Question

27 points please help me out which are equivalent

Answer 1

a)

`8(x + 5)`

b)

`13y + 10`

Explanation:

Hope it helps you<3

Answer 2

(a) 1st, 2nd

(b) 4th

Explanation:

(a) Option 1: Expanding with the distributive property, we have

`8(x+5)=8x+8\cdot 5\\~~~~~~~~~~~~=8x+40,`

which is equivalent.

Option 2: Multiplying the terms gives

`8\cdot x+8\cdot 5= 8x+40`,

which is equivalent.

Option 3: We don't know what x is, so there is no way to write
`48x` as
`8x+40`. This is not equivalent.

Option 4: Expanding with the distributive property gives

`8(5x+1) = 8\cdot 5x+8\cdot1\\~~~~~~~~~~~~~=40x+8,`

which is not equivalent.

(b) First, we combine like terms in the given expression:

`12+14y-2-y=12-2+14y-y\\~~~~~~~~~~~~~~~~~~~~~~~=10+(14-1)y\\~~~~~~~~~~~~~~~~~~~~~~~=10+13y.`

Looking at the given answer choices, only the fourth option is equivalent.