Question

a number machine uses a rule to change numbers. the table shows the results.
number machine results

in (k)	out (m)
5	17
7	19
11	23

which could be the rule the number machine used?
a $k + 12 = m$
c $k + 12 = m$
b $k - 12 = m$
d $k \times 12 = m$

Explanation:

Step1: Test Option A (k + 12 = m)

Substitute k = 2: \(2 + 12 = 14\), which matches the out value 14.
Substitute k = 5: \(5 + 12 = 17\), which matches the out value 17.
Substitute k = 7: \(7 + 12 = 19\), which matches the out value 19.
Substitute k = 11: \(11 + 12 = 23\), which matches the out value 23.

Step2: Test Option B (k - 12 = m)

Substitute k = 2: \(2 - 12 = -10
eq 14\), so B is incorrect.

Step3: Test Option D (k × 12 = m)

Substitute k = 2: \(2 × 12 = 24
eq 14\), so D is incorrect. (Note: Option C seems to be a duplicate of A here, likely a typo, but A works as shown.)

Answer:

A. \(k + 12 = m\)