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lys-0071 [83]
3 years ago
7

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

years passed since January 1, 2011. For which time interval would the company make a loss?
Mathematics
1 answer:
zavuch27 [327]3 years ago
3 0
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.
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Answer:

The value of x = 12.

Step-by-step explanation:

We know that two angles are termed as supplementary when the sum of the measure of their angles is 180°.

We also know that a straight line angle measures 180°.

It is clear that the angles 72° and 9x° line on a straight line. Thus, the sum of the measure of their angles is 180°.

Therefore,

9x° + 72° = 180°

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Therefore, the value of x = 12.

5 0
2 years ago
Factoring quadratics 4x^2-13x+3=0
ozzi

Answer:

X=3,1/4

Step-by-step explanation:

4x²-(12+1)x+3=0

or,4x²-12x-x+3=0

or,4x(x-3)-1(x-3)=0

or,(4x-1)(x-3)=0

Either,4x-1=0➡️ 4x=1

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6 0
2 years ago
Read 2 more answers
HELP ASAP.
8090 [49]

Hey there!

#1 ⬇️

6 × 6 × 6 × 6 × 6

6 × 6 = 36

36 × 36 × 6

36 × 36 = 1,296

1296 × 6 = 7,776

Answer: 7,776 ☑️

#2 ⬇️

3 × 3 × 3 × 3

3 × 3 = 9

9 × 9 = 81

Answer: 81 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

6 0
2 years ago
Pls help i don’t get it , ill mark brainlist
professor190 [17]

Answer:

100 and 2

Step-by-step explanation:

If we are trying to reduce the radical, we know that 100 times 2 is 200.Therfore,Those are two possible numbers to reduce the radical.

                                             Hope this is right !

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2 years ago
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The area of a square can be tripled by increasing the length and width by 10 inches. What is the original length of the square?
trapecia [35]
The new square has length: 10 + l, where l is the original length of the square, and it's area is (10 + l)^2;
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Then, 3 x l^2 = 100 + 20 x l + l^2;
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l^2 - 10l - 50 = 0 (we use the quadratic equation formula);
The only positive solution is l = 5(1+ \sqrt{3} );


5 0
3 years ago
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