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x, is isolated like you want the simply states
:
that x has the value of anything greater than -2 and less than 4.....that is the solution set.
It would look something like this on the number line. The -2 and 4 should be hollow circles since they are not inclusive and everything in between those numbers are a solution.

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let n be the number of nickels and q be the number of quarters
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.05n+.25q=7.70
.05q+.25n=4.90---->.25n+.05q=4.90
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mulitply 1st equation by -5
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-.25n+-1.25q=-38.5..revised eq 1
.25n+ .05q=4.90
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-1.2q=-33.6
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quarters
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.05n+.25(28)=7.70
:
.05n=.70
:
nickels
:

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divide by 2 the original coordinates would be a(-4,-3/2) b (-3/2,0) c (-1,3/2)
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a scale factor of 3 would produce (a(-12,-9/2) b (-9/2,0) c (-3,9/2)
simply by multiplying by 3

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the hint just means it doesnt have to equal 29000.
so with the labels that they gave.
:

what that is saying is 120 pounds per acre of honeydew +150 pounds per acre of onions+ 180 pounds per acre of lettuce cannot exceed 29000 pounds of nitrogen.

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or meaning D and H are directly related
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and have a constant value of 113.523

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a)add 10 to both sides of equation
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now divide both sides by -9 remembering that dividing by a
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negative reverses the inequality sign.
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b) distribute the middle term 3(x-1)=3x-3
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now add 3 to all terms
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now divide all terms by 3 to isolate the x
:

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ok the easiest way to set this up is with proportions
:
lets call votes kim receives k and votes amy receives a
:
--->2k=3a---->k=3a/2......eq 1
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----->a+8=2(k-8)--->a+8=2k-16--->a-2k=-24....eq 2
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lets substitute k's value in eq 1 into eq 2
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a-2(3a/2)=-24
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a-3a--24
:
-2a=-24
:
votes for amy
:
votes for kim
Total of people who voted

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....multiply all terms by 1-t
:

:
.....subtract s from both sides
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....divide by -s on both sides
:

:

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solving by elimination is simply adding or subtracting one equation from another
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with the intention of eliminating one of the variables.
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so lets line the equations up one under the other to have a better look at each variable.
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x+7y=30....eq 1
9x+6y=99....eq 2
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ok as you observe these equations we try to do the least amount of manipulation as possible to reach our goal.....we can either multiply eq 1 by -9 and add the equations together thus eliminating the x terms, or we could multiply eq 1 by - and eq 2 by -7 and add the two equations togethr to eliminate the y terms. I choose the first choice
:so -9(x+7y=30) equals -9x-63y=-270..so that is our revised eq 1. lets line them up again.
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-9x-63y=-270
9x+ 6y=99
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so you see how if we add these two equations together that the x terms are eliminated because -9x+9x=0. We are left with -63y+6y=-270+99--->
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-57y=-171...dividing by -57 gives us
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.
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now we take y's value and plug it back into either original equation to solve for x I choose eq 1
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x+7(3)=30
:
x+21=30
:

:
:

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.......-(-1-i) = 1+i
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so
:
or

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5-2=3feet gain per day...200/3=66.66 this number gives us a reasonable place to start....remember it jumps 5 feet before it loses 2.
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lets start at day 64 just to give our selves room 64 times 3=192 which is 8 feet from reaching our goal. day 65 starts like this 92+5=97(oh, so close)but then we lose 2 at the end of the day...97-2=95...Damn......
at the end of 65 days the frog will have climbed up 195 feet. On day 66 will the frog finally reach its goal?... the frog leaps and what to his wonder 195+5=200. He made it......damn that must have been tiring....turdles pace..lol

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this is a direct proportion problem
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5/40=10/x.....cross multiply and solve for x
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5x=400
:
minutes

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multiply both sides by 7
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your left with
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dividing both sides by -2
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252 divided by -2=126

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art can do 1/30 job per minute
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bob.......1/40 job per minute
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carl.......1/60 job per minute
those are all rates.....lets call time=t
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t/30+t/40+t/60=1(job)
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4t+3t+2t=120...muliply each term by 120
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9t=120
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or 13 and 1/3 minutes to do the entire job...

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you must first figure the earnings per share which would be
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earnings(1.5million)/number of shares(1 million
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eps=$1.5 (earnings per share)
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a PE(price per earnings) ratio is simply what your pay in multiples above what the earnings are.....if the earnings are 1.5 dollars per share a 15 PE or multiple would be 15 times that amount
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therefore $ is the price that would be paid on Ted's stock if the equaled the industry PE multiple of 15.

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lets call our intergers a and a+2
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2(a+a+2)=260
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2(2a+2)=260
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4a+4=260
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4a=256
:
integer 1
:
integer 2
:

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since and we are left with the difference of squares here
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factoring
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lets line up the terms that have like variables
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-15wy -5wy)so factor out a -5 and w -5w(3y+x)
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so factor out an x.........x(x+3y)
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do you see any terms that are alike.... that we can factor out of these terms......yes (3y+x)
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so
factors to
:

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you need to multiply each term by (x-5)(x-4)
:
you should get distribute this
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and end up with

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=49 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9, 5.5. Here's your graph:

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:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=404 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9.04987562112089, -11.0498756211209. Here's your graph:

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completing the square
factoring
vertex is at(4,-5)

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2.10000(x+1)(x+1)+3500(x+1)=15569.75------>where x is the interest rate
.... dealing with a quadratic formula.....
when you solve this email me and I will let you know if you have the correct answer.

:

:

:
drop the negative value
:
or 8.5%

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=635010000 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.0849702377437334, -2.43497023774373. Here's your graph:

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let us call P profit and P=4000
:

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x intercept is found when y is set to zero
:
5x-0=-5
:
5x=-5
:
x intercept (-1,0)

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lets call residents,commercial and industrial r,c,and i
:
5r/day
5c/day
2i/day
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7000/5=1400 work days
2500/5=500 work days
500/2=250 work days
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total work days to appraise the 10000 appraisals is 2150 work days
if each person works 240 days a year then the number needed would be
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2150/240=8.95 rounding up
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9 appraisers are needed assuming of course each appraiser can do any of the 3 types of appraisals....

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in my opinion it is the distributive property. You see it in almost every problem.

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2+3n...where n is the natural numbers
:
101st term
:
2+3(101)=305

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2.10000(x+1)(x+1)+3500(x+1)=15569.75------>where x is the interest rate
.... dealing with a quadratic formula.....
when you solve this email me and I will let you know if you have the correct answer.

:

:

:
drop the negative value
:
or 8.5%

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=635010000 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.0849702377437334, -2.43497023774373. Here's your graph:

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I set up the equations you solve
:
d=rt........in both instances distance is equal
lets call the rate of the slow trip r and time t
lets call the rate of the fast trip r+10 and time(t-1)
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so 200=rt...eq 1
...200=(r+10)(t-1)..eq 2
:change eq 1 to t=200/r and substitute it into eq 2 and solve for r...this will involves a quadratic equation again
:

:

:

:

:

throw out negative value
so mph and =50mph
:

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=8100 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 40, -50. Here's your graph:

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:
:
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Let s= speed of the boat in still water
The current =3 mi/hr
we know that d=rt or d/r=t for this problem we must break this up into 2 parts
(distance upriver)/(rate going upriver)
+ (distance downriver)/(rate going downriver) = 9 hrs
:the we know the distance is 60 each way
the rate going up stream is 60/s-3
the rate going down stream is 60/s+3
:
so we have again a quadratic equation
:
:
multiply each term by (s+3)(s-3)
:




:
drop the negative value
:
so mph

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=17316 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13.9772373998204, -0.643904066487102. Here's your graph:

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lets call the numerator a and the denominator b
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a/b=1/4--->4a=b....eq 1
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(a+3)/(b+3)=1/3--->3a+9=b+3--->3a=b-6...eq 2
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take b's value from eq 1 and plug it into eq 2
:
3a=4a-6
:


6/24=1/4
(6+3)/(24+3)=9/27=1/3

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let x be the number of maintenance agreements and P=profit
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P=11(x))-34(1/20)(x)
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P=11x-17/10(x)
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P=97/10(x) so for 100 contracts
:
P=97(100)/10=$970 bucks

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lets assume that A=t you have is A-t
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S=(n/2)(A-t)...multiply both sides by 2
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2S=n(A-t)...divide by n on both sides
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2S/n=A-t....now add t to both sides
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