Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).
= P(x) divided by ![(x+2)](https://tex.z-dn.net/?f=%28x%2B2%29)
Step 1: Find a
To find a we will have to convert (x+2) into (x - a) form
i.e. (x+2) = (x - (-2))
therefore, a = -2
Step 2: Substitute value of a in P(x),
By substitution we get,
![2(-2)^{4}+(-2)^{2}-10(-2)-1](https://tex.z-dn.net/?f=2%28-2%29%5E%7B4%7D%2B%28-2%29%5E%7B2%7D-10%28-2%29-1)
= ![2(16) + 4 +20 -1](https://tex.z-dn.net/?f=2%2816%29%20%2B%204%20%2B20%20-1)
= ![32 +4 + 20 - 1](https://tex.z-dn.net/?f=32%20%2B4%20%2B%2020%20-%201)
=
= Remainder
Hence, Remainder is 55.
Answer:
function
Step-by-step explanation:
The question is incomplete. The complete question is :
Nate starts a lawn-mowing business. In his business, he has expenses and revenue. Nate's expenses are the cost of the lawn mower and gas, and his revenue is $25 per lawn. At what point will Nate's revenue exceed his expense?
Cost of lawn mower = $ 200
Cost of gasoline = $ 2 per lawn
Solution :
Given :
Cost of the lawn mower = $ 200
The cost of gasoline expense for one lawn = $ 2
The revenue generated for one lawn = $ 25
So let the number of lawn to be mowed = x
Therefore the total expenses = ![$200+2x$](https://tex.z-dn.net/?f=%24200%2B2x%24)
So, the total revenue = ![$25x$](https://tex.z-dn.net/?f=%2425x%24)
The point for which the revenue will exceed the total expenditure will be :
![$25x \geq 200+2x$](https://tex.z-dn.net/?f=%2425x%20%5Cgeq%20200%2B2x%24)
So at ![x=9, \ 225 > 218](https://tex.z-dn.net/?f=x%3D9%2C%20%20%5C%20225%20%3E%20218)
Thus the revenue exceeds the total expenditure after mowing 9 number of lawns.
Answer:
![D = \left[\begin{array}{ccc}9&11\\-14&5\end{array}\right]](https://tex.z-dn.net/?f=D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%2611%5C%5C-14%265%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:
![D + \left[\begin{array}{ccc}-1&-15\\0&7\end{array}\right] = \left[\begin{array}{ccc}8&-4\\-14&-12\end{array}\right].](https://tex.z-dn.net/?f=D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-15%5C%5C0%267%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-4%5C%5C-14%26-12%5Cend%7Barray%7D%5Cright%5D.)
Solving for D:
![D = \left[\begin{array}{ccc}8&-4\\-14&12\end{array}\right] - \left[\begin{array}{ccc}-1&-15\\-0&7\end{array}\right] = \left[\begin{array}{ccc}9&11\\-14&5\end{array}\right]](https://tex.z-dn.net/?f=D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-4%5C%5C-14%2612%5Cend%7Barray%7D%5Cright%5D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-15%5C%5C-0%267%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%2611%5C%5C-14%265%5Cend%7Barray%7D%5Cright%5D)
Then, the solution is the fourth option.
![D=\left[\begin{array}{ccc}9&11\\-14&5\end{array}\right]](https://tex.z-dn.net/?f=D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%2611%5C%5C-14%265%5Cend%7Barray%7D%5Cright%5D)
Answer:
i think B
Step-by-step explanation:
because if we think logically...the price have to more than 10-28.All answer except B are illogical for me i think
hope its help