Answer:
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-(-1))/(-2-4)
m=(3+1)/-6
m=4/-6
simplify
m=-2/3
y-y1=m(x-x1)
y-(-1)=-2/3(x-4)
y+1=-2/3(x-4)
y+1=-2/3x+8/3
y=-2/3x+8/3-1
y=-2/3x+8/3-3/3
y=-2/3x+5/3
y-(-2/3x)=5/3
y+2/3x=5/3
2/3x+y=5/3
3(2/3x+y)=3(5/3)
2x+3y=5
2x+3y-5=0
Answer:
Step-by-step explanation:
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
10 square centimeters.
Step-by-step explanation:
The area of a rectangle=base*height. 5*2=10 square centimeters.
Answer:
6/15
Step-by-step explanation:
draw a tree diagram.
the only path with no white is highlighted
multiply them
2/3 x 3/5 = 6/15
