Which expression is equivalent to 30(12x−2)+40(34y−4)

Question

Which expression is equivalent to  30(12x−2)+40(34y−4)
 (1 point)
Responses

15x+30y−220
15 x plus 30 y minus 220

15x+30y−64
15 x plus 30 y minus 64

45xy−220
45 x y minus 220

15x−30y−220

GPT-4o mini · Answer

To simplify the expression $ 30(12x - 2) + 40(34y - 4) $, we can distribute the constants into the parentheses. 1. Distributing $ 30 $ into $ (12x - 2) $: $$ 30(12x) - 30(2) = 360x - 60 $$ 2. Distributing $ 40 $ into $ (34y - 4) $: $$ 40(34y) - 40(4) = 1360y - 160 $$ Now, combining the two results: $$ 360x - 60 + 1360y - 160 $$ Next, combine like terms: $$ 360x + 1360y - 60 - 160 = 360x + 1360y - 220 $$ Since the expression simplifies to $ 360x + 1360y - 220 $, this can also be factored or simplified further if needed. However, none of the provided responses seem to match this directly. To look for equivalent expressions, we can break it down slightly and find factors, or perhaps express it in terms of smaller coefficients where possible. From the provided options, it seems none of those match the full expression: - $ 15x + 30y - 220 $ - $ 15x + 30y - 64 $ - $ 45xy - 220 $ - $ 15x - 30y - 220 $ Among these options, let's re-evaluate the first option for further simplification: Notice that $ 360x $ can be expressed as $ 15 \times 24x $, and $ 1360y $ can be expressed as $ 30 \times 45.33y $, but neither gives us an easy breakout to equivalent simple forms available. Based on re-evaluating individual terms, I suggest reviewing them again as none absolutely seem equivalent. Therefore, from the original distribution calculation, **the equivalent expression is not fully contained within provided responses, leading to results not being comparable directly but simplifying shows:** $$ 360x + 1360y - 220 $$ In sum, none of the responses correctly translate back to this primary factorization correctly without losing structure. If you require further assistance or specific comparative breakdowns, I'd be glad to assist!

mav welborn · Answer

whats the closest answer

GPT-4o mini · Answer

Let's find the closest answer among the options provided, based on our earlier calculations.

Based on our calculations, we simplified the original expression $ 30(12x - 2) + 40(34y - 4) $ to:

\[ 360x + 1360y - 220 \]

When we look at the provided options:

$ 15x + 30y - 220 $
$ 15x + 30y - 64 $
$ 45xy - 220 $
$ 15x - 30y - 220 $

None of them matches $ 360x + 1360y - 220 $ directly, but we can compare their forms:

The first option, $ 15x + 30y - 220 $, is the most relatable since:

It maintains the same constant term of $-220$.
The coefficients of $x$ and $y$ are both smaller, potentially representing a simplified version if independent variables.

Comparatively:

The coefficients $15x$ and $30y$ are technically factors of the larger $360x$ and $1360y$, so it could represent a very general aspect but does not hold direct multiplicative relations as simplified results.

Thus, while none are proportionately accurate to express the entirety of the expression, the closest answer among the provided selections is:

$15x + 30y - 220$.