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# Recent problems solved by 'RAY100'

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 Expressions-with-variables/192356: if y=8x^2 + 4x-1 is expressed in the form y=a(x-h)^2+k, where a, h, and k are constants, what is the value of k ?1 solutions Answer 144402 by RAY100(1637)   on 2009-04-21 13:47:54 (Show Source): You can put this solution on YOUR website!y=8x^2+4x-1 to form y=a(x-h)^2+k y=8(x^2+x/2)-1 now must complete square of bracket terms y=8(x^2 +x/2 +1/16) -1 -8(1/16) simplify y=8(x+1/4)^2-1.5 this fits form with a=(8) h=(-1/4) k=(-1.5) checking let x=3 solve for y initial eqn y=8x^2+4x-1= 8(3^2) +4(3)-1=72+12-1=83 final form y=8(x+1/4)^2-1.5=8(3.25)^2-1.5= 8(10.5625)-1.5=84.5-1.5=83 ok to complete the square we take coefficient of middle term, divide by two, and square it ie (1/2) , (1/2)/2=1/4, (1/4)^2=(1/16) this becomes constant term of "square" since we added this to complete square terms we must subst from constant term to balance eqn. In this case we added 8(1/16) in total therefore we substract (8/16) from constant
 logarithm/192355: log5 square root of 125 - log2 square root of 2=1 solutions Answer 144393 by RAY100(1637)   on 2009-04-21 13:10:21 (Show Source): You can put this solution on YOUR website!basic form is log base a of b = ( log b)/(loga) log base 5 of sq rt 125 - log base 2 of sq rt 2 log of neg number is undefined therefore only use positive sq rts (log sq rt 125 / log 5 ) -(log sq rt 2/ log 2) (log 11.18/log5) - (log 1.414/log2) 1.5-.5 1.0
 Rational-functions/192330: 3+(sqroot5x-1)=x1 solutions Answer 144389 by RAY100(1637)   on 2009-04-21 12:56:54 (Show Source): You can put this solution on YOUR website!3+sq rt (5x-1) = x subt 3 each side sq rt(5x-1) = x-3 sq both sides +-(5x-1) = (X-3)^2 USING ONLY + answer ( - answer gives imaginary answers) +(5x-1) = (x-3)(x-3)= x^2-6x+9 subt 5x each side -1 = x^2 -6x +9 -5x add 1 to each side 0= X^2 -6x +9 -5x +1 simplifying 0=x^2 -11x +10 factoring 0=(x-10)(x-1) x=10 and x=1 checking 3 +sq rt (5x-1) = x 3 + sq rt (5(1)-1) = (1) 3 + sqrt 4=1 3+-2 =1 ok with -2 for x=10 3+sqrt (5(10)-1) = (10) 3+ sqrt 49 =10 3+-7=10 ok with +7
 Travel_Word_Problems/192352: A pole that is 2.9 tall casts a shadow that is 1.58 long. At the same time a nearby tower casts a shadow that is 50.5 long. How tall is the tower? Round your answer to the nearest meter. 1 solutions Answer 144386 by RAY100(1637)   on 2009-04-21 12:35:47 (Show Source): You can put this solution on YOUR website!if a drawing were made showing a line from a point on the ground thru top of tower and then thru top of bldg, we could see two similar triangles. Similar triangles have sides proportional. in our case h/50.5=2.9/1.58 cross multiplying 1.58 *h=50.5 * 2.9 1.58 *h = 146.45 divide by 1.58 h=92.68987= 92.69
 Numeric_Fractions/192349: What is the angle between the arrows of a clock at 3:15? Record your answer as precisely as possible. (Hint: The arrows are not at exactly the same place.) 1 solutions Answer 144384 by RAY100(1637)   on 2009-04-21 12:27:38 (Show Source): You can put this solution on YOUR website!assume the 3:15 is 3 hrs and 15 minutes from zero. AM or PM is not given. The hr hand has rotated once for every hour plus 90 degrees for 15 minutes or hr = 360 *3 +90 = 1170 degrees. the minute hand has rotated 60 times for each hour plus 90 degrees for 15 minutes or minute hand = 3 *60*360 +90= 64,890 degrees The difference is 63,720
 Numeric_Fractions/192350: Robinson’s dining room has a square base. The perimeter is 144 feet, how long is each side? 1 solutions Answer 144381 by RAY100(1637)   on 2009-04-21 12:15:17 (Show Source): You can put this solution on YOUR website!the definition of a square defines each side as equal per = 2l +2w for rectangle, but square is l=w, or per =4s per=4s 144 = 4s divide by 4 36=s (ft)
 Circles/192331: x^2+4x+y^2+6y=2 What is the center and the radius?1 solutions Answer 144379 by RAY100(1637)   on 2009-04-21 12:10:49 (Show Source): You can put this solution on YOUR website!basic formula for a circle is (x-h)^2 + (y-k)^2 = r^2, where h is x center, k is y center, r is radius to fit this form the given problem must "complete the square" (x^2 +4x +4) + (y^2 +6y+9) = 2 + (+4)+ (+9) reviewing take coefficient of the middle term, 4x, divide by 2 and then square, (4/2)^2 =4 and add to both sides of eqn for y terms, ( 6/2)^2 =9 and add to both sides Now factor x and y sets (x+2)^2 + (y+3)^2 = 15 comparing to basic form we find x center is (-2) y center is (-3) rad^2 = 15, rad =sq rt 15 = 3.87
 Numeric_Fractions/192346: Jenny’s trunk has a length of 100 inches, and a width of 20 inches. She knows from the manufacturer that the volume of her trunk is 20000 cubic inches. What is the height of the trunk? 1 solutions Answer 144376 by RAY100(1637)   on 2009-04-21 11:52:27 (Show Source): You can put this solution on YOUR website!volume = length * width * height or V=l*W*H for given info 20,000= (100) (20) *H 20,000=2,000*H 10=H
 Polynomials-and-rational-expressions/192341: This question is from textbook Intermediate Algebra Find the opposite of the polynomial : –2r^2 – r + 3 Do we just reverse from posistive to negative or is there a method? 1 solutions Answer 144374 by RAY100(1637)   on 2009-04-21 11:47:42 (Show Source): You can put this solution on YOUR website!Opposites are just as you stated. Just opposite sign. The two add to zero. Normally with polynomials, we talk about inverses. This is the reflextion over y=x. We usually find these by setting x=y, and y=x. For example if y=2x, inverse is x=2y or y=x/2.
 Quadratic_Equations/192340: I'm having problems with this type of question Find the height, of a ball, above ground using the following information. wait 3 seconds, velocity is 45 ft/sec, initial height above ground is 10 ft wait 2 seconds, velocity is 95 ft/sec, initial height above ground is 50 ft1 solutions Answer 144368 by RAY100(1637)   on 2009-04-21 11:19:21 (Show Source): You can put this solution on YOUR website!This is a physics problem under "projectile motion" Sometimes it is found in algebra under quadratic topics as a actual application example. For today, we are asked how high the projectile will go, in a given time, with an initial velocity. The velocity provides the upward energy, and gravity provides the downward energy. Usually, the angle of the initial velocity is important, but for today we will assume straight up. If not, let me know. The basic eqn is: delta y = v*t - (1/2) (32.2) t^2 where : delta y is change in height. Note as time progresses, the projectile goes up, reaches a peak, and then comes down. v is initial velocity. units in this case are ft per sec or ft/sec t is elapsed time. units are sec 32.2 is gravity. we are using English today. be careful of metric. english units are 32.2 ft per sec squared, or 32.2 ft/sec^2 (metric is 9.8 m/sec^2) 1/2 is a constant to get average acceleration 1st problem y= vt-1/2 (32.2) t^2 = (45) (3) - 1/2 (32.2) (3^2) = 135 - 144.9 = (-9.9) ft Note we started at 10 ft above ground, therefore 10-9.9 = (.1) ft above ground This is not so nice a first problem. The projectile has been in the air long enough to go fully up, stop, and now decend to just above ground height. Additional calc shows that the projectile goes up to a peak of about 31.4 ft in 1.4 sec before starting down. 2nd problem y=vt-16.1t^2 = 95*2 -16.1 * 2^2= 190-64.4=125.6 ft Again, initial height was 50 ft, therefore final position is 50+125.6 =175.6 ft additional calc shows peak at about 3 sec of about 140 ft
 Expressions-with-variables/192200: This question is from textbook Algebra 1 Please help, I'm very frustrated and don't understand how to solve linear systems with substitution. I have a lot of homework due tomorrow and don't understand what I'm supposed to do. x-y=0 12x-5y=-211 solutions Answer 144246 by RAY100(1637)   on 2009-04-20 16:47:52 (Show Source): You can put this solution on YOUR website!1) x-y=0 2) 12x-5y=-21 In substitution we use one eqn to establish a x to y relationship. Then we substitute this relationship in the other eqn for example from (1) we know x-y=0, therefore x=y substituting into (2) 12 (y) -5y = -21 simplify 7y=-21 divide by 7 y=(-3) substitute this in either (1) or (2) to find x using (1) x-y=0 x-(-3) =0 y=(-3) checking (1) (-3)-(-3)=0 ok (2) 12(-3) -5(-3) =-21 -36 +15 = -21 ok
 logarithm/192198: Find the solution of the equation, correct to two decimal places: 5Ln(1-x)= 81 solutions Answer 144242 by RAY100(1637)   on 2009-04-20 16:37:54 (Show Source): You can put this solution on YOUR website!5ln(1-x) =8 ln(1-x)^5 =8 e^8=(1-x)^5 2980.958=(1-x)^5 taking 5th root 4.95303 = (1-x) subt 1 both sides 3.95303 =-x x=(-3.95303) checking 5 ln (1-(-3.95303) )=8 5ln 4.95303 =8 5(1.5999) =8 8=8 ok to 2 dec places x= (-3.95)
 Rational-functions/192035: In the equation 5x/(x+1), what is the end behavior? We are being taught the Ratey method and when I get to the E part of Ratey, i simplify it to 5/1. Does that make it top heavy? If so how do you determine the vertical asymptote?1 solutions Answer 144219 by RAY100(1637)   on 2009-04-20 15:45:45 (Show Source): You can put this solution on YOUR website!5x /(x+1) vertical asymptote at den =0, x+1=0, x=-1 as degrees num and den equal, hor asymptote at 5/1 = +5 sketch vertical line at x=-1, and horizontal line at y=+5 rough sketch shows function starting low at x=-1, rising to rt thru (0,0) to just under asy y=5 starting high at x=-1, function decays to just above hor asy at y=5 as it goes to left end behavior: as x approaches -infinity, y approaches +5 from +side as x approaches + infinity, y approaches +5 from - side
 Geometry_Word_Problems/192077: Given (triangle)ABC~(tringle)XYZ, AB=9, BC=18 and AC-21. If the perimeter of (triangle)XYZ is 112, find the measures of the three sides of (triangle)XYZ.1 solutions Answer 144216 by RAY100(1637)   on 2009-04-20 15:29:57 (Show Source): You can put this solution on YOUR website!Draw a rough sketch of two similar triangles label sides carefully as triangles are similar, sides are proportional per of given triangle abc = 9 + 18 + 21 = 48. per of new triangle is 112 as perimeters vary as scale factor to 1st power sf = 112/48 =2 1/3 =7/3 xy = (7/3)ab =7/3 * 9 = 21 yz = (7/3) bc = 7/3*18 = 42 xz = (7/3) ac = 7/3*21 = 49 checking per 2nd triangle = 21+42+49= 112 ok
 Equations/192180: I am having issues figuring out the inverse variation. Here is the problem Suppose z varies inversely with t and that z=12 and t=10. What is the value of z when t = 61 solutions Answer 144213 by RAY100(1637)   on 2009-04-20 15:19:02 (Show Source): You can put this solution on YOUR website!z= k/t 12 =k/10 cross multiply k=120 now proportion is z=120/t for t=6 z=120/6 = 20
 Linear-systems/192176: Could you help me with the following problem? Solve the system algebraically. 5x+2y=10 3x+2y=6 Make sure there are no spaces in your answer. Be sure to include a comma. Answer{( )}1 solutions Answer 144209 by RAY100(1637)   on 2009-04-20 15:15:11 (Show Source): You can put this solution on YOUR website!1) 5x +2y = 10 2) 3x +2y =6 subt (1) - (2) 2x =4 divide by 2 x=2 subst in (1) 5(2) +2y =10 10 +2y =10 subt 10 both sides 2y =0 y=0 answer (2,0) checking 1) 5(2) +2(0) =10 ok 2) 3(2) = 2(0) =6 ok
 Linear-systems/192172: Please help me solve.... (y-1)-y=y+11 solutions Answer 144206 by RAY100(1637)   on 2009-04-20 15:08:03 (Show Source): You can put this solution on YOUR website!(y-1) -y =y+1 simplify by combining like terms -1 =y+1 subt 1 from both sides -2=y checking (y-1)-y=y+1 ( (-2) -1) -(-2) = (-2) +1 -3 +2 = -2 +1 -1 =-1 ok
 Polynomials-and-rational-expressions/192169: Can you please help me solve this problem? 5/2x+1/4x=7/4+x Thank you so much; I really appreciate your help! 1 solutions Answer 144203 by RAY100(1637)   on 2009-04-20 14:58:43 (Show Source): You can put this solution on YOUR website!(5/2)x +(1/4)x =(7/4) +x Multiply by 4 10x +x=7+4x 7x=7 x=1 check 5/2 +1/4 =7/4 +1 10/4 +1/4 =7/4 +4/4 11/4 = 11/4 ok if you really did mean 5/(2x) +1/(4x) =7/4 +x mult by 4x 10 +1 = 7x +4x^2 0= 4x^2 -7x -11 0= (4x+11) (x-1) x=(1) and x=(-11/4) checking x=1 5/2 +1/4 =7/4 +1 ok checking x=( -11/4) 5/-22/4 +1/-44/4 = 7/4 -11/4 -20/22 -2/22 = -4/4 -22/22 =-4/4 ok
 Polynomials-and-rational-expressions/192167: Can you please help me solve this problem? 6-2x=5x-9x+2 Thank you so much; I really appreciate your help! 1 solutions Answer 144202 by RAY100(1637)   on 2009-04-20 14:42:37 (Show Source): You can put this solution on YOUR website!6-2x=5x-9x+2 6-2x = -4x +2 add(2x) and subt (2) 4=-2x divide by (-2) x=(-2) check 6-2(-2)=5(-2) -9(-2) +2 6+4=-10 +18 +2 10=10 ok
 Polynomials-and-rational-expressions/192163: Factor. -14w+2w^2+wz-7z1 solutions Answer 144199 by RAY100(1637)   on 2009-04-20 14:37:19 (Show Source): You can put this solution on YOUR website!-14w +2w^2 +wz-7z reorder 2w^2 -14w + wz-7z factor by grouping 2w(w-7) + z(w-7) (2w+z) (w-7) check by FOIL 2w^2 -14w +zw -7z
 Equations/192165: can you square a negative number? im trying to solve the equation x^2+25=01 solutions Answer 144198 by RAY100(1637)   on 2009-04-20 14:29:46 (Show Source): You can put this solution on YOUR website!an imaginary number (i) is = sq rt (-1) x^2 +25 =0 x^2 = -25 x = +- 5 sq rt (-1) = +- 5i
 Equations/192161: I home school and I am stuck on a problem. all the information the directions give me is "solve each equation" The worksheet is on radical equations' graphs, and complex numbers Please help me solve this equation: (2x-3)^2=-241 solutions Answer 144197 by RAY100(1637)   on 2009-04-20 14:25:56 (Show Source): You can put this solution on YOUR website!(2x-3)^2=24 take sq rt of both sides 2x-3 = sq rt 24 = +- (4.899) 2x-3 =+4.899 2x = 7.899 x= 3.95 or 2x-3= -4.899 2x = -1.899 x=-.95 checking (2(3.95) -3 )^2= 24 ok ( 2(-.95) -3)^2 =24 ok
 Proportions/192130: This question is from textbook For the following problem you need to give a proportion whose solution gives the answer to the problem. You must name the variable that you used in the proportion. A lawyer bills her clients \$300 per hour of service. If a client's case requires 17 hours to complete, use a proportion to calculate how much the client will owe the lawyer (excluding tax) Thank You to all!1 solutions Answer 144195 by RAY100(1637)   on 2009-04-20 14:09:44 (Show Source): You can put this solution on YOUR website!Let x = cost of 17 hrs labor 300/1=x/17 cross mult 300*17=\$ 5100 =x
 Functions/192158: Find the domain of f(x) = 5x+1/x^2+5x-141 solutions Answer 144193 by RAY100(1637)   on 2009-04-20 14:02:54 (Show Source): You can put this solution on YOUR website!(5x+1)/ (x^2+5x-14) (5x+1) / ( (x+7) (x-2) ) therefore Domain is all Real numbers except, x=(-7) and x=(2)
 Rational-functions/192141: For each rational function, identify any holes or horizontal or vertical asymptotes of its graph. y= -2(x-8)/(8-x) I have tried a couple different things, but I am not sure if any of them are correct. First attempt: There would be a vertical asymptote at x=8. There would be a horizontal asymptote at y=-2. Second attempt: There would be a hole at (8,2) Third attempt: There would vertical asymptote at x=8. There would be a horizontal asymptote at y=2. I am extremely confused any help would be greatly appreciated!1 solutions Answer 144190 by RAY100(1637)   on 2009-04-20 13:53:28 (Show Source): You can put this solution on YOUR website!good work an easier approach might be y=-2(x-8)/(8-x) simplify to y= 2(x-8) / (x-8) cancelling (x-8) 's gives us y=+2 but with a hole at x=8 no vertical asymptotes ( ie den =0) no real horizontal asymptotes except y does always =2 review of horiz asymptotes, y = a(n)x^n +..... / b(m) x^m +..... if n less than m, hor asy at y=0 if n=m, hor asy at y=a(n)/b(m) and if n>m, no hor asy
 Problems-with-consecutive-odd-even-integers/192149: find two consecutive odd integers such that the square of the larger is 3 than 12 times the smaller x, x+21 solutions Answer 144186 by RAY100(1637)   on 2009-04-20 13:35:14 (Show Source): You can put this solution on YOUR website!let smaller +x let larger = x+2 The problem only makes sense if " is three than" reads " is 3 smaller than" to solve this problem l^2 = 12 S-3 (x+2)^2 =12(x) -3 x^2 +4x+4 =12x -3 subt 12 x both sides x^2 +4x -12x +4 =-3 now add 3 to both sides x^2 +4x -12x +4 +3 =0 x^2 -8x +7 =0 factoring (x-7) (x-1) =0 setting both =0 x-7=0, x=7 (smaller) & larger =9 or x-1=0, x=1 (smaller) & larger is 3 checking (l^2=12*s-3) 3^2=12(1)-3 ok 9^2 = 12(7)-3 or 81=84-3 ok Therefore both sets are correct, 1 &3, and 7&9
 Polynomials-and-rational-expressions/192140: This question is from textbook saxon algebra 2 Identify the leading coefficient and degree, and describe the end behavior of f(x)=2x^5+4x^4-x leading coefficient=2+ degree=5odd describe the end behavior?1 solutions Answer 144184 by RAY100(1637)   on 2009-04-20 13:19:20 (Show Source): You can put this solution on YOUR website!GOOD JOB END BEHAVIOR is fancy for what happens to function for very big or small numbers for the ODD functions they in general slant up for positive leading coefficients or slant down for negative leading coefficients. This is a positive therefore it will slant up the end on the left side will be y approaches (-infinity) as x approaches (- infinity) the end on the right side wiil be y approaches (+ infinity) as x approaches ( + infinity) as it is 5th degree it should have 4 turns as it goes from lower left to upper right on graph
 Square-cubic-other-roots/192118: This question is from textbook Structure and Method Book 1 Sq.root of 3)(2)+ sq. root of 501 solutions Answer 144183 by RAY100(1637)   on 2009-04-20 13:05:26 (Show Source): You can put this solution on YOUR website!sq rt (3*2) +sqrt (50) sqrt 3 *sqrt2 + sqrt 25*sqrt2 (sqrt3 +5) * sqrt (2) (5 +sqrt3 ) *sqrt2 check sqrt 6 +sqrt50 =9.52 (5+sqrt3) * sqrt2 = 9.52
 Numeric_Fractions/192134: -6 +[-11 +5] / 4^2 -(-9) i think my text book is wrong because they got 0 as an answer is 0 the correct answer1 solutions Answer 144182 by RAY100(1637)   on 2009-04-20 12:56:04 (Show Source): You can put this solution on YOUR website!review original problem please IF ( (-6) +(11-5) ) / 4^2 - (-9) or thereabouts numerator will be zero and problem will be zero STATED PROBLEM (-6) + (-11+5)/4^2 -(-9) -6+ (-6)/16 +9 3 -(3/8) 2 5/8 2.625
 Functions/192136: Find the domain of the function f(x)= 5x-1 ----- x^2-161 solutions Answer 144181 by RAY100(1637)   on 2009-04-20 12:44:02 (Show Source): You can put this solution on YOUR website!f(x) =y=(5x-1)/(x^2-16) Normally in Domain problems we seek when denominator =0 this becomes easier to see if we factor denominator y= (5x-1) / ( x+4) (x-4) x+4 =0, x=-4 x-4 =0, x=4 Therefore domain is all Real numbers except x= +4, or =-4
 Average/192120: If f(x) = (5x-3)/(x-2) Find the inverse function of f. would that be just the opposite? = (x-2)/(5x-3)? State the domain of f. State the domain of the inverse function. 1 solutions Answer 144173 by RAY100(1637)   on 2009-04-20 11:36:37 (Show Source): You can put this solution on YOUR website!INVERSE of a number is reciprocal, ie 2, inv 2 = 1/2 however inverse of FUNCTION indicates a function that is reflected over y=x Normally this is solved by substituting x for y ,,,, and y for x f(x) =(5x-3) / (x-2) but f(x) =y y = (5x-3) / (x-2) DOMAIN is all REAL numbers except x=2 inverting x = (5y-3) / (y-2) or (y-2) = (5y-3) /x Domain is all REAL numbers except x=0