Answer:
72
Step-by-step explanation:
If the rates d and c are flowers per day, we have ...
150/d = 120/c
d -c = 18
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Multiplying the first equation by cd/30, we have ...
5c = 4d
Multiplying the second equation by 4 gives ...
4d -4c = 72
Adding these equations together, we get ...
5c +4d -4c = 4d +72
Simplifying and subtracting 4d leaves ...
c = 72
Charlie can plant 72 flowers per day.
Answer:
True
Step-by-step explanation:
Subtracting a number is identical to adding its opposite.
-2 -5 = -2 +(-5)
The statement is True.
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If you doubt this, you can have your calculator tell you what the answers are.
You have to build the triangles.
They are such that:
h is the common height
x is the horizontal distance from the plane to one stone
Beta is the angle between x and the hypotenuse
Then in this triangle: tan(beta) = h / x ......(1)
1 - x is the horizontal distance from the plane to the other stone
alfa is the angle between 1 - x and h
Then, in this triangle: tan (alfa) = h / [1 -x ] ...... (2)
from (1) , x = h / tan(beta)
Substitute this value in (2)
tan(alfa) = h / { [ 1 - h / tan(beta)] } =>
{ [ 1 - h / tan(beta) ] } tan(alfa) = h
[tan(beta) - h] tan(alfa) = h*tan(beta)
tan(beta)tan(alfa) - htan(alfa) = htan(beta)
h [tan(alfa) + tan(beta) ] = tan(beta) tan (alfa)
h = tan(beta)*tan(alfa) / (t an(alfa) + tan(beta) )
Calculate the price per gallon: first case is $97.45/5 gal = $19.49/gal
The second case is $21.95/gal.
Everything else being equal, I would buy the cheaper one for $19.49/gal