Which of these describes the equation –18x + 9y = –416?
2 answers:
Answer:
We conclude the equation is linear because it can be rewritten in the form .
Hence, option D is correct.
Step-by-step explanation:
The slope-intercept form of the line or linear equation
where
is the slope
is the y-intercept
<u>Important Tip:</u>
The graph of a linear equation is always a straight line.
Convert the given equation in the slope-intercept form
subtract 18x from both sides
simplify
divide both sides by 9
Now, comparing the equation with a slop-intercept form of linear equation
- The slope m = -2
- The y-intercept b = -416/9
Therefore, we conclude the equation is linear because it can be rewritten in the form .
From the attached graph, is also clear that the graph of the equation is a straight line.
Hence, option D is correct.
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Area of a regular polygon = 1/2 x apothem x perimeter
We know that each side is 10, because if you draw a segment from the center to a vertex it creates a 30-60-90 triangle (those are the angles). This type of triangle has a ratio for its sides where the longer side is radical three times as long as the shorter leg. This shorter leg happens to be half of a side of the polygon. Knowing that the polygon has 6 sides, we can multiply 10 by 6 to get the perimeter.
Area of polygon = 1/2 x apothem x perimeter = 1/2 x 5
x 60
=30 x 5
= 30 x 5 x <span>1.73205080757
= 150 x </span><span>1.73205080757
= </span><span>259.807621135
To the nearest tenth of a cm, the area of the polygon is 260 cm squared</span>
We know that each side is 10, because if you draw a segment from the center to a vertex it creates a 30-60-90 triangle (those are the angles). This type of triangle has a ratio for its sides where the longer side is radical three times as long as the shorter leg. This shorter leg happens to be half of a side of the polygon. Knowing that the polygon has 6 sides, we can multiply 10 by 6 to get the perimeter.
Area of polygon = 1/2 x apothem x perimeter = 1/2 x 5
=30 x 5
= 30 x 5 x <span>1.73205080757
= 150 x </span><span>1.73205080757
= </span><span>259.807621135
To the nearest tenth of a cm, the area of the polygon is 260 cm squared</span>