Choose the system of equations that matches the following graph:
2 answers:
Answer:
C. and
Step-by-step explanation:
We are given the graph of the system of equations given by,
.
After simplifying the equations, we get,
i.e.
i.e.
i.e.
And,
i.e.
i.e.
or
Hence, we get the system of equations,
and
Now, we will check the point of intersection of the new equations,
Multiplying first equation by 7 and second equation by 2 and then subtracting both equations,
We get,
gives
i.e. y = -3
So, 2x-4y=0 gives 2x-4×(-3)=0 i.e. 2x=-12 i.e. x= -6
Thus, the intersection point is (-6,-3).
So, the new system of equation matches the graph.
Hence, option C is correct.
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Check the picture below.
we know that AL is an angle bisector, so the angle at A gets cuts into two equal halves, we also know the angle at B is 30°, so the triangle ABC is really a 30-60-90 triangle, meaning the angle at A is really a 60° angle, cut in two halves gives us 30° and 30° as you see in the picture.
if the angles at A and B, inside the triangle ABL, are equal, twin angles are only made in an isosceles by twin sides, that means that AL = BL.
Looking at the triangle ALC, we can see is also another 30-60-90 triangle, and we can just use the 30-60-90 rule to get x=CL.
