The system of equations Y =-3x+2 and Y = 3x-6 is shown on the graph below.

Basically in order to create nine 0's, the previous step had to have all 0's or all 1's. There is no other way possible, because between any two equal bits you insert a 0.

If we consider two cases for the second-to-last step:

There were 9 0's:

We obtain nine 0's if all bits in the previous step were the same, thus all bit were 0's or all bits were 1's. If the previous step contained all 0's, then we have the same case as the current iteration step. Since initially the circle did not contain only 0's, the circle had to contain something else than only 0's at some point and thus there exists a point where the circle contained only 1's.

There were 9 1's:

A circle contains only 1's, if every pair of the consecutive nine digits is different. However this is impossible, because there are five 1's and four 0's (we have an odd number of bits!), thus if the 1's and 0's alternate, then we obtain that 1's that will be next to each other (which would result in a 1 in the next step). Thus, we obtained a contradiction and thus assumption that the circle contains nine 0's after iteratins the procedure is false. This then means that you can never get nine 0's.

To summarize, in order to create nine 0's, the previous step had to have all 0's or al 1's. As we didn't start the arrange with all 0's, the only way is having all 1's, but having all 1's will not be possible in our case since we have an odd number of bits.

5 0

3 years ago

Ashley and Kristin are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls

rodikova [14]

The cost of one roll of plain wrapping paper is $5 and one roll of shiny wrapping paper costs $16.

Step-by-step explanation:

Step 1; Assume that the cost of one roll of plain wrapping paper is $x and a roll of shiny wrapping paper costs $y. so we have the following equations from the given data

4x + 3y = 68, take this as equation 1.

9x + 2y = 77, take this as equation 2

Step 2; We multiply equation 1 with 2 and equation 2 with 3 so we can cancel out the variable y in both equations. By doing this we get

8x + 6y = 136, take this as equation 3,

9x + 2y = 77, this is equation 4.

If we subtract 4 from 3, we cancel out the y variable and can calculate the value of x.

-19x = -103 , x = $\frac{-95}{-19}$ = 5.

Step 3; Substituting this value of x in any of the previous equations we will get x's value. Here this value of y is substituted in equation 1.

4 (5) + 3y = 68, 20 + 3y = 68 , 3y = 48, y= 16.

So we have x = $5 and y = $16.

5 0

3 years ago

What is 19 plus 8 times 5 plus 8

NemiM [27]

Answer:

19+8*5+8=67

Step-by-step explanation:

when you add 19 with 8 then you times it with 5 then add 8 you get 67

5 0

3 years ago