A student submitted the following answer to the graphing systems problem:
1 answer:
Answer: No, she is not correct.
Step-by-step explanation:
Since we have given that
First we check the consistency of system of equations:
here ,
so, it becomes,
So, it is consistent and it is an intersecting lines.
So, it would have a unique solution.
From Eq(1), we have,
Put it in eq(2), we have
So, x=4 and
so, the solution point of this line will be (4,12).
No, she is not correct.
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Answer:
5 cm
Step-by-step explanation:
If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.
If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.
Consider two right triangles ABO and ACO. In these triangles:
- AO is common hypotenuse;
- ∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;
- OB=OC as radii of the circle k(O).
By HL theorem, triangles ABO and ACO are congruent. Then
- ∠OAB=∠OAC=30°;
- AC=AB=5 cm.
Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.
Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus
∠CBA=∠BCA=1/2(180°-60°)=60°.
Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.
