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Rate-of-work-word-problems/300150: It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence?
I tried solving this as an inverse work-rate problem using
1/A + 1/B = 20 but I can't get it to work.
1 solutions
Answer 215441 by richwmiller(9143)   on 2010-05-03 21:56:15 (Show Source):
You can put this solution on YOUR website!20/x+20/(x+9)=1
The one means one job
We are trying to find what fraction of the job Jack does and what fraction of the job Mike does. Together it has to add up to one whole job or 100% of the job
20/x is how much Mike does in the4 20 hour job
20/(x+9) is the part Jack does since he takes longer.
jack can do it in x+9 hours and so he does 1/(x+9) in one hour.
in 20/(x+9) he does his part of the 20 hour job
so we multiply 20/x by (x+9)/(x+9)
and we multiply 20/(x+9) by x/x
(20*(x+9)+20x)/x*(x+9)=1
(40x+180)=x^2+9x
0=x^2-31x-180
we want factors of -180 that add up to -31
-18 and 10 sum -8
-36 and 5 -31
ok
(x-36)*(x+5)=0
x=36 and x=-5
reject negative
x=36
20/36+20/45=1
5/9+4/9=1
jack take 45 hours alone and mike takes 36 alone
and together they take 20 hours
in 20 hours jack does 4/9 of the job and mike does 5/9
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Quadratic_Equations/300155: i don't understand some of the quadratic equation steps, like:
* when to use the two different equations.
*when do i know that there are no solutions
*if i got a fraction for x do i turn it into a decimal?
*if i don't have to turn it into decimal is there a chance that i can get a real big number? how can i work that out?
*when i use the long equation(the one with the square root on it) im looking for the vertex in the parabola or what.. i don't understand?
Please help me im doing kind of bad in Algebra because i don't understand this quadratic equations
Maria Rivera
1 solutions
Answer 215434 by richwmiller(9143) on 2010-05-03 21:37:24 (Show Source):
You can put this solution on YOUR website!
I like your questions
I hope I understand your questions
For every unknown (a different letter), you need another equation.
Let's say you just have x then you only need one equation .
If you have x and y then you need two equations
If you have x, y, and z then you need three equations.
Do you mean when are there no real solutions or no solutions?
There are always solutions to a quadratic equation.
The determinant (b^2-4ac) will tell you what type (real, imaginary, rational, irrational) and how many there are.
Answers can be left in fraction form. They are more exact than the decimal form.
Sometimes the teacher will want an answer in decimal form rounded to one or two places because there are roots with radicals etc.
What do you mean by a really big number? And what is wrong with really big numbers? Wouldn't you like a really big number of dollars?
The vertex will have an x and a y in the point such as (3,4)
the 3 is the x and the 4 is the y
-b/2a is the x value of the vertex when the equation is in the form ax^2+bx+c=0 or ax^2+bx=c
then plug in that value of x to find the y of the point y=ax^2+bx+c or
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Rate-of-work-word-problems/299707: Together, two pipes can fill a swimming pool in 4 hours. Separately, the smaller pipe requires 6 more hours to fill the pool than the larger pipe. How many hours does it take for each pipe alone to fill the pool?
1 solutions
Answer 215261 by richwmiller(9143) on 2010-05-03 06:30:17 (Show Source):
You can put this solution on YOUR website!4/x+4/(x+6)=1
(8(x+3))/(x (x+6)) = 1
(8 (x+3))=(x (x+6))
8x+24=x^2+6x
x^2-2x-24
(x-6)*(x+4)=0
reject x=-4
x=6
one pipe takes 6 hours and the other takes 12
4/6+4/12=1
2/3+1/3=1
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Average/298994: The average of a set of 11 numbers is 11. If two numbers are removed the average of the remaining numbers is 10. What is the sum of the two numbers removed?
1 solutions
Answer 214979 by richwmiller(9143) on 2010-05-01 09:28:39 (Show Source):
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Circles/298989: I am a Mom I can not figure out how to do the area of a sector of a circle I have a central angle of 140 and a radius of 6 in and I know the answer is 43.96 but I can not do the math to make it come out to 43 so I can't explain to my child how to do this...so frustrated please help me
1 solutions
Answer 214978 by richwmiller(9143) on 2010-05-01 08:54:49 (Show Source):
You can put this solution on YOUR website!Area of a circle is pi*r^2
3.14 is pi
r=6
what part of the circle do we want? 140/360
(36*3.14)*140/360=
36/360=1/10
140/10=14
3.14*14=43.96
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Average/298878: My exam grade is 82, possible points is 100, average score is 92. There are nine students in the class, what is the highest score and what is the lowest score.
1 solutions
Answer 214957 by richwmiller(9143) on 2010-04-30 22:55:15 (Show Source):
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Linear-equations/298936: It has been over 40 years since I have had algebra. Below is a problem my son needs to solve. If you can provide the answers hopefully I will begin to remember how equations work so I can help him with the rest of his problems. Thanks.
The equation for profit P in terms of the number of boxes sold s is:
P = 5s - (100 + 2s). The number of boxes sold also depends on the number of choir members.
a. Suppose each member sell 11 boxes. Write an equation that will predict profit from the number of choir members n. (Hint: Firts find an expression for the number of boxes sold)
b. Write an equivalent expression for profit in part (a). Explain what the variables and numbers represent.
c. Suppose the choir has 47 members. What is the profit?
d. Suppose the profit is $1,088. How many choir members are there?
e. In part (d), how many boxes were sold?
Barbara Best
1 solutions
Answer 214954 by richwmiller(9143) on 2010-04-30 22:49:20 (Show Source):
You can put this solution on YOUR website!I suspect that there is something wrong with your equation/formula. It can be reduced. Formulas are in their reduced form
P=5s-(100+2s)
P=3s-100
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Quadratic_Equations/298730: 2. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
Thank you so much for your assistance
1 solutions
Answer 214806 by richwmiller(9143) on 2010-04-30 09:30:42 (Show Source):
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Graphs/298725:
Find the equations for the following lines and then graph them using any graphing utility
Parallel to 6x - 4y + 12 = 0, and passing through the line x = 3
6 times (3)-4y+12=0
18-4y+12=0 y=30/4 or 7.5
30-4y=0
30=4y
6x-4y+12=0 -4y/-4 = 6x+12/-4
4y=6x+12 y=6/-4x + 12 y=1.5x+12
slope = 6/-4 solution (3, 7.5)
So I was able to get this much not sure if it is correct however I am lost when it comes to the graphing and the part of the problem whre it states passing through the line x=3
any help is much appreciated and needed Thank you
Eric
1 solutions
Answer 214800 by richwmiller(9143) on 2010-04-30 08:59:44 (Show Source):
You can put this solution on YOUR website!Please don't yell. We can hear you. We have new batteries in the hearing aids.
HELLO I AM LOST ON THIS PROBLEMI I WAS ABLE TO COME UP WITH PART OF THE ANSWER BUT I AM NOW STUCK. I ALSO HAVE NO CLUE HOW TO GRAPH THIS ANY HELP WOULD BE APPRECIATED.
All Caps is internet yelling.
If it passes through x=3 that means the new line at some time has x=3
the original line has the equation 6x - 4y + 12 = 0
it has a slope of -a/b=-6/-4=3/2
The new line will also have a slope of 3/2
and an x of 3
y=3x/2 is our new line
We are pretty sure it will pass through x=3
But how can we be sure?
The only lines that won't pass through x=3 are parallel with x=3 x=3 has an undefined slope since y never changes.
Our line has a slope of 3/2 so they do intersect.
As a further test we can see if the original line passes through x=3
by plugging in 3 for x in the original equation but it is not necessary.
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Polynomials-and-rational-expressions/298715: A rancher in Dallas decides to build a silo inside his corral. The rectangular corral measures 25 meters by 15 meters and the silos base is circular with a diameter of 2 meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built?
1 solutions
Answer 214796 by richwmiller(9143) on 2010-04-30 07:58:02 (Show Source):
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Miscellaneous_Word_Problems/298712: A cat, a fox and a dog share a portion of 450 grams of meat. If two foxes eat as much as three cats and two cats eat as much as a dog, how many grams of meat does the fox eat?
1 solutions
Answer 214790 by richwmiller(9143) on 2010-04-30 07:34:35 (Show Source):
You can put this solution on YOUR website!c+f+d=450
2f=3c
2c=d
c = 100, d = 200, f = 150
The other tutor was ok with x+x/2+3x/4=450
x=200 which is my d
For some reason he multiplied part of the equation by 4 but not all
and got
4x+2x+3x /4 = 450
if he had continued correctly
4x+2x+3x = 1800
9x=1800
x=200
each fox is 3x/4=600/4=150 which is my f
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Expressions-with-variables/298667: The area of a square can be quadrupled by increasing the length by 12cm and the width by 2cm.
What are the dimensions of the square?
( area of the square is  )
I'm not sure if my start was correct but I started off with  , and then  ..
1 solutions
Answer 214772 by richwmiller(9143) on 2010-04-29 23:30:49 (Show Source):
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Quadratic_Equations/298677: Sue can paint a barn by herself in X days. Mary can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x = 5.
1 solutions
Answer 214770 by richwmiller(9143) on 2010-04-29 23:23:20 (Show Source):
You can put this solution on YOUR website!y/x+y/2x=1
2y+y=2x
3y=2x
y=2x/3
y/5+y/10=1
2y+y=10
3y=10
y=10/3
it takes them 10/3 (3 1/3 )days together if x=5
so they complete 3/10 in one day
so they complete 3x/2 in one day
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Equations/298653: If y varies directly as x, and y = 1/3 when x = 4, write an equation for this relationship:
a. y = (4/3)x
b. y = (1/12)x
c. y = (3/4)x
d. y = 4/3x
Would the answer be b or d ? I am guessing b but I am not sure what the difference is between b and d since they seem to produce the same answer.
1 solutions
Answer 214768 by richwmiller(9143) on 2010-04-29 23:16:07 (Show Source):
You can put this solution on YOUR website!x=4 y=1/3
a. y = (4/3)x
1/3=4/3*4
1/3=16/3 no
b. y = (1/12)x
1/3=1/12*4=4/12
1/3=1/3 maybe
c. y = (3/4)x
1/3=3/4*4
1/3=3 no
d. y = 4/3x
1/3=4/3*4
1/3=1/3
maybe
d is an inverse relationship not direct
leaving b as you wanted
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Equations/298332: I have solved this problem, but I doubt if I did this in the correct manner or even if the problem is correct.
Here is the problem as stated: [(37*8.9)(4-2(3-1))]-5(2/(2-7))(5)= ?
This is my work below:
[(37*8.9)(4-2(3-1))]-5(2/(2-7))(5)= ? (original problem)
1.) 37*8.9 = 329.3 (I start by going left to right - multiplying the first set of parentheses)
2.) (3-1) = 2 (I than remember to always work the inner most part of the problem)
3.) (4-2+2) = 2 (According to my instructor, when it comes to multiplication/division and addition/subtraction, one is able to go from left to right rather than adding or subtracting first. I am not sure if this is correct, but here this is done by his teaching)
4.) (2-7)=-5 (I than move on to the right side of the equal sign)
5.) 2/-5=-0.4 (I than finish what is inside of the parentheses)
6.) 329.3+4-5(-0.4)(5) (This is what I have thus far into the equation)
7.) -5(-0.4)=2
329.3+4+2(5)
8.) 2(5)=10
329.3+4+10
9.) 343.3 (After I combine the last 3 terms)
So... I'm pretty sure that there is something I missed while working the problem. Please help me understand what I might have done wrong. Thanks!
1 solutions
Answer 214646 by richwmiller(9143) on 2010-04-29 13:18:34 (Show Source):
You can put this solution on YOUR website!I got 10 as my answer which you have to admit is a nice small even number.
I would not do it left to right.
Follow pemdas rules of order of operations
I would also hold off on making numbers bigger. There is often a way to cancel things if you leave them in factored form
Actually let's do the right hand side
5(2/(2-7))(5)
2-7=-5
-5*2/-5*5
=10
(4-2(3-1))
3-1=2
4-2*2=0
I was right to hold off on multiplying
anything times 0 =0 so we are left with ten
so how you changed 4-2*2 in4-2+2
(4-2+2) = 2 so instead of zero you got 2
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Miscellaneous_Word_Problems/298288: The polynomial 0.041h-0.018a-2.69 can be used to estimate the lung capacity, in liters, of a female with height h, in centimeters, and age a, in years. Find the lung capacity of a 50 year old women who is 170 centimeters tall.
Her lung capacity is_ liters?
I am not sure how to solve this polynomial.
1 solutions
Answer 214645 by richwmiller(9143) on 2010-04-29 12:49:17 (Show Source):
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Signed-numbers/298322: I need your help with an order of operations problem. First, I would like to state that I tried to work the problem, but was unable to come up with an answer. I know that the order of operations follows this list; parentheses(1), exponents(2), multiplication(3), division(4), addition(5), and subtraction(6). Using this knowledge has helped me break the problem down somewhat, but not completely.
Here is the problem as stated:  What number replaces the question mark? (The y represents the question mark. I was not able to punch the question mark in instead of the y because of a syntax error.)
I can deduce that the problems in the parentheses must be evaluated first, however, I'm not quite sure how to go about this. By combining like terms, I can see that 18x would combine with 3x, and 216 would combine with 36. However, they problems do not provide me with a classic distributive property solution.
Would you be able to enlighten me as far as what I can do when another situation such as this presents itself? Thanks!
1 solutions
Answer 214643 by richwmiller(9143) on 2010-04-29 12:35:45 (Show Source):
You can put this solution on YOUR website!solve 27x^3+216=(3x+y)(9x^2-18x+36) for y
factor
27*(x^3+8)=27*(x+2)*(x^2-2 x+4)
(9x^2-18x+36) =9*(x^-2x+4)
27*(x+2)*(x^2-2x+4) = 9*(x^2-2x+4)*(3x+y)
27/9=3
which you can see can be reduced to
3(x+2)=3x+y
3x+6=3x+y
6=y
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Functions/298275: Could you please provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10.
1 solutions
Answer 214642 by richwmiller(9143) on 2010-04-29 12:22:48 (Show Source):
You can put this solution on YOUR website!x=9 is not a function
(9,0) (9,2) (9,1) (9,4) (9,5)
In a function, each x yields one y
y=9 is a function however.
You can have many x's for one y
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