Answer:
(3rd listed choice) Paula's notes are incorrect. Step 4a should be "If the result does not define y as a function of x, then f does not have an inverse," and step 4b should be "If the result defines y as a function of x, then f has an inverse."
Step-by-step explanation:
If f(y) = x can be solved for a relation for y that is a function, then f(x) has an inverse. It will be the function defined by y.
Answer:

Step-by-step explanation:
The equation of a circle in standard form:

(h, k) - center
r - radius
We have the endpoints of the diameter: (-1, 6) and (5, -4).
Midpoint of diameter is a center of a circle.
The formula of a midpoint:

Substitute:

The center is in (2, 1).
The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.
The formula of a distance between two points:

Substitute the coordinates of the points (2, 1) and (5, -4):

Finally we have:

Answer:
The length of LM,hypotenuse is 55.866ft
Step-by-step explanation:
Given that LN=39ft and MN=40ft so you can solve it using Pythogoras' Theorem:
side²+side² = hypo²
LN² + MN² = LM²
hypo² = 39²+40²
= 3121
LM = √3121
= 55.866ft (3d.p)
The solution to the quadratic equation are option C) x= -5 and option E) x=3.
<u>Step-by-step explanation</u>:
The given quadratic equation is x²+2x-15 = 0.
Using the factorization method,
- product of the roots should be -15.
- Sum of the roots should be 2.
⇒ -15 = 5
-3
⇒ 2 = 5+(-3)
(x+5)(x-3) = 0
Therefore, x = -5 and x = 3
Answer:
x equals 25 hope this helps