Hello from MrBillDoesMath!
Answer:
Choice A, 1/4
Discussion:
Consider the perfect square
(x + a)^2 = x^2 + (2a)x + a^2
The constant term (a^2) equals 1/2 the coefficient of x (i.e. 2a), squared.
Let's apply this idea to x^2 + x
x^2 + x = => as 2 * 1/2 = 1
x^2 + ( 2 * 1/2)x =
( x^2 + (2* 1/2)x + ( 1/2) ^2 ) - (1/2) ^2 =
as constant term to add is 1/2 coefficient of x (that is, 1/2) and
(1/2)^2 - (1/2)^2 = 0
(x + 1/2) ^ 2 - (1/2)^2
In other words add the constant (1/2)^2 = 1/4, which is Choice A.
Thank you,
MrB
I don’t understand the question can you give more detail
If AP and PB are in a 1:2 ratio, it means that PB is twice AB.
So, AP must fit three times into AB, meaning that P must be at one third of the way between A and B.
Answer:
The sum of the arithmetic series is 2717.
Step-by-step explanation:
The sum of an arithmetic sequence is given by:
Where <em>k</em> is the number of terms, <em>a</em> is the initial term, and <em>x</em>_<em>k</em> is the last term.
There are 22 terms, the first term is 7, and the last term is 240. Hence, the sum is:
In conclusion, the sum of the arithmetic series is 2717.
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