9514 1404 393
Answer:
2. (b) 6 feet by 18 feet
3. -5, -1
Step-by-step explanation:
2. Perhaps the easiest way to answer this is to check to see what the areas are of the offered choices:
a) 7·19 = 133 . . . . numbers are odd, so the answer is odd, incorrect
b) 6·18 = 108 . . . . correct choice
c) 12·24 = 288
d) 5·17 = 85 . . . . again an odd number
__
If you were to solve this by factoring, you would be looking for factors of 108 that have a difference of 12.
108 = 1·108 = 2·54 = 3·36 = 4·27 = 6·18 = 9·12
The differences are 107, 52, 33, 23, 12, 3. The dimensions you want are 6 and 18 feet.
_____
3. Completing the square is easier if the quadratic has a leading coefficient of 1. Here, all of the coefficients are divisible by 2, so we can simplify this to ...
x^2 +6x = -5 . . . . . . divide both sides by 2
Now, we complete the square by adding the square of half the linear term coefficient.
x^2 +6x +9 = 4 . . . . add (6/2)^2 = 9 to both sides
(x +3)^2 = 4 . . . . . write as a square
x +3 = ±2 . . . . . . . take the square root
x = -3 ±2 = -5, -1 . . . . add -3 to both sides
The solutions are -5 and -1.
