Answer:
First, plug-in x and y as 3sinθ-2 and 3cosθ+4 into the equation, respectively:
Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:
We can factor out 3^2 = 9 from both equations:
We know from a trigonometric identity that 
, meaning we can reduce the equation to:
And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sinθ-2 and y=3cosθ+4.
Hope this helped you.
Answer:
(5,0)
Step-by-step explanation:
an x-intercept is where the line crosses the x-axis. in this case it crosses it multiple time so other possible answers could be (1,0) or (-1,0)
X + x + 2 = 14
2x + 2 = 14
2x = 12, x = 6
Solution: the smallest of the two integers is 6
Answer:
Step-by-step explanation:
We know that the diameter of the fountain is 3 feet and that it is in the center of the pond.
We know that the area of a circumference is:
where r is the radius of the circumference.
further
d = 2r
Where d is the diameter of the circumference.
Then the radius 
of the source is 1.5 ft.
The radius 
of the pond is 1.5 + 3 = 4.5 ft
Finally the area of the pond is equal to the area of the ring that is shown in the image
Answer:
<h2>
2x + 3y = 33 </h2>
Step-by-step explanation:
As we move from (-2, 5) to (1, 3), x increases by 3 and y decreases by 2.
Hence, the slope of this line is m = rise / run = -2/3.
Start with the slope-intercept form y = mx + b.
Substitute 3 for y and 1 for x and -2/3 for m:
3 = (-2/3)(1) + b.
Remove fractions by mult. all three terms by 3:
9 = -2 + b, so b = 11, and y = (-2/3)x + 11
Again, mult. all three terms by 3:
3y = -2x + 33, or, in standard form,
<h2>
2x + 3y = 33 </h2>
