Consider the table of values.

x y
-2 0
-1 2
0 6
1 12
2 20
3 30
4 42

select the statement that is true about the table.

a.
the relationship between the variables in the table is linear because the first differences are constant.
b.
the relationship between the variables in the table is quadratic because the second differences are constant.
c.
the relationship between the variables in the table is linear because the second differences are constant.
d.
the relationship between the variables in the table is quadratic because the first differences are constant.

B.  The relationship between the variables in the table is quadratic because the second differences are constant.

Step-by-step explanation:

We have to look for the differences in the y values of the given table.

The y values are:

0, 2, 6, 12, 20, 30, 42

The differences between the consecutive values are:

2, 4, 6, 8, 10, 12

These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:

2, 2, 2, 2, 2

These are the second differences. The second differences are constant. So this means the given relationship is quadratic.

Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.

answer: the answer is e

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .