello, I go to the Moring Star Online Homeschooling Academy. And need sever help with Exponents.. I am having questions that look like this: j-7^2k^9^3kl _____________ -j^4k^2l I do not understand how to do these.. This is one of many problems they are telling me to use: To complete these problems, use the rules you have learned as necessary in this order: Power of Quotients Rule (AKA: Power of Fractions Rule) Zero Exponent Rule Power Rule Expand or evaluate any exponents Product Rule Quotient Rule I have no idea how to even start a problem like this! I was wondering if you could give me a few pages to print out of how to do each step step-by-step explanatory help.. Can you send me a link or something. ASAP.. Thanks. I appreciate your help... VICTORIA P.S. If you could send me some rules and exaples of negative numbers with that Id really appreciate it :)1 solutions Answer 58514 by scott8148(6628)   on 2007-05-11 16:58:15 (Show Source): You can put this solution on YOUR website!try this link I found with google ... http://www.math.com/school/subject2/lessons/S2U2L2DP.html
 Travel_Word_Problems/81580: a car traveled at an average rate of 40 mph and then reduced its average rate to 30mph for the rest of the trip. if the 180 mile trip took five hour, determine how long the car traveled at each rate. 1 solutions Answer 58454 by scott8148(6628)   on 2007-05-10 21:37:32 (Show Source): You can put this solution on YOUR website!let t equal the time at 40 mph ... so 5-t is the time at 30 mph ... the total distance is the sum of the distances at the two rates 40*t+30*(5-t)=180 ... 40t+150-30t=180 ... 10t=30 ... t=3 ... 3 hrs at 40 mph and 2 hrs at 30 mph
 Percentage-and-ratio-word-problems/81581: how many cubic centimeters of a 25% antibotic solution should be added to 10 cubic centimetrs of a 60% antibiotic solution in order to get a 30% antibiotic solution?1 solutions Answer 58452 by scott8148(6628)   on 2007-05-10 21:31:05 (Show Source): You can put this solution on YOUR website!x cc's of 25% solution added to 10 cc's of a 60% solution gives (10+x) cc's of a 30% solution .25x+.6(10)=.3(10+x) ... .25x+6=3+.3x ... 3=.05x ... x=60
 Linear-equations/81574: Conside the linear equation D=RT, where D is distance in miles, R is speed in miles per hours. If I traveled at a speed of 50 miles per hour, find the time it takes me to catch up to a car traveling at 30 miles per hour that had a 200 mile head start.1 solutions Answer 58450 by scott8148(6628)   on 2007-05-10 21:22:21 (Show Source): You can put this solution on YOUR website!see 81572
 Linear-equations/81572: Conside the linear equation D=RT, where D is distance in miles, R is speed in miles per hours. If I traveled at a speed of 50 miles per hour, find the time it takes me to catch up to a car traveling at 30 miles per hour that had a 200 mile head start.1 solutions Answer 58448 by scott8148(6628)   on 2007-05-10 21:21:40 (Show Source): You can put this solution on YOUR website!when you catch the first car, you will have traveled the same distance ... the time it takes to catch up is your travel time ... this is the time that the first car travels AFTER the 200 mile head start 50*t=30*t+200 ... 20t=200 ... t=10 hours
 Geometry_proofs/81613: This question is from textbook Geometry Write a proof argument for part (b) of the sufficient conditions for a parallelogram theorem: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. given: that the opposite sides are congruent. prove: that the figure ABCD is a parallelogram I drew in diagonals in the figure ABCD and labeled the point where they intersect E. please help me solve this proof and provide the justifactions this is very important. PLEASE try to get this back to me by the end of May 10th thank you very much1 solutions Answer 58443 by scott8148(6628)   on 2007-05-10 21:08:25 (Show Source): You can put this solution on YOUR website!you can prove that the 2 triangles formed by drawing the diagonal are congruent by SSS ... you are given that the opposite sides are congruent and the diagonal is congruent to itself using the congruency of the two triangles, you can prove that the alternate angles at the ends of the diagonal are congruent (corresponding parts of congruent triangles are congruent) ... this proves the parallelism of the opposite sides by equal alternate interior angles
 Rate-of-work-word-problems/81406: Can anyone please help me with this problem? Two motorcycles each make the same 220 mile trip, but one travels 5 mph faster than the other. Find the rates of each motorcycle, if the slower one takes 24 minutes longer to complete the trip than the faster one. Show set-up, and equation work. Thanks.1 solutions Answer 58375 by scott8148(6628)   on 2007-05-10 01:27:07 (Show Source): You can put this solution on YOUR website!distance=rate X time ... let r=rate of slower motorcycle ... let t=time of faster motorcycle (in hours) for slower ... 220=r*(t+.4) ... t=(220/r)-.4 ... (24 min=.4 hr) for faster ... 220=(r+5)*t ... substituting t from slower gives ... 220=(r+5)*((220/r)-.4) FOILing gives 220=220-.4r+(1100/r)-2 ... 0=-.4r-2+(1100/r) ... multiplying by r gives dividing by -.4 gives ... using quadratic formula gives r=-55 and r=50 ... the negative value is unrealistic ... so slower=50 and faster=55
 Sequences-and-series/81427: One number is 6 more than another. If the sum of the smaller number and 3 times the larger number is 34, find the two numbers.1 solutions Answer 58367 by scott8148(6628)   on 2007-05-10 00:15:13 (Show Source): You can put this solution on YOUR website!let n equal the smaller number ... n+(3(n+6))=34 ... n+3n+18=34 ... 4n=16 ... n=4 so the numbers are 4 and 10
 Equations/81439: Write the equation of the line with slope -1/2 and y-intercept (0, 3).1 solutions Answer 58366 by scott8148(6628)   on 2007-05-10 00:06:20 (Show Source): You can put this solution on YOUR website!the general form is y=mx+b ... where m is the slope and b is the y-intercept in this case ... y=-(1/2)x+3
 Quadratic-relations-and-conic-sections/81488: This question is from textbook Algebra 2 I can not figure out how to write an equation for parabola focus (3,8),directrix y=41 solutions Answer 58340 by scott8148(6628)   on 2007-05-09 20:53:17 (Show Source): You can put this solution on YOUR website!a parabola is made up of points that are equidistant from a given point (focus) and a given line (directrix) the "distance formula" gives the distance between (x,y) and (3,8) as the distance between (x,y) and y=4 is y-4 ... x is not involved setting these equal gives ... squaring both sides gives ... ... so ........THIS ANSWER HAS BEEN CORRECTED (with my apologies)
 Graphs/81463: I'd really appreciate some help with my algebra, my middle school teacher just confuses me:( Here's the equation: find the y intercept and x intercept if y=2x-51 solutions Answer 58326 by scott8148(6628)   on 2007-05-09 20:08:45 (Show Source): You can put this solution on YOUR website!the y-intercept is where the line crosses the y axis, x is equal to zero ... y=2(0)-5 ... y=-5 the x-intercept is where the line crosses the x axis, y is equal to zero ... 0=2x-5 ... 5=2x ... x=5/2
 Volume/81482: how do i find the volume of a hexogonal cynlinder1 solutions Answer 58325 by scott8148(6628)   on 2007-05-09 20:01:36 (Show Source): You can put this solution on YOUR website!find the area of the hexagon (6 equilateral triangles) and multiply by the length of the cylinder
 Travel_Word_Problems/81421: I don't know if I am putting this in the right area but I need your help I can not do this I have been trying for ever please help me? The height h in feet of an object after t seconds is given by the function h=-16t^2+90t+3 How long will it take the object to hit the ground? round your answer to the nearest thousandth.1 solutions Answer 58321 by scott8148(6628)   on 2007-05-09 19:46:07 (Show Source): You can put this solution on YOUR website!the object "hits the ground" when it is at height 0 ... so set h=0 and solve for t ... using quadratic formula ... so t=-0.033 and t=5.658 ... the negative value is unrealistic
 Linear-equations/81209: This question is from textbook ALGEBRA 1 Hi,My question is how do you write an equation of the line in point-slope form that passes through the given point and has the given slope. (2,-1),m = 31 solutions Answer 58213 by scott8148(6628)   on 2007-05-08 15:03:11 (Show Source): You can put this solution on YOUR website!the equation has the general form ... y-(y coordinate)=m(x-(x coordinate)) in this case ... y-(-1)=3(x-2) ... y+1=3x-6 ... y=3x-7
 Graphs/81146: The boundary line of y>3 is graphed, how do I determine the correct half-plane and complete the graph?1 solutions Answer 58174 by scott8148(6628)   on 2007-05-07 23:05:54 (Show Source): You can put this solution on YOUR website!since this is a "greater than" inequality with no "equal to", the boundry line is dashed as opposed to solid to determine the correct half-plane, pick a point (I use the origin, if possible) on one side of the line and see if it satisfies the inequality ... if it does, then shade that side; if it doesn't, shade the other side
 Numeric_Fractions/81097: Factor completely. 18a(3) + 12a(2) + 2a1 solutions Answer 58173 by scott8148(6628)   on 2007-05-07 22:53:22 (Show Source): You can put this solution on YOUR website!factoring out 2a gives the remaining quadratic is a perfect square and factors into so the complete factoring is (2a)(3a+1)(3a+1)
 Mixture_Word_Problems/81119: This question is from textbook Find the length of a pendulum that makes one swing in three seconds?1 solutions Answer 58170 by scott8148(6628)   on 2007-05-07 22:43:04 (Show Source): You can put this solution on YOUR website!see 81126
 Mixture_Word_Problems/81126: This question is from textbook Find the length of a pendulum that makes one swing in three seconds?1 solutions Answer 58169 by scott8148(6628)   on 2007-05-07 22:42:00 (Show Source): You can put this solution on YOUR website!the formula for a simple pendulum is ... where T=period, L=length, g=gravitational acceleration solving for L gives ... so ... L equals approximately 7.30 feet
 Quadratic-relations-and-conic-sections/81128: How do I find the vertex of the following parabola f(x)= -x^2 + 9x -51 solutions Answer 58165 by scott8148(6628)   on 2007-05-07 22:23:47 (Show Source): You can put this solution on YOUR website!the vertex is on the axis of symmetry; the general equation of which is x=-b/2a ... in this case, x=-9/(-2), or x=4.5 so the x value for the vertex is 4.5 ... to find the y value, just substitute into the equation ... so y=15.25 ... vertex is (4.5,15.25)
 Vectors/81011: Two cables hold a 975 lb crate. The tension T1 and T2 equals 575lbs. Find ang le theta. I don't know if you can do this problelm without a picture. The picture is a thin long rectangular shape with T1 and T2 forming a triangle from this rectangle (the sides) and the crate (975lbs) is at the tip of the triangle. The angle theta is under the rectangular shape being the left and right angles of the triangle, if that makes sense?1 solutions Answer 58138 by scott8148(6628)   on 2007-05-07 13:49:57 (Show Source): You can put this solution on YOUR website!the weght of the crate is equally distributed between the cables, so each cable supports 975/2 or 487.5 lb 487.5 is the vertical component of the tension, which means that 575*sin(theta)=487.5 theta approximately equals 60 degrees
 Vectors/81010: Find the resultant using the component method for the given vectors A = 32degrees 3200lbs B = 36degrees 1300lbs C = 35degrees 2100lbs I added the 3 vectors using the head to tail method but not sure how to add three vectors, this is what I did: Ax =3200lb(cos32 degrees) =Ax = 2560 Ay = 3200(sin 32 degrees) =Ay = 1600 Bx = 1300lb (cos 36 degrees) = Bx = 1051.7 By - 1300 (sin 36 degrees) Its not finished but is that the way to do it?1 solutions Answer 58136 by scott8148(6628)   on 2007-05-07 13:38:23 (Show Source): You can put this solution on YOUR website!yes, you are doing it correctly ... find the x and y components of the three vectors and then add them Rx=Ax+Bx+Cx and Ry=Ay+By+Cy ... you can calculate the angle for R using Rx and Ry ... tan=Ry/Rx
 Problems-with-consecutive-odd-even-integers/81047: This question is from textbook Elementary Algebra The product of two consecutive even integers is 72.1 solutions Answer 58134 by scott8148(6628)   on 2007-05-07 13:26:00 (Show Source): You can put this solution on YOUR website!since 6*8=48 and 8*10=80, there appears to be something amiss with this problem if it were just consecutive integers (not even), then 8*9=72
 Geometry_Word_Problems/81026: A bacterial culture grows according to the formula P=Poa^t. If it takes 5 days for the culture to triple in size, how long did it take to double?1 solutions Answer 58133 by scott8148(6628)   on 2007-05-07 13:18:57 (Show Source): You can put this solution on YOUR website!if a^5=3, then taking the fifth root of both sides gives a=3^(1/5) ... so if a^x=2 ... (3^(1/5))^x=2 3^(x/5)=3^(log2/log3) ... x/5=log2/log3 ... x=5log2/log3 ... x is approximately 3.15
 Polynomials-and-rational-expressions/81031: I have to find the length of x. express my answer in simplified radical form. 51ft is the top 45ft is the bottom x is the smaller side on the side so i came up with x^2+45ft^2=51ft^2 =x^2+20.25+26.01 =x^2=46.26 I thought the answer of the four will be 68ft but it comes out to 46.24 but my answers to choose from is 18ft 24ft 10ft 68ft1 solutions Answer 58132 by scott8148(6628)   on 2007-05-07 12:56:10 (Show Source): You can put this solution on YOUR website!your initial equation is correct, but it looks like you made some errors with decimal points and algebra ... ... ... so x=24
 Quadratic_Equations/81046: This problem is not from my book. I have tried to answer it but don't feel I am correct, and I need every point possible to pass this course. Problem What is the minimum product of two numbers whose difference is 4? What are the numbers? Here is what I have done. n(n+1)=-4 n^2 + n = -4 n^2 + n - 4 = 0 (n+1)(n-4) The numbers are 1, -4, the minimum product is -4 Thank you so much for your help. Like I said I don.t think my solution is correct. 1 solutions Answer 58131 by scott8148(6628)   on 2007-05-07 12:43:30 (Show Source): You can put this solution on YOUR website!if the difference is 4 (not 5), then the numbers are n and n+4 (not n+1) ... so y=n(n+4) setting y=0 gives n=0 and n=-4 ... the minimum value for y is midway between these values (on the axis of symmetry) at n=-2 so the numbers are -2 and 2, and the product (which you did find) is -4