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Lana71 [14]
2 years ago
5

Combine the like terms to create an equivalent expression: -k-(-8k)

Mathematics
2 answers:
Gelneren [198K]2 years ago
6 0
-k+8k
7k. Is the answer
mamaluj [8]2 years ago
4 0

Answer and Step-by-step explanation:

We are given the terms -1, k, -1, -1, and 8k.

<u>Here is where those terms are found.</u>

-1(<u>k</u>) -1( -1(8k) )

<u>Distribute all of the negative ones.</u>

-k -(-8k)

-k + 8k   _*

* How did we get positive 8k?

- When multiplying two negative numbers, which in this case was -1 and -8k, the result is positive. Thus, giving us positive 8k.

<u>Now, combine like terms.</u>

7k

The answer is 7k.

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

<em><u></u></em>

<em><u>I hope this helps!</u></em>

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A company manufactures running shoes and basketball shoes. The total revenue (in thousands of dollars) from x1 units of running
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Answer:

x_1 =2 , x_2=7

Step-by-step explanation:

Consider the revenue function given by R(x_1,x_2) = -5x_1^2-8x_2^2 -2x_1x_2+34x_1+116x_2. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).

\frac{dR}{dx_1} = -10x_1-2x_2+34 =0

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From the first equation, we get, x_2 = \frac{-10x_1+34}{2}.If we replace that in the second equation, we get

-16\frac{-10x_1+34}{2} -2x_1+116=0= 80x_1-2x_1+116-272= 78x_1-156

From where we get that x_1 = \frac{156}{78}=2. If we replace that in the first equation, we get

x_2 = \frac{-10\cdot 2 +34}{2}=\frac{14}{2} = 7

So, the critical point is (x_1,x_2) = (2,7). We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives  and check if the criteria is fulfilled in order for it to be a maximum. We get that

\frac{d^2R}{dx_1dx_2}= -2 = \frac{d^2R}{dx_2dx_1}

\frac{d^2R}{dx_{1}^2}=-10, \frac{d^2R}{dx_{2}^2}=-16

We have the following matrix,  

\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right].

Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is (-10)\cdot (-16) - (-2)(-2) = 156>0 and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum

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