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schepotkina [342]
3 years ago
11

Find x. Side splitter theorem

Mathematics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

x = 9

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\frac{8}{8+4} = \frac{x-3}{x} , that is

\frac{8}{12} = \frac{x-3}{x} ( cross- multiply )

12(x - 3) = 8x

12x - 36 = 8x ( subtract 8x from both sides )

4x - 36 = 0 ( add 36 to both sides )

4x = 36 ( divide both sides by 4 )

x = 9

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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
The time interval is Jan. 1, 2014 to Jan. 1, 2015.
3 0
2 years ago
Pentagon jklmn is translated five units up. what is the name of the image after translation?
mrs_skeptik [129]

There will not be any specific name given to that image after translation

<u>Step-by-step explanation:</u>

  • Whatever may be the transformation, either it may be rotation, reflection or translation, the size or shape of the image will not change no matter what the condition is and hence the name of that image will also not change and remains constant.
  • Thus we can conclude that the name of the image will always tend to remain constant and not changes.

4 0
3 years ago
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