Answer:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:
3 - 1
x = -----------
2
and
-1
y = ----------
2
The center is at x = 1 and y = -1/2: (1, -1/2).
b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):
diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,
radius = (1/2)√65.
square of the radius = r² = 65/4
The general equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r². In this case, the equation is:
(x - 1)² + (y + 1/2)² = 65/4
Answer:

Step-by-step explanation:
Given
Let the three sides be a, b and c
Such that:

Required
Find c such that a, b and c do not form a triangle
To do this, we make use of the following triangle inequality theorem



To get a valid triangle, the above inequalities must be true.
To get an invalid triangle, at least one must not be true.
Substitute: 



The results of the inequality is:
and 
Rewrite as:
and

This means that, the values of c that make a valid triangle are 1 to 9 (inclusive)
Any value outside this range, cannot form a triangle
So, we can say:
, since no options are given
Answer:
x=2-y/2
y=12/7-6x/7
Step-by-step explanation:
We are given a relationship between the sides of a rectangle, that is, the length of one of its sides is 5 less two times its width, and we are asked to find an expression for the area. Let's remember that the area of a rectangle is equal to the product of the length of its side by its width. Let "w" be the length of the rectangle and "L" its lenght, then the area is given by the following formula:

We can use the relationship given in the problem, that is, its length being five less two times its width, that is:

Replacing in the formula for the area we get:

Now we use the distributive law: