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Here is your answer:

But I would still like you to thanks EP and to answer my question as to why you believed it to be wrong.

Even if it is just that you put it in an answer box and it was wrong.  You should always give your reason.

72 degrees clockwise or  360-72 counterclockwise.

But you only want the little one.

How about saying thanks.

EP obviously put a lot of time into your answer.

Also, please state why you believe it to be wrong.

The following should help:

As follows:

The members are  : Mr.L, Mrs.L, 1st child, 2nd child & 3rd child.

• Either Mr.L or Mrs.L sits in driver's seat

                     No. of possibilities = 2

• Only 3rd child can't sit in other front seat and either M.L or Mrs.L already sits in drivers' 

                     No. of possibilites in other front seat = (5-2) = 3

• Of the remaining 3 anyone can seat in any 3 seats in any order 

                     No. of arrangements in the back seats = 3! = 6

Thus total seating arrangements \(=2×3×6\)

                                                     \(=36\)

~ Hope you got it :)  

Thank you

In 2004 = $290 billion

In 2005 \(=(1+{7\over 100})*290\)

             \(=310.3\)

In 2006 \(={107\over 100}×310.3\)

             \(=332.02\)

In 2007 \(={107\over 100}×332.021\)

             \(=355.26\)

... and so on

As you might have observed the above series forms a GP with

1st term a₁ = 290 and common ratio r = 10.7

In order to find amount of money in 2018 (14 yrs later), we've to find the 15th term i.e. a₁₅ 

⇒ \({a}_{15}= a × r^{14}\)

           \(=290 × (10.7)^{14}\)

           \(=$ 74777490355836152.54\) billion       (approx.) 

~Hope you got it :) 

If you really do not speak English.

It may be helpful for us to know what language or languages you do speak.

I have a passing interest in this question too.

What does it even mean?

If I was to totally guess the answer I'd say the area is 3 times that of the original.  2.5*3 = 7.5

But like I said. I have no idea what I am talking about.

This question may have been asked by a child who has never used algebra.

It is easier to use algebra for a person who knows how BUT here is how another way to do it.

the first one has             2 circles, 2 trangles and another triangle and it adds to 21

the second one has       2 circles, 2 trangles and another circle and it adds to 19

So the triangle must be bigger than the circle by 2.  (because that is the only difference)

So if I replace each of the triangles in the second one with  a circle plus 2 more I get

5 circles + 2+2 = 19

If 5 circles plus 4 more equals 19 then

5 circles must equal 15

so one circle must be 3       (because 3+3+3+3+3=15)

Find the determinant of the following matrix.

\(\begin{pmatrix} 2 & 2 & 4 & 2 \\ 3 & 0 & 5 & 0 \\ 0 & 2 & 0 & 2 \\ 0 & 2 & 0 & 5 \\ \end{pmatrix}\)

\(\begin{array}{|rcll|} \hline \begin{vmatrix} 2 & 2 & 4 & 2 \\ 3 & 0 & 5 & 0 \\ 0 & 2 & 0 & 2 \\ 0 & 2 & 0 & 5 \\ \end{vmatrix} &=&2* \begin{vmatrix} 0 & 5 & 0 \\ 2 & 0 & 2 \\ 2 & 0 & 5 \\ \end{vmatrix} -3* \begin{vmatrix} 2 & 4 & 2 \\ 2 & 0 & 2 \\ 2 & 0 & 5 \\ \end{vmatrix} \\ &=&2*(-5)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} -3*(-4)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&(-10+12)* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&2* \begin{vmatrix} 2 & 2 \\ 2 & 5 \\ \end{vmatrix} \\ &=&2*(2*5-2*2) \\ &=&2*(10-4) \\ &=&2*6 \\ &=& \mathbf{12} \\ \hline \end{array}\)

this question does not make sense.

Attn: mworkhard,

I know you are a valuable member of the forum and maybe I should keep my thoughts to myself......... but really ...

The heading 'quick'   Come on!   Why did you need to sound so demanding?

Then.

"thats wut i got just checking!!"

No "thank you."  no   "I wanted to see if there was a better way to do it"

Did you even look at catmg's or CPhill's working?

You gave your question a point but you did not give a point to either answerer.

I suppose any response is better than no response but you're better than this!

The sequence \((a_n)\) satisfies \(a_1=3\) and
\(a_{n}=\dfrac{a_{n-1}-1}{a_{n-1}+1}\)
for all \(n \ge 2\). Find \(a_{100}\)

\(\begin{array}{|rclclcr|} \hline a_1 && && &=& \color{red}3 \\\\ a_2 &=& \dfrac{a_1-1}{a_1+1} &=& \dfrac{3-1}{3+1}&=& \dfrac{1}{2} \\\\ a_3 &=& \dfrac{a_2-1}{a_2+1} &=& \dfrac{\dfrac{1}{2}-1}{\dfrac{1}{2}+1}&=& -\dfrac{1}{3} \\\\ a_4 &=& \dfrac{a_3-1}{a_3+1} &=& \dfrac{-\dfrac{1}{3}-1}{-\dfrac{1}{3}+1}&=& -2 \\\\ a_5 &=& \dfrac{a_4-1}{a_4+1} &=& \dfrac{-2-1}{-2+1}&=& \color{red}3 \\\\ a_6 &&&=& a_2 &=& \dfrac{1}{2} \\\\ a_7 &&&=& a_3 &=& -\dfrac{1}{3} \\\\ a_8 &&&=& a_4 &=& -2\\\\ a_9 &&&=& a_5 &=& \color{red}3 \\ \dots \\ \hline \end{array}\)

\(\mathbf{100} \text{ is divisible by } 4 \text{, so } a_{100} = a_{8} = a_{4} = \mathbf{-2}\)

Key idea:  : Let  y = Total paid for Plan A =  B ,   at x minutes use

we compare  two equations of plan A & B  and solve for x minutes use

Plan A :     y =   0.10 x 

Plan B:      y = (0.05)x + 20

0.10x  =  (0.05)x + 20

x =  400    

(Meaning:  Plan B will be cheaper after 400 min.  )

At x =  400  is the intercept between Plan A and B.  The slope of Plan B is increase slower than the Plan A

  Red line  y = (0.05)x + 20 . 

X^2 + 2x + 3 = x^2-x-20

3x = -23

x= -23/3

Sent from my Android with Tapatalk

                                            Plan A            Plan B  

Cost for 100 minutes (¢)      1,000        2,000 +    500 = 2,500  

Cost for 200 minutes (¢)      2,000        2,000 + 1,000 = 3,000  

Cost for 300 minutes (¢)      3,000        2,000 + 1,500 = 3,500  

Cost for 400 minutes (¢)      4,000        2,000 + 2,000 = 4,000  

You can see that, starting with the 401^st minute, Plan B is the cheaper plan.  

_.

Can you send working?

$a_{100} = \boxed{1/6}$

Nice work xc !   Here is a simple venn perspective:

The $x^2$ term is $(-4x^2)(-7) + (5x)(tx) + (-5)(x^2)$ which is equal to $(28+5t-5)x^2$.  Since the product has no $x^2$, we have $28+5t-5=0$.  Solving for $t$ gives $t=-23/5$.

Divide  x^2 + 2x + 3    into     2x^5 + 3x^4 + 7x^3 + 6x^2 + 15x + 9   to get:

2x3 - x^2 +3x + 3