Without graphing, classify the following system as independent, dependent, or inconsistent. y=-3x+4 and 6x+2y=8
1 answer:
Answer:
Dependent
Step-by-step explanation:
and
Lets solve the second equation for y and then substitute it in first equation
Subtract 6x on both sides
Divide by 2 on both sides
Now we plug it in first equation for y
Add 3x on both sides
Both sides are same, they are equal. the system has infinite solutions.
They are said to be dependent
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Answer:
Step-by-step explanation:
we know that
In the triangle abc
if
then
Because, the sum of the interior angles in a triangle must be equal to 180 degrees
therefore
Triangle abc is a right triangle
see the attached figure to better understand the problem
The sine of angle a is equal to divide the opposite side to angle a by the hypotenuse
so
The cosine of angle b is equal to divide the adjacent side to angle b by the hypotenuse
so
therefore
When two angles are complementary, the sine of one angle is equal to the cosine of the other angle and the cosine of one angle is equal to the sine of the other angle
so
The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)
The distance between both lighthouses is 5783.96 m
I've added an attachment that represents the scenario.
From the attachment, we have:
Convert to degrees
Convert to degrees
So, the measure of angle S is:
---- Sum of angles in a triangle
The required distance is distance AB
This is calculated using the following sine formula:
Where:
So, we have:
Make AB the subject
Hence, the distance between both lighthouses is 5783.96 m
Read more about bearing and distance at:
