When reading a book, charlie made a list by writing down the page number of the last page he finished reading at the end of each day. (he always finished reading a page that he started.) his mom thought his list indicated the amount of pages he had read on each day. at the end of the $8^{\text{th}}$ day of reading, she added the numbers on his list and thought charlie had read 432 pages. if charlie started reading the book on page one, and he read the same amount of pages each day of this eight- day period, how many pages did he actually read by the end of the $8^{\text{th}}$ day?

96 pages.

Step-by-step explanation:

We know that Charlie read the same amount of pages each day, if we call N the number of pages read each day, his first number on the list was N, the second number was N + N = 2N, the third number was N + N + N = 3N

His mom sums up these numbers and gets 432. Therefore we have that:

N + 2N + 3N + 4N + 5N + 6N + 7N + 8N = 432

36N = 432

N = 12.

Now we know that Charlie read 12 pages per day. With this information we can conclude that by the end of the 8th day he read:

12 pages x 8 = 96 pages.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.