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# Recent problems solved by 'checkley77'

checkley77 answered: 12560 problems
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 Geometry_Word_Problems/205194: Please help with me find an equation of line l and solve for y when Line l goes through (0,0) and is perpendicular to the line through (0,6) and (-5,0). I am stumped because I don't think there is a slope for the first line. Any help is greatly appreciated.1 solutions Answer 154918 by checkley77(12569)   on 2009-08-03 10:51:52 (Show Source): You can put this solution on YOUR website!(0,6)(-5,0) The equation for this line is: Y=mX+b m=slope=(y2-y1)/(x2-x1)=(0-6)/(-5-0)=-6/-5=6/5 ans. 6=6/5*0+b 6=b ans. for the y intercept. y=6x/5+6 is the equation for this line. (red line) A perpendicular line will have a slope=-5/6 passing through (0,0). 0=-5/6*0+b 0=b ans. for the y intercept for this line. y=-5x/6+0s the equation for thjis line. (green line) (graph 300x300 pixels, x from -6 to 6, y from -6 to 6, of TWO functions 6x/5 +6 and y = -5x/6).
 Money_Word_Problems/205203: Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total receipts were \$824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?1 solutions Answer 154916 by checkley77(12569)   on 2009-08-03 10:35:41 (Show Source): You can put this solution on YOUR website!2x*3+x*2=824 6x+2x=824 8x=824 x=824/8 x=103 ans. for the number of student tickets sold. 28103=206 ans. for the number of adult tickets sold. Proof: 206*3=103*2=824 618+206=824 824=824
 Graphs/205225: This question is from textbook Solve this by graphing 2x-y=4 and 2x-y=31 solutions Answer 154915 by checkley77(12569)   on 2009-08-03 10:30:47 (Show Source): You can put this solution on YOUR website!2x-y=4 -y=-2x+4 y=2x-4 (red line) 2x-y=3 -y=-2x+3 y=-2x-3 (green line) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -2x -4 and -2x -3). There is no unique solution for x & y beause these 2 lines do not intersect.
 Quadratic_Equations/205121: Solve 16x = x^2 by factoring1 solutions Answer 154868 by checkley77(12569)   on 2009-08-02 17:57:16 (Show Source): You can put this solution on YOUR website!16x = x^2 Divide both sides by x. 16x/x=x^2/x 16=x ans.
 Polynomials-and-rational-expressions/205142: xover 3=4 over x+11 solutions Answer 154867 by checkley77(12569)   on 2009-08-02 17:52:37 (Show Source): You can put this solution on YOUR website!x/3=4/(x+1) x(x+1)=3*4 x^2+x=12 x^2+x-12=0 (x+4)(x-3)=0 x+4=0 x=-4 ans. x-3=0 x=3 ans.
 Money_Word_Problems/205163: P=R-C Profit=Revenue- Cost Solve for C Suppose your profit for one day is \$1,281 and the cost of running the business for the day is \$1,463. What is the revenue for that day? Explain1 solutions Answer 154866 by checkley77(12569)   on 2009-08-02 17:49:29 (Show Source): You can put this solution on YOUR website!p=r-c c=r-p ans. 1,281=r-1,463 r=1,281+1,463 r=\$2,744 ans. for the days revenue.
 Rational-functions/205147: z^2/8 - 7z/8 = 1 Can you please solve and show the work on how to slve this problem please1 solutions Answer 154865 by checkley77(12569)   on 2009-08-02 17:44:33 (Show Source): You can put this solution on YOUR website!z^2/8 - 7z/8 = 1 (z^2-7z)/8=1 z^2-7z=8 z^2-7z-8=0 (z-8)(z+1)=0 z-8=0 z=8 ans. z+1=0 z=-1 ans. Proofs: 8^2/8-7*8/8=1 64/8-56/8=1 (64-56)/8=1 8/8=1 1=1 -1^2/8-7*-1/8=1 1/8+7/8=1 8/8=1 1=1
 Quadratic_Equations/205148: Hi, I need help solving this problem. A rectangular piece of cardboard 11 inches by 14 inches is made into a box by cutting idential squares from each corner and folding up the sides. If the bottom of the box turns out to haave an area of 80 in^2, what size squares were cut from the corners? I am setting up my problem as: 80 = (w-11)(w-14) but I am not sure if I am barking up the wrong alley (so to speak). Any help or suggestions would be greatly appreciated. Thank you - Lori1 solutions Answer 154864 by checkley77(12569)   on 2009-08-02 17:39:22 (Show Source): You can put this solution on YOUR website!(11-2x)(14-2x)=80 154-28x-22x+4x^2=80 4x^2-50x+154-80=0 4x^2-50x+74=0 Using the quadratic equation we get: x=(50+-sqrt[-50^2-4*4*74])/2*4 x=(50+-sqrt[2,500-1,184])/8 x=(50+-sqrt1,316)/8 x=(50+-36.2767)/8 x=(86.2767)/8 x=10.78 not an ans. x=(50-36.2767)/8 x=13.7233/8 x=1.7154 in. is the size of the square removed from the 4 corners. Proof: (11-2*1.7154)(14-2*1.7154)=80 (11-3.43)(14-3.43)=80 7.57*10.57=80 80~80
 Coordinate-system/205141: This question is from textbook Longman mathematics foe IGCSE book 1 Write downthe equations of the lines that are parallel to 2y=5x+7, passing through (0,-3.5) 1 solutions Answer 154862 by checkley77(12569)   on 2009-08-02 17:25:50 (Show Source): You can put this solution on YOUR website!Parallel to 2y=5x+7, & passing through (0,-3.5) 2y=5x+7 y=5x/2+7/2 y=2.5x+3.5 (red line) This line has a slope=2.5. Thus any parallel line also has a slope=5/2. Y=mX+b is the equation of the parallel line through (0,-3.5) with a slope=5/2. -3.5=2.5*0+b -3.5=b which is the y intercept of the parallel line. y=2.5x-3.5 (green line). (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2.5x +3.5 and 2.5x -3.5).
 Quadratic_Equations/205156: I have a word problem that says: A rectangular scrapbook page has an area of 180 inches squared. If the length of the page is two less than twice the width, find the width of the page. 1 solutions Answer 154861 by checkley77(12569)   on 2009-08-02 17:17:25 (Show Source): You can put this solution on YOUR website!L*W=180 L=2W-2 (2W-2)W=180 2W^2-2W-180=0 2(W^2-W-90)=0 2(W-10)(W+9)=0 W-10=0 W=10 ANS. L=2*10-2 L=20-2 L=18 ANS. PROOF 18*10=180 180=180
 Travel_Word_Problems/205157: This question is from textbook Intermediate Algebra A Train Leaves Los Angeles at 2:00 PM. A second train leaves the same station in the same direction at 4:00 PM. The second train travels 24mph faster than the first. If the second train overtakes the first at 7:00pm, what is the speed of each of the two trains? Please Help! Thank you.1 solutions Answer 154860 by checkley77(12569)   on 2009-08-02 17:15:47 (Show Source): You can put this solution on YOUR website!D=RT SEEING AS THE DISTANCES ARE THE SAME WE HAVE: 5R=3(R+24) 5R=3R+72 5R-3R=72 2R=72 R=72/2 R=36 MPH. IS THE SPEED OF THE FIRST TRAIN. 36+24=60 MPH. IS THE SPEED OF THE SECOND TRAIN. PROOF: 5*36=3(60) 180=180
 Quadratic_Equations/205158: I have a word problem that says: A rectangular scrapbook page has an area of 180 inches squared. If the length of the page is two less than twice the width, find the width of the page. 1 solutions Answer 154859 by checkley77(12569)   on 2009-08-02 17:10:18 (Show Source): You can put this solution on YOUR website!L*W=180 L=2W-2 (2W-2)W=180 2W^2-2W-180=0 2(W^2-W-90)=0 2(W-10)(W+9)=0 W-10=0 W=10 ANS. L=2*10-2 L=20-2 L=18 ANS. PROOF 18*10=180 180=180
 Quadratic_Equations/205159: 1.65=1+8t-5tē1 solutions Answer 154858 by checkley77(12569)   on 2009-08-02 17:06:22 (Show Source): You can put this solution on YOUR website!1.65=1+8t-5tē 5t^2-8t-1+1.65=0 5t^2-8t+.65=0 Using the quadratic equation: We get: t=(8+-sqrt[-8^2-4*5*.65])/2*5 t=(8+-sqrt[64-13])/10 t=(8+-sqrt51)/10 t=8+-7.1414)/10 t=(8+7.1414)/10 t=15.1414/10 t=1.5141 ans. t=(8-7.1414)/10 t=.8586/10 t=.08586 ans.
 Graphs/205140: What is the solution of the system 9y-6x=12 6x-9y=-121 solutions Answer 154857 by checkley77(12569)   on 2009-08-02 16:48:07 (Show Source): You can put this solution on YOUR website!9y-6x=12 9y=6x+12 y=6x/9+12/9 y=2x/3+4/3 (red line) 6x-9y=-12 -9y=-6x-12 9y=6x+12 y=6x/9+12/9 y=2x/3+4/3 (green line) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2x/3 +4/3 and 2x/3 +4/3). As you can see these 2 lines (equations) are identical with many solutions for both x & y. One set is (-2,0) & (0,4/3)
 Expressions-with-variables/205144: x/6=-101 solutions Answer 154855 by checkley77(12569)   on 2009-08-02 16:35:47 (Show Source): You can put this solution on YOUR website!x/6=-10 x=-10*6 x=-60 ans.
 Coordinate-system/205018: This question is from textbook Longman Mathematics foe IGCSE book1 Write down the equations of the line that are parallel to y=8x-14, passing through (0,8.4)1 solutions Answer 154818 by checkley77(12569)   on 2009-08-02 10:50:08 (Show Source): You can put this solution on YOUR website!y=8x-14 (red line) A parallel line passing through (0,8.4) will have a slope=8 8.4=8*0+b 8.4=b which is the y intercept. y=8x+8.4 (green line) (graph 300x200 pixels, x from -6 to 5, y from -15 to 10, of TWO functions 8x -14 and 8x +8.4).
 Equations/205087: 18x - 12y = 18 x = y - 12 what is x? What is y? 1 solutions Answer 154817 by checkley77(12569)   on 2009-08-02 10:36:00 (Show Source): You can put this solution on YOUR website!18x - 12y = 18 x = y - 12 Substituting (y-12) for x in the first equation we get: 18(y-12)-12y=18 18y-216-12y=18 6y=18+216 6y=234 y=234/6 y=39 ans. x=39-12 x=27 ans. Proof: 18*27-12*39=18 486-468=18 18=18
 Miscellaneous_Word_Problems/205089: How many rectangular pieces of wood of size 20 cm by 45 cm can be cut from a plywood sheet of 120 cm by 240 cm?1 solutions Answer 154816 by checkley77(12569)   on 2009-08-02 10:31:43 (Show Source): You can put this solution on YOUR website!240/45=5.3 120/20=6 5*6=30 pieces ans. Alternate possibility: 240/20=12 120/45=2.67 12*2=24 pieces
 Exponents-negative-and-fractional/205091: how to solve this 8.7x 10 to the negative 4th power1 solutions Answer 154815 by checkley77(12569)   on 2009-08-02 10:20:31 (Show Source): You can put this solution on YOUR website!10^(-4)=.0001 8.7*.0001=.00087 ans.
 Rectangles/205093: The length of a rectangle is 3yd more than twice its width, and the area of the rectangle is 77yd^2 . Find the dimensions of the rectangle1 solutions Answer 154814 by checkley77(12569)   on 2009-08-02 10:15:56 (Show Source): You can put this solution on YOUR website!L=2W+3 L*W=AREA (2W+3)W=77 2W^2+3W=77 2W^2+3W-77=0 (2W-11)(W+7)=0 2W-11=0 2W=11 W=11/2 W=5.5 ANS. FOR THE WIDTH. L=2*5.5+3 L=11+3 L=14 ANS. FOR THE LENGTH. PROOF: 5.5*14=77 77=77
 Miscellaneous_Word_Problems/204973: A painting canvas has a length 8 inches longer than its width. If the area is 84 in^(2), what are the dimensions of the canvas?1 solutions Answer 154733 by checkley77(12569)   on 2009-07-31 20:30:53 (Show Source): You can put this solution on YOUR website!L=W+8 LW=84 (W+8)W=84 W^2+8W-84=0 (W+16)(W-6)=0 W-6=0 W=6 ANS. FOR THE WIDTH. L=6+8=14 ANS. FOR THE LENGTH. PROOF: 6*14=84 84=84
 Functions/204837: f(x)= -2x^3-2x find x if f(x) =-491 solutions Answer 154622 by checkley77(12569)   on 2009-07-30 17:43:57 (Show Source): You can put this solution on YOUR website!f(x)=-2x^3-2x find x if f(x)=-49 f(-49)=-2(-49^3)-2*-49 f(-49)=-2*-117,649+98 f(-49)=235,298+98 f(-49)=235,396 ans.
 Polynomials-and-rational-expressions/204713: x2 + 3x -10 x2 + 5X +6 ___________ X __________ x2 + 8x +15 x2 + 4X +41 solutions Answer 154503 by checkley77(12569)   on 2009-07-29 10:27:35 (Show Source): You can put this solution on YOUR website!x2 + 3x -10 x2 + 5X +6 ___________ X __________ x2 + 8x +15 x2 + 4X +4 [(x+5)(x-2)/(x+5)(x+3)] [(x-2)/(x+3)]
 Polynomials-and-rational-expressions/204594: The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio? 1 solutions Answer 154501 by checkley77(12569)   on 2009-07-29 10:18:55 (Show Source): You can put this solution on YOUR website!(x+2)/x=8/5 8x=5(x+2) 8x=5x+10 8x-5x=10 3x=10 x=10/3 x=3.3333 ans. for the width. 3.3333+2=5.3333 ans. for the length. Proof: 5.3333/3.3333=8/5 1.6~1.6
 Square-cubic-other-roots/204595: simplify (4-2i)(3-3i)1 solutions Answer 154500 by checkley77(12569)   on 2009-07-29 10:13:19 (Show Source): You can put this solution on YOUR website!(4-2i)(3-3i) 12-6i-12i+6i^2 12-18i+6(-1) 12-18i-6 6-18i 6(1-3i) ans.
 Miscellaneous_Word_Problems/204598: The height of a rectangular window is 1.5 times its width. The window is 2400 square inches. Find the dimensions of the window.1 solutions Answer 154499 by checkley77(12569)   on 2009-07-29 09:57:32 (Show Source): You can put this solution on YOUR website!x(1.5x)=2400 1.5x^2=2400 x^2=2400/1.5 x^2=1600 x=40 ans. for the width. 40*1.5=60 ans. for the height. Proof: 40*60=2400 2400=2400
 Rational-functions/204599: Solve the rational equation x + 1 = 5 _ _ x 2 and check1 solutions Answer 154498 by checkley77(12569)   on 2009-07-29 09:51:12 (Show Source): You can put this solution on YOUR website!x + 1 = 5 _ _ x 2 (x*x+1)/x=5/2 (x^2+1)/2=5/2 x^2+1=5 x^2+1-5=0 x^2-4=0 (x-2)^2=0 x-2=0 x=2 ans. Proof: 2+1/2=5/2 (2*2+1)/2=5/2 (4+1)/2=5/2 5/2=5/2
 Square-cubic-other-roots/204607: Simpligy br factoring: sqrt 245k^7q^81 solutions Answer 154497 by checkley77(12569)   on 2009-07-29 09:45:10 (Show Source): You can put this solution on YOUR website!sqrt 245k^7q^8 (7k^3q^4)sqrt5k ans.
 Square-cubic-other-roots/204609: Add or subtract. Then simplify by collecting like radical terms, if possible. 21sqrt5 - 13sqrt51 solutions Answer 154496 by checkley77(12569)   on 2009-07-29 09:42:16 (Show Source): You can put this solution on YOUR website!21sqrt5-13sqrt5 (21-13)sqrt5 8sqrt5 ans.
 Numeric_Fractions/204620: 2 5/2 - 2 3/21 solutions Answer 154495 by checkley77(12569)   on 2009-07-29 09:37:41 (Show Source): You can put this solution on YOUR website!2 5/2 - 2 3/2 (2*2+5)/2-(2*2+3)/2 (4+5)/2-(4-3)/2 9/2-1/2 8/2=4 ans.
 Quadratic_Equations/204683: f(x)=2x squared1 solutions Answer 154494 by checkley77(12569)   on 2009-07-29 09:31:10 (Show Source): You can put this solution on YOUR website!f(x)=2x squared (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 2x^2).