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Dennis_Churaev [7]
3 years ago
12

you are charged $16.05 after tax for a meal. Assume sales tax is 7%, what was the menu price for the meal?

Mathematics
2 answers:
Anton [14]3 years ago
7 0

1.07x=16.05

16.05/1.07=15

15=x

Anton [14]3 years ago
7 0

The menu price for the meal is $15.

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A model predicts the profit, p of a company as p(x) = x3 – 3x2 – 16x + 48, where p is in thousands of dollars and x is number of
zavuch27 [327]
The first step is to determine the zeros of p(x).
From the Remainder Theorem, 
p(a) = 0  => (x-a) is a factor of p(x), and x=a is a zero of p(x).

Try x=3:
p(3) = 3^3 - 3*3^2 - 16*3 + 48 = 27 - 27 - 48 + 48 = 0
Therefore x=3 is a zero, and (x-3) is a factor of p(x).

Perform long division.
                    x²             -  16
      -------------------------------------
x-3 |  x³  -  3x²  -  16x  +  48
         x³  -  3x²
        -----------------------------------
                         -  16x  + 48
                         -  16x  +  48         

Note that x² - 6 = (x+4)(x-4).

Therefore the complete factorization of p(x) is
p(x) = (x-3)(x+4)(x-4)

To determine when p(x) is negative, we shall test between the zeros of p(x)
   x      p(x)       Sign
----  ---------    ---------
  -4          0    
   0        48         +
   3           0
3.5   -1.875         -
   4           0

p(x) is negative in the interval x = (3, 4).

Answer
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How much is the percent increase from 1 to 4?
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Answer:

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5 0
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∠1 ​ and ∠2 are supplementary. ∠1=124°∠2=(2x+4)° Select from the drop down menu to correctly answer the question.
Alex_Xolod [135]
Remark
Supplementary angles add up to 180o. 

Givens
<1 = 124
<2 = 2x + 4

I imagine you are looking for either x or <2. 

Equation
<1 + <2 = 180          Substitute the givens
124 + 2x + 4 = 180  Collect like terms on the left.
128 + 2x = 180         Subtract 128 from both sides
2x = 180 - 128          Collect like terms on the right   
2x = 52                     divide by 2
x = 52/2
x = 26 <<<<<<<<< answer

<1 = 124
<2 = 2x + 4 = 2*26 + 4
<2 = 52 + 4
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