An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 3 plays, 4 poetry books, and 4 nonfiction books.

Step 1 of 2 : If she wants to include no more than 2 plays, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Step 2 of 2 : If she wants to include all 4 poetry books, how many different

reading schedules are possible? Express your answer in scientific notation

rounding to the hundredths place.

She wants to pick 10 books. She picks all 4 poetry books and therefore needs

to pick 6 more from the 5+5+7=17 other (non-poetry) books.

So she can pick the remaining 6 (non-poetry) books in (17 CHOOSE 6) = 17C6

= 12376 ways.

For each of the 12376 ways to pick the 10 books to read, she can arrange the

order to read them in -- in (10 POSITION 10)=10P10=10!=3628800 ways.

(17C6)(10!)=12376*3628800 = 4.49×1010

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

equal to

step-by-step explanation: