Question

select the correct answer.

mark and nina own different flower shops, which both open at the same time in the morning.

function (m) models the number of roses mark has at his flower shop, and function (n) models the number of roses in ninas flower shop, (x) hours after the shops open.
(m(x) = 616 - 24x)
(n(x) = 552 - 36x)

which function correctly represents how many more roses mark has at his flower shop than nina has at hers, (x) hours after opening?

(a) ((m - n)(x) = 64 - 60x)
(b) ((m - n)(x) = 64 - 16x)
(c) ((m - n)(x) = 64 + 12x)
(d) ((m - n)(x) = 64 - 12x)

Explanation:

⚡ Using what you learned: Operations with Polynomial Functions

Step 1: Set up the difference function

To find how many more roses Mark has than Nina, subtract Nina's function \( n(x) \) from Mark's function \( m(x) \):

$$ (m - n)(x) = m(x) - n(x) $$

Step 2: Substitute and simplify

Substitute the given functions into the expression:

$$ (m - n)(x) = (616 - 24x) - (552 - 36x) $$

Distribute the negative sign:

$$ (m - n)(x) = 616 - 24x - 552 + 36x $$

Combine like terms:

$$ (m - n)(x) = (616 - 552) + (-24x + 36x) $$

$$ (m - n)(x) = 64 + 12x $$

Answer:

$$ (m - n)(x) = 64 + 12x $$