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# Recent problems solved by 'checkley77'

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 Travel_Word_Problems/313919: Two bicyclists start at the same time at a given point and travel in the same direction at average speeds of 8 miles per hour and 10 miles per hour. After how long are the bicyclists 5 miles apart?1 solutions Answer 224451 by checkley77(12569)   on 2010-06-13 18:39:06 (Show Source): You can put this solution on YOUR website!D=RT D=8T D=10T-5 8T=10T-5 8T-10T=-5 -2T=-5 T=-5/-2 T=2/5 T=2.5 HOURS THEY WILL BE 5 MILES APART. PROOF: 8*2.5=10*2.5-5 20=25-5 20=20
 Linear-equations/313939: Please help me solve this equation world problem If a plane can travel 480 miles per hour with the wind and 440 miles per hour against the wind, find the speed of the plane in still air1 solutions Answer 224449 by checkley77(12569)   on 2010-06-13 18:28:37 (Show Source): You can put this solution on YOUR website!s+w=480 s-w=400 add, -------------- 2s=880 s=880/2 s=440 mph. speed of the plane in still air. (480-440)=40 mph. speed of the wind.
 Square-cubic-other-roots/313925: Find the distance between (-1,7) and (-3,6). a)10.07 b)13.15 c)15.28 d)2.231 solutions Answer 224447 by checkley77(12569)   on 2010-06-13 18:13:29 (Show Source): You can put this solution on YOUR website!(-1,7) and (-3,6). X distance=(-3+1)=2 Y distance=(7-6)=1 1^2+2^2=c^2 1+4=c^2 c^2=5 c=sqrt5 c=2.236 ans. D).
 test/313950: 3(2x-5)=12+4x1 solutions Answer 224446 by checkley77(12569)   on 2010-06-13 18:07:54 (Show Source): You can put this solution on YOUR website!3(2x-5)=12+4x 6x-15=12+4x 6x-4x=12+15 2x=27 x=27/2 x=13.5 ans. Proof: 3(2*13.5-5)=12+4*13.5 3(27-5)=12+54 3*22=66 66=66
 Numbers_Word_Problems/313959: The three angles in a triangle always add up to 180°. If one angle in a triangle is 48° and the second is 2 times the third, what are the three angles?1 solutions Answer 224445 by checkley77(12569)   on 2010-06-13 18:04:07 (Show Source): You can put this solution on YOUR website!48+2*48+x=180 48+96+x=180 144+x=180 x=180-144 x=36 degrees ans. for the third angle.
 Numbers_Word_Problems/313960: A car rental agency charges \$150 per week plus \$.20 per mile to rent a car. How many miles can you travel for \$250?1 solutions Answer 224444 by checkley77(12569)   on 2010-06-13 17:57:36 (Show Source): You can put this solution on YOUR website!150+.20x=250 .20x=250-150 .20x=100 x=100/.20 x=500 miles ans. Proof: 150=.20*500=250 150+100=250 250=250
 test/313945: 7x-(5x-4)=121 solutions Answer 224443 by checkley77(12569)   on 2010-06-13 17:54:18 (Show Source): You can put this solution on YOUR website!7x-(5x-4)=12 7x-5x+4=12 2x=12-4 2x=8 x=8/2 x=4 ans. Proof: 7*4-(5*4-4)=12 28-(20-4)=12 28-16=12 12=12
 Linear-equations/313951: 3x2 +18x + 21= x(x + 5)1 solutions Answer 224442 by checkley77(12569)   on 2010-06-13 17:50:02 (Show Source): You can put this solution on YOUR website!3x^2 +18x + 21= x(x + 5) 3x^2+18x+21=x^2+5x 3x^2-x^2+18x-5x+21=0 2x^2+13x+21=0 (2x+7)(x+3)=0 2x+7=0 2x=-7 x=-3.5 ans. x+3=0 x=-3 ans.
 Linear-systems/313946: what is the y-intercept and vertex of y=x^2+2x?1 solutions Answer 224441 by checkley77(12569)   on 2010-06-13 17:44:59 (Show Source): You can put this solution on YOUR website!y=x^2+2x (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, x^2 +2x). Y intercept=0 VERTEX=(-1,-1)
 Miscellaneous_Word_Problems/313948: A rectangular window is 10 inches longer than it is wide. If the area of the window is 1200 square inches, find the length and the width.1 solutions Answer 224440 by checkley77(12569)   on 2010-06-13 17:39:02 (Show Source): You can put this solution on YOUR website!W=L+10 A=LW A=L(L+10) 1,200=L^2+10L L^2+10L-1,200=0 (L-30)(L+40)=0 L-30=0 L=30 ANS. FOR THE WIDTH. W=30+10=40 ANS. FOR THE LENGTH. PROOF: 1,200=30*40 1,200=1,200
 Rectangles/313597: Three squares have sides of different integer lengths, a, b, and c. The total area of the three squares cannot be (A) 14 (B) 29 (C) 50 (D) 88 (E) 1011 solutions Answer 224308 by checkley77(12569)   on 2010-06-12 18:18:07 (Show Source): You can put this solution on YOUR website!1+4+9=14 4+9+16=29 9+16+25=50 1+36+64=101 ANSWER D)88. (A) 14 (B) 29 (C) 50 (D) 88 (E) 101
 decimal-numbers/313674: Given the sequence 7, 14, 28, 56, ..., which expression shown would give the tenth term?1 solutions Answer 224306 by checkley77(12569)   on 2010-06-12 18:11:14 (Show Source): You can put this solution on YOUR website!L=A*R^(N-1) L IS THE LAST NUMBER. A=THE FIRST NUMBER. R IS THE RATIO. N IS THE Nth TERM. L=7*2^(10-1) L=7*2^9 L=7*512 L=3,584 IS THE 10th TERM IN THE SEQUENCE.
 Polynomials-and-rational-expressions/313676: bill leaves nightclub at 60mph. sue leaves 1 minute later at 90mph. how many minutes before they meet?1 solutions Answer 224304 by checkley77(12569)   on 2010-06-12 17:50:28 (Show Source): You can put this solution on YOUR website!D=RT D=60T FOR BILL. D=90(T-1/60) FOR SUE. 60T=90(T-1/60) 60T=90T-90/60 60T-90T=-1.5 -30T=-1.5 T=-1.5/-30 T=.05 HOURS OR IN 3 MINUTES SUE WILL CATCH BILL. PROOF: 60*.05=90(.05-1/60). 3=90(.05-.01667) 3=90*.0333 3=3
 Unit_Conversion_Word_Problems/313700: how many bricks would it take to skirt a 76x30 foot mobile home if the bricks are 9x2.5 inches1 solutions Answer 224303 by checkley77(12569)   on 2010-06-12 17:23:36 (Show Source): You can put this solution on YOUR website!76*30=2,280 ft^2 9*2.5=22.5 in^2 22.5/12*12=22.5/144=.15625 ft^2 per brick. 2,280/.15625=14,592 bricks will be required.
 Graphs/313564: graph this problem a.) y = 2x – 1 b.) y = (–3/4)x + 5 c.) y = x2 – 4 y = –3x2 – 6x – 5 1 solutions Answer 224302 by checkley77(12569)   on 2010-06-12 17:17:47 (Show Source): You can put this solution on YOUR website!a.) y = 2x – 1 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 2x -1). b.) y = (–3/4)x + 5 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -3x/4 +5). c.) y = x^2 – 4 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, x^2 -4). d.) y = –3x^2 – 6x – 5 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -3x^2 -6x -5 )
 Travel_Word_Problems/313574: two sculptures are similar. The height of one sculpture is four times the height of the other sculpture. The smaller sculpture is 2.5 feet tall. How tall is the larger sculpture?1 solutions Answer 224301 by checkley77(12569)   on 2010-06-12 17:09:33 (Show Source): You can put this solution on YOUR website!4*2.5=10 FEET TALL FOR THE TALLEST SCULPTURE.
 Miscellaneous_Word_Problems/313593: A box containing 5 oranges weighs 1.678 kilograms. The same box with 10 oranges in it weighs 2.278 kilograms. How much does the empty box weigh? (Assume all oranges weigh the same.) (A) 0.300 kg (B) 0.539 kg (C) 0.600 kg (D) 1.078 kg (E) 1.356 kg 1 solutions Answer 224300 by checkley77(12569)   on 2010-06-12 17:05:31 (Show Source): You can put this solution on YOUR website!10X+Y=2.278 5X+Y=1.678 SUBTRACT THIS EQUATION --------------------------- 5X=.6 X=.6/5 X=.12 KG. WEIGHT OF AN ORANGE. 10*.12+Y=2.278 1.2+Y=2.278 Y=2.278-1.2 Y=1.078 KG. WEIGHT OF THE BOX. ANSWER D).
 Numbers_Word_Problems/313600: The sum of all the digits used in writing the integers from 1 to 10 is 46. What is the sum of all the digits used to write the integers from 1 to 50? (A) 230 (B) 240 (C) 270 (D) 284 (E) 3301 solutions Answer 224299 by checkley77(12569)   on 2010-06-12 16:54:47 (Show Source): You can put this solution on YOUR website!THE SUM OF THE DIGITS OF ALL INTEGERS FROM 1 TO 50=330 ANS E).
 Rectangles/313613: Solve the following application problem (show your equation and then your solution). Round answers to nearest thousandths and properly label your answer as well. The length of a rectagle is 2 cm. more than 3 times its width. If the area of the rectange is 95 cm^2, find the dimensions of the rectangle.1 solutions Answer 224298 by checkley77(12569)   on 2010-06-12 16:43:13 (Show Source): You can put this solution on YOUR website!L=3W+2 A=LW 95=(3W+2)W 95=3W^2+2W 3W^2+2W-95=0 W=(-2+-SQRT[2^2-4*3*-95])/2*3 W=(-2+-SQRT[4+1,140])/6 W=(-2+-SQRT1,144)/6 W=(-2+-33.823)/6 W=(-2+33.823)/6 W=31.823/6 W=5.304 ANS. W=(-2-33.823)/6 W=-35.823/6 W=-5.967 ANS.
 Rectangles/313614: Solve the following application problem (show your equation and then your solution). Round answers to nearest thousandths and properly label your answer as well. A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 15ft by 25ft. The total area, garden plus walkway, is to be 650ft^2. What must be the width of the walkway? 1 solutions Answer 224294 by checkley77(12569)   on 2010-06-12 16:30:37 (Show Source): You can put this solution on YOUR website!(15+2X)(25+2X)=650 375+50X+30X+4X^2=650 4X^2+80X+375-650=0 4X^2+80X-275=0 X=(-80+-SQRT[80^2-4*4*-275])/2*4 X=(-80+-SQRT[6,400+4,400])/8 X=(-80+-SQRT10,800)/8 X=(-80+-103.923)/8 X=(-80+103.923)/8 X=23.923/8 X=2.99 ANS. FOR THE WIDTH OF THE WALKWAY.
 Problems-with-consecutive-odd-even-integers/313618: Ten consecutive integers are arranged in order from least to greatest. If the sum of the first five integers is 200, what is the sum of the last five integers ? 1 solutions Answer 224290 by checkley77(12569)   on 2010-06-12 16:17:18 (Show Source): You can put this solution on YOUR website!X+X+1+X+2+X+3+X+4=200 5X+10=200 5X=200-10 5X=190 X=190/5 X=38 ANS. FOR THE FIRST INTEGER. 38+1=39 ANS. THE SECOND INTEGER. 38+2=40 ANS. FOR THE THIRD INTEGER. 38+3=41 ANS. FOR THE FOURTH INTEGER. 38+4=42 ANS. FOR THE FIFTH INTEGER. 43+44+45+46+47=225 ANS. FOR THE SUM OF THE NEXT FIVE INTEGERS.
 test/313619: Find an equation of variation in which y varies directly as x and y=12 when x=1/3. Then find the value of y when x=20.1 solutions Answer 224289 by checkley77(12569)   on 2010-06-12 16:10:52 (Show Source): You can put this solution on YOUR website!(1/3)/12=20/X CROSS MULTIPLY. X/3=12*20 X/3=240 X=720 ANS.
 test/313621: The distance d traveled by a car varies directly as the time t. A car travels 60 km in 2/3 hr. How far will it travel in 6 hr?1 solutions Answer 224288 by checkley77(12569)   on 2010-06-12 16:05:44 (Show Source): You can put this solution on YOUR website!(2/3)/60=6/X CROSS MULTIPLY. 2/3X=360 X=360/(2/3) X=360*3/2 X=180*3=540 MILES CAN BE DRIVEN IN 6 HOURS.
 test/313628: Find an equation of the line containing the pair of points (-6,3) and (1,1).1 solutions Answer 224287 by checkley77(12569)   on 2010-06-12 15:58:46 (Show Source): You can put this solution on YOUR website!(-6,3) and (1,1) Y=mX+b m=slope=(y2-y1)/x2-x1) m=(1-3)/(1+6) m=-2/7 ans. for the slope. 1=-2/7*1+b 1=-2/7+b b=1+2/7 b=7/7+2/7=9/7 ans. for the y intercept. Y=-2X/7+9/7 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -2x/7 +9/7).
 Miscellaneous_Word_Problems/313635: Last month a factory produced 800 tv's. This month they producted 1,064 tv's. The increase in production from last month to this month is what percentage? An electronic device that perviously sold \$21 has been reduced to \$17.43. The price reduction rounded to the nearest percent is what?1 solutions Answer 224285 by checkley77(12569)   on 2010-06-12 15:48:25 (Show Source): You can put this solution on YOUR website!1,064/800=1.33 OR A 33% INCREAE. 1-(17.43/21)=1-.83=.17 OR 17% REDUCTION.
 Miscellaneous_Word_Problems/313636: the length of a rectagular parking lot is 4 meters less than twice its width and the perimeter is 316 meters, find the length of the parking lot.1 solutions Answer 224282 by checkley77(12569)   on 2010-06-12 15:41:44 (Show Source): You can put this solution on YOUR website!L=2W-4 P=2L+2W 316=2(2W-4)+2W 316=4W-8+2W 6W=316+8 6W=324 W=324/6 W=54 ANS. FOR THE WIDTH. L=2*54-4 L=108-4=104 ANS. PROOF: 316=2*104+2*54 316=208+108 316=316
 Circles/313643: Find the area of a circle with radius 3 units. Give your answer in terms of and as a decimal rounded to the nearest tenth. Use 3.14 for the approximation of . 1 solutions Answer 224281 by checkley77(12569)   on 2010-06-12 15:38:20 (Show Source): You can put this solution on YOUR website!A=PI*R^2 A=3.14*3^2 A=3.14*9=28.3 ANS.
 Exponential-and-logarithmic-functions/313646: What is 5(3+4)/35+12/4 7+{20-(7+6)} 9+{13(2)-(3-12)} 12/2-{6-(7(3))}1 solutions Answer 224280 by checkley77(12569)   on 2010-06-12 15:36:38 (Show Source): You can put this solution on YOUR website!5(3+4)/35+12/4 5*7/35=3 35/35+3 1+3=4 ANS. ----------------- 7+{20-(7+6)} 7+20-13 27-13=14 ANS. ----------------- 9+{13(2)-(3-12)} 9+{26-(-9)} 9+{26+9} 9+35=44 ANS. ------------------- 12/2-{6-(7(3))} 6-{6-21} 6-{-15} 6+15=21 ANS.
 Triangles/313653: 1)The base of a parallelogram is 10 inches.The height is 2 inches more than half the base.Find the are. 2)The height of a parallelogram is 4.5cm.The base is twice the height.What is the area? 3)The area of a parallelogram is 6 ft squared.The height is 5ft.How long is the base? 4)The are of a parallelogram is375 cm squared.The base is 25cm. Find the height. 1 solutions Answer 224279 by checkley77(12569)   on 2010-06-12 15:31:47 (Show Source): You can put this solution on YOUR website!1) AREA=B*H AREA=10*(10/2+2) AREA=100/2+20 AREA=50+20=70 IN^2. ANS. 2) AREA=2*4.5*4.5 AREA=40.5 IN^2 ANS. 3) 6^2=B*5 36=5B B=36/5 B=7.2 FT. ANS. 4) 375=25H H=375/25 H=15 cm^2. ans.
 Travel_Word_Problems/313673: An athlete runs 105 miles south and 80miles west. How ,far is he from the starting point.1 solutions Answer 224276 by checkley77(12569)   on 2010-06-12 15:23:11 (Show Source): You can put this solution on YOUR website!105^2+80^2=C^2 11,025+6,400=C^2 17,425=C^2 C=SQRT17,425 C=132.004 MILES. ANS. FOR THE DISTANCE FROM THE STARTING POINT.
 Equations/313678: the perimeter of a rectangle is 24 cm. the are of the same rectangle is 20 sq. cm. find the sides of the rectangle without using calculus.1 solutions Answer 224274 by checkley77(12569)   on 2010-06-12 15:19:20 (Show Source): You can put this solution on YOUR website!24=2L+2W 20=LW OR L=20/W REPLACING L IN THE FIRST EQUATION BY (20/W) & SOLVE FOR W. 24=2(20/W)+2W 24=40/W+2W 24=(40+2W*W)/W 24=(40+2W^2)/W CROSS MULTIPLY. 24*W=40+2W^2 24W=40+2W^2 2W^2-24W+40=0 2(W^2-12W+20)=0 2(W-10)(W-2)=0 W-10=0 W=10 ANS. L=20/10=2 ANS. W-2=0 W=2 ANS. L=20/2=10 ANS. PROOF: 20=2*10 20=20 24=2*10+2*2 24=20+4 24=24