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# Recent problems solved by 'scott8148'

scott8148 answered: 6619 problems
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 Miscellaneous_Word_Problems/118784: There are two boats that start out on opposite sides of a river at the same time. Each one is heading across the river to the other side. They each go a constant speed throughout the entire problem (so ignore having to slow down to turn around, and ignore current, etc.), but they are not necessarily the same speed as each other. When each boat reaches its opposite bank, it immediately turns around and heads back to where it started. The boats thus pass each other twice. The first time they pass, they are 700 yards from one of the banks of the river. The second time they pass, they have each turned around after reaching their respective opposite shores and have started back toward where they each began. When they pass the second time, they are 300 yards from the other bank of the river. How wide is the river?1 solutions Answer 86927 by scott8148(6628)   on 2008-01-05 23:41:38 (Show Source): You can put this solution on YOUR website!the distances traveled by the boats are proportional to their speeds ___ since the speeds are constant, the ratio of the distances is constant let w="width of river" ___ river is >700 yd wide let x and y be the boat distances at first meeting ___ x=700, y=w-700 at second meeting ___ x=w+300, y=2w-300 ratio of distances is constant, so 700/(w-700)=(w+300)/(2w-300) ___ 1400w-210000=w^2-400w-210000 1400w=w^2-400w ___ 1800w=w^2 ___ 1800=w my first attempt at a solution had the x and y values at the first meeting reversed ___ this resulted in a width <700
 Equations/118696: This question is from textbook Algebra 1 I need help with ... four more than two thirds of the number is 22. Find the number. how do i make an equation for this problem?1 solutions Answer 86822 by scott8148(6628)   on 2008-01-04 22:37:56 (Show Source): You can put this solution on YOUR website!"four more than two thirds of the number" ___ (2/3)x+4 "is 22" ___ =22 (2/3)x+4=22
 Finance/118692: This question is from textbook Algebra Number 6: Phil can furnish the garage in 12 hours, and Rick can do it in 10 hours. They work together for 3 hours. How long will it take Rick to finish the job alone?1 solutions Answer 86821 by scott8148(6628)   on 2008-01-04 22:33:59 (Show Source): You can put this solution on YOUR website!in the time that they work together, Phil does 3/12 (25%) and Rick does 3/10 (30%) this leaves 45% of the job to do ___ 45% of 10 hr is 4.5 hr
 Geometric_formulas/118694: The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon 1.) 120 2.)150 I am at a complete lost here, could someone help me please? Where would I start?1 solutions Answer 86820 by scott8148(6628)   on 2008-01-04 22:28:55 (Show Source): You can put this solution on YOUR website!the interior and exterior angles are supplementary (they add to 180°) the sum of the exterior angles of a polygon is 360° 1.) 180-120=60 ___ 360/60=6 ___ hexagon
 Quadratic_Equations/118664: explain why a^0 =1 for any nonzero value of a.1 solutions Answer 86792 by scott8148(6628)   on 2008-01-04 13:05:26 (Show Source): You can put this solution on YOUR website!when quantities having the same bases are divided, the exponents are subtracted (2^6)/(2^2)=2^(6-2) ___ (2^6)/(2^2)=2^4 ___ 64/4=16 if the exponents are the same ___ (2^3)/(2^3)=2^(3-3) ___ (2^3)/(2^3)=2^0 ___ 8/8=1 in this case, a=2 ___ a can be any value except for zero (division by zero is undefined)
 Exponents/118663: Whaqt is the remainder when 2008^2007 is divided by 51 solutions Answer 86790 by scott8148(6628)   on 2008-01-04 12:53:14 (Show Source): You can put this solution on YOUR website!look at the units digit for powers of 8 8^1=8 8^2=64 8^3=512 8^4=4096 8^5=32768 ___ same units digit as 8^1 ___ the units digit repeats in a 4 number pattern 8-4-2-6 2007 divided by 4 leaves a remainder of 3 ___ so the units digit of 2008^2007 is 2 ___ this is the remainder when 2008^2007 is divided by 5
 Mixture_Word_Problems/118643: PART C LQCKRfRNLEM Imagine you are at a school that has lockers. There are 1,000 lockers, all shut and unlocked, and 1,000 students - HERE’S THE PROBLEM: 1) Suppose the first student goes along the row and opens every locker. 2) The second student then goes and shuts every other locker beginining with the number 2 3) The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.) 4) The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the thousand students have followed the pattern with the thousand lockers. At the end, which lockers will be open and which will be closed? Why? fl\ 1 solutions Answer 86765 by scott8148(6628)   on 2008-01-04 02:06:42 (Show Source): You can put this solution on YOUR website!looking at a few lockers will reveal the pattern... ___ c is closed, o is open L1 ___ o-1 L2 ___ o-1, c-2 L3 ___ o-1, c-3 L4 ___ o-1, c-2, o-4 L5 ___ o-1, c-5 L6 ___ o-1, c-2, o-3, c-6 L7 ___ o-1, c-7 L8 ___ o-1, c-2, o-4, c-8 L9 ___ o-1, c-3, o-9 L10 ___ o-1, c-2, o-5, c-10 look at the OPEN lockers ___ 1, 4, 9 ___ see a pattern? ___ WHY? factors for numbers occur in pairs, like for 12 __ 1,12 __ 2,6 __ 3,4 ___ the first factor opens and the second closes, so the locker ends up closed but for perfect squares, one of the pairs is the same number ___ for 36 __ 1,36 __ 2,18 __ 3,12 __ 4,9 __ 6,6 ___ so there is no close to go with the open
 Quadratic_Equations/118528: A rectangular lawn has dimensions 30m by 40m. A strip of uniform width is to be placed around the perimeter. How wide should the strip be so that exactly half the lawn gets mowed? I tried (2x-30)(2x-40) and found x=5m but I was marked wrong by my teacher :(1 solutions Answer 86649 by scott8148(6628)   on 2008-01-03 12:53:00 (Show Source): You can put this solution on YOUR website!5m is correct, but what was your technique? the lawn is 30 by 40 or 1200 sq m, so half would be 600 sq m (30-2x)(40-2x)=600 ___ 1200-140x+4x^2=600 ___ 600-140x+4x^2=0 x^2-35x+150=0 ___ (x-30)(x-5)=0
 Polynomials-and-rational-expressions/118537: Find a trimonial that represents the area of a paralleogram whose base is 3x+2 meters and whose height is 2x+3 meters.1 solutions Answer 86646 by scott8148(6628)   on 2008-01-03 12:40:08 (Show Source): You can put this solution on YOUR website!area=base X height ___ a=(3x+2)(2x+3) FOILing gives a=6x^2+13x+6
 Polynomials-and-rational-expressions/118536: Find a trimonial that represents the area of a paralleogram whose base is 3x+2 meters and whose height is 2x+3 meters.1 solutions Answer 86645 by scott8148(6628)   on 2008-01-03 12:39:32 (Show Source): You can put this solution on YOUR website!area=base X height ___ a=(3x+2)(2x+3) FOILing gives a=6x^2+13x+6
 Quadratic_Equations/118534: An arithmetic sequence has t4=4 and t10=5.5. What is the 88th term for the sequence? I said 25 but I only guessed correctly, I don't understand how to do it :(1 solutions Answer 86644 by scott8148(6628)   on 2008-01-03 12:36:06 (Show Source): You can put this solution on YOUR website!in an arithmetic sequence, the difference between consecutive terms is constant there are 6 terms from t4 to t10, so the difference is (5.5-4)/6 or .25 there are 84 terms from t4 to t88, so t88=t4+(84(.25))___ t88=4+21
 Quadratic_Equations/118531: A flare is fired as a stress signal and its height ,h in metres above the ground, t seconds after firing, is provided in the table below. Algebraically determine the quadratic function that defines the height of the flare above the ground t seconds after firing, and use it to determine the flare's height at 2.4 seconds. t---0 1 2 3 4 h---2 97 182 257 322 I tried y=-2ak^2 97=-2a(1)^2 97/-2=-2a/-2 a=-48.5 and was completly lost :( Please Help Me :)1 solutions Answer 86641 by scott8148(6628)   on 2008-01-03 12:28:35 (Show Source): You can put this solution on YOUR website!the general equation is h=at^2+bt+c by plugging in values from the table, you can find the values for a, b, and c when t=0, h=c ___ so c=2 when t=1, 97=a+b+2 ___ 95=a+b ___ 95-a=b when t=2, 182=4a+2b+2 ___ 180=4a+2b ___ 90=2a+b substitution gives 90=2a+(95-a) ___ -5=a ___ 95-(-5)=b ___ 100=b h=-5t^2+100t+2 in the real world, the a term is half the gravitational acceleration (negative because gravity is downward) ___ the b term is the initial velocity of the flare ___ and the c term is the initial height (probably the height of the person shooting the flare)
 Quadratic_Equations/118494: This question is from textbook What is X squared - X =6?1 solutions Answer 86613 by scott8148(6628)   on 2008-01-02 21:39:20 (Show Source): You can put this solution on YOUR website!subtracting 6 gives X^2-X-6=0 factoring gives (X-3)(X+2)=0 so X=3 and X=-2
 Quadratic_Equations/118493: What is S squared - S = 0 ?1 solutions Answer 86611 by scott8148(6628)   on 2008-01-02 21:36:10 (Show Source): You can put this solution on YOUR website!factoring gives S(S-1)=0 so S=0 and S=1
 Parallelograms/118474: these are the corrdinates of three points (0,10),(30,10),(20,-30) find a fourth point so that the four points form the vertices of a parallelogram. how would you do this? how many different points could be the fourth vertex?what are the coordinates of these points? write your answers below. show the different possible parallelograms in different colors on the grid. Luke and his mom..1 solutions Answer 86609 by scott8148(6628)   on 2008-01-02 21:31:42 (Show Source): You can put this solution on YOUR website!if you draw a triangle, using the three points as the vertices, ___ you can visualize two sides of the triangle as sides of a parallelogram ___ and the third side of the triangle as a diagonal of the parallelogram since there are 3 possible diagonals, there are 3 possible parallelograms ___ remember, the diagonals of a parallelogram bisect each other ___ (they cross at their midpoints) let the first two points form a diagonal ___ the midpoint is ((0+30)/2,(10+10)/2) or (15,10) ___ this is also the midpoint of the other diagonal let (x,y) be the missing vertex ___ so (x+20)/2=15 and (y-30)/2=10 ___ x=10 and y=50 ___ the missing vertex is (10,50) you can repeat this for the other 2 "diagonals"
 Radicals/118403: Find the distance between each pair of points (-3, 0)and (4, 0) Just double checking my answers. I came up with two different answers and I dont know which one is right. One answer is c = square root of 1 2nd answer is d = square root of 71 solutions Answer 86524 by scott8148(6628)   on 2008-01-01 17:46:32 (Show Source): You can put this solution on YOUR website!since the points have the same y-coordinate, the distance is the difference in the x-coordinates ___ this is 7 if you used the "distance formula", you should check which terms were plugged in where
 Quadratic_Equations/118362: What is the maximum area of a triangle having 15cm as the sum of its base and height ? Please Help :)1 solutions Answer 86481 by scott8148(6628)   on 2007-12-31 14:25:44 (Show Source): You can put this solution on YOUR website!b+h=15 ___ b=15-h area=bh/2 ___ a=(15-h)(h)/2 ___ a=(15/2)h-(1/2)h^2 maximum area is on the axis of symmetry ___ h=(-15/2)/(2(-1/2)) ___ h=15/2 b=15-h ___ b=15-(15/2) ___ b=15/2 a=(15/2)(15/2)/2 ___ a=225/8
 Quadratic_Equations/118360: The sum of a number and three times another number is 18. Find the numbers if their product is a maximum. Please Help :)1 solutions Answer 86477 by scott8148(6628)   on 2007-12-31 12:30:15 (Show Source): You can put this solution on YOUR website!let x=number, y="other number" ___ x+3y=18 ___ x=18-3y product=x*y ___ p=(18-3y)y ___ p=18y-3y^2 maximum is on the axis of symmetry ___ y=-b/2a ___ y=-18/(2(-3)) ___ y=3 x+3(3)=18 ___ x=9
 Geometry_Word_Problems/118356: Beginning witha fixed length of fence, a free-standing rectangular enclosure is built so that it encircles the maximum area. Show that this enclosure is actually a square. Remember that all squares are rectangles.1 solutions Answer 86474 by scott8148(6628)   on 2007-12-31 11:55:37 (Show Source): You can put this solution on YOUR website!let 2k="length of fence", y="length of enclosure", x="width of enclosure" perimeter=2x+2y ___ 2k=2x+2y ___ k=x+y ___ k-y=x area=x*y ___ a=(k-y)y ___ a=ky-y^2 the maximum area is at the axis of symmetry ___ y=-k/(2(-1)) ___ y=k/2 x+y=k ___ x+(k/2)=k ___ x=k/2 x=y ___ width=length ___ definition of square
 Quadratic_Equations/118354: Identify the axis of symmetry, create a suitable table of values, and sketch the graph for the following table. y=x^2-5x+3 I have the axis of symmetry of x=5/2 I know how to graph this equation. I need help with creating a suitable table of values. I am confused with this. Please help. 1 solutions Answer 86473 by scott8148(6628)   on 2007-12-31 11:39:37 (Show Source): You can put this solution on YOUR website!a "suitable" table of values would probably be centered around the vertex (axis of symmetry), ___ and would show the zeroes (for x and y) (0,3), (1,-1), (2,-3), (5/2,-13/4), (3,-3), (4,-1), (5,3) ___ listed in table form
 Polynomials-and-rational-expressions/118299: Solve the polynomial inequality z^3-6z^2+9z<0?1 solutions Answer 86454 by scott8148(6628)   on 2007-12-30 23:40:27 (Show Source): You can put this solution on YOUR website!factoring gives ___ z(z-3)(z-3)<0 z must be <0 because the two (z-3) factors will always have a result >=0
 Systems-of-equations/118187: 1a) At the school play on Fri. night 120 tickets were sold. Student tickets cost \$5 each, and Adult tickets colst \$7 each. the total sale for the evening was \$670. How many of each type of tickets were sold? 1b) Write a sytem of equations that represents this problem, then solve and asnwer the question. Answer for 1a- amount of Student tickets sold is 85 amount of Adult tickets sold is 35 Could you please help me with 1b I'am not exactly sure how to do it :( 1 solutions Answer 86292 by scott8148(6628)   on 2007-12-27 22:29:25 (Show Source): You can put this solution on YOUR website!let x=students and y=adults ___ x+y=120 ___ x=120-y 5x+7y=670 ___ 5(120-y)+7y=670 ___ 600-5y+7y=670 ___ 2y=70
 Systems-of-equations/118189: This question is from textbook Fubd of Alg and Trig This is an application that falls under this category. I have worked it to the end but need a little guidance. An airline that flies from LA to Albuquerque with a stopover in Phoenix charges a fare of \$45 to Pheonix and a fare of \$60 from LA to Albuq. A total of 185 passengers boarded the plane in LA and fares totaled \$10,500. How many passengers got off of the plane in Pheonix? This is how I sat the problem up: x+y= 185 45x+60y= 10,500 I know this problem should be solved using elimination. So I mult E1 by -45 in order to eliminate. -45(x+y)= 185 -45x-45y= 185 45x+60y= 10,500 With this I end up with.. 15y=10,685 then I divided by 15 but got a decimal...am I doing this right?1 solutions Answer 86291 by scott8148(6628)   on 2007-12-27 22:24:18 (Show Source): You can put this solution on YOUR website!you didn't multiply the WHOLE equation by -45 (what about the 185?)
 Quadratic_Equations/118188: This question is from textbook Strategies for problem solving workbook It's a story where you are supposed to pull out information to build and a quadratic equation step-by-step, and then possible solve it. Here's the story; "A retailer spent \$48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for \$3 above the original cost per mug, she made a total profit of \$22. Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased." Step 1) If the price for n mugs is \$48, how can we express the cost per mug? I figured it out to be: 48/n=y Step 2) we are told that the retailer, in order to make a specific profit, sells the remaining mugs for \$3 more than the original cost per mug. using this information, and your answer to step 1, how can we express the selling price per mug? I figured it out as: n(y+3)=70, this is from cost \$48 for all mugs plus the profit of \$22. Step 3) Since two of the mugs were broken in the store, how can we represent the number of mugs available for sale? I figured it be: n-2 Step 4) Using your answers from step (2) and (3)construct an expression for the the amount of money made on the sale of the remaining mugs. I figured that out to be: n-2+n(y+3)=70 Step 5) The profit on the mugs can be found by subtracting the cost of the mugs from the amount of money made on the sale of the mugs. Write an eqution that states this relationship between the money made, the cost, and the profit. I know the equation has to equal -48+70=22, but how... is it like: -48+(n-2)+n(y+3)=22 Then to top this off rewrite the equation that you wrote in step (5) in the standard form of a quadratic equation. Please tell me if I'm on the right track, or at least help get to the track?1 solutions Answer 86290 by scott8148(6628)   on 2007-12-27 22:20:09 (Show Source): You can put this solution on YOUR website!1) an expression, not an equation ___ 48/n is correct 2) 3 more than the original cost per mug is 1) plus 3 ___ (48/n)+3 or (48+3n)/n 3) n-2 is correct 4) again, an expression ___ number of mugs times cost per mug ___ (n-2)((48+3n)/n) 5) now, an equation ___ 22=(n-2)((48+3n)/n)-48 22n=(n-2)(48+3n)-48n ___ 70n=48n+3n^2-96-6n ___ 3n^2-28n-96=0 ___ (3n+8)(n-12)=0
 Word_Problems_With_Coins/118146: HI please help me with this A parking meter accepts only Quarters and dollars. If there are 31 coins and a value of \$ 20.50 how many quarters and dollars are there. thanks for any help coming my way1 solutions Answer 86288 by scott8148(6628)   on 2007-12-27 21:55:04 (Show Source): You can put this solution on YOUR website!let x=quarters, so 31-x=dollars ___ working in cents to avoid decimals x(25)+(31-x)(100)=2050 ___ 25x+3100-100x=2050 ___ -75x=-1050
 Geometry_Word_Problems/117103: The length of a rectangular piece of sheet is 2 in. longer than the width. Find the exact dimensions if the area of the sheet is 168 square in.1 solutions Answer 86205 by scott8148(6628)   on 2007-12-26 15:27:14 (Show Source): You can put this solution on YOUR website!let x=width, so x+2=length ___ x(x+2)=168 ___ x^2+2x-168=0 (x+14)(x-12)=0
 Miscellaneous_Word_Problems/117139: A circle in the standard (x,y) coordinate plane is tangent to the y-axis at 9. What is the equation of the circle in standard form?1 solutions Answer 86203 by scott8148(6628)   on 2007-12-26 15:21:14 (Show Source): You can put this solution on YOUR website!(x-r)^2+(y-9)^2=r^2
 Quadratic-relations-and-conic-sections/117178: This is tricky for me, A parabola has a vertical axis and passes through the points (0,3), (1,7) and (-2,-17). Find the equation of the parabola. use y=ax^2+by+c1 solutions Answer 86202 by scott8148(6628)   on 2007-12-26 15:13:26 (Show Source): You can put this solution on YOUR website!there are three unknowns; a, b, and c ___ you can generate three equations using the points and y=ax^2+bx+c (0,3) ___ 3=a(0)^2+b(0)+c ___ 3=c (1,7) ___ 7=a(1)^2+b(1)+3 ___ 4=a+b ___ 4-a=b (-2,-17) ___ -17=a(-2)^2+b(-2)+3 ___ -20=4a-2b ___ -20=4a-2(4-a) ___ -20=4a-8+2a ___ -12=6a ___ -2=a ___ 6=b
 Numbers_Word_Problems/118104: A boat travels 1 km upstream and 1km back. The time for the round trip is 10 hours. The speed of the stream is 2 km/hr. What is the speed of the boat in still water?1 solutions Answer 86201 by scott8148(6628)   on 2007-12-26 14:57:13 (Show Source): You can put this solution on YOUR website!let x=speed of boat in still water ___ time=distance/rate (1/(x+2))+(1/(x-2))=10 ___ (x-2)+(x+2)=10(x-2)(x+2) ___ 4x=10x^2-40 0=5x^2-2x-20
 Length-and-distance/117316: This question is from textbook Glencoe Geometry Using graph paper, graph the question and plot the given ordered pair. Then construct a perpendicular segment and find the distance from the point to the line. 24. y = 4x, (5, 3) I have no idea what y = 4x could mean except that maybe y was four times whatever x was, and that was the ordered pair. If so, I have no idea how to figure out what x is. Thanks in advance!1 solutions Answer 86200 by scott8148(6628)   on 2007-12-26 14:38:42 (Show Source): You can put this solution on YOUR website!the given ordered pair is the point (5,3) the ordered pairs from y=4x are the ones you describe, the y value is 4 times the x value ___ (0,0), (-1,-4), (1,4), (-3,-12), (3,12), etc. ___ these points form a line the distance from the point to the line is the distance along a perpendicular to the line that passes through the point the slope of the line is 4, so the slope of the perpendicular is -1/4 ___ the equation of the perpendicular is y-3=(-1/4)(x-5) or 4y=-x+17 the point of intersection is found using 4(4x)=-x+17 ___ 16x=-x+17 ___ x=1, so y=4 the distance is between (1,4) and (5,3)
 Graphs/117371: This question is from textbook Algebra 1 Write an equation for each relation in function notation.(-2,0) (1,3) (2,4)1 solutions Answer 86197 by scott8148(6628)   on 2007-12-26 14:13:53 (Show Source): You can put this solution on YOUR website!f(x)=x+2