Answer:
D.6
Step-by-step explanation:
Answer:
The amount invested in the mutual fund that earned 5% was $1,000
The amount invested in the mutual fund that earned 3% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested in the mutual fund that earned 5%
y ----> the amount invested in the mutual fund that earned 3%
we know that
---->
----> equation A


----> equation B
Solve the system by substitution
substitute equation A in equation B
Solve for x

<em>Find the value of y</em>


therefore
The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800
<span>We want to show that f(g(x)) = x and g(f(x)) = x.
So to do that, we need to calculate f(g(x)) and g(f(x)) explicitly.
Let's begin with f(g(x))
Now, f(g(x)) = f(4/x), by definition of g, as g(x) = 4/x
What then is f(4/x) equal to? Use the definition of f.</span>
Answer:
![\left[\begin{array}{ccc}4&19&-5\\7&0&-14\end{array}\right] + \left[\begin{array}{ccc}-8&7&0\\-1&17&6\end{array}\right] = \left[\begin{array}{ccc}-4&26&-5\\6&17&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2619%26-5%5C%5C7%260%26-14%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%267%260%5C%5C-1%2617%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%2626%26-5%5C%5C6%2617%26-8%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
To add two matrices you just need to add the corresponding entries together. In this case, we have that:
![\left[\begin{array}{ccc}4&19&-5\\7&0&-14\end{array}\right] + \left[\begin{array}{ccc}-8&7&0\\-1&17&6\end{array}\right]=\left[\begin{array}{ccc}4-8&19+7&-5 + 0\\7-1&0+17&-14+6\end{array}\right] = \left[\begin{array}{ccc}-4&26&-5\\6&17&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2619%26-5%5C%5C7%260%26-14%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%267%260%5C%5C-1%2617%266%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-8%2619%2B7%26-5%20%2B%200%5C%5C7-1%260%2B17%26-14%2B6%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%2626%26-5%5C%5C6%2617%26-8%5Cend%7Barray%7D%5Cright%5D)
Then, we conclude that the sume of the two matrices is:
![\left[\begin{array}{ccc}4&19&-5\\7&0&-14\end{array}\right] + \left[\begin{array}{ccc}-8&7&0\\-1&17&6\end{array}\right] = \left[\begin{array}{ccc}-4&26&-5\\6&17&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2619%26-5%5C%5C7%260%26-14%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%267%260%5C%5C-1%2617%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%2626%26-5%5C%5C6%2617%26-8%5Cend%7Barray%7D%5Cright%5D)