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# Recent problems solved by 'richwmiller'

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 Mixture_Word_Problems/282535: Two different chemicals are to be mixed, Chemical 1 is 25% citrate acid, and Chemical 2 is 37% ascorbic acid. A 24 milliliters of mixture solution is desired with 30% of acid in it. 1 solutions Answer 205165 by richwmiller(9132)   on 2010-03-18 17:28:55 (Show Source): You can put this solution on YOUR website!.25x+.37y=24*.30 x+y=24 x=14 y=10
Quadratic_Equations/282540: i need help and a couple of things explained better if possible
this is what my textbook says:
By drawing a suitable graph, find the roots of these quadratic functions. Check each root by substitution:
this is what we have been told to find by our teacher
where does x²-x=0 cut the y-intercept
where it cuts the x-axis
locate the turning point (an axis of symmetry)
i dont know how to do any of it so there is nothing i can write to show what i have done so far ?
thanks if you get back to me x
1 solutions

Answer 205163 by richwmiller(9132)   on 2010-03-18 17:24:23 (Show Source):
You can put this solution on YOUR website!
There are some problems with your wording.
x^2-x=0
x*(x-1)=0
the two roots are x=0 and x=1
that is where the parabola crosses the x axis
(0,0) and (1,0)
x intercept is when y =zero the zeroes or roots of the equation
y intercept is when x=0
Nothing cuts the y intercept. Perhaps you want to know the y intercept where x=0 or where it cuts(crosses) the y axis.
1/2^2-1/2
1/4-1/2=-1/4
 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=1 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1, 0. Here's your graph:

 Linear-equations/282548: 4. The equation a = 640s gives the relationship between s square miles and a acres. Pam owns 7.5 square miles of farmland. How many acres does she own? 1 solutions Answer 205153 by richwmiller(9132)   on 2010-03-18 17:09:00 (Show Source): You can put this solution on YOUR website!some website rules one problem per submission no similar problems max 4 submissions daily a=640s plug in 7.5 for s a=640*7.5 and calculate acres
 Expressions-with-variables/282434: a=y-x^2 ____ 2 make x the subject of the formula1 solutions Answer 205070 by richwmiller(9132)   on 2010-03-18 11:56:08 (Show Source): You can put this solution on YOUR website!a=y-(x^2/2) get x^2 on one side by itself a-y=-x^2/2 multiply by -2 -2(a-y)=x^2 sqrt(-2(a-y)=x x=sqrt(2(y-a)) x=-sqrt(2(y-a))
 Linear-equations/282427: 4x=5y as an linear equation. how to graph and what are the points? 1 solutions Answer 205067 by richwmiller(9132)   on 2010-03-18 11:48:03 (Show Source): You can put this solution on YOUR website!plug in 0 for x and find y 4x=5y solve for x x=5/4*y pick a multiple of 4 for y and find x pick 4 for y 4x=5*4 x=5 now you have two points, plot them and draw a line through them.
 Linear-equations/282430: I have a question and i dont have a clue how to do it so would love some help if possible. Find the equation of this line with y-intercept=-1 and passing through (-1;-2) Would Love Helppppp1 solutions Answer 205064 by richwmiller(9132)   on 2010-03-18 11:44:12 (Show Source): You can put this solution on YOUR website!see this problem and 3 solutions http://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.282417.html
 Geometry_Word_Problems/281882: The radius of a circular flower garden is 4 meters. How many meters of edging will be needed to surround the garden? A) 7.14 meters B) 12.56 meters C)25.12 meters D)50.27 meters E)3.14 meters 1 solutions Answer 205061 by richwmiller(9132)   on 2010-03-18 11:36:51 (Show Source): You can put this solution on YOUR website!c=2 pi r c=2*3.14*4 c=8*3.14 We can approximate 8*3=24 the only answer even close is 25.12 since "none of the above' is not a choice it must be 25.12. and yes 3.14*8=25.12 if you didn't know that 8*14 is 112 you should know that 8*7=56 and 2*56=112
Quadratic_Equations/282422: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
The product of two consecutive positive integers is 272. Find the integers.
1 solutions

Answer 205058 by richwmiller(9132)   on 2010-03-18 11:28:39 (Show Source):
You can put this solution on YOUR website!
x*(x+1)=272
x^2+x-272=0
16 and 17
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 1 and the last term -272 to get -272. Now we need to ask ourselves: What two numbers multiply to -272 and add to 1? Lets find out by listing all of the possible factors of -272

Factors:

1,2,4,8,16,17,34,68,136,272,

-1,-2,-4,-8,-16,-17,-34,-68,-136,-272, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -272.

(-1)*(272)=-272

(-2)*(136)=-272

(-4)*(68)=-272

(-8)*(34)=-272

(-16)*(17)=-272

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

||||||||||
 First Number | Second Number | Sum 1 | -272 | 1+(-272)=-271 2 | -136 | 2+(-136)=-134 4 | -68 | 4+(-68)=-64 8 | -34 | 8+(-34)=-26 16 | -17 | 16+(-17)=-1 -1 | 272 | (-1)+272=271 -2 | 136 | (-2)+136=134 -4 | 68 | (-4)+68=64 -8 | 34 | (-8)+34=26 -16 | 17 | (-16)+17=1

We can see from the table that -16 and 17 add to 1. So the two numbers that multiply to -272 and add to 1 are: -16 and 17

breaks down to this (just replace with the two numbers that multiply to -272 and add to 1, which are: -16 and 17)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 1x out of the first group and factor a 17 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

Notice how foils back to our original problem . This verifies our answer.

 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=1089 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 16, -17. Here's your graph:

 Linear-equations/282417: My Teacher has been of for ages and came in the other day to give us a homework sheet but the thing is we havent learnt any of this stuff so have looked everywhere on the internet for examples but cant find any so thought i would try this site. The question is: Find the equation of this line with the y-intercept=2 and passing through (2;6) Would love if you could help with this question as i find it easier to work out the following questions if i can see how one was done first :) Thanks Youu1 solutions Answer 205054 by richwmiller(9132)   on 2010-03-18 11:13:16 (Show Source): You can put this solution on YOUR website!You seem to know that we are dealing with linear equations. Have you heard of y=mx+b? m is the slope and b is the y intercept? Have you heard of this to find slope? (y-y)/(x-x)=m So we know two points. (2,6) and (0,2) Where did I get (0,2)? the y intercept 2 is when x=0. That means (0,2) (y-y)/(x-x)=m 6-2/2-0=4/2=2 slope is 2 plug in the new info slope =2 and old info y intercept=2 y=mx+b y=2x+2 done
 Probability-and-statistics/282405: Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm.1 solutions Answer 205049 by richwmiller(9132)   on 2010-03-18 11:02:16 (Show Source): You can put this solution on YOUR website!There are no minimum and maximums when length and width are known. A=L*W A=4.15*7.34=30.461
 decimal-numbers/282412: how do i figure out this simple problem? 25 divided by .5?1 solutions Answer 205047 by richwmiller(9132)   on 2010-03-18 10:51:51 (Show Source): You can put this solution on YOUR website!There are many ways 1-we could use a calculator 2- 25/.5= 250/5=50 We could change .5 to 1/2 3-25/1/2=25*2=50 Remember multiplying by the reciprocal is the same as dividing by the number. The reciprocal of 1/2 is 2 So dividing by 1/2 is the same as multiplying by 2
Quadratic_Equations/282408: Factor completely. Remember to look first for a common factor. Check by multiplying. If a polynomial is prime, state this.
27m^2 - 36 + 12
This is what I have got so far if I am heading in the right direction please let me know and what I do next if not help me figure this one out.
27m^2 - 36 + 12
=3(9x^2 - 12x + 4)
=3[(3x)^2 - 4*3 + 2^2]
That's all I got so far.
1 solutions

Answer 205046 by richwmiller(9132)   on 2010-03-18 10:46:18 (Show Source):
You can put this solution on YOUR website!
first i suspect that you copied the problem incorrectly
27m^2 - 36 + 12
I suspect it should be
27m^2 - 36m + 12
You perform some magic with the equation changing m's to x's
and then the last line is completely a mystery what you are doing and why you are doing it.
assuming it should be
27m^2 - 36m + 12
3*(9m^2-12m+4)
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 9 and the last term 4 to get 36. Now we need to ask ourselves: What two numbers multiply to 36 and add to -12? Lets find out by listing all of the possible factors of 36

Factors:

1,2,3,4,6,9,12,18,36,

-1,-2,-3,-4,-6,-9,-12,-18,-36, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 36.

1*36=36

2*18=36

3*12=36

4*9=36

6*6=36

(-1)*(-36)=36

(-2)*(-18)=36

(-3)*(-12)=36

(-4)*(-9)=36

(-6)*(-6)=36

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 | 36 | 1+36=37 2 | 18 | 2+18=20 3 | 12 | 3+12=15 4 | 9 | 4+9=13 6 | 6 | 6+6=12 -1 | -36 | -1+(-36)=-37 -2 | -18 | -2+(-18)=-20 -3 | -12 | -3+(-12)=-15 -4 | -9 | -4+(-9)=-13 -6 | -6 | -6+(-6)=-12

We can see from the table that -6 and -6 add to -12. So the two numbers that multiply to 36 and add to -12 are: -6 and -6

breaks down to this (just replace with the two numbers that multiply to 36 and add to -12, which are: -6 and -6)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 3m out of the first group and factor a -2 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

which can also be written as since the factors repeat themselves

Notice how foils back to our original problem . This verifies our answer.

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 27 and the last term 12 to get 324. Now we need to ask ourselves: What two numbers multiply to 324 and add to -36? Lets find out by listing all of the possible factors of 324

Factors:

1,2,3,4,6,9,12,18,27,36,54,81,108,162,324,

-1,-2,-3,-4,-6,-9,-12,-18,-27,-36,-54,-81,-108,-162,-324, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 324.

1*324=324

2*162=324

3*108=324

4*81=324

6*54=324

9*36=324

12*27=324

18*18=324

(-1)*(-324)=324

(-2)*(-162)=324

(-3)*(-108)=324

(-4)*(-81)=324

(-6)*(-54)=324

(-9)*(-36)=324

(-12)*(-27)=324

(-18)*(-18)=324

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

Now which of these pairs add to -36? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -36

||||||||||||||||
 First Number | Second Number | Sum 1 | 324 | 1+324=325 2 | 162 | 2+162=164 3 | 108 | 3+108=111 4 | 81 | 4+81=85 6 | 54 | 6+54=60 9 | 36 | 9+36=45 12 | 27 | 12+27=39 18 | 18 | 18+18=36 -1 | -324 | -1+(-324)=-325 -2 | -162 | -2+(-162)=-164 -3 | -108 | -3+(-108)=-111 -4 | -81 | -4+(-81)=-85 -6 | -54 | -6+(-54)=-60 -9 | -36 | -9+(-36)=-45 -12 | -27 | -12+(-27)=-39 -18 | -18 | -18+(-18)=-36

We can see from the table that -18 and -18 add to -36. So the two numbers that multiply to 324 and add to -36 are: -18 and -18

breaks down to this (just replace with the two numbers that multiply to 324 and add to -36, which are: -18 and -18)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 9m out of the first group and factor a -6 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

Notice how foils back to our original problem . This verifies our answer.

 Travel_Word_Problems/282399: Car A travels 180 miles in the same time it takes Car B to travel 120 miles. If one car is going 20 mph faster than the other car, find both speeds. 1 solutions Answer 205044 by richwmiller(9132)   on 2010-03-18 10:23:45 (Show Source): You can put this solution on YOUR website!(x+20)t=180 x*t=120 t=3 hours x=40 mph x+20=60 mph
 Polygons/282400: how do you find the value of x in a ploygon1 solutions Answer 205040 by richwmiller(9132)   on 2010-03-18 10:12:25 (Show Source): You can put this solution on YOUR website!Is a ploygon anything like a polygon? It all depends on what x means and what you know about the "ploygon"
 decimal-numbers/282398: how do you do this problem? i just need an example and im on my way! 40% of 50= thank you1 solutions Answer 205039 by richwmiller(9132)   on 2010-03-18 10:08:20 (Show Source): You can put this solution on YOUR website!" of " means multiply. 40%=.40=4/10=2/5 4/10 or 2/5 are the easiest forms to use here .40*50=20.00=20 2/5*50=2*10=20 4/10*50=4*5=20
 Numeric_Fractions/282396: I am trying to understand how to divide fractions. can you help me with this problem? 2/4 divided by 1/5= thank you1 solutions Answer 205036 by richwmiller(9132)   on 2010-03-18 10:02:43 (Show Source): You can put this solution on YOUR website!let's look at some examples first and see what we notice. if we divide 20 by 5 we get 4 20/5=4 but 20 *1/5 also equals 4 so dividing by a number is the same as if we multiply by the reciprocal so if we divide by 1/5 we can also multiply by 5 if we divide by 5 we can multiply by 1/5 2/4 divided by 1/5 is the same as multiplying by 5 2/4*5=10/4 BTW 2/4 -1/2 so 1/2*5=10/4=2.5 or 2 1/2
 Polynomials-and-rational-expressions/282391: what is the factorization of 9x^4 - 3x^2? I came up with the answer being..3x^2(x2 - 3). Just wanted to make sure this is right.1 solutions Answer 205032 by richwmiller(9132)   on 2010-03-18 09:57:25 (Show Source): You can put this solution on YOUR website!Did you check your answer by multiplying it out? 3x^2*(x^2-3) gives you what? 3x^4-9x^2 if you factor 3x^2 from 9x^4 you get 3x^2 not x^2 if you factor 3x^2from the second term you get 1 not 3
 Numeric_Fractions/282393: how do you do this problem...1/2 x 4/6= thanks!1 solutions Answer 205031 by richwmiller(9132)   on 2010-03-18 09:51:46 (Show Source): You can put this solution on YOUR website!1/2*4/6=4/12=1/3
 Numeric_Fractions/282387: 3/8 + 3/8 + 17/321 solutions Answer 205030 by richwmiller(9132)   on 2010-03-18 09:50:14 (Show Source): You can put this solution on YOUR website!first combine like terms 6/8+17/32 conv3erts 8th's to 32nd 24/32+17/32 41/32 1 9/32
 Exponential-and-logarithmic-functions/282352: 2x+(x+2)y=540 what is x and what is y1 solutions Answer 205029 by richwmiller(9132)   on 2010-03-18 09:46:02 (Show Source): You can put this solution on YOUR website!This one equation with two unknowns . No one unique solution is possible. There are at least 24 integer solutions. There are at least 5 integer solutions where both x>0 and y >0 0 < x < 270, y = -(2 (x-270))/(x+2)
 Numeric_Fractions/282360: This is the problem and they want an algebra solution. Three tired and hungry men went to sleep with a bag of apples. One man woke up, ate 1/3 of the apples, then went back to sleep. Later a second man woke up and ate 1/3 of the remaining apples, then went back to sleep.Finally,the third man woke and ate 1/3 of the remaining apples. When he was finished there were 8 apples left. How many apples were in the bag originally?1 solutions Answer 205028 by richwmiller(9132)   on 2010-03-18 09:38:13 (Show Source): You can put this solution on YOUR website!This problem appears every couple weeks. x-x/3-1/3(x-x/3)-1/3(x-x/3-1/3(x-x/3))=8 x=27 first guy ate 1/3*27=9 leaving 18 next guy ate 18/3=6 leaving 12 3rd guy at 12/3=4 leaving 8 A simpler way to calculate by working backwards 2/3x=8 x=12 2/3x=12 x=18 2/3x=18 x=27
 Polynomials-and-rational-expressions/282385: which one is correct? or 1 solutions Answer 205026 by richwmiller(9132)   on 2010-03-18 09:29:11 (Show Source): You can put this solution on YOUR website!10x^2*10x^7=100x^9 we have 10*10*x^2*x^7 so we have 100*x^9
 Travel_Word_Problems/282361: The time required to drive from Duluth to Fargo varies inversely with the speed of the car. If the trip takes 6.25 hours at 40 mph, what speed is required to make the trip in 4 hours? A) 6.4 mph B) 0.625 mph C) 25.6 mph D) 8.44 mph E) 62.5 mph 1 solutions Answer 205024 by richwmiller(9132)   on 2010-03-18 09:26:49 (Show Source): You can put this solution on YOUR website!r*t=d t=d/r 6.25*40=x*4 6.25*10=x 62.5=x E) 62.5 mph
 Triangles/282383: the measure of each three angles of a triangle are represented by x,2x,and x+60, find the numerical measure of each angle 1 solutions Answer 205022 by richwmiller(9132)   on 2010-03-18 09:22:50 (Show Source): You can put this solution on YOUR website!x+2x+x+60=180 4x+60=180 4x=120 x=30 2x=60 x+60=90
 Expressions-with-variables/282381: Factor the Polynomial Completely. 64x^3 + y^3 I know this uses the "Sum of Cubes" formula... a^3+b^3= (a+b)(a^2-ab+b^2), but I'm not sure how to start this.1 solutions Answer 205021 by richwmiller(9132)   on 2010-03-18 09:21:23 (Show Source): You can put this solution on YOUR website!a^3=(4x)^3 b^3=y^3 a=4x b=y
 Average/282382: What is the average? A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What is the average score for all 50 students who took the test? 1 solutions Answer 205020 by richwmiller(9132)   on 2010-03-18 09:19:16 (Show Source): You can put this solution on YOUR website!(35*80+15*70)/50
 Linear-systems/282366: You can rent a mid size car from Company A for \$250 per week with unlimited mileage. A similar car can be rented from Company B for \$150 per week plus 25 cents for each mile driven. How many miles must you drive in a week in order for the rental fee for Company B to be equal to that for Company A? A) 330 miles B) 150 miles C) 160miles D) 400 miles E) None of the above. 1 solutions Answer 205019 by richwmiller(9132)   on 2010-03-18 09:17:06 (Show Source): You can put this solution on YOUR website!250=150+x/4 100=x/4 400=x d) 400 miles
Polynomials-and-rational-expressions/282331: Please solve this problem and show the steps in solving it. 12y^2 - 5y = 2.
1 solutions

Answer 205016 by richwmiller(9132)   on 2010-03-18 09:08:12 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 12 and the last term -2 to get -24. Now we need to ask ourselves: What two numbers multiply to -24 and add to -5? Lets find out by listing all of the possible factors of -24

Factors:

1,2,3,4,6,8,12,24,

-1,-2,-3,-4,-6,-8,-12,-24, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -24.

(-1)*(24)=-24

(-2)*(12)=-24

(-3)*(8)=-24

(-4)*(6)=-24

Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5

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 First Number | Second Number | Sum 1 | -24 | 1+(-24)=-23 2 | -12 | 2+(-12)=-10 3 | -8 | 3+(-8)=-5 4 | -6 | 4+(-6)=-2 -1 | 24 | (-1)+24=23 -2 | 12 | (-2)+12=10 -3 | 8 | (-3)+8=5 -4 | 6 | (-4)+6=2

We can see from the table that 3 and -8 add to -5. So the two numbers that multiply to -24 and add to -5 are: 3 and -8

breaks down to this (just replace with the two numbers that multiply to -24 and add to -5, which are: 3 and -8)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 3y out of the first group and factor a -2 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
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