Answer:
Move the decimal two times to the left and you get 1.5638
∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.
Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².
∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find
![\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm](https://tex.z-dn.net/?f=%5Csin%2830%5E%5Ccirc%29%20%3D%20%5Cdfrac%7Bh%7D%7B4%5C%2C%5Crm%20cm%7D%20%5Cimplies%20h%3D%202%5C%2C%5Crm%20cm)
where
is the length of the altitude originating from vertex O, and so
![\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%20b2%5Cright%29%5E2%20%2B%20h%5E2%20%3D%20%284%5C%2C%5Cmathrm%7Bcm%7D%29%5E2%20%5Cimplies%20b%20%3D%204%5Csqrt3%20%5C%2C%5Crm%20cm)
where
is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².
So, the total area of the shaded region is
(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²
dishwasher:
1200*0.15 = 180
1200-180 =$1,020
area:
middle section 6x6 = 36
left triangle 6*6*0.5 = 18
right triangle Area=base x height/2 = 6x6/2 = 18
36 +18 +18 =
72 in^2
The range of the possible values of x is:
x > 4
For the given triangle:
AB = 4x + 25
BC = 3x - 2
AC = 9x - 5
The sum of two of the sides of the triangle should be greater than the length of the third side
That is:
AC + BC > AB
9x - 5 + 3x - 2 > 4x + 25
12x - 7 > 4x + 25
Collect like terms
12x - 4x > 25 + 7
8x > 32
x > 32/8
x > 4
Therefore, the range of the possible values of x is:
x > 4
Learn more triangle theorems here: brainly.com/question/2102943
Answer:
1
Step-by-step explanation:
A coin only has two outcomes. Meaning that she has a 50/50 chance of landing on each side. So, 50% of 20 is 10. According to the theoretical probabilty, the coin would have landed on heads 10 times and tails 10 times. So, for that to be true Maria would have had to land on tails one more time.