3 years ago

The commutative property can be expressed as

Mathematics

1 answer:

AleksAgata [21]3 years ago

5 0

!.!.!!..!.!.!.!!.!.!.!.!.!.!.!.!!..!!..!.!!.!.!.!.!.!.!.!.!.!..!. A

You might be interested in

Between the two of them, they teach 35 yoga classes each week. if erica teaches 13 fewer than twice as many as bo, how many clas

Nutka1998 [239]

Assume x are Erica's classes & y are Bo's classes.
x+y=35
x=2y-13
Replacing the value of x into the first equation
2y-13+y=35
3y=35+13
y=16 classes
x=2*16-13=19 classes

7 0

3 years ago

Which expression is equivalent to 60 Σ n=1 (2n − 1)2 ? Check all that apply.

Hunter-Best [27]

9514 1404 393

Answer:

B, D

Step-by-step explanation:

The quadratic expands to ...

(2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1

The coefficients can be factored out of the sum, so ...

∑(4n²) = 4∑n² for example

The sum of 60 ones is 60:

$\displaystyle\sum_{n=1}^{60}{1}=1+1+1+\dots+1=60$

So, the sum can be written as ...

$\displaystyle\sum_{n=1}^{60}{(2n-1)^2}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+\sum_{n=1}^{60}{1}}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+60}$