Answer:
Theory
Step-by-step explanation:
The Perpendicular Bisectors in a triangle,(as the name suggests) perpendicularly bisect the sides of triangle
The point at where all 3 meet is called the Circumcenter
The distance of the Circumcenter from any vertex is same and is equal to circumradius(R)
If a circle is drawn with Circumcenter as center and R as radius, it circumscribes the triangle
The Angle Bisectors in a triangle, are dropped from the vertex to the opposite side.(as the name suggests) It bisects the angle at the vertex of the triangle.
The point at where all 3 meet is called The Incenter
The distance of the Incenter from any of the sides is same and is equal to Inradius(r)
If a circle is drawn with Incenter as center and r as radius,it inscribes the triangle
The angle bisector divides the side it intersects in the ratio of the ratio of other 2 sides
b.6/8
c.5/6
d.9/12
y > One-halfx + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded.
(–1, 3)
(0, 2)
(1, 2)
(2, –1)
(2, 2)
The ordered pairs which make both the inequalities true are (1, 2).
Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given two linear inequalities,
y < 5x + 2 and y > 1/2 x + 1
Consider y < 5x + 2.
(-1, 3) ⇒ 3 < -5 + 2 ⇒ 3 < -3, which is not true.
(0, 2) ⇒ 2 < 0 + 2 ⇒ 2 < 2, which is not true
(1, 2) ⇒ 2 < 5 + 2 ⇒ 2 < 7, which is true
(2, -1) ⇒ -1 < 10 + 2 ⇒ -1 < 12, which is true
(2, 2) ⇒ 2 < 10 + 2 ⇒ 2 < 12, which is true
Consider y > 1/2 x + 1.
Substitute the points which are true for first inequality in this one.
(1, 2) ⇒ 2 > 1/2 + 1 ⇒ 2 > 3/2, which is true
(2, -1) ⇒ -1 > 1 + 1 ⇒ -1 > 2, which is not true
(2, 2) ⇒ 2 > 1 + 1 ⇒ 2 > 2, which is not true.
Hence the point is (1, 2) which is true for both inequalities.
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Answer:
(0,2) and (1,2)
Step-by-step explanation: