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# Recent problems solved by 'richwmiller'

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 Miscellaneous_Word_Problems/280728: Stan and Hilda can mow the lawn in 30 min if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone?1 solutions Answer 204027 by richwmiller(9135)   on 2010-03-14 17:57:53 (Show Source): You can put this solution on YOUR website!.5/h+.5/s=1 2h=s s=1.5 hours and h=.75 hours stan would take 1 hour 30 minutes alone
 Mixture_Word_Problems/280702: How many liters of water must be added to 7 liters of a 20% acid solution to obtain a 10% acid solution?1 solutions Answer 204018 by richwmiller(9135)   on 2010-03-14 17:44:47 (Show Source): You can put this solution on YOUR website!we can look at the problem from the point of view of water or acid. water .8*7+x=(7+x)*.90 x=7 liters of pure water acid .2*7=.1*(7+x) x=7 liters of water as expected
 Square-cubic-other-roots/280696: Find the three cube roots of 125. Show all work. Express exact answers in polar point form. Thanks!1 solutions Answer 204010 by richwmiller(9135)   on 2010-03-14 17:17:58 (Show Source): You can put this solution on YOUR website!+5 is the only real cube root of 125 x = 5/2 (-1-i sqrt(3)) x = 5/2 (-1+i sqrt(3)) x=-2.5-4.33013i x=-2.5+4.33013i
 Miscellaneous_Word_Problems/280699: Mutt and Jeff need to paint a fence. Mutt can do the job alone 4 hours faster than Jeff. If together they work for 13 hours and finish only 1/2 of the job, how long would Jeff need to do the job alone1 solutions Answer 204008 by richwmiller(9135)   on 2010-03-14 17:09:37 (Show Source): You can put this solution on YOUR website!double the hours to finish the job 26/m+26/j=1 m=j-4 j=54.0768 hours m=50.0768 hours
 Linear-systems/280624: find the slope and the y-intercept f(x)=-9x-101 solutions Answer 203969 by richwmiller(9135)   on 2010-03-14 14:16:00 (Show Source): You can put this solution on YOUR website!y=-9x-10 y=mx+b where b= y intercept and m=slope
 Radicals/280622: Really need help on this question use the equation y=30/x,where y equals the amount of time to complete a job and x represents the number of people working. how many people does it take to complete the job in 5hours?1 solutions Answer 203968 by richwmiller(9135)   on 2010-03-14 14:13:37 (Show Source): You can put this solution on YOUR website!just plug in 5 for y and solve for x y=30/x 5=30/x multiply both sides by x 5x=30 divide both sides by 5 x=6
 Age_Word_Problems/280621: John is twice as old as his sister Mary. Mary's age is 1/6 the age of her mother. Their mother is 30. How old are John and Mary? 1 solutions Answer 203964 by richwmiller(9135)   on 2010-03-14 14:08:27 (Show Source): You can put this solution on YOUR website!j=2s s=m/6 m=30 s=30/6=5 j=2*5=10
 Linear-equations/280619: write an equation (y=Mx+b) or the line that passes through the given point P and has the given slope. P(0,5) slope=2 1 solutions Answer 203963 by richwmiller(9135)   on 2010-03-14 14:05:00 (Show Source): You can put this solution on YOUR website!Curiously, in the USA, the m for slope is always lower case. b= y when x=0 since we have the point 0,5 b=5 y=2x+5
 Exponents-negative-and-fractional/280613: 1/3 x -3/41 solutions Answer 203960 by richwmiller(9135)   on 2010-03-14 13:47:04 (Show Source): You can put this solution on YOUR website!do you mean . or and is there a question?
 Miscellaneous_Word_Problems/280604: in a class the ratio of boys to girls is 3:2. If there are 11 more boys than girls,how many pupils are in the class?1 solutions Answer 203957 by richwmiller(9135)   on 2010-03-14 13:38:29 (Show Source): You can put this solution on YOUR website!3/2=b/g b=11+g 3/2=(11+g)/g 3g/2=11+g 3g=22+2g g=22 b=11+22=33 boys =33 and girls =22 there are 55 in the class
 Systems-of-equations/280606: Show the steps that you would take to solve the following algebraically 3/(x-3)=x/(x-3)-3/2 What potential solution did you obtain? Explain why this is this not a solution.1 solutions Answer 203954 by richwmiller(9135)   on 2010-03-14 13:31:52 (Show Source): You can put this solution on YOUR website!Is this what you mean? multiply by (x-3) 3=x-3*(x-3)/2 3=x-(3x-9)/2 6=2x-3x+9 -3=-x x=3 It looks like x=3 but it can't be x=3 since the denominator in the original equation would be 0 (3-3)
 Quadratic-relations-and-conic-sections/280601: find vertex of the parabola y=4x squared - 16x - 111 solutions Answer 203953 by richwmiller(9135)   on 2010-03-14 13:22:56 (Show Source): You can put this solution on YOUR website!y=4x^2-16x-11 vertex x=-b/2a x=-(-16)/2*4 x=16/8=2 y=4*2^2-16*2-11 y=16-32-11 y=-16-11 y=-27 (2,-27)
 Numbers_Word_Problems/280592: if a number is subtracted from 4 more than twice itself, the result is 30. what is the number?1 solutions Answer 203952 by richwmiller(9135)   on 2010-03-14 13:16:40 (Show Source): You can put this solution on YOUR website!2x+4-x=30 x=26 the number is 26 2*26+4=56 52+4=56 56-26=30
 Miscellaneous_Word_Problems/280595: aunt joanie has a 3x6 garden that she would like to triple the area of by adding some amount onto 2 sides1 solutions Answer 203950 by richwmiller(9135)   on 2010-03-14 13:12:16 (Show Source): You can put this solution on YOUR website!3*6=18 18*3=54 (3+x)*(6+x)=54 x=3 add three to each side 6*9=54
 expressions/280593: 1/8= blank over 321 solutions Answer 203949 by richwmiller(9135)   on 2010-03-14 13:06:36 (Show Source): You can put this solution on YOUR website!1/8=x/32 8x=32 x=4 1/8=4/32
 Rectangles/280598: what is 2/3 of 10. shade 2/3 of the diagram? the diagram is a rectangle divide into 10 equal parts.1 solutions Answer 203948 by richwmiller(9135)   on 2010-03-14 13:04:42 (Show Source): You can put this solution on YOUR website!2*10/3 20/3=6.7
 Rectangles/280596: the perimeter of a rectangle is 26cm. the length is 8cm. what is its width?1 solutions Answer 203947 by richwmiller(9135)   on 2010-03-14 13:03:19 (Show Source): You can put this solution on YOUR website!2*(l+w)=p 2*(8+w)=26 8+w=13 w=5
 Finance/280587: The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. Find the length of the three sides 1 solutions Answer 203946 by richwmiller(9135)   on 2010-03-14 12:59:09 (Show Source): You can put this solution on YOUR website!I guess I can't help you. I fail to see the finance involved. c=6+a a=b-2 a^2+b^2=c^2 a = 4*(1+sqrt(3)), b = 2*(3+2sqrt(3)), c = 2*(5+2sqrt(3))
 Polynomials-and-rational-expressions/280579: 28x^3-23x^2-57x-18/7x+3 1 solutions Answer 203945 by richwmiller(9135)   on 2010-03-14 12:47:35 (Show Source): You can put this solution on YOUR website!nice expression! what about it? Do you mean (28x^3-23x^2-57x-18)/(7x+3) It reduces to and then factors to Which becomes
Polynomials-and-rational-expressions/280572: Can you please find two examples of prime polynomials?
Given a polynomial such as x^2 + 4x + 8 how would I decide if this is factorable or not? What logic would you use to come up with your answer? What about a more complicated polynomial such as 3x^2 + 12x + 4? How would you decide if this is prime or not?
1 solutions

Answer 203943 by richwmiller(9135)   on 2010-03-14 12:36:45 (Show Source):
You can put this solution on YOUR website!
Neither of your equations are factorable even though this solver might say they are. This solver considers all real numbers factorable, whereas we normally only consider the equations factorable if there are whole numbers in the factors.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -16 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -16 is + or - . The solution is Here's your graph:

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=96 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.367006838144548, -3.63299316185545. Here's your graph:

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 3 and the last term 4 to get 12. Now we need to ask ourselves: What two numbers multiply to 12 and add to 12? Lets find out by listing all of the possible factors of 12

Factors:

1,2,3,4,6,12,

-1,-2,-3,-4,-6,-12, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 12.

1*12=12

2*6=12

3*4=12

(-1)*(-12)=12

(-2)*(-6)=12

(-3)*(-4)=12

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 12

||||||
 First Number | Second Number | Sum 1 | 12 | 1+12=13 2 | 6 | 2+6=8 3 | 4 | 3+4=7 -1 | -12 | -1+(-12)=-13 -2 | -6 | -2+(-6)=-8 -3 | -4 | -3+(-4)=-7

None of these factors add to 12. So the quadratic cannot be factored.

 Percentage-and-ratio-word-problems/280567: In 2001 2 women skied 1675 miles in 89 days across the land mass of Antartica. They still had to ski 508 miles. About what percent of their total distance remained.1 solutions Answer 203942 by richwmiller(9135)   on 2010-03-14 12:26:16 (Show Source): You can put this solution on YOUR website!1675+508=d=2183 508*100/2183=23.27%
 Complex_Numbers/280571: (3-4i)^21 solutions Answer 203940 by richwmiller(9135)   on 2010-03-14 12:22:16 (Show Source): You can put this solution on YOUR website!(3-4i)*(3-4i) use FOIL 9-12i-12i+16*(-1) -7-24i
 Polynomials-and-rational-expressions/280570: The base of a triangle is 6cm greater than the height. The areas is 20cm^2 Find the height and length of the base height of triangle is ____ cm. base of triangle is ____ cm.1 solutions Answer 203938 by richwmiller(9135)   on 2010-03-14 12:18:58 (Show Source): You can put this solution on YOUR website!A=1/2*Base*height 20=1/2*(6+h)*h h=4 cm base=10 cm check 20=1/2*10*4 20=20
 Rate-of-work-word-problems/280513: James and Wendy can paint a house in three-fourths the time that it takes James working alone. Wendy takes 12 days to paint a house alone.the rate in houses per day at which James paints alone is A 2 b 1/2 c 4 d 1/4 e 1/6 1 solutions Answer 203937 by richwmiller(9135)   on 2010-03-14 12:13:12 (Show Source): You can put this solution on YOUR website!x/12+x/j=1 x=3j/4 j=4 and x=3 James takes 4 days alone and together they take 3 days Answer: James can paint 1/4 house per day check 3/12+3/4=1 1/4+3/4=1 When working together James does 3/4 of the house and Wendy does 1/4 ok
 Numbers_Word_Problems/280524: The sum of two numbers is 10. The smallest possible value of the sum of the square of the first number plus two times the second number is: (A)9 (B) 18 (C) 19 (D) 20 (E) 23 1 solutions Answer 203936 by richwmiller(9135)   on 2010-03-14 12:01:31 (Show Source): You can put this solution on YOUR website!a+b=10 a^2+2b=y a^2-2a+20=y vertex is 1,19 so the lowest is 19
 Travel_Word_Problems/280553: amy travels 450 miles at a certain speed. If the car had gone 15 mph faster, the trip would have take 1 hour less. Find amys speed. Show your work. I know that D=RT So 450=RT I am not sure where to go from here because this does not work 450=(15+r)(t-1) ---- any suggestions? I appreciate the help, thank you1 solutions Answer 203935 by richwmiller(9135)   on 2010-03-14 11:55:19 (Show Source): You can put this solution on YOUR website!There is nothing wrong with your equation 450=(r+15)*(t-1) You forgot the original info. r*t=450 r=75 and t=6 check r*t=450 75*6=450 450=450 now check the second equation 90*5=450 450=450 ok The trip would not have been one hour less because Amy would have gotten stopped and ticketed or most likely ended up as a traffic fatality (dead). What a terrible problem for math!
 Linear_Equations_And_Systems_Word_Problems/280555: A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shipped to furniture stores. The shop can produce at most 30 dinner tables and coffee tables combined each week. If the shop sells dinner tables for \$120 and coffee tables for \$150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?1 solutions Answer 203934 by richwmiller(9135)   on 2010-03-14 11:46:54 (Show Source): You can put this solution on YOUR website!9+13 tables are already assigned which leaves 8 more to go. Choose coffee tables for max income 9*120+21*150=4230 1080+3150=4230 \$4230 is the max
 Functions/280563: Is this relation a function? {(2,4), (3,2), (4,6), (5,4)} 1 solutions Answer 203933 by richwmiller(9135)   on 2010-03-14 11:42:06 (Show Source): You can put this solution on YOUR website!one problem per submission
 Coordinate-system/280558: What co-ordinate would be on the lines y=4x+1 and y=6x-4? And how do you work out that answer?1 solutions Answer 203932 by richwmiller(9135)   on 2010-03-14 11:40:47 (Show Source): You can put this solution on YOUR website!set them equal to each other and solve for x 4x+1=6x-4 5=2x 2.5=x now substitute 2.5 for x in either equation y=4*2.5+1 y=11 (2.5,11)
 Geometry_Word_Problems/280560: what is the width of a 22 inch monitor that is 11 inches high1 solutions Answer 203931 by richwmiller(9135)   on 2010-03-14 11:36:33 (Show Source): You can put this solution on YOUR website!Assuming that the 22 inches is the diagonal. 11^2+w^2=22^2 121+w^2=484 w^2=363 w=about 19 inches
 Linear-equations/280559: Graph the equation and identify the y-intercept. y= -3/4x-3 The y-intercept is?1 solutions Answer 203930 by richwmiller(9135)   on 2010-03-14 11:32:58 (Show Source): You can put this solution on YOUR website!y=mx+b where m is the slope and b is the y intercept when x=0 b=-3 and m=-3/4