Answer:
D
Step-by-step explanation:
Remember that the sum of the interior angles of a triangle will always total 180.
Therefore:
Let’s solve for <em>x: </em>
Combine LIke Terms:
Add:
Subtract 80 from both sides:
Divide both sides by 25:
Therefore, the value of <em>x </em>is 4.
Now, to find A, we can substitute it for A.
A is measured by:
Substitute 4 for <em>x</em> and evaluate:
Hence, our answer is D.
Answer:
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the area of the enlarged garden
y ----> the area of the original garden
we have that
If Tessa multiplies each dimension by 2, then the scale factor equals 2.
substitute
The area of the enlarged garden will be equal 4 times the area of the original garden
so
If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.
therefore
Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two
182.5 is the maximum revenue.
What do revenue means?
Revenue = p(x) × x = ( 300 - x /30)x
⇒R(x) = 300x - x²/30
R'(x) =
300 - x /15 = 0
⇒ x = 300 . 15 = 4500
∴ Max Revenue = R(4500) = 300 . 4500 - 4500²/30 = 675000 $
Profit = Revenue - cost
P(x) = 300x - x²/30 - (75000 + 60x)
P'(x) = d/dx ( 300x - x²/30 - ( 75000 + 60x)
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60z))
= 300 - x /15 -60
= 240 - x /15
P'(x) = 0 ⇒ x = 240 . 15 = 3600
P(3600) = 300 .3600 - 3600²/30 - (75000 +60 . 3600) =357000
∴ Max profit is 357000$ when 3600 sets are manufactured
After taxation , p(x) = 300x - x²/30 - ( 75000 + 60x) -5x
P'(x) = 300x - x²/30 - ( 75000 + 60x) -5x
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60x ) - d/dx (5x)
= 300 - x/15 - 60 -5 = 235 - x/15
P'(x) = 0 ⇒ x = 235 . 15 = 3525
Pmax = P(3525) = 300 .3525 - 3525²/30 - ( 75000 + 60 .3525) - 5 .3525= 678375/2 (Decimal ; 339187.5)
P(3525) = 300 - 3525/30 = 365/2 = 182.5
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