Question

lesson 5 | session 4
2 an architect is trying different dimensions for the room shown below. write an algebraic expression the architect can use to find the area of the room. then find the area when x is 6 m. show your work.
(there is a diagram of a room here)
solution
3 what is the value of 2 + b(a² + 4) when a = 2 and b = 4?
a 22
b 34
c 2
d 48
zara chose d as the correct answer. how might she have gotten that answer?

Explanation:

Step1: Substitute \(a = 2\) and \(b = 4\) into the expression \(2 + b(a^2 + 4)\)

First, calculate \(a^2\) when \(a = 2\): \(a^2 = 2^2 = 4\)
Then, substitute into the parentheses: \(a^2 + 4 = 4 + 4 = 8\)

Step2: Multiply by \(b\)

Now, multiply this result by \(b = 4\): \(b(a^2 + 4)=4\times8 = 32\)

Step3: Add 2

Finally, add 2: \(2 + 32 = 34\)
To see how Zara got D (48), she might have made a mistake in order of operations. For example, if she calculated \(2 + b = 6\) first, then \(a^2 + 4 = 8\), and then \(6\times8 = 48\), ignoring the correct order of operations (parentheses first, then multiplication, then addition).

Answer:

The value of the expression is 34, so the correct option is B. 34. Zara might have miscalculated the order of operations, e.g., adding 2 and \(b\) first before multiplying by \((a^2 + 4)\).