Can someone explain how to get the answers to these problems please!?

Question

NOTE: I am not asking for the answer, I would like to try to figure out the answer myself, because I want to understand what I have to do. If you give me the answer, though, please tell me how you got that answer so I can learn it ..thanks!

1. 4,7,3,4,...
In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference between the previous two terms. If the nth term is the first term of the sequence that is equal to zero, what is the value of n ?

2. If the average (arithmetic mean) of q, r, s, and t is 10, what is the average of s-r, 3r+t, 10-r and 6+q ?


3. If x^10= 5555 and x^9/y= 5, what is the value of xy?


math class is soooo hardd..
thanks for the help

Answer 1

Not sure on #1.

2)
The mean of the 4 given numbers is:
(q + r + s + t) / 4 = 10

so... you want to find:

[(s - r) + (3r + t) + (10 - r) + (6 + q)] / 4

Simplify inside the parentheses:
s - r + 3r + t + 10 - r + 6 + q
= s + (-r + 3r - r) + t + q + (10 + 6)
= s + r + t + q + 16
= (q + r + s + t) + 16

So, now you have:
[(q + r + s + t) + 16] / 4
= (q + r + s + t) / 4 + (16 / 4)
= (10) + 4
= 14

3)
x^10 = 5555
x^9 / y = 5

Solve the second one for x^9.
x^9 / y = 5
x^9 = 5y

Now...
x^10
= x^9 * x
= (5y)(x)
= 5xy

Also...
x^10 = 5555
so...
5xy = 5555
xy = 1111

Answer 2

This is not hard, it requires patience.

do the first one like this:
7-4 = 3, 3-7= 4, 4-3=1, 1-4=3, 3-2=2, 2-3=1, 1-1=0

4 7 3 4 1 3 2 1 1 0

the nth term is the 10th term where the sequence =0
n=10

s-r+3r+t+10-r+6+q= s + r +t +q +16
since AVG of s+q+r+t = 10 then
(s+q+r+t)/4 =10
s+q+r+t = 40
put this into the first equation:
40 + 16 = 56

Now, find the new average=
56 / 4 = 14 (use the 4 because of the 4 terms in the question)



3. Note that if you divide the first value by the second you will get the xy you are looking for so:
(x^10) /(x⁹/y)= (xy) = 5555/5 = 1111/1
xy = 1111

Answer 3

1. simply do it manually
4,7,3,4,1,3,2,1,1,0
then n = 10


2. try to get the sum of the given:
s - r + 3r + t + 10 - r + 6 + q = s + r + t + q + 16

Now, q + r + s + t = 40 ... since the average is 10.

then s + r + t + q + 16 = 56 ... this is the sum.
divide by 4, you get the average: 14.

§
3. [x^9/y] / [x^10] = 1/(xy) = 5/5555 = 1/1111
thus xy = 1111

Answer 4

1. continue writing out the sequence: 4, 7, 3, 4, 1, 3, 2..... and then count how many numbers there are including the zero

2. Add up the expressions and see what you have

3. xy = x^10/(x^9/y) = ?????

Answer 5

The trick is to transform the entire numbers into decimals first. subsequently a million will become a hundred and we deduct 36 from that obtaining sixty 4. Then we replace the decimal. a million could be expressed as a million.00 we could desire to subtract 0.36 enable us to multiply the two words via a hundred a hundred - 36 = sixty 4 we could desire to divide it via a hundred to get decrease back the end result 0.sixty 4 It looks complicated yet is honestly ordinary in case you undergo in strategies the thought and coaching.