Answer:
Step-by-step explanation 1 and 4
To write the equation of a line, we use the equation: y = mx +b.
m is the slope of the line, which can be calculated using the equation:
m = (y2 - y1)/(x2 - x1)
We can choose any two points on the line to put into this equation. The red dots are at (0,0) and (-6,-2), so we will use those, but you would get the same answer by using any other pair of coordinates on the blue line.
m = (-2 - 0)/(-6 - 0) = 2/6 = 1/3
b is the y-intercept of the line. The y-intercept is the y-coordinate when the line crosses the y-axis. It crosses the y-axis at (0,0), so the y-intercept is 0.
Now, we plug our values back into the full equation to get the equation of the line.
y = mx + b
y = (1/3)x + 0
So the final answer is y = (1/3)x or y = x/3, depending on how you want to write it.
Answer:
1
Step-by-step explanation:
First, convert all the secants and cosecants to cosine and sine, respectively. Recall that
and
.
Thus:


Let's do the first part first: (Recall how to divide fractions)

For the second term:

So, all together: (same denominator; combine terms)

Note the numerator; it can be derived from the Pythagorean Identity:

Thus, we can substitute the numerator:

Everything simplifies to 1.
Answer:
Step-by-step explanation:
Sum
-2d + 1 + 6d + 4
Solving like terms
4d + 5
Difference
-2d + 1 - 6d - 4
-8d - 3
Let the measure of side AB be x, then, the measue of side AE is given by

.
Now, ABCD is a square of size x, thus the area of square ABCD is given by

Also, AEFG is a square of size

, thus, the area of square AEFG is given by

<span>The sum of the areas of the two squares ABCD and AEFG is given by

Therefore, </span>the number of square units in the sum of the areas of the two squares <span>ABCD and AEFG is 81 square units.</span>