Given the matrix
![\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D20%2630%5C%5C15%265%5C%5C5%262%5Cend%7Barray%7D%5Cright%5D%20)
representing the number of thousands of gallons of regular and premium oil sold by the three stations of Tiger oil company and the matrix
![\left[\begin{array}{c}500\\600\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D500%5C%5C600%5Cend%7Barray%7D%5Cright%5D%20)
representing dolloars per thousands of gallons of regular and premium oil sold by Tiger oil company.
T<span>he matrix for total dollar volume of sales using matrix multiplication is given by:
![\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right] \left[\begin{array}{c}500\\600\end{array}\right]= \left[\begin{array}{c}20(500)+30(600)\\15(500)+5(600)\\5(500)+2(600)\end{array}\right] \\ \\ = \left[\begin{array}{c}10000+18000\\7500+3000\\2500+1200\end{array}\right] =\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D20%2630%5C%5C15%265%5C%5C5%262%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D500%5C%5C600%5Cend%7Barray%7D%5Cright%5D%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D20%28500%29%2B30%28600%29%5C%5C15%28500%29%2B5%28600%29%5C%5C5%28500%29%2B2%28600%29%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D10000%2B18000%5C%5C7500%2B3000%5C%5C2500%2B1200%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D28000%5C%5C10500%5C%5C3700%5Cend%7Barray%7D%5Cright%5D)
Therefore, the total dolar </span><span>volume of sales is per thousand of gallons of oil is given by:
![\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D28000%5C%5C10500%5C%5C3700%5Cend%7Barray%7D%5Cright%5D)
</span>
Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:
C(n) = 1200 + 45n.
Now, we have to solve for n when C(n) = 4800, hence:
1200 + 45n = 4800
45n = 3600
n = 3600/45
n = 80.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
x + y - 5z = 52
Step-by-step explanation:
Given data:
Point on the plane (3,4,-9)
parallel to x + y -5z = 1
Finding the normal vector
(1 , 1 , -5)(x, y , z) = 1
the normal vector is (1 , 1 , -5)
<em>formula for finding equation the plane given the normal vector (a,b,c) and point (m,n,o) is as </em>
<em>a(x - m) + b(y - n) + c(z-o)=0</em>
Substituting the data we have
1(x-3) + 1( y- 4) - 5(z+9) =0
x-3 +y -4 -5z -45 = 0
x + y - 5z = 45 +4 +3
x + y - 5z = 52
Answer:
she ate 4 slices
Step-by-step explanation:
First Answer:
A)fails the vertical line test at (2,3) and (2,-2)
Second Answer:
B) not a function
=========================================
Further Explanation:
It is possible to pass a single vertical line through this red curve. So it is not a function because it fails the vertical line test. One specific line goes from (2,3) to (2,-2) but there are infinitely other lines to choose from. In order to pass the vertical line test, it must be impossible to pass a vertical line through more than one point on the curve. A function is where any given input leads to exactly one output. In the case of (2,3) and (2,-2), the input x = 2 leads to more than one output (y = 3 and y = -2) at the same time
