Answer:
t^2 + 30t - 15/t^2 + 25
Step-by-step explanation:
Given:
Faiz's total online shipping bill comes to £45.71.
He then receives discount of £15.90.
To find:
How much does he have to finally pay after the discount?
Solution:
We have,
Amount of bill = £45.71
Discount amount = £15.90
Now,
Final payment = Amount of bill - Discount amount
= £45.71 - £15.90
= £29.81
Therefore, Faiz's have tp pay £29.81 after discount.
Answer:
88
Step-by-step explanation:
Answer:
![\sum_{n=1}^{25}(3n-2)=925]](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B25%7D%283n-2%29%3D925%5D)
Step-by-step explanation:
The given series is 
The first term of this series is



The second term is



The common difference is

The sum of the first n-terms is given by;
![S_n=\frac{n}{2}[2a_1+d(n-1)]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a_1%2Bd%28n-1%29%5D)
The sum of the first 25 terms of the series is
![S_{25}=\frac{25}{2}[2(1)+3(25-1)]](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%7D%7B2%7D%5B2%281%29%2B3%2825-1%29%5D)
![S_{25}=\frac{25}{2}[2+3(24)]](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%7D%7B2%7D%5B2%2B3%2824%29%5D)
![S_{25}=\frac{25}{2}(74)]](https://tex.z-dn.net/?f=S_%7B25%7D%3D%5Cfrac%7B25%7D%7B2%7D%2874%29%5D)
![S_{25}=925]](https://tex.z-dn.net/?f=S_%7B25%7D%3D925%5D)
Part I - First synthetic division
You need to use synthetic division to come up with an expression for a and b:
(x + 2) is a factor, and the remainder is 7, so we can draw a synthetic division table...
coefficients = 1 for X^3; A for X^2; B for X^1; and 3
-2 | 1 A B 3
-2 -2(A-2) 4(A-2)-2B
1 (A-2) -2(A-2)+B 4(A-2)-2B + 3
Remainder = 7
<u>So...</u>
4(A-2)-2B + 3 = 7
4 * (A - 2) - 2B + 3 = 7
4A - 8 - 2B = 4
4A - 2B = 12
2A - B = 6
Proved
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Part II - Second Synthetic Division
We draw another synthetic division table, this time with (x - 1), so the number on the left hand side will be +1
1 | 1 A B 3
1 (A+1) A+B+1
1 (A+1) A+B+1 A+B+4
Remainder = 4
<u>So...</u>
A + B + 4 = 4
A + B = 0
<u>A = -B
</u>
-------------------------------------------------------------------------------------------------------------------
Part III - Solving for A and B with our two simultaneous equations
We know that<u> </u><u>A = -B</u><u /> and we also know that 2A - B = 6
Since we know that A is equal to -B We can substitute in A for -B, to get:
2A - B = 6
Therefore...
2A + A = 6
3A = 6
<u>A = 2</u>
Again, as we know that A = -B, and as we have found that A = 2, we can see:
A = -B
Therefore...
2 = -B
<u>B = -2
</u>
So our final answer is <u>A = 2, B = -2</u><u />
Hopefully this answer is more useful than the last one, and isn't so confusing!