Answer:
Central angle = θ = 2.5 radians
Step-by-step explanation:
The radian measure of central angle is given by
Where s is the arc length, r is the radius of circle and θ is angle in radians
We are given an arc length of 5 units
We are given radius of 2 units
Therefore, the central angle in radians is
Bonus:
Radian is a unit which we use to measure angles.
1 Radian is the angle that results in an arc having a length equal to the radius.
Degree is another unit that we use to measure angles.
There are 360° in a circle.
There are 2π radians in a circle.
Answer:
7x²-3x
Step-by-step explanation:
What is the are of the shaded region. The inner square is a width of x and a length of x+7. The outer square is a length of 4x and a width of 2x + 1.
Area of a square = Length * Length
Area of the inner square = x (x+7)
Area of the inner square = x²+7x
Area of the outer square = 4x(2x+1)
Area of the outer square = 8x²+4x
Area of the shaded region = Area of outer square - Area of inner square
Area of the shaded region = (8x²+4x)-(x²+7x)
Area of the shaded region = 8x²+4x-x²-7x
Area of the shaded region = 7x²-3x
This gives the area of the shaded region
<h3>
Answer: 60 muffins</h3>
=========================================================
Explanation:
x = some positive whole number
2x = amount Helen baked initially
5x = amount Rebecca baked initially
Notice that the ratio 2x:5x reduces to 2:5 after dividing both parts by x.
So (2x)/(5x) = 2/5
Helen then bakes another 12 muffins, bumping the 2x up to 2x+12. The ratio is now 1:2, which means,
(amount Helen bakes)/(amount Rebecca bakes) = 1/2
(2x+12)/(5x) = 1/2
2(2x+12) = 5x*1 .... cross multiply
4x+24 = 5x
24 = 5x-4x
24 = x
x = 24
From here, we then can say,
- Helen = 2x+12 = 2*24+12 = 48+12 = 60
- Rebecca = 5x = 5*24 = 120
Helen baked 60 muffins and Rebecca baked 120 muffins. We see that 60:120 reduces to 1:2 after dividing both parts by the GCF 60.
Furthermore, note how
- 2x = 2*24 = 48
- 5x = 5*24 = 120
- 48:120 reduces to 2:5 after dividing both parts by 24
This helps confirm we have the correct answer.
833
Seravalle____________Chiesanuova______________San Marino
|---------------------------------------------------------------------|
982
so the distance from Chiesanuova to Serravalle is :
982 - 833 = 149 miles <==
Answer:
(x-4) (x-3) (x+3)
Step-by-step explanation:
x^3 - 4x^2 - 9x + 36
Make 2 groups
x^3 - 4x^2 - 9x + 36
We can factor out x^2 from the first group and -9 from the second group
x^2 (x-4) - 9(x-4)
Now factor out (x-4)
(x-4) (x^2 -9)
This may be an answer choice but we can still factor
(x^2 -9) is the difference of squares
(x^2-9) = (x-3) (x+3)
Replacing this
(x-4) (x-3) (x+3)