Step 1
<u>Find the slope of the given line</u>
we have

Isolate the variable y
Subtract
both sides


Divide by
both sides

the slope of the given line is

Step 2
Find the equation of the line that passes through the point
and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to

we have

substitute in the equation


or 
therefore
<u>the answer is</u>
or

Equation of circle is (x - a)^2 + (y - b)^2 = r^2; where (a, b) is the center and r is the radius.
r^2 = (2 - 3)^2 + (-1 - 4)^2 = (-1)^2 + (-5)^2 = 1 + 25 = 26
Equation is (x - 2)^2 + (y + 1)^2 = 26
30 x 30........................
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function
as compared to the graph of
.
We can write our transformed function as:


Now let us compare our transformed function with parent function.
Let us see rules of transformation.
,
,
Scaling of a function: 
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Answer:

Step-by-step explanation:
Given that:

for 
That means, angle
is in the 3rd quadrant.
To find:
Value of cot(t)
Solution:
First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.
In 3rd quadrant, tangent and cotangent are positive.
All other trigonometric ratios are negative.
Let us have a look at the following identity:

here, 
So, 

But, angle
is in 3rd quadrant, so value of
