3. Give a property of real numbers (associative, commutative, or distributive) or a property of equality
(addition or multiplication) that justifies each step in the following equation:
3x+1+ 2x - 7= x+22
(1) 3x + 2x +1-7 = x+
(2) x(3+2) - 6 = x+22
5x-6=X+22
(3) 5x-6+6 = x+22+
5x = x+28
(4) 5x - x = x + 28
(5) x(5-1) = 28
4x=28
(6) 34x=-=-28

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

do you have a picture of the table

b, 20 yards

step-by-step explanation:

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5