 # Chikis

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1. That is an error. I mean to write ₦2000 and not ₦20 000. Please pardon me for that error. It there in the problem. I copied the the original words in the post i and put the concerned section in bold. You can see it below. A man's income is N 180 000 per anum. He is allowed a tax-free income in the following: personal allowance N 72 000, child allowance N 4 500 for each child under 18 years for a maximum of 4 children, dependent relatives allowance to a maximum of N 18 000. Calculate the amount of tax the man will pay if has 5 children under 18 years and the taxable income is 10% for the first N 20 000, 15 % for over N 20 000 and up to N 40 000, 20% for over 40 000 and up to N 60 000, and 25% for over ₦60 000. Have you seen it?
2. A man's income is N 180 000 per anum. He is allowed a tax-free income in the following: personal allowance N 72 000, child allowance N 4 500 for each child under 18 years for a maximum of 4 children, dependent relatives allowance to a maximum of N 18 000. Calculate the amount of tax the man will pay if has 5 children under 18 years and the taxable income is 10% for the first N 20 000, 15 % for over N 20 000 and up to N 40 000, 20% for over 40 000 and up to N 60 000, and 25% for over N 60 000. Here is my work: Man's income = N 180 000 Personal allowance =N 72 000 Child allowance (4 children maximum) = N 4 x N 4 500 = N 18 000 Dependent relatives allowances = N 18 000 Total tax free allowances: N 72 000 + N 18 000 + N 18 000 = N 108 000 Taxable income N 180 000 - N 108 000 = N 72 000 To calculate the tax on the taxable income: N 72 000 = N 20 000 + N 40 000 + N 12 000 Tax rate on the first N 20 000 is 10% = N 20 000 Tax rate over N 20 000 up to N 40 000 is 15% = N 6000 My problem now is what do I do with the remaining N 12 000 since it is less than N 40 000 and not even over N 65 000? Somebody help me please
3. And I say give me the value of of a and n, in which it is not true.All I can say is that $\frac{-a+n}{a+n}$ and $-\left(\frac{a+n}{a+n}\right)$ are the same and diffrent in some cases. The first expression is factored to get the second expression. True or force? I will only say that the expression are the same and different.
4. Okay, what about when $-\frac{a-n}{a+n}$is equal to $-\left(\frac{a+n}{a+n}\right)$. The fraction becomes -1. Am sure you agree to this one.Okay, coming to when a = 2 and n = 1, if we put the values in the expression, $-\left(\frac{a+n}{a+n}\right)$, we have $-\left(\frac{2+1}{2+1}\right)$ $=-\left(\frac{3}{3}\right)$. This gives -(1) = -1. What do you have to say about this one?
5. No I can't. Could you explain why? Or should I take it that the rule is to use the factors of the constant term.
6. When $x=2$ $\rightarrow$ $2(2)^3+(2)^2-13(2)+6$ $\rightarrow$ $16+4-26+6=0$ $\rightarrow$$26-26=0$ $\therefore$ $x-2$ is a factor of $2x^3+x^2-13x+6$ When $x=-3$ $2(-3)^3+(-3)^2-13(-3)+6$ $=2(-27)+9+39+6$ $=-54+48+6$ $=-54+54=0$ $\therefore$$x+3$ is a factor of $2x^3+x^2-13x+6$ But what is the easiest method for finding the values of x? Or would one be always doing trial and error method?
7. $\frac{3(x+y)(x-y)}{y^2-2xy-3x}$ Well the solution to the problem above is $\frac{(y-x)}{(x-\frac{y}{3})}$. The issue now is that I cannot give any justification to the solution. Any help here?
8. We are just complicating issue by making this topic long. What I understand and see here is that when you have $\frac{a-n}{a+n}$ and you multiply the expression by $-1$, it becomes $\frac{-a+n}{a+n}$ The numerator and denominator cancels out to give $-1$ What are we still aguing here? How do you mean? Give a particular example.
9. What does the r and f stand for? Or what does $f( r)$ stand for?
10. It says that $x-r$ is a factor of a polynomial $f( x)$ if $f( r)=0$
11. I want to use the factor theorem to find the factors $2x^3+x^2-13x+6$ How do I do that?
12. $\frac{3}{x+1}+\frac{4}{x+5}$ $=\frac{3(x+5)+4(x+1)}{(x+1)(x+5)}$ $=\frac{3x+15+4x+4}{(x+1)(x+5)}$ $=\frac{7x+19}{(x+1)(x+5)}$ If the above is what you meant, I have done it and seen that it came out correctly. Thank you.
13. Oh! Sorry! I made a mistake there. I intended writing $\frac{3(x+y)(x-y)}{y^2-2x-3x}$ before I typed that trash. Now that the mistake has been corrected, can the denominator be factored out completely to see the terms that could cancel out?
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