Multiplying a function by a constant factor (10 in this example) stretches the graph relative to the x-axis. If f(x) would be a sine, you would blow up the amplitude from -1..+1 to -10..+10.
Answer:
-136
Step-by-step explanation:
We have to find the determinant of the following matrix:
![\left[\begin{array}{ccc}-4&5&6\\0&4&4\\-2&-5&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C0%264%264%5C%5C-2%26-5%264%5Cend%7Barray%7D%5Cright%5D)
We can find the determinant by expanding via 1st column. i.e. by taking each element of 1st column and multiplying it by its co-factor matrix as shown below:
det
= ![(-4 \times det \left[\begin{array}{cc}4&4\\-5&4\end{array}\right]) - (0 \times (-4 \times det \left[\begin{array}{cc}5&6\\-5&4\end{array}\right]))+ ((-2) \times det\left[\begin{array}{cc}5&6\\4&4\end{array}\right])\\\\ =-4 \times (16 + 20)-(0)+(-2 \times 20-24)\\\\ =-4(36)+(-2(-4))\\\\ =-144+8\\\\ =-136](https://tex.z-dn.net/?f=%28-4%20%5Ctimes%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%264%5C%5C-5%264%5Cend%7Barray%7D%5Cright%5D%29%20-%20%280%20%5Ctimes%20%28-4%20%5Ctimes%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%266%5C%5C-5%264%5Cend%7Barray%7D%5Cright%5D%29%29%2B%20%28%28-2%29%20%5Ctimes%20det%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%266%5C%5C4%264%5Cend%7Barray%7D%5Cright%5D%29%5C%5C%5C%5C%20%3D-4%20%5Ctimes%20%2816%20%2B%2020%29-%280%29%2B%28-2%20%5Ctimes%2020-24%29%5C%5C%5C%5C%20%3D-4%2836%29%2B%28-2%28-4%29%29%5C%5C%5C%5C%20%3D-144%2B8%5C%5C%5C%5C%20%3D-136)
The notation det() stands for determinant of the matrix.
Therefore, the determinant of the given matrix is -136
It can be easily assumed that most information's are already given in the question. Based on those information's, the answer can be deduced.
rt = [(3/4)r] * (t + 12)
4rt = 3r (t + 12)
4rt = 3rt + 36r
4rt - 3rt = 36r
rt = 36r
t = 36
From the above deduction we can conclude that the time taken by Carmen to ride to the market is 36 minutes
Then
Time taken by Carmen to ride home = 36 + 12 = 48 minutes
Answer:
Correct
Step-by-step explanation:
I think you are right.
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