Answer: To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)
y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)
y = (x+2)² ⇒⇒⇒ take the square root to both sides
√y = x+2
x = √y - 2 ⇒⇒⇒ x becomes a function of y
final step:
∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function
So, as a conclusion:
f(x) = y = x² + 4x + 4 ⇒⇒⇒ the given function
f⁻¹(x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function
The answer is 4.5 l
To calculate this, we will use the Boyle's law using constant k, pressure P, and volume V:
PV = k
We can forget temperature since it is constant.
We have:
P1V1 = k
P2V2 = k
So, P1V1 = P2V2
P1 = 3 atm
V1 = 1.5 l
P2 = 1 atm
V2 = ?
_____
P1V1 = P2V2
3 atm * 1.5 l = 1 atm * V2
4.5 atm/l = 1 atm * V2
V2 = 4.5 atm l / 1 atm
V2 = 4.5 l
Answer:
56
Step-by-step explanation:
Lowest Common Multiple= 56
The answer is (3, -7). If the function is written in the form y = a(x –
h)^2 + k, the vertex will be (h, k). Let's write the function 8x^2 – 48x
+ 65 in the form of a(x – h)^2 + k. g(x) = 8x^2 – 48x + 65. g(x) = 8x^2
– 48x + 72 - 72 + 65. g(x) = (8x^2 – 48x + 72) - 7. g(x) = (8 * x^2 – 8
* 6x + 8 * 9) - 7. g(x) = 8(x^2 - 6x + 9) - 7. g(x) = 8(x - 3)^2 - 7.
The function is now in the form a(x – h)^2 + k, where a = 8, h = 3, and k
= -7. Thus, the vertex is (3, -7).
In fraction is 3/4 and 3/4
Decimal is .75 and .75