Answer:
Option B is the correct answer
Step-by-step explanation:
After removing squares with side 4 inch long, the open box will have following dimensions:
Length = x + 9 - 4 - 4 = (x + 1) in
Width = x - 4 - 4 = (x - 8) in
Height = side of square = 4 in
It is given that volume of the open box is 64 cubic inches.
Answer:
x = 3 is extraneous
Step-by-step explanation:
Given
= x - 5 ( square both sides to clear the radical )
4x - 8 = (x - 5)² ← expand using FOIL
4x - 8 = x² - 10x + 25 ( subtract 4x - 8 from both sides )
0 = x² - 14x + 33 ← in standard form
0 = (x - 11)(x - 3) ← in factored form
Equate each factor to zero and solve for x
x - 11 = 0 ⇒ x = 11
x - 3 = 0 ⇒ x = 3
As a check
Substitute these values into the equation and if both sides are equal then they are solutions
x = 11
left side = =
= 6
right side = 11 - 5 = 6
Thus x = 11 is a solution
x = 3
left side = =
= 2
right side = 3 - 5 = - 2 ≠ 2
Thus x = 3 is an extraneous solution
