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This is a simple ratio question, because you are looking for the ratio beween E and M you simply have to divide the two numbers.
38/95=0.4
Now that you know the ratio is .04 simply multiply it with the weight of the person on earth
0.4x100=40
A 100 lb person would weigh 40 pounds on mars.

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To solve this question you must first find the quantity of liquid that is not alcohol in the first solution.
Because the 40kg solution is 70% alcohol 30% of the solution is a fixed variable.
30% of 40kg = 12kg.

The second solution is 85% alcohol. Because we can not change the fixed variable the 15% of the new solution weighs 12kg
if 15% of the new solution weigs 12kg then the entire solution weighs 80kg.
because your original solution weighs 40kg, and your new solution weighs 80kg, you would need 40kg of pure alcohol added to the old solution to increase the concentration from 70% to 85%.

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To solve this question you must first find a linear equation.
Let the speed of the slower train equal (x)
the faster train is 25mph faster than (x) so train 2=(X)+25
Because 4 hours elapsed we can state that (4)(X) distance has occured for the slower train and (4)(x+25) has occured for the faster train.
Because we are looking for the total distance between them we can add them to find the total distance.
train x+train Y= XY
(4x)+(4y)=456
because y (faster train) is represented by x+25. substitute the value.
your linear equation is below
4(X)+(4)(x+25)=456
expand the brackets and simplify the equation and solve
4x+4x+100=456
8x+100=456
8x=356
x=44.5
so the slower train is traveling at 44.5mph and the faster one is traveling at 69.5.
You can test this by substituting the numbers into your equation (4x)+(4y)=456
(4)(44.5)+(4)(69.5)=456.
Solved.

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the quickest way to solve this is to list the factors of 35
1x35
5X7
there are only 2 sets of factors relating to 35 and only 1 set has a differece of 2 that is 5,7

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To solve this question you are looking for the base of a right angle triangle.
you are given the opposite side of the triangle (10km)
and are looking for the adj side of the triangle to 5 degrees
because you are using the opp and adj sides of the triangle you use your trig functions. knowing tangent uses opp and adj sides you can make an equation

we are given the opposite side of 10 and are looking for the adj side. to find the adj side you use the cross mulitplication rules to rearrange the equation
so

if your calculator is in degree mode you will get the answer 114.3km
Good Luck

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To solve this question it is easier to make a set of simple equations.
because perimeter is x+y+z we can make the equation

now we can make equations for the other parts of the question
because BC is the length of Ab we can make the equation

now we can add on the other part of the equation. because BC is 2cm longer than AC we can derive the equation

now you have the 3 equations below



the simplest way to solve is to substitute the 2 lower equations into the top equation in place of their respective variables. so you substitute (2/3)BC in place of AB in the top equation.
you get

simplify

divide by 8/3
BC=9
Now because you have BC solved substitute into the other equations to solve for the remainder sides


so AC=11
and AB=6
the lengths of the 3 sides of the triagle are 9,11,6

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first thing to do with this question is to simplify brackets by expanding the 4 into them

Now simplify the question

remove the 6 from the right side by subtracting from both sides


now bring the 8 to the other side by adding it

so by dividing 12 from each side
check this answer by substituting it into the first equation


7=7
Then when the equation is verified.

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Word problems are tricky to understand. The easiest way to derive an equation is to go step by step.
the first equation you can find is simple.
y=x-4
where x is the larger number and y is the smaller one
so if y is the smaller number 10x y subtracting 3x the larger number x looks like this
10y-3x=51
so your two equations are below
y=x-4
10y-3x=51
because you have y isolated you can substitute it in for the second equation
10y-3x=51
10(x-4)-3x=51
expand the brackets
10x-40-3x=51
simplify
7x-40=51
bring the 40 to the other side
7x=91
divide by 7
x=13
because you have the larger number subtract 4 to find the smaller number
your two numbers are (13 and 9)

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You know that there are 5280 feet in a mile.
You can find the distance in miles that the ball traveled from the pitchers mound to the plate by dividing.

now you find how many hours elapsed
note that 60 seconds in a min and 60 mins in an hour
now by dividing the time by the distance you can find the mph of the ball

the ball traveled aprox 103 mph

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For this question it is simple substitution
P=6000
R=.03
T= 2 an.
Assuming that it is not compounded after the first year you substitute the values into the simple interest formula
I=PRT
I=(6000)(.03)(2)
I=360

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to graph this question you first must isolate y from each side

bring the x to the other side

divide by -2

Repeat the same for the next line


Bring x to the other side

divide by 4

by substituting in your x value into your isolated equations you can find the y coordinate.
ex.
for the equation
you are given a random x value of 4
place 4 in for x and you get the y value


now plot (4,-1) on your graph, and repeat for other points until you can draw your graph.

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Because you are looking for the speed of the plane in mph. you should convert the data into full hours. assuming the planes stay at a constant speed. 2x the time should equal 2x the distance
So if in 1/2 an hour the planes are 275 miles appart in one hour they will be 550 miles appart.
because one plane travels 50 mph faster than the other, 550 is the same as x+(x+50) where x represents the speed of the slower plane.
because this is a simple linear equation you can combine the terms

to

take the 50 to the other side

divide by 2

so the slower plane is traveling at 250mph, and the faster plane is traveling 50mph faster so the second plane is traveling at 300mph
you can check this answer in the question
at 1/2 (250mph) plane 1 is 125miles from the origin
at 1/2 (300mph) plane 2 is 150miles from the origin
because they are in opposite directions they are 275 miles appart.

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To solve this problem you need 2 pieces of data.
1. The amount of time that passes
2. The temperature drop over that amount of time

Because you measure the time from noon (12) to (5) there has been a 5 hour time difference.
to find the temperature change subtract 58 from 70 and you get 12 degrees.
now divide the temperature by the time
is your answer. in decimal form 2.4 degrees per hour.

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The right angle triangle formula is
because c= hypotenuse
and you have a side a/b
you can isolate the other side by making the equation
by quaring the information you have you can fill in the equation

and by square routing the answer you find a
A=3
so your third side is equal to 3

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A product means that you multiply the numbers change "a number" to x and you can form the equation
9x+17=-1
subtract 17 from each side
9x=-18
divide by 9 from each side
x=-2
so your number is -2

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Start by making "a number"=x "twelve less"=-12 and "equal" to =
by changing the words into their literal meaning you get the equation
-12+2x=-1
add 12 to each side
-12+2x=-1
+12 +12
________________
2x=11
divide by 2
x=5.5 or 11/2
so your number is 5.5

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There are two possible answers for this question.
If the aquarium has a glass lid, more glass will be needed
If the aquarium has no glass lid (like normal) less glass will be needed.
To find the two solutions find the area of each side. Because the sides are paired, you only have to calculate the area 3 times.
We start with the sides
200cm*600cm=120000cm squared*2 =240000cm squared
the small sides
200cm*300cm=60000cm*2= 120000cm squared
and the top and bottom
300cm*600cm= 180000cm....
with no glass lid the amount of glass needed is 540000cm squared
with a glass lid the amount of glass needed is 720000cm squared

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To find the Tuition rate from the previous year, divide 2007s tuituion by 7%
so
13910/1.07= 13000
so the tuition is 13000 in 2006

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x + y = 1
x - y = 3
simply add all the terms
2x=4
x=2
substitute in 2 for x
2+y=1
y=-1

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To add find a common denominator for the term

in this case the common denominator is (x-5)
to get a common denominator multiply 7 by (x-5)

when you simplify the numberator you get

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To find the amount of hours worked each month, simply multiply the weekly hours by 4.3 (4.3 weeks in a month)
48x4.3 206.4 hours
to find the wage, divide the monthly salary by the amount of hours worked.
$2528/206.4
his hourly wage is $12.25 rounded to the nearest cent.

Find the horizontal asymptote of the rational 
function  
Possible answers: 



 
Thank you. Exactly what is a asymptote? Can anyone 
explain the simplest way to solve this problem?

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Hello,
Because you have a linear function with a division equation, the asymptote is located where the equation is undefined. this occurs when the function is divisable by 0. because no equation is valid when you divide by 0 that is your asymptote.
to find this simply look at the bottom half of your equation

the value that makes the bottom half 0 is (1/2) ... 4(1/2)-2=0
so your asymptote is 1/2

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The easiest way to solve this is by converting the terms into standard form and then placing them back into notation form.
9.8E-4 is the same as 0.00098 as the decimal moves 4 forward
2.1E2 is teh same as 210 as the decimal moves 2 back
3.1E-1 is the same as 0.31 as the decimal moves 1 back
multiply these to form one term
0.00098x210x0.31= 0.063798 because you are only given 2 significant digits you round to the 2nd placing in this case you round it up to 0.064
to get the term back into standard notation move the decimal back 2 places you get the answer

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(5m - 6n + 7)(2m - 3n - 4)
to multiply out this term we use a method known as foiling. You multiply each term in the first equation by each term in the second equation.
I will break this down step by step.
Take 5m and multiply it.
5m(2m - 3n - 4)
10m^2-15mn-20m (hold onto this we will use it later.)
now -6n
-6n(2m - 3n - 4)
-12mn+18n^2+24n(hold onto this we will use it later.)
now we will multiply out 7.
7(2m - 3n - 4)
14m-21n-28
You now take all the results from the foil process and line them up.
10m^2-15mn-20m-12mn+18n^2+24n+14m-21n-28
you combine all like terms
10m^2+18n^2-27mn-6m+3n-28
this is your answer

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To solve this question you must first find the amount he makes in an hour
$160/40h=$4.00/h
if it was increased by 25%, take his wage (100%) add 25% to the value. because percents are decimals, 100% can be written as 1.0 and 25% can be written as .25
to find the new value multiply $4 by 1.25 (125%)
4x1.25 =$5/h
now multiply it by the amount of hours he will spend working (60)
5x60=$300/week

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Use a system of equations to solve
a+2b=5
a-b=0
isolate a from the first equation
a=5-2b
substitute into the second formula
5-2b-b=0
5-3b=0
3b=5
b=5/3
now add this to your first equation
a+(2(5/3))=5
a+10/3=5
a=5/3
both a and b are 5/3

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lwt us convert the whole question into feet. I mile=5280 feet
so the x distance on a graph will be 17160 feet
the slope of the graph can be found by the equation rise/run or Y2-Y1/X2-X1
fisrt you must find the 2 points on the graph to find the slope.
these were given in your data,
the first position is x, this is at zero. and Y is at 1800 feet so you have the point (0,1800)
the second point is also given, where x is 17160 feet away, and where he stopped y=0
so your two points are (0,1800) and (17160,0)
so in the equation you will get
0-1800/17160-0=slope
the slop of your graph is (+/-)0.104895 where depending on your view is positive or negative.

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the first information about the amount of the house is un-needed to answer the question. all you need is the amount cost per month.
because the 20 year period has 240 months. it would cost
240x$752.40=$180 576
and the 30 year period has 360 months it would cost
360x$660.60=$237 816
so the home owner would save $57 240 taking out the 20 year mortgage.

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4(8-t)=20
6(2x-1)=4(2x+5)
7(2w-3)-5(3w-1)=0
I belive you are looking to solve for the variable in each case.
on the first.
4(8-t)=20
expand the brackets.
32-4t=20
subtract 32 from each side
-4t=-12
switch signs to make T positive
4t=12
divide out 4
t=3
next
6(2x-1)=4(2x+5)
expand brackets
12x-6=8x+20
put similar terms on different sides
12x-8x=20+6
4x=26
divide out 4.
x=6.5
the last one
7(2w-3)-5(3w-1)=0
expand the brackets
14w-21-15w+5=0
place similar terms on opposite sides
14w-15w=21-5
-w=18
switch signs to make w positive.
w=-18

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no, when multiplying negatives with a positive the answer is always negative, when multiplying two negatives, the answer is positive.

to solve this question we must expand the terms into the brackets.

we can combine these terms

add x to both sides,

add 13 to both sides

divide out 4 to isolate x

good luck

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in a rectangular prism there is always 2 opposite sides that have the same area,
to find the surface area, the sides, multiply by LxW and multiply by 2.
since there are 3 sets of sides we have to make 3 calculations and add the together.
LxW is one set
LxH is another set
WxH is the third set
set 1=(2)x(8)x(5)
set 1 surface area is 80cm squared
set 2=(2)x(8)x(3)
set 2 surface area is 48cm squared
set 3=(2)x(5)x(3)
set 3 surface area is 30cm squared
to find the total surface area, add the numbers together.
the total surface area of the cube is 158cm squared