Answer by YourHope:
Hi! :)
The graph shows f(x) = [1/2]^x and its translation, g(x). Which describes the translation of f(x) to g(x)?
Translation of four units up! The f(x) function cannot possibly be f(x)=1/2, though, because that would be a horizontal line through y = 1/2 and that function is clearly not a horizontal line. So whatever f(x) is really, add 4 to the tail end of it to show its translation!
:)
We found a counterexample, so the statement is false.
<h3>
Is the statement true?</h3>
Let's use the matrix:
![\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-2%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C%200%260%260%261%20%5Cend%7Barray%7D%5Cright%5D)
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
![\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%2F2%260%260%260%5C%5C0%26-1%260%260%5C%5C0%260%26-1%260%5C%5C%200%260%260%26-1%20%5Cend%7Barray%7D%5Cright%5D)
If we multiply it by 2, we get:
![\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%26-2%260%260%5C%5C0%260%26-2%260%5C%5C%200%260%260%26-2%20%5Cend%7Barray%7D%5Cright%5D)
The adjoint of that is the original matrix, actually:
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
If you want to learn more about matrices:
brainly.com/question/11989522
#SPJ1
Answer: 79
Step-by-step explanation:
If the sum of the first and last is 64, their average is 32. They will have a difference of 6, so the first number is 29 and the last is 35. The numbers are therefore 29, 31, 33, 35.
Answer:
there are 51 cars and 34 trucks
hope this helps
Step-by-step explanation:
