X² + mx + m A perfect square trinomial is where:x² - is the square of the first term binomialmx - is twice the product of the binomials first and last termm - is the square of the last term binomial
x² + mx + m = (x + 1)²
(x + 1)² ⇒ (x+1)(x+1) = x(x+1) +1(x+1) ⇒ x² + x + x +1 = x² + 2x + 1
Answer:
Explanation:
Binomial expansion is:

Here in given expression we have a=x , b=-2y and n = 13
general formula for binomial expansion is:

Since, 
r should be one number less than the term we need to find so it will become the number we need to find like here we have to find 9th term so, r=8
substituting the values in the genral formula we will get

After substituting the values we will get

After simplification we will get
which will be the 9th term of the expansion
Answer=6
Given the information, the following equation can be made, where x is equal to the number of cases she needs to buy.
160=16+24x
subtract 16 from both sides
144=24x
divide both sides by 24
6=x
She will have to buy 6 cases to have a total of 160 water bottles.
The complete question in the attached figure
we know that
the root mean square speed, is the square root of the average (mean) of all of the square of the speeds of individual particles in a gas.
step 1
find the square of the speeds of individual particles
2.8²----> 7.84
3.2²---->10.24
5.8²----> 33.64
7.3²----> 53.29
7.4²---> 54.76
average=[7.84+10.24+33.64+53.29+54.76]/5-----> 159.77/5----> 31.954
step 2
find the square root of the average
√31.954=5.65
therefore
the answer isthe option b) 5.7 m/s