1/2a - 7 + 1/2a = 1/3
1/2a + 1/2a = 1/3 + 7
2/2a = (1 + 21)/3
a = 22/3
4x + 6 + 5x + 3 = 90
9x +9 = 90
( Subtract 9 from 9 and 90 )
9x = 81
( Divide 9x and 81 by 9 )
x = 9
Hope this helps.
Answer:
- r = 12.5p(32 -p)
- $16 per ticket
- $3200 maximum revenue
Step-by-step explanation:
The number of tickets sold (q) at some price p is apparently ...
q = 150 + 25(20 -p)/2 = 150 +250 -12.5p
q = 12.5(32 -p)
The revenue is the product of the price and the number of tickets sold:
r = pq
r = 12.5p(32 -p) . . . . revenue equation
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The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...
p = (0 +32)/2 = 16
The theater should charge $16 per ticket.
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Maximum revenue will be found by using the above revenue function with p=16.
r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue
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<em>Additional comment</em>
The number of tickets sold at $16 will be ...
q = 12.5(32 -16) = 200
It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.
For this case we have an equation of the form:
Where,
v0: initial value in assets
b: depreciation rate
t: time in years.
Substituting values we have:

For year 8 we have:

Rounding off we have:
V (t) = 83401
Answer:
the value of V0 and b are:
V0 = $ 408,000
b = 0.82
the value of the assets after 8 years is:V (t) = 83401 $
The coordinates of the corners in the scale drawing of the desing are:
H = (2,0)
I = (0,0)
J = (0,4)
K = (2,4)
That makes the lengths of the segments be:
HI = 2 - 0 = 2
JK = 2 - 0 =2
JI = 4 - 0 = 4
KH = 4 - 0 = 4
Now check the segments of the actual cover:
H'I' = 10 - 0 = 10
K'J' = 10 - 0 = 10
J'I' = 16 - 0 = 16
K'H' = 16 - 0 = 16
Now check corresponding segments meet proportionality criterium, which is needed for similarity:
H'I' / HI = 10 /2 = 5
K'J' / KJ = 10 / 2 = 5.
So far we this is fine.
JI / J'I' = 16 / 4 = 4............ then not, the ratio is not the same ratio of the other two segments, which implies that the scale used for the vertical segments is different to the scale used for the horizontal segments, driving to a non similar figure.
Answer: no, because the corresponding sides are not proportional