Answer:
Jessica spent 10 months in Spain and 8 months in Colombia.
Step-by-step explanation:
Let x be the number of months Jessica lived in Spain, then she lived 18 - x months in Colombia.
She learned an average of 160 words per month when she lived in Spain, so she learned 160x words in Spain.
She learned an average of 200 words per month when she lived in Colombia, so she learned 200(18-x) words in Colombia.
In total, she learned a total of 3,200 new words, thus
![160x+200(18-x)=3,200\\ \\160x+3,600-200x=3,200\\ \\160x-200x=3,200-3,600\\ \\-40x=-400\\ \\x=10](https://tex.z-dn.net/?f=160x%2B200%2818-x%29%3D3%2C200%5C%5C%20%5C%5C160x%2B3%2C600-200x%3D3%2C200%5C%5C%20%5C%5C160x-200x%3D3%2C200-3%2C600%5C%5C%20%5C%5C-40x%3D-400%5C%5C%20%5C%5Cx%3D10)
Jessica spent 10 months in Spain and 8 months in Colombia.
Hello,
the second score is 85, and the third is 86.
Hope this helps!
Answer:
IV
Step-by-step explanation:
Since the cost is the same for weights in one interval, it will form a step function
Answer:
![\left[\begin{array}{ccc}0&-1\\-1&-2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%5C%5C-1%26-2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Thinking process:
We will need to test the different geometric transformations.
Let's see how this can be done:
Let the shear transformation be represented by the matrix S such that ![S(e_{2}) = e_{2} + 2e_{1}](https://tex.z-dn.net/?f=S%28e_%7B2%7D%29%20%3D%20e_%7B2%7D%20%2B%202e_%7B1%7D)
Then, let the image be reflected by the reflection R, such that:
R =
is reflected across the point ![x_{1} = x_{2}](https://tex.z-dn.net/?f=x_%7B1%7D%20%20%3D%20x_%7B2%7D)
then the vector will be = ![\left[\begin{array}{ccc}-1\\0\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5C%5C0%5C%5C%5Cend%7Barray%7D%5Cright%5D)
This is the mirror image.
Then it means that
and ![R (e_{2}) = -e_{1}](https://tex.z-dn.net/?f=R%20%28e_%7B2%7D%29%20%3D%20-e_%7B1%7D)
Thus, the standard matrix is given by: ![\left[\begin{array}{ccc}0&-1\\-1&-2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%5C%5C-1%26-2%5C%5C%5Cend%7Barray%7D%5Cright%5D)