Answer:
r = 1/3
= 1
Step-by-step explanation:
1 + 1/3 + 1/9 + 1/27 + 1/ 81
In this series a is the first term = 1
r is the common ratio = 2nd term/1st term = 3rd term/ 2nd term
r = 1/3 ÷ 1 = 1/9 ÷ 1/3
r = 1/3
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<u>Given</u>:
Given that FGH is a right triangle. The sine of angle F is 0.53.
We need to determine the cosine of angle H.
<u>Cosine of angle H:</u>
Given that the sine of angle F is 0.53
This can be written as,

Applying the trigonometric ratio, we have;
----- (1)
Now, we shall determine the value of cosine of angle H.
Let us apply the trigonometric ratio
, we get;
----- (2)
Substituting the value from equation (1) in equation (2), we get;

Thus, the cosine of angle H is 0.53
Answer:



Step-by-step explanation:
Given

See attachment
Solving (a): 
To solve for
, we make use of:

The relationship between both angles is that they are complementary angles
Make
the subject

Substitute
for 


Solving (b): 
To solve for
, we make use of:
The relationship between both angles is that they are complementary angles

Solving (c): 
To solve for
, we make use of:

The relationship between both angles is that they are alternate exterior angles.
So:

The answer is that there are no solutions to the equations. They are parallel to each other and never cross. They can also be called inconsistent
If we need our line to pass through point C, then we have to use the x and coordinates of point C in our new equation. If that line is to be perpendicular to AB, we also need to find the slope of AB and then take its opposite reciprocal. First things first. Point C lies at (6, 4) so we will use x = 6 and y = 4 in our equation in a bit. The coordinates of A are (-2, 4) and the coordinates of B are (2, -8) so the slope between them is

which is -3. The opposite reciprocal of -3 is 1/3. That's the slope we will use along with the points from C to write the new equation. We will do this by plugging in x, y, and m (slope) into the slope-intercept form of a line and solve for b.

and 4 = 2 + b. So b = 2. That's the y-intercept, the point on the y axis where the line goes through when x is 0. Therefore, the point you're looking for is (0, 2).