Look at the table. make a conjecture about the sum of the first 20 positive even numbers.

Hence, the conjecture for the sum of first 20 positive integer is:

20×21=420

Step-by-step explanation:

The table is given as:

2                        = 2 =1.2

2+4                    = 6 = 2.3

2+4+6                = 12 = 3.4

2+4+6+8            = 20 = 4.5

2+4+6+8+10      = 30 = 5.6

Hence, we see the pattern as:

2+4+6++2n= n(n+1)

which is the sum of first n even positive integers.

Hence, we are asked to find the sum of first 20 positive even numbers that is we are asked to find the sum when n=20.

i.e. the sum of:

2+4+6+8++40=20(20+1)

2+4+6+8++40=20×21=420.

Hence, the conjecture for the sum of first 20 positive integer is:

20×21=420

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180