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# Recent problems solved by 'scott8148'

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 Linear-systems/90560: My questions is what is the answer to : If f(x) = -2x + 7, what is f(x+3)? Thank you for your time...1 solutions Answer 65764 by scott8148(6628)   on 2007-07-28 21:31:47 (Show Source): You can put this solution on YOUR website!f(x+3)=-2(x+3)+7=-2x-6+7=-2x+1
 Travel_Word_Problems/90558: Please solve,wordproblemsare so difficult. :) Thank you! The trip upstream from A to B takes 4.5 hrs, and the trip back downstream takes 2 hrs. Its 18 miles from A toB. What is the speed of the current and what is the speed of the boat in still water? Thank you!1 solutions Answer 65762 by scott8148(6628)   on 2007-07-28 21:28:50 (Show Source): You can put this solution on YOUR website!let b=boat, c=current ... speed upstream=18/4.5=4 ... speed downstream=18/2=9 b+c=9 ... b-c=4 ... b+c+(b-c)=9+4 ... 2b=13 ... b=6.5 ... c=9-b ... c=2.5
 Geometry_Word_Problems/90479: The shorter parallel side of a trapezoid is equal to its height and the longer side is 3/2 times as long. If the area is 80, find the lengh of the shorter side.1 solutions Answer 65760 by scott8148(6628)   on 2007-07-28 21:06:04 (Show Source): You can put this solution on YOUR website!let x=shorter side ... area=(average of sides)(height) ... 80=((x+3x/2)/2)(x) ... 80=5x^2/4 320=5x^2 ... 64=x^2 ... 8=x
 Linear_Equations_And_Systems_Word_Problems/90471: Please help me figure the following problem out. Thank you A software company that sells a word processing program for personal computers. They have found that their montly profit in dollars, P, from selling x copies of the program is approximated by P(x)= -0.6x^2+2160x-10800 Find the number of copies of the program that should be sold in order to maximize the profits?1 solutions Answer 65757 by scott8148(6628)   on 2007-07-28 20:59:10 (Show Source): You can put this solution on YOUR website!the maximum value for P lies on the axis of symmetry of the function ... the equation is x=-b/2a in this case, x=-2160/(2(-0.6)) ... x=1800
 Linear-equations/90452: i need help with the following: A line passing through (–8, 2) and (–1, y) is perpendicular to a line with slope . Find the value of y. thank you 1 solutions Answer 65754 by scott8148(6628)   on 2007-07-28 20:48:59 (Show Source): You can put this solution on YOUR website!you need to provide the slope value
 Linear-equations/90450: i need help with the following please: Write the equation of the line with x-intercept (–1, 0) and undefined slope. i am lost with it thank you 1 solutions Answer 65753 by scott8148(6628)   on 2007-07-28 20:47:34 (Show Source): You can put this solution on YOUR website!an undefined slope means a vertical line ... passing through (-1,0) ... the equation of the line is x=-1
 Problems-with-consecutive-odd-even-integers/90266: THANK YOU SCOTT!!1 solutions Answer 65545 by scott8148(6628)   on 2007-07-26 23:24:35 (Show Source): You can put this solution on YOUR website!you're welcome
 Miscellaneous_Word_Problems/90213: the length of the side of a square is 3meters less than the length of the side of another square. The difference of their areas is 117 square meters. find the length of a side of each square.1 solutions Answer 65474 by scott8148(6628)   on 2007-07-26 16:17:57 (Show Source): You can put this solution on YOUR website!let s equal the smaller square ... (s+3)^2-s^2=117 ... s^2+6s+9-s^2=117 ... 6s=108 ... s=18 ... s+3=21
 Graphs/90223: This question is from textbook Beginning Algebra I need to identify the axis of symmetry, create a suitable table of values and sketch a graph including the axis of symmetry for: y = x^2 - 5x +3 I know the formula to find the axis is x = -b/2a thus x = -(-5)/2(1) = 5/2 From here on out I'm lost. I get really confused whenever fractions are involved. I'm not sure what numbers to choose for my values and why to choose those numbers. Any help would be appreciate.1 solutions Answer 65472 by scott8148(6628)   on 2007-07-26 16:11:29 (Show Source): You can put this solution on YOUR website!you've got the hard part ... for your table of values, choose numbers for x that are equally spaced around the axis of symmetry like 2, 3, 1, 4, 0, 5 ... then plug these values into the original equation to get matching y values
 Quadratic_Equations/90112: If the sides of a square are decreased by 2cm, the area is decreased by 36 cm^2. What were the dimensions of the original square? Thank you1 solutions Answer 65471 by scott8148(6628)   on 2007-07-26 16:07:23 (Show Source): You can put this solution on YOUR website!let s equal the original side length ... (s-2)^2=s^2-36 ... s^2-4s+4=s^2-36 ... -4s=-40 ... s=10
 Graphs/90218: This question is from textbook Beginning Algebra I need to identify the axis of symmetry, create a suitable table of values and the sketch a graph including the axis of symmetry for y = x^2 - 5x + 3. I know the formula to find the axis is x = -b/2(a)thus... x = -(-5)/2(1) = 5/2 From here on out I'm lost. I get really confused when there is a fraction. I don't which values to choose and why to choose them. Please help.1 solutions Answer 65469 by scott8148(6628)   on 2007-07-26 15:56:39 (Show Source): You can put this solution on YOUR website!you've got the hard part ... for your table of values, choose numbers for x that are equally spaced around the axis of symmetry like 2, 3, 1, 4, 0, 5 ... then plug these values into the original equation to get matching y values
 test/90053: Use inductive reasoning to predict the next number in each sequence. 3, 7, 11, 15, _____________ 1, -2, 4, -8 ________________1 solutions Answer 65382 by scott8148(6628)   on 2007-07-25 18:41:52 (Show Source): You can put this solution on YOUR website!in the first sequence, you add 4 to get from one term to the next ... so the missing term is 19 in the second sequence, you multiply by -2 to get the next term ... so the missing term is 16
 Linear-systems/90047: Write a system of linear equations, and then use the system to solve the problem. A cup of uncooked rice contains 15 g of protein and 810 calories. A cup of uncooked soybeans contains 22.5 g of protein and 270 calories. How many cups each should be used for a meal containing 9.5 g of protein and 324 calories?1 solutions Answer 65378 by scott8148(6628)   on 2007-07-25 18:30:15 (Show Source): You can put this solution on YOUR website!let r equal cups of rice and s equal cups of soybeans r(15)+s(22.5)=9.5 ... r(810)+s(270)=324 ... multiply first equation by -12 and add the second equation -180r-270s+810r+270s=-114+324 ... 630r=210 ... r=1/3 ... from first equation (1/3)(15)+s(22.5)=9.5 ... s(22.5)=4.5 ...s=1/5
 Functions/89921: It has been a long time since I have done any algebra. A friend of mine is taking an algebra course and I could help him if I could just get started by recalling a simple equation. Once this is explained to me, the ball will start rolling. Thank you. f(x)=2x(3)^-7 find f(1)^x1 solutions Answer 65297 by scott8148(6628)   on 2007-07-25 00:23:58 (Show Source): You can put this solution on YOUR website!maybe your notation is rusty; please check the problem and resubmit liberal use of parentheses is fine
 Travel_Word_Problems/89938: It is the year 2074 and the electric truck is a reality. Jeff is an independent truck driver who delivers vehicles from the factory to the dealers in his very flat state. Jeff’s truck (with him and his lunch box in it) weighs 8,000 lbs. From Jeff’s house in Small Town to the automobile factory, which is 120 miles away, his truck consumes 99.86 kW-h of energy. He loads up 6 vehicles with a nominal weight each of 3000 lbs. His closest customer, dealership Rip-U-Off, is 200 miles away and Jeff’s truck consumes another 543 kW-h getting there. He delivers X trucks to Mr. Rip-U-Off and continues on to dealership U-Bought-It to deliver the rest of the vehicles. U-Bought-It is 300 miles from Rip-U-Off and Jeff’s truck consumed 436.89 kW-h to get to it. Jeff returns home with his empty truck and consumes 41.61 kW-h to get home (he was so busy that had no time to eat his lunch). This is a challenging problem. Let’s not get frustrated trying to solve it right, but rather let’s spend time formulating it and discussing the possibilities. Of course, the easy questions are: · How many vehicles did each dealer get? and · How far is Jeff’s home from the U-Bought-It dealership? The bonus question is which of the two dealers received a smuggled shipment of potatoes in the trunk of one of the vehicles and how much did the shipment weigh?1 solutions Answer 65296 by scott8148(6628)   on 2007-07-25 00:17:19 (Show Source): You can put this solution on YOUR website!the energy that Jeff's truck uses is proportional to the distance he drives and the weight of the load e=kdw k is the constant of proportionality and is determined for the truck from Jeff's initial trip k=e/(dw) k=99.86/(120*8000) ... using the equation e=kdw, you can plugin values from the legs of the trip to find the weights Jeff's trip home at the end is with the same weight as the beginning so the distance is porportional to the energy each dealer gets 3 cars ... Jeff's house is 50 miles from U-Bought-It ... Rip-You-Off got 100 lbs of potatoes
 Percentage-and-ratio-word-problems/89939: A small private school has 500 students. Two thirds of the soccer players are girls. One third of the boys play soccer. One hundred of the girls do not play soccer. How many boys are in this school?1 solutions Answer 65294 by scott8148(6628)   on 2007-07-24 23:17:24 (Show Source): You can put this solution on YOUR website!let b equal number of boys, so number of girls is 500-b 1/3 of the boys play soccer and twice as many girls as boys play soccer ... 100 of the girls do not play soccer so 500-b-100 girls play soccer and this number is twice a large as the 1/3 of the boys that play 500-b-100=2(b/3) ... 400=5b/3 ... 1200=5b ... 240=b
 Complex_Numbers/89821: How would you graph a graphical interpretation of the problem (5-6i) and (-3+i)? I worked the problem and came up with 2-5i, but am unsure how to graph it.1 solutions Answer 65248 by scott8148(6628)   on 2007-07-24 17:45:21 (Show Source): You can put this solution on YOUR website!graph first point ... use first point as an "origin" and graph the second point this is the same technique as adding vectors ... the tail of the second vector starts at the head of the first
 Systems-of-equations/89878: When my professor explains this I understand. When I get home, it is like written in Hebrew or something. Can you please explain to me (in detail) how to solve a problem like this? I am trying to solve for (x,y,z). My final in is tomorrow and I need to know this stuff. Thanks in advance. x+y+2z=11 x+y+3z=14 x+2y-z=51 solutions Answer 65246 by scott8148(6628)   on 2007-07-24 17:36:39 (Show Source): You can put this solution on YOUR website!first you take two pairs of equations and eliminate one of the variables multiply third equation by 2 and add to first equation 2x+4y-2z+x+y+2z=10+11 ... 3x+5y=21 ... z is eliminated multiply third equation by 3 and add to first equation 3x+6y-3z+x+y+3z=15+14 ... 4x+7y=29 ... z is eliminated next, you take the pair of new equations and eliminate one of the variables multiply first new equation by 4 and second new equation by -3 and add 12x+20y-12x-21y=84-87 ... -y=-3 ... y=3 take this value to one of the new equations to find x ... 3x+5(3)=21 ... x=2 take values of y and x to an original equation to find z ... 2+3+2z=11 ... z=3
 Exponents/89817: How do you determine the units digit of 3 to the 99th power???1 solutions Answer 65235 by scott8148(6628)   on 2007-07-24 16:47:22 (Show Source): You can put this solution on YOUR website!3^1=3 ... 3^2=9 ... 3^3=27 ... 3^4=81 ... 3^5=243 (same units digit as 3^1) the unit digits repeat in a pattern of four ... 99 divided by 4 is 24 with a remainder of 3 so the units digit for 3^99 is the third units digit in the pattern, which is 7
 Rate-of-work-word-problems/89847: HOw many ounces of a 5% solution would you need to mix with a 10% solution to get 60 ounces of a 9% solution? as far as i've gotten: x+y=60 .05+.10=.09 .05+.10=.09 (60) 5.4 1 solutions Answer 65233 by scott8148(6628)   on 2007-07-24 16:32:41 (Show Source): You can put this solution on YOUR website!first equation ok ... third equation kind of on track ... why two variables? let x equal amount of 5% solution ... then 60-x equals the amount of 10% solution expanding on your third equation ... .05(x)+.10(60-x)=.09(60) multiplying by 100 gives 5x+600-10x=540 ... -5x=-60 ... x=12
 Miscellaneous_Word_Problems/89742: Please help me figure this out. I have done this over and over and I am missing something. I know this is easy...but I must have a brain fart. The problem states: A writer is writing an article for a magazine which is 21,000 words, he uses two different size fonts. Using the small font a page holds 1,500 words, using the large font a page holds 1,200 words. He is alloted 16 pages, how many pages must be in a small font? Please help. Thank you!1 solutions Answer 65178 by scott8148(6628)   on 2007-07-23 22:28:44 (Show Source): You can put this solution on YOUR website!brain fart, huh? hope its not catching let s equal small font ... s(1500)+(16-s)(1200)=21000 ... dividing by 300 gives s(5)+(16-s)(4)=70 5s+64-4s=70 ... s=6 checking ... 6(1500)+10(1200)=21000 ... 9000+12000=21000
 Rational-functions/89696: How would you write an equation in standard form for an ellipse with foci(5,0)and (-5,0) and y- intercepts of 7 and -7?1 solutions Answer 65176 by scott8148(6628)   on 2007-07-23 22:18:39 (Show Source): You can put this solution on YOUR website!this ellipse is centered at the origin with the foci on the y-axis so the equation will be of the form a is the semi-major axis, in this case a=7 ... c is the distance from center to focus, c=5 b^2=a^2-c^2 ... b^2=49-25 ... b^2=24 so the equation is
 Linear-equations/89728: In Problem 26, your best bet is to sketch a graph on paper with all the known information – you know the coordinates of the solution, and should be able to easily determine the y-intercept of the second equation - important since this would give you two points on the same line, from which you should then be able to find m. In the first equation, you’ll have to do some math to find the value of its slope – but watch out for the value of b, because here (HINT), it may not be the same as the value of the y-intercept. Also, we’re only looking for the values of m and b – no graph needs to be submitted for this problem! 26) Find values for m and b in the following system so that the solution to the system is (-3, 4). 5x + 7y = b mx + y = 22 1 solutions Answer 65172 by scott8148(6628)   on 2007-07-23 22:00:01 (Show Source): You can put this solution on YOUR website!solution is (-3,4) so 5x+7y=b ... 5(-3)+7(4)=b ... -15+28=b ... 13=b mx+y=22 ... m(-3)+4=22 ... -3m=18 ... m=-6
 Problems-with-consecutive-odd-even-integers/89693: Sorry! I put thwe wrong email address. The correct one is PayJ3@aol.com "Prove the product of 4 consecutive integers plus 1 is the square of an odd number (always)"1 solutions Answer 65169 by scott8148(6628)   on 2007-07-23 21:33:33 (Show Source): You can put this solution on YOUR website!let x equal the first integer ... x(x+1)(x+2)(x+3)+1=x^4+6x^3+11x^2+6x+1 since this is a perfect square and the coefficients of the first and last terms are 1, the factors must be of the form x^2+bx+1 (x^2+bx+1)^2=x^4+2bx^3+(b^2+2)x^2+2bx+1 ... so b=3 ... x^2+3x+1=x(x+3)+1 integers that are separated by an odd amount (3) must be odd and even; so their product must be even ... adding 1 makes it odd ALWAYS
 Problems-with-consecutive-odd-even-integers/89691: Hi! I'm sorry for not giving anymore information but this is an extra credit question for my class and there is no book from which the question came from (at least not one given to the students). "Prove the product of 4 consecutive integers plus one is the square of an odd number (always)." THANK YOU!1 solutions Answer 65168 by scott8148(6628)   on 2007-07-23 21:31:34 (Show Source): You can put this solution on YOUR website!let x equal the first integer ... x(x+1)(x+2)(x+3)+1=x^4+6x^3+11x^2+6x+1 since this is a perfect square and the coefficients of the first and last terms are 1, the factors must be of the form x^2+bx+1 (x^2+bx+1)^2=x^4+2bx^3+(b^2+2)x^2+2bx+1 ... so b=3 ... x^2+3x+1=x(x+3)+1 integers that are separated by an odd amount (3) must be odd and even; so their product must be even ... adding 1 makes it odd ALWAYS
 Linear-equations/89682: This question is from textbook Question: Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the point rises, falls, is horizontal, or is vertical. (6,-4)and(4,-2) I will need this by this evening if possible. I need to submit a similar one as this by tomorrow. Thank you so much. Teha 1 solutions Answer 65138 by scott8148(6628)   on 2007-07-23 18:13:52 (Show Source): You can put this solution on YOUR website!the slope is the change in y (rise) divided by the change in x (run) in this case, (-2-(-4))/(4-6) ... 2/(-2) ... or -1 ... this is a falling slope, going down from left to right
 Linear-systems/89663: 6x-4y=10 2y+5=3x Solve by using any method and I'm getting no solution and wanted to make sure.1 solutions Answer 65137 by scott8148(6628)   on 2007-07-23 18:05:28 (Show Source): You can put this solution on YOUR website!you are CORRECT ... there is no unique solution
 Coordinate-system/89671: Write the equation of the circle that has a diameter whose endpoints are (3,-5) and (-7,3). Write the equation in General Form which is: x2+y2+Dx+Ey+F=0 The "2's" are exponents. I am stumped on this last bit of work I need to know. Can you please help me? Thanks!1 solutions Answer 65136 by scott8148(6628)   on 2007-07-23 18:00:58 (Show Source): You can put this solution on YOUR website!an equation for a circle centered at (h,k) with a radius of r is (x-h)^2+(y-k)^2=r^2 the center of this circle is the midpoint of the diameter ... ((3-7)/2,(-5+3)/2) or (-2,-1) the radius is the distance from the center to one of the ends ... r^2=(-2-3)^2+(-1-(-5))^2 ... r^2=25+16=41 so (x+2)^2+(y+1)^2=41 ... x^2+4x+4+y^2+2y+1=41 ... x^2+y^2+4x+2y-36=0
 Linear-equations/89680: Point A (4,1)is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB? A.(-6,1) B.(4-,-1) C.(-4,3) D.(-2,1) E.(8,1) Note:Please explain step by step for each problem. 1 solutions Answer 65134 by scott8148(6628)   on 2007-07-23 17:41:41 (Show Source): You can put this solution on YOUR website!x=2 is a vertical line ... to be perpendicular, the line AB must be horizontal so B has the same y-coordinate as A if x=2 bisects AB then 2 is midway between the x-coordinates of A and B ... (4+x)/2=2 ... 4+x=4 ... x=0 B is (0,1) ... none of the above
 Mixture_Word_Problems/89664: How many ounces of a 20% alcohol solution must be mixed with 5 ounces of a 50% alcohol solution to get a mixture that is 30% alcohol? I have my first equation set up as 20% + 50% =30% I then get confused and need help please.1 solutions Answer 65133 by scott8148(6628)   on 2007-07-23 17:19:14 (Show Source): You can put this solution on YOUR website!you have the concentrations but not the amounts switch to decimals and try .2(x)+.5(5)=.3(x+5)
 Coordinate-system/89667: The questions state: Find all values of y such that the distance between (3,y) and (-2,9) is 12. I am stumped and need help PLEASE! thanks!1 solutions Answer 65132 by scott8148(6628)   on 2007-07-23 17:13:44 (Show Source): You can put this solution on YOUR website!(3,y) defines a vertical line at x=3 ... all the points at a distance of 12 units from point (-2,9) is a circle since the line is less than 12 units from the point, the line will intersect the circle in two places the general formula for a circle of radius r centered at (h,k) is (x-h)^2+(y-k)^2=r^2 ... in this case (3-(-2))^2+(y-9)^2=144 25+(y-9)^2=144 ... (y-9)^2=119 ... ...