Final answer:
To determine which expressions are equivalent to 40x+30y, we must look for expressions that have the same coefficients and variables, or can be factored or simplified to match. An equivalent expression, which factors out the greatest common divisor, is 10(4x + 3y).
Step-by-step explanation:
The student is asking which expressions are equivalent to the algebraic expression 40x+30y. To find equivalent expressions, we can look for expressions that have the same terms but might be factored differently or expressions with terms that have been simplified or combined.
An example of an equivalent expression to 40x+30y would be to factor out the greatest common divisor of the coefficients 40 and 30, which is 10. This gives us:
10(4x + 3y)
We can confirm that this expression is indeed equivalent to 40x+30y by distributing the 10 back into the parentheses:
10 * 4x + 10 * 3y = 40x + 30y
Since the resulting expression is the original one, we have proven that the factored expression is equivalent. No other expressions are provided in the question, so we cannot evaluate other options.