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# Recent problems solved by 'checkley77'

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 test/229346: I am learning to prove lines parallel. How do i know if a line is or segments are parallel? the assignment wants me to answer with a theorem or postulate. Can some one please explain to me how i will figure that out?1 solutions Answer 170062 by checkley77(12569)   on 2009-10-20 19:10:15 (Show Source): You can put this solution on YOUR website!LINES ARE PARALLEL IF THEIR SLOPES ARE EQUAL. EXAMPLE: Y=3X/5+3 (RED LINE) Y=3X/5-4 (GREEN LINE) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 3x/5 +3 and 3x/5 -4).
 Numeric_Fractions/229349: How do you solve the equation 3/2x=6 1 solutions Answer 170060 by checkley77(12569)   on 2009-10-20 19:05:18 (Show Source): You can put this solution on YOUR website!3/2x=6 3X/2=6 3X=6*2 3X=12 X=12/3 X=4 ANS. PROOF: 3/2*4=6 12/2=6 6=6
 Volume/229266: The volumes of two cubes differ by 259 cu meters. If the edges of one cube are each 4 meters greater than the edges of the other, what is the sum of the lengths of one edge of each cube?1 solutions Answer 170058 by checkley77(12569)   on 2009-10-20 19:02:56 (Show Source): You can put this solution on YOUR website!X^2-Y^2=259 X=Y+4 (Y+4)^2-Y^2=259 Y^2+8Y+16-Y^2=259 8Y=259-16 8Y=243 Y=243/8 Y=30.375 ANS FOR THE SMALLER SQUARE SIDES. X=30.375+4 X=34.375 ANS FOR THE LARGER SQUARE SIDES. PROOF: 34.375^2-30.375^2=259 11.81.64-922.64=259 259=259
 Rectangles/229273: An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3. Find the sides of the two squares.1 solutions Answer 170053 by checkley77(12569)   on 2009-10-20 18:47:37 (Show Source): You can put this solution on YOUR website!(2X)^2+(3X)^2=52 4X^2+9X^2=52 13X^2=52 X^2=52/13 X^2=4 X=2 ANS FOR THE SIDES OF THE SMALLER SQUARE. PROOF: (2*2)^2+(3*2)^2=52 4^2+6^2=52 16+35=52 52=52
 Travel_Word_Problems/229278: Twp cyclists start biking from a trails start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?1 solutions Answer 170051 by checkley77(12569)   on 2009-10-20 18:38:45 (Show Source): You can put this solution on YOUR website!D=RT D=6T D=10(T-3) 6T=10(T-3) 6T=10T-30 6T-10T=-30 -4T=-30 T=-30/-4 T=7.5 HOURS THEY WILL MEET. PROOF: 6*7.5=10(7.5-3) 45=10*4.5 45=45
 Travel_Word_Problems/229287: Stan can drive from Atlas to Billings at a constant rate in four hours. If he increases his rate by 15 miles per hour, he could complete the trip in three hours. Find the number of miles between Atlas and Billings.1 solutions Answer 170048 by checkley77(12569)   on 2009-10-20 18:34:17 (Show Source): You can put this solution on YOUR website!D=RT D=R*4 D=(R+15)3 4R=3R+45 4R-3R=45 R=45 MPH IS THE RATE FOR THE 4 HOUR TRIP. D=45*4=180 MILES IS THE DISTANCE BETWEEN ATLAS & BILLINGS. D=(45+15)3 D=60*3 D=180 DITTO.
 Travel_Word_Problems/229288: Jack starts at the summit of Mt. Mickinley (elevation 20,320) and travels down the mountain at a rate of 4 feet per second. Jill starts at the bottom at the same time and travels up the mountain at a rate of 1 foot per second. At what elevation, in feet, will they meet?1 solutions Answer 170047 by checkley77(12569)   on 2009-10-20 18:28:51 (Show Source): You can put this solution on YOUR website!4x+1x=20,320 5x=20,320 x=20,320/5 x=4,064 sec. after they start they will meet. 1*4,064=4,064 feet is the meeting altitude. Proof: 4*4064=16,256 feet below the peak. 16,256+4,064=20,320 20,320=20,320
 absolute-value/229289: -|3n-5| is greater than or equal to 7n-15 I don't understand how to show the absolute value when it is negative. Please show good, concise steps.1 solutions Answer 170043 by checkley77(12569)   on 2009-10-20 18:22:34 (Show Source): You can put this solution on YOUR website!-|3n-5|>=7n-15 -3n+5>=7n-15 -3n-7n>=-15-5 -10n>=-20 n<=-20/-10 [Note: when dividing by a negative value the > sign changes to a < sign] n<=2 ans. Proof: Let n=1.9 -[3*1.9-5]>=7*1.9-15 -[5.7-5]>=13.3-15 -[.7]>=-1.7 -.7>=-1.7 -------------------------- -[3n-5]>=-(7n-15) -3n+5>=-7n+15 -3n+7n>=15-5 4n>=10 n>=10/4 n>=2.5 ans. Proof: Let x=2.6 -[3*2.6-5]>=-(7*2.6-15) -(7.8-5]>=-(18.2-15) -(2.8)>=-3.8 -2.8>=-3.8
 Inequalities/229290: Expenses. The sophomore class is planning a picnic. The cost of a permit to use a city park is \$250. To pay for the permit, there is a fee of \$.75 for each sophomore and \$1.25 for each guest who is not a sophomore. Two hundred sophomores plan to attend. Write and solve an inequality to find how many guests must attend for the sophomores to pay for the permit.1 solutions Answer 170038 by checkley77(12569)   on 2009-10-20 18:08:07 (Show Source): You can put this solution on YOUR website!200*.75+1.25x>250 150+1.25x>250 1.25x>250-150 1.25x>100 x>100/1.25 x>80 minimum number of non sophomores are required to raise the \$250 fee. Proof: 200*.75+1.25*80>250 150+100=250 250=250
 Linear-equations/229292: y=2x+31 solutions Answer 170035 by checkley77(12569)   on 2009-10-20 18:00:07 (Show Source): You can put this solution on YOUR website!y=2x+3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 2x +3).
 Linear-equations/229194: Find the equation of a line parallel to 4y=2x+6 through the point (-4,5)1 solutions Answer 170031 by checkley77(12569)   on 2009-10-20 17:53:45 (Show Source): You can put this solution on YOUR website!4y=2x+6 through the point (-4,5) y=2x/4+6/4 y=x/2+3/2 this line has a slope=1/2. (red line) Thus a parallel line will also have a slope=1/2. Y=mX+b 5=1/2*-4+b 5=-2+b b=5+2 b=7 Y=X/2+7 the equation for the parralel line through (-4,5). (green line). (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions x/2 +3/2 and x/2 +7).
 Linear-equations/229195: Find the x and y intercept points of -3x-2y=121 solutions Answer 170028 by checkley77(12569)   on 2009-10-20 17:44:19 (Show Source): You can put this solution on YOUR website!-3x-2y=12 -2y=3x+12 y=3x/-2+12/-2 y=-3x/2-6 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -3x/2 -6). Intercepts: (-4,0) & (0,-6)
 Money_Word_Problems/229217: You invested \$8000, part at 5% and part at 6%. The total interest earned in one year what \$468. How much was invested at each rate?1 solutions Answer 170023 by checkley77(12569)   on 2009-10-20 17:29:23 (Show Source): You can put this solution on YOUR website!.06x+.05(8,000-x)=468 .06x+400-.05x=468 .01x=468-400 .01x=68 x=68/.01 x=6,800 amount invested @ 6%. 8,000-6,800=1,200 amount invested @ 5%. Proof: .06*6,800+.05*1,200=468 408+60=468 468=468
 Miscellaneous_Word_Problems/229219: When 30% of a number is added to the number, the result is 54.6. What is the number?1 solutions Answer 170021 by checkley77(12569)   on 2009-10-20 17:25:01 (Show Source): You can put this solution on YOUR website!.3x+x=54.6 1.3x=54.6 x=54.6/1.3 x=42 ans. Proof: .3*42+42=54.6 12.6+42=54.6 54.6=54.6
 Linear-systems/229220: solve linear system 3x-y=-2 5x+2y=151 solutions Answer 170020 by checkley77(12569)   on 2009-10-20 17:22:27 (Show Source): You can put this solution on YOUR website!3x-y=-2 multiply by 2 & add. 5x+2y=15 6x-2y=-4 ------------- 11x=11 x=11/11 x=1 ans. 3*1-y=-2 3-y=-2 -y=-2-3 -y=-5 y=5 ans. Proof: 5*1+2*5=15 5+10=15 15=15
 Linear-systems/229223: substitution and elimination 2x+y=-5 -x+3y=61 solutions Answer 170017 by checkley77(12569)   on 2009-10-20 17:19:04 (Show Source): You can put this solution on YOUR website!2x+y=-5 -x+3y=6 multiply by 2 & add. -2x+6y=12 2x+y=-5 ----------------- 7y=7 y=7/7 y=1 ans. 2x+1=-5 2x=-5-1 2x=-6 x=-6/2 x=-3 ans. Proof: -(-3)+3*1=6 3+3=6 6=6
 Equations/229226: 4m^2+8m+2=0 solve using quadraratic formula1 solutions Answer 170013 by checkley77(12569)   on 2009-10-20 17:15:06 (Show Source): You can put this solution on YOUR website!4m^2+8m+2=0 m=(-8+-sqrt[8^2-4*4*2])/2*4 m=(-8+-sqrt[64-32])/8 m=(-8+-sqrt32)/8 m=(-8+-5.657)/8 m=(-8+5.657)/8 m=-2.343/8 m=-.29289 ans. m=(-8-5.657)/8 m=-13.657/8 m=-1.7071 ans.
 Rectangles/229229: The length of a rectangle is 8 in. more than its width. the perimeter of the rectangle is 24 in. what anr the width and length of the rectangle?1 solutions Answer 170005 by checkley77(12569)   on 2009-10-20 17:00:36 (Show Source): You can put this solution on YOUR website!L=W+8 2L+2W=24 2(W+8)+2W=24 2W+16+2W=24 4W=24-16 4W=8 W=8/4 W=2 ANS. FOR THE WIDTH. L=2+8=10 ANS. FOR THE LENGTH. PROOF: 2*10+2*2=24 20+4=24 24=24
 Percentage-and-ratio-word-problems/229233: find the absolute and relative change (as a percentage) if the numbers of daily newspapers was 2338 in 1900 and 1317 in 20051 solutions Answer 170001 by checkley77(12569)   on 2009-10-20 16:55:45 (Show Source): You can put this solution on YOUR website!(2338-1317)/2338=1021/2338=.4367 Absolute reduction=1,021. Percentage reduction=(-43.67%)