A farmer is going to plant more than 50 acres in corn this year. If a represents the number of acres planted in corn, write an inequality to describe all possible values of a.

a>50A is greater than 50

a<50a<50

a≥50A is greater than or equal to 50

a≤50

+ 1) is an even number.

Take any n ∈ N, then n is either even or odd.

• Suppose n is even ⇒ n = 2m for some m ⇒ n(n + 1) = 2m(n + 1) ⇒ n(n + 1) is even.

• Suppose n is odd ⇒ n+ 1 is even ⇒ n+ 1 = 2m for some m ⇒ n(n+ 1) = 2nm ⇒ n(n+ 1)

is even. QED

2. The sum of the first n natural num

Step-by-step explanation:

a>50A is greater than 50

a<50a<50

a≥50A is greater than or equal to 50

a≤50

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

-2

7 - 9 = -2

reversed:

-2 + 9 = 7