Circle D circumscribes ABC and ABE. Which statements about the triangles are true?
1 answer:
The true statements about these triangles are: B. I and II.
<h3>How to identify the true statements?</h3>Based on the diagram (see attachment), we can logically deduce the following points in accordance with circle theorem:
- The tangents drawn from a point out side the circle are the same (equal).
- The perpendicular bisectors of triangle ABC would have an intersection at the same point (center D) as those of triangle ABE.
- The distance from point C to point D is the same as the distance from point D to point E i.e CD = DE since both are radii of the circle.
In conclusion, we can logically deduce that the true statements about these triangles are I and II only.
Read more on perpendicular bisectors here: brainly.com/question/16965212
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Answer:
The system of linear equations has infinitely many solutions
Step-by-step explanation:
Let's modified the equations and find the answer.
Using the first equation:
we can multiply by 2 in both sides, obtaining:
which can by simplified as:
which is equal to:
Considering the second equation:
Taking into account that from the first equation we know that: , we can express the second equation as:
, which can be simplified as:
Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:
if
This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.
For example, if k=0 then
which give us y=-4, and, because:
if y=-4 then
Now let's try with k=-1, then:
which give us y=-8, and, because:
if y=-8 then
.
Then, the system of linear equations has infinitely many solutions