Carlos claims that every number and its opposite are located on both the positive side of a number line and the negative side of a number line. In the table below, determine if the example supports or refutes Carlos's claim. Select supports or refutes for each example. 1. -24 and it’s opposite
Supports or Refutes

2. 605 and it’s opposite
Supports or Refutes

3. 0 and it’s opposite
Supports or Refutes

i believe the answer is d.

hope it you! : d

step-by-step explanation:

what is the figure? attach a picture.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.