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The whole length of wire is ft
ft is used for the equilateral triangle
is used for the circle
-----------------
The area of the triangle is
The base is . The height is


----------------------
The area of the circle is
To find , find the circumference



and


Hope I got it

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I would start by multiplying both sides by
the LCD,

add to both sides

Subtract from both sides

Divide both sides by

--------------------
Also, doing it the other way:



OK

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The distance formula is:

given:
P1 ( -2,-5 )
P2 ( -2, 3 )





------------
The slope is ( change in y ) / ( change in x )
slope =
slope =
slope =
When is in the denominator of a slope, that
means the slope is infinite, and that means it is a vertical line
through ( -2, y ) where y can be anything

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Let = the original price of the drill
given:





The original pice was $80
check:




OK

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percentage means per one hundred, so


Multiply both sides by

60% own cats
---------------
But, if you haven't had algebra yet,


60% own cats

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It's kind of a general question, but I'll try.
Suppose you have a rectangle that is
3 meters on one side and 5 meters on the other side
The area of the rectangle is square meters
----------------
To convert the area to square centimeters,
( meters ) x ( 100 centimeters / meter )
centimeters
and
centimeters
To get the area, multiply
square centimeters
-----------------
To convert the area to square millimeters,
( meters ) x ( 1000 millimeters / meter )
millimeters
and
millimeters
To get the area, multiply
square millimeters
-----------------
Hope this helps.

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Find out what 1 acre sells for

1 acre sells for $166.67

22 acres sell for $3,666.67

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Let = the speed of the current
= the boat's speed going upstream
= the boat's speed going downstream
given:
Going upstream:
(1)
Going downstream:
(2)
------------------------
Substitute (1) into (2)

Multiply both sides by





The current's speed is 2.286 mi/hr

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You need 2 equations, 1 for the first 210 miles
and another for the last 160 miles
Let = his time in hrs for the 1st 210 miles
Let = his speed for the 1st 210 miles
= his time in hrs for the last 160 miles
= his speed for the last 160 miles
--------------------------------------
Equation for the first 210 miles:
(1)
Equation for the last 160 miles
(2)
----------------------------
(2)
(2)
and
(1)
Substitute (1) into (2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
complete the square
(2)
(2)
(2)
Take the square root of both sides
(2)
(2)
and, since
(1)
(1)
(1)
(1)
His speed for the 1st 210 miles was 35 mi/hr
check:
(2)
(2)
(2)
(2)
(2)
OK

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the library started with an unknown number of books
The cash donation allowed them to double that number, so
then they had books
Then a book collector gave the library 4028 books, so then
they had books
The total after that was books, so




The library started with 23,743 books

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they could not have all ordered large cones
since that adds up to
---------
There can't be 4 large cones since that adds
up to and that would only
leave 65 cents for the 5th cone
--------
Can there be 3 large cones and 2 mediums?

No, that's too much
--------
Can there be 3 large, 1 medium and 1 small?

Still too much
--------
Can there be 3 large and 2 small?

Too much
--------
That means there can be at most 2 large cones
Can there be 2 large and 3 mediums?

Too much
---------
Can there be 2 large and 3 small?

Too low
---------
Can there be 2 large, 2 small and 1 medium?
Too small
---------
Can there be 2 large, 2 medium, and 1 small?
Too much
----------
It looks like there can only be 1 large
Can there be 1 large and 4 mediums?

Too much
----------
Can there be 1 large, 3 medium, 1 small?


They bought 3 medium cones

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You were correct, but you have 2 unknowns and
only 1 equation. The other equation is:

Multiply both sides of this equation by
and subtract from the other equation




and, since



200 balcony tickets were sold
125 1st floor tickets were sold

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Plot the point (0,3)
If you make this the vertex ( turning point ) and
the parabola spills water ( does not look like a cup )
then the curve has to cross the x-axis twice and
that makes the roots real, and equally spaced on
either side of the y-axis.
The equation would look like

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It sounds like it could be either one.
The x-coordinate of the vertex is at
where the equation looks like

The turning point is at (0,-7), so


Now I have



------------
It looks like can be any (+) or (-)
number since it just controls the shape
( narrow or wide ) and the direction
( open down or open up )
I'll say
answer
Here's the plot:

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Let = liters of 30% solution needed
Let = liters of 80% solution needed
given:
(1)
(2)
-------------------------
(2)
(2)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
(2)
(1)


and, since
(1)
(1)
(1)
42 liters of 30% solution are needed
28 liters of 80% solution are needed
check answer:
(2)
(2)
(2)
(2)
OK

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This is a parabola with a minimum and not a maximum
I can tell because the squared term is positive. If I changed it
to then it would have a maximum.
The vertex is the (x,y) point at the minimum ( or maximum )
---------------
The x-coordinate of the vertex occurs halfway
between the roots, which are
the two solutions to
---------------
To get a deeper understanding of this look at the
quadratic formula which gives these two solutions
---------------


Now I'll separate the terms in each solution:


-----------------------------------------
Now what you have is:
= ( x coordinate of the vertex ) + ( the positive correction )
= ( x coordinate of the vertex ) - ( the negative correction )
-------------------
So, you can see that is the x-coordinate of the vertex
when the form of the equation is
-------------------
I can apply this to your problem






--------------------
Now you know the vertex is at ( -2, y ). To find y, plug
into the equation




---------------
The vertex is at ( -2, -5 )
Here's a plot of the equation:

The vertex is where is should be

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-------------
By substitution:



and, since



Ryan is 18 and
Sam is 5

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Add the rates of pumping to get the rate
pumping together
( blood pumped by small pump ) / ( pumping time ) + ( blood pumped by large pump ) / ( pumping time )
= ( blood pumped with both pumps ) / ( pumping time )
------------------------------

Multiply both sides by



It will take 12 minutes with both pumps hooked up

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You need 2 equations- one for Norma
and one for Marietta
Let = time for both
Let = the speed of Norma's boat
= speed of Marietta's boat
---------------------------------
Norma's equation:
(1)
Marietta's equation:
(2)
---------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
and, since
(1)
(1)
(1)
Norma is rowing at 7.5 mi/hr
check:
(2)
(2)
(2)
(2)
(2)
OK

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kcu suro frews naehj two nkuods ehc tiB

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liter of nitric acid in 48% solution
The concentration is:


The concentration is 34.8%

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( seats made ) / ( time to make them ) = ( seats made ) / ( time to make them )

Multiply both sides by


min
-------------
You can also solve this way:
it will take him half as long to make just 1 seat
or min
16 seats will take him 16 times as long, or
min

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actually, you can't graph
It is an equation, but it doesn't relate 2 variables.
What you really mean is
Here's the plot:

Now if you want to find the roots,
is what you





and

------------------
In decimals:


and


These values match up OK with the x-intercepts ( roots )

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Let = the Daughter's age now
is the Father's age now
= the Daughter's age in years
= the Father's age in years
------------------
The thing about ages is that the difference between
their ages will always remain the same, years, so







The Daughter's age is 2 now
The Father's age is 28 now
check:





OK

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Think of the boat as standing still and the
helicopter approaching at the sum of their speeds



The helicopter will take 2 hrs

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Let = time spent canoeing
Let = time spent driving
Let = his speed driving

(a)


------------------------
(b)







The trip will take 41.1 minutes

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Let = the age of the youngest brother
The other brothers are:




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





-------------
The brother's are 3,5,7, and 9

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Set up the ratio:
( 1 loaf of banana bread ) / ( 2/3 cup oil ) = ( x loaves banana bread ) / ( 3 cups oil )


Multiply both sides by


You can make 4 and 1/2 loaves of banana bread with 3 cups of oil

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Let = amount invest @ 8%
= amount invested @ 10%
given:





Randy invested $110 @8% and $220 @10%

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Just call 45 min 3/4 hr
You need 2 equations, one for home to Metro
and one for Metro to work
Let = the distance from Metro to work
= the distance from home to Metro
Let = time spent on Metro
= time spent on bike ( home to metro )
-------------------
Equation for home to Metro:
(1)
Equation for Metro to work:
(2)
---------------
(1)
Substitute (2) into (1)
(1)
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
From work to Metro is 59.454 mi
check answer:
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
(1)
(1)
OK
Hope I got it

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Let the fraction =
given:
(1)
(2)
-----------------------------
Substitute (1) into (2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
and, since
(1)
(1)
(1)
The fraction is
check answer:
(2)
(2)
(2)
(2)
OK