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d=rt. we know the distance in both cases is 50. Lets call the local trains rate r and its time t. So the express's rate would be 2r and its time t-1
:
50=rt..........eq 1
50=2r(t-1).....eq 2
:
lets rewrite eq 1 as t=50/r and plug that value into eq 2
:
----->----

---->
MPH-speed of the local train
MPH-speed of the express
:

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y-(-2)=3/4(x-0)
:
y+2=3/4x
:
y=3/4x-2
:

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ok........we know that the volume of the cylinder is
so what we need is to take the outer volume and subtract out the inner volume to get the thickness volume. we know that the volume of the clay(200) will be equal to outer volume-inner volume.
We also know that the outer radius which is the unknown here minus the inner radius will give the measurement of the thickness of the pencil holder. I used 3.14 as appx value of
:




cm...this isnt exactly 4 because of approximations
cm....thickness of pencil holder

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5.75+5.75x=6.75 where x is the interest rate increase
:
5.75x=1
:
x=.174 or 17.4% over 4 years....so to find out an annualize rate we need to
:
divide by 4
:
% per annum

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78 cents
:
3 pennies
1 nickel
2 dimes
2 quarters

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5n:.......5,10,15,20,25
3n+2:.....5,8,11,14,17
7n-4:.....3,10,17,24,31

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no.....in the equation y>3 point(5,-2) -2>3 is not a true statement....the point does satisfy the x+y<5 but it has to satisfy both if you consider both equations together. If you consider them seperately it does not satisfy the first but does satisfy the 2nd

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well the answer is 9
: remember the middle rung can only be counted once so we need to account for that
:
if x is the total distance from one rung to the other
:
(1/2)x=3-5+6+1/2........the 1/2 is so that the middle rung is counted once
:
x/2=4.5
:
steps

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ok lets find the slope first m=rise/run or change in y/change in x.
:
m=3-7/0-5=4/5
:
so any line parallel to a line thru these two point must have the same slope of . Any line perpendicular to a line passing through these point have to have the - inverse of the slope 4/5 which is

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take any two point and write an equation find slope first....I will use the first two points change in y /change in x is the slope. 3-4/-6-2=1/8 is the slope. now take one of the points(of the two we just used to find the slope), and plug it into point slope formula(I am using the first point)
:
y-4=(1/8)(x-2)
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we dont need to re write this we just take the third point (-3,1) and check and see if it works in the equation ....if it does it is on the same line...if not then a straight line doesn not pass thru these 3 points.
:
1-4=(1/8)(-3-2)
:
-3=1/8(-5)
:
-3=-5/8.......which is not a true statement therefore they do not all lie on the same line.

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given
:
multiplying factors
:
combining like terms
:
multiplication by a negative 1

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:
factoring out a 27
:
combining terms
:

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let the number of tickets sold to non seniors and seniors , be n and s respectively
:
n+s=400.........eq 1
7n+5s=2600......eq 2
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lets rewrite eq 1 to s=400-n and place that value into eq 2.
:

:
distribution
:
combining terms
:
number of non senior ticket sold

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bx-2=k........first add 2 to both sides of the equation
:
bx=k+2......next we divide both sides by b
:

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10368(.07)=725.76 round and add this to the original amount
:
10368+726=11094
:
11094(.07)=776.58 round and add to new amount
:
costs of college in 2 years

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you are simply adding or subtracting one equation from another trying to eliminate one of the variables. Sometimes you have to manipulate one equation or the other or both to accomplish the elimination.
:
2x+y=5
x-y=7------. these two equation need no help add one to the other and y-y=0 and your left with 2x+x=7+5 and you can solve for x. once you solve for x you can plug its value back into either original equations and solve for y
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3x+3y=9...eq 1
x-y=10....eq 2----in this case if you multiply all terms in eq 2 by 3 you will get 3x-3y=30........as you can see if you now add the two equations together the y's will again be eliminated because 3y-3y=0 and your left with 3x+3x=9+30 and again you follow the same procedure.
hope that helps

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just plug the numbers in where ever there is an x replace it with 1
:

:

:
is answer to f(1)

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well if you figure it to be 11 years
formula is total amount(27,500) times n being the number of years of depreciation. In general depreciation equals where T is the Total being depreciated, x is the rate of depreciation, and n is the number of years.
:
gives us a percentage of .167
:
multiply that by 27500 and the appx value is dollars

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if the ratio of the world is the same for these 9th grade boys then 2/5 of the 9th graders(we will call the total t) will not be able to distinguish red from green. number that cannot distinguish red from green we will call c and we have the number that fit this category as 14
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equation would be .4(t)=c
:
.4t=14
:
ninth graders

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to be divisible by 9 the digits added together must be divisible by 9 and to be divisible by 12 it must be even.
along with units digit being < tens digit....let see if we can come up with something.
ones unit must be 0,2,4,6,or 8.
if 0 then tens unit can be 1-9 case1
if 2 then tens unit can be 3-9 case2
if 4 then tens unit can be 5-9 case3
if 6 then tens unit can be 7-9 case4
if 8 then tens unit can be 9 case5
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108 is covered in case1 because 0<8
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lets work backwards
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case5: 98----9+8=17 to be divisible by 9 hunderds unit has to be 1 and 198
is not divisible by 12
:
case4:96,86,76...96---9+6=16 to be div by 9 100's unit has to be 3 and that is more than 200. 86 ...8+6=14 to be div by 9 100's unit has to be 4....to big
same problem with 76
:
case3:94,84,74,64,54...9+4, 8+4,7+4,6+4,5+4 all present problems with #'s larger than 200
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case2:92,82,72,62,52,42,32 ...92,82,and 72 all get throw out because #'s larger than 200. 62 is 6+2=8..to be divisble by 9 100's unit must be 1...162..not divisible by 12 take 52,42,32 end up with being over 200
:
case1:90,80,70,60,50,40,30,20,10... 90 larger than 200...80 is 8+0=8 in order to be divisible by 9 100's unit has to be 1. 180.......guess what this number is divisible by 9 and 12 and is less than 200
applying divisibility rules for the rest of the numbers in this case make all the numbers to large >200
:
SO WE HAVE GONE THROUGH ALL THE CASES AND 180 is the only one that qualified
there could be a simpler way but I will have to think on that

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no not necessarily you can make two 90 degree angles with acb and ade and get very different angles for b and e. In the drawing below you can see that AB and AE are congruent and ACB congrent to ADE both at 90 degrees. but angle B and E are clearly not congruent

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jointly simply means directly with 2 or more variables. Any direct variations take the form a/b=k and any inverse proportions take on the form ab=k
:
so where k is the constant of variation

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given
:
added 5 to each side

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for y =3
:

:

:

:
for y=3
now if this reads all terms to the 3rd power..because the way you wrote it was unclear.
=.138 for y=3

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given
:
distribute
:
subtract 15 from both sides
:
factor
:
2y-3=0--->add 3 to each side--->2y=3--->divide by 2 on each side y=3/2
y+5=0--->subract 5 from each side--->y=-5
:

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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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, 0. Here's your graph:

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given....... x intercepts are found when y is 0
:
so x intercepts are 2 and 3.
:
vertex (-B/2A , C - B^2/4A) (5/2(1),6-(25/4)...(5/2,-1/4)
so the vertex is below the x axis
:

vertex for x is -2/2(-1)=1 plug that into equation to find y
:
=0....so vertex is at (1,0) which is on the x axis meaning there is no x intercepts
there is one x intercept at x=1
:

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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: 1, 1. Here's your graph:

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we need a problem before we can answer

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y=mx+b....first subtract b from both sides
:
y-b=mx...next divide by m
: