A function is initially defined by the set of coordinate pairs ((-3,7), (1,5), (4,13)). Which coordinate pair below, if added to this set, prevents the set from representing a function? 1) (2,5) 2) (5,0) 3) (-1,8) 4) (1,4)

We conclude that if we add (1, 4) to this set, it prevents the set from representing a function.

Step-by-step explanation:

Given the initial function

{(-3, 7), (1, 5), (4, 13)}

We know that the given function indicates the relation in which each input has only one output.

i.e.

at x = -3, y = 7

at x = 1, y = 5

at x = 4,y = 13

Thus, it represents a function, becaus there is no repetitive inputs.

The only way the above function will no longer be a function we bring a point, adding of which makes the initial function having repetitive inputs.

i.e. if we add (1, 4) to the initial set, the relation will no longer be a function.

because induction of the point (1, 4) causes repetitive inputs because x = 1 is already present in the set.

so adding the point (1, 4)

{(-3, 7), (1, 4), (1, 5), (4, 13)}

Now, check the points (1, 4) and (1, 5).

It is clear that there are multiple outputs for x = 1. In other words, the input is no more a unique value as x=1 has been repeated multiple times.

Therefore, we conclude that if we add (1, 4) to this set, it prevents the set from representing a function.

a

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 .