Answer:
z = 7/3 is extraneous.
Step-by-step explanation:
√(z^2+8) = 1 - 2z
z^2 + 8 = (1 - 2z)^2
z^2 + 8 = 1 -4z + 4z^2
3z^2 - 4z - 7 = 0
3z^2 + 3z - 7z - 7 = 0
3z(z + 1) - 7(z + 1) = 0
(3z - 7)(z + 1) = 0
3z = 7, z = -1
z = 7/3, -1.
One of these might be extraneous.
Checking:
√(z^2+8) = 1 - 2z, if z = -1:
√(1 + 8) = 3, -3
1 - 2(-1) = 3. So its not z = -1
if z = 7/3
√((7/3)^2 + 8) = 13.44
1 - 2(7/3) = -3.66
So its z = 7/3
Profit is revenue minus costs so...
P(x)=20x-7x-10
P(x)=13x-10
X>_0 y>_-4 your domain is the opposite of whats inside of the radical, in this case it’s zero but if the number was -5 you would say x>_ 5. Your range is whatever number is in the back, which is negative 4. But you have to pay attention, if there is a negative before the radical your range will be y<_ the number. But here, there isn’t a negative sign in the front of the radical so it’s just y>_ -4.