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The speed of the train is becoming
less and less over a certain distance
which they tell you is m
You could make a plot of this as time
on the horizontal axis and distance
traveled on the vertical, but it is easier
to plot distance on the horizontal and
velocity on the vertical.
Let m/sec
Let m/sec
Let the point at which is measured
= m
Let the point at which is measured
= m
-----------------------
In general, the slope of the line is



--------------------------
The general form of the equation for velocity vs distance
would be:

You can see that when , , and
when ,
--------------------------
When the train has stopped, it's velocity is zero, so



This says the train has gone m from where
the 15 m/sec measurement was made. The problem wants to
know how far it went after the 7 m/sec measurement was made
m
The train went more meters before coming to rest
Here is the plot of the line:

Notice that when , and
when ,

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Let beginning =
Let middle =
Let end =
given:
(1)
(2)
(3)
-----------------
There are 3 unknowns and 3 equations, so
it should be solvable
Substitutute (2) in (1)
(1)
Substitute (3) in (1)
(1)
Multiply both sides by
(1)


And, from (2)


From (3)


The beginning is 14 min
The middle is 42 min
The end is 84 min
check:
(1)


(2)
(2)


(3)
(3)

OK

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Let her investment =
given:



Her investment was $400

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(1) You have to get the given equation into
the form , where is the slope
Any line parallel to the given line
will have the same slope.




Now I know the general form I want is

Now plug in (4,-2) to find



The solution is
(2)
Start with the general form

From the given info, can be anything, so I pick
Given: (3,5)


is one possible answer

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First I'll write 2 equations: 1 for walking and 1
for jogging:
Walking:
(1)
If the distance from A to B is mi, then
the distance jogged is mi
Jogging:
(2)
-------------------
given:
mi/hr
mi/hr
hrs
-------------------
I'll rewrite (1) and (2)
(1)
(2)
Add the equations

By substitution:




By substitution into (1):



hrs answer
check answer:
Suppose mi
(1)

(2)






From answer:



OK

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The number either begins with or
If the tens digit is , the units digit is or less
If the tens digit is , the units digit is or less
and
If the product of the digits, the tens digit can't be ,
since is the most the product can be
and
George's number must be , since
which is OK, and which fails the 2nd test

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The problem is asking "What is left over after
I divide 45 by 2 2/3 as many times as I can?"
2 2/3 =


This is telling me that 2 2/3 cups goes into 45 cups
16 times with .875 left over. What fraction is .875?
(divide top and bottom by )
(divide top and bottom by )
There is 7/8 of a cup left over

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Percent means "per 100". Rewrite the question as:
"what per 100 of 155,000 is 6,750?
Now replace "what per 100" with




It is 4.355%

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You can write 2 equations, 1 for driving to the house and
1 for returning. The distance is unknown, but it's the
same for both trips. I'll call the distance
I'll call the time to drive to the house . Since the
total driving time is hrs, the time to drive back
is
Driving to the house:
(1)
Drive from the house:
(2)
given:
mi/hr
mi/hr
-------------------------
Now I can write:
(1)
(2)
I can set (1) and (2) equal to eachother:




It took 6.5 hrs to drive to the house.
Now find


mi
You drove the same distance coming back, so
the total distance is


You drove 715 mi
check answer:





OK

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(A)

(B)
The solution is the region bounded by the line (including
the line), the y-axis and the x-axis

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Add their rates of doing dishes
Call the "dishes" 1 job
For Jimmy:
is his rate (1 dishwashing job/20 min)
For Susie:
is her rate (1 dishwashing job/15 min)
Working together:
(1/x is 1 dishwashing job/x min)
Now solve for
Multiply both sides of the equation by



Working together, they can do the dishes in 6 min

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This is a distance = rate x time problem
given:
rate = km/hr
time = hrs
-------------------
first part:
distance =
the 2nd part says the time is hrs
distance =
distance = km

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In words:
(kg of salt in final solution)/(total kg of final solution) = 5%
Let = kg of water that needs to be evaporated
given:
Salt in original solution: kg
------------------------------------
The final solution has kg of salt plus water
The original kg of salt never changes, so It
stays at kg
I can't finish- have to go

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You can't solve it because there are 2 unknowns.
If there were 1 unknown, you could solve it. You
can get either or alone on one side,
however. I'll find in terms of

Subtract from both sides


To simplify, divide both sides by , and
change the > sign to a < sign.

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(1)
(2)
Multiply both sides of (2) by and
add to (1)
(1)
(2)

Now substitute this value for in either
(1) or (2) to find
(1)
(1)

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The formula is

The discriminant is

Where






Since the discriminant is positive (), and it is not zero,
there are 2 real solutions
If the discriminant were zero, there would be 1 real solution.

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A 160% increase resulted in pansies
Let = number of pansies that had bloomed before nightfall


73 had bloomed before nightfall

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Add their rates of working to get the rate that they work together
In words:
(part of the house Joe can paint)/(time it takes to paint it)
plus
(part of the house his Father can paint)/(Father's time to paint it)
equals
(One house painted)/(Their time working together to paint one house)
Given:
Joe's rate of painting:
(the means one house)
Father's rate of painting:

--------------------

Multiply both sides by


days
It takes them 4 days working together

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If this is and is not true
If this is true

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Let the length of the rectangle =
Let the width of the rectangle =
The circumference,
given:
ft






This is the quadratic equation- you could pick your
own letters instead of and

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Use your calculator to take the square root of it.
If the square root is an integer,then that number
you took the square root of is a perfect square.

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Let = Mother's age
Let = Daughter's age
Let = Son's age
given:



This is 3 equations and 3 unknowns, so it's solvable
By substitution:


Again, by substitution:



and, since,



also,



The Mother is 32, the Daughter is 4, and the Son is 8

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For the commercial plane:



For the fighter:

hrs

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Find the ratio of the increase in price to the original price in simplest form.
The increase in price is
The original price is

That is my reading of it, anyway

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You will need a compass to draw the circle. The
compass automatically gives you the center of
the circle. It is where the point of the compass
sticks into the paper. Once you have drawn a circle,
you will need a protractor that has angles marked
off on it. It looks like a half circle with 0 degrees
to 180 degrees marked off in 1 degree units.
Now you need to look at the data that you want to
put into a pie chart. Only certain kinds of data
can be arranged into a pie chart. All the separate data
items have to add up to 100% of something.
An example is a person's budget of spending and saving
from monthly income.
For example:
food: $300/month
rent: $1000/month
entertainment: $150/month
savings: $50/month
If this adds up to monthly income, then it's 100% of income
and can be put into a pie chart.
The way to do this is to turn the data into pie slices with this
formulas:
(food amount)/(total budget) x 360 degrees
(rent amount)/(total budget) x 360 degrees
(entertainment)/(total budget) x 360 degrees
(savings)/(total budget) x 360 degrees
----------------------------------
What is the total budget?
300 + 1000 + 150 + 50 = 1500
so,
food: 300/1500 x 360 = 72 degrees
rent: 1000/1500 x 360 = 240 degrees
entertainment: 150/1500 x 360 = 36 degrees
savings: 50/150 x 360 = 12 degrees
-----------------------------------
These are the pie slices and they should add up to a full pie,
or 360 degrees:
72 + 240 + 36 + 12 = 360 degrees
Now draw a straight line from the center of the circle to
the outer edge. Use the protractor to create 72 degrees
from this line and draw the line at 72 degrees.
Now go around the circle, marking off 240, 36, and 12
degrees to make up a full circle. Label the pie slices
72 degrees: food
240 degrees: rent
and so on

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Let = number of solid-color ones sold
Then = number of print ones sold
given:
Sales of solid-color ones =
Sales of print ones sold =

-----------------------------





31 solid-color ones and 9 print ones were sold
check:




OK

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answer

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Complete the square





and


The roots are 1 and -5
Here's a plot:

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If is
Profit as a function of units, then the break
even point is where there is zero Profit.


Multiply both sides by

You can complete the square also

Multiply both sides by





Take square root of both sides


and


There is a break-even point after 12 units and another
after 737 units
Here's a plot:

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I just solved this one. See tutors > josmiceli > solutions