Question

gianna is substituting t = 2 and t = 7 to determine if the two expressions are equivalent.
5(2t+3) 5t+25
which statement is true?
both expressions are equivalent to 35 when t=2.
both expressions are equivalent to 85 when t=7.
both expressions are equivalent to 60 when t=7.
the expressions are equivalent.

Explanation:

Step1: Substitute \( t = 2 \) into \( 5(2t + 3) \)

First, calculate the expression inside the parentheses: \( 2t+3 = 2\times2 + 3 = 4 + 3 = 7 \). Then multiply by 5: \( 5\times7 = 35 \). Now substitute \( t = 2 \) into \( 5t + 25 \): \( 5\times2 + 25 = 10 + 25 = 35 \). So both expressions equal 35 when \( t = 2 \).

Step2: Substitute \( t = 7 \) into \( 5(2t + 3) \)

Calculate inside the parentheses: \( 2\times7 + 3 = 14 + 3 = 17 \). Multiply by 5: \( 5\times17 = 85 \). Substitute \( t = 7 \) into \( 5t + 25 \): \( 5\times7 + 25 = 35 + 25 = 60 \). So they are not equal when \( t = 7 \).

Answer:

Both expressions are equivalent to 35 when \( t = 2 \) (the first option).