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geniusboy [140]
3 years ago
7

Solve and show steps! (x^2 - x - 12) / (x-4)

Mathematics
1 answer:
emmainna [20.7K]3 years ago
6 0

Answer:

x+3

Step-by-step explanation:

           x2 - x - 12

Simplify   ———————————

              x - 4    

Trying to factor by splitting the middle term

1.1     Factoring  x2 - x - 12  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -12  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12  

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -1 .

     -12    +    1    =    -11  

     -6    +    2    =    -4  

     -4    +    3    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  3  

                    x2 - 4x + 3x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-4)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-4)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x-4)

            Which is the desired factorization

Canceling Out :

1.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 x + 3

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Answer:

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Figure the rates per hr.

110/3 = 36 2/3

160/5 = 32.

So, the rates are not the same.

Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.

In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).

We're given two pairs of values:

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The next step is to fit a line to them.

y = mx+b is the general equation for a line.

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Call the change in x, dx (for delta x).

m = dy/dx = 50/2 = 25

The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.

We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.

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Checking this formula at x=3, we know it is 110.

Checking it at x=5, we obtain:

y = 25*5 + 35 = 125 + 35 = 160.

That checks.

Now to figure an 8-hr job, set x=8 and use the equation"

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y = 235.

That means an 8-hr job costs $235.

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