Find an equation of the line that (a) has y-intercept of -8 and (b) is parallel to the line 6 x − 1 y = 7 6x-1y=7 . Write your a
1 answer:
Answer:
The equation of the line in the slope-intercept form is:
Step-by-step explanation:
The slope-intercept form of the equation of a line is
As y intercept is -8, we have
Since the line is parallel to , then it has the same slope.
Let's put this equation in form and find the slope
Thus, the slope is :
Now we can finish the equation of the line in the slope-intercept form
∵
, b = -8
Therefore, the equation of the line in the slope-intercept form is:
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Answer:
The area of the shaded region is about 58.9 square inches.
Step-by-step explanation:
To solve this question, let's recall some facts.
We know that the area of a circle can be defined as the following:
where r is the radius of the circle.
We too know that circles have a diameter and a radius. The diameter of a circle is the distance a line that connects two points on a circle with its center, and the radius is half of the diameter.
We also know that figures can touch each other, or be in tangent with each other. For the sake of simplicity, we're going to assume that the shaded circles are in tangent with each other, or touch each other. Because they touch each other, these three circles can share 5 in. of the 15 in. rectangle. This means that the circles are 5 in. in diameter, or 2.5 in in radius.
Now, we can solve the problem.
Because we have 3 circles, each with 2.5 in. radii, we can have the following expression which represents the total area of these circles:
After approximation, I can conclude that the area of the shaded region is 58.9 square inches.