They are both 8 spaces away from 0 in opposite directions.
Answer:
a. 29.3 units²
Step-by-step explanation:
The area of a circle is A = πr².
The area of each triangle is A = ½bh.
The vertex angle of each triangle is 360/5 = 72°. If we cut the triangle in half, we can use trig to write:
sin 36° = (½b) / r
b = 2r sin 36°
And:
cos 36° = h / r
h = r cos 36°
Substituting, we get the area of each triangle is:
A = r² sin 36° cos 36°
A = ½ r² sin 72°
The radius of the circle is 8. So the area of the circle minus the area of the 5 triangles is:
A = π (8)² − 5 (½) (8)² (sin 72°)
A ≈ 48.9 units²
Three fifths of the area is shaded, so:
⅗ A ≈ 29.3
A + b + c = 180
a = 2b
b = c + 4
Substitute the b equation into the a equation
a = 2(c + 4)
a = 2c + 8
Substitute equations a and b into the first equation
2c + 8 + c + 4 + c = 180
4c = 168
c = 42
Find the other angles using c
b = 42 + 4
b = 46
a = 2(42) + 8
a = 92
Therefore angle a is 92 degrees, angle b is 46 degrees, and angle c is 42 degrees.
Answer:
(7/15,−13/5)
Equation Form:
x=7/15,y=−13/5
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.