This is a circle with the radii forming a piece of pizza that is the sector, and the chord goes from the endpoint of one radii to the endpoint of the other radii which is the base of a triangle that uses the radii as sides. So we have to find the area of the sector and then subtract from it the area of the triangle, leaving the area between the segment and the outside of the circle. For the area of the sector...we need the central angle. if we look to the triangle that is formed with the chord and the 2 radii, we see that all the sides of that triangle measure 8". If all the sides are the same, by the converse of the Isosceles Triangle Theorem, then all the angles are the same measure as well. This means that this is an equiangular triangle and all the angles measure 60 degrees (by the Triangle Angl-sum Theorem all the angles of a triangle add up to equal 180). So the central angle is 60. Our formula for the sector then is this: which simplifies to . Now we will go to the triangle formed by the chord and the 2 radii. The formula for a triangle is . We know the base is 8. That was given to us as the measure of the chord. The height, however, is a different story. If we extract this triangle and drop an altitude from the vertex angle to the base, that is the height we are looking for the h in our formula. If all the angles of the whole triangle are 60 degrees, when we drop the altitude, we are cutting that vertex angle exactly in half. So half of our whole triangle is a 30-60-90 triangle, with the base angle as 60 degrees. The side across from the 60 degree angle in the Pythagorean triple is the square root of 3. So filling in our formula for the area we have which simplifies down to . Now go back to the beginning where we said that the area of that little bit of the circle between the chord and the outside of the circle was found by subtracting the area of the triangle from the area of the sector. Leaving it in the form in which you need it looks like this: . There you go!
Answer: C
Step-by-step explanation:
Given
Nancy bought the bag with 1100 beads to make necklaces
She found another bag with 700 beads
So, the total number of beads is the sum of two i.e. 1800 beads
It takes 50 beads per necklace
The number of necklaces that can be formed is
Answer:
20 miles
Step-by-step explanation:
Let x = amount charge each mile
y = total price paid
Since the Uber charged $1.10 for each mile, we multiply x by 1.1 like this 1.1x
Also, $2 were already charged so we add 2 to the total price
y = 1.1x + 2
Since the Lyft charged $0.95 for each mile, we multiply x by 0.95 like this 0.95x
Also, $5 were arleady charged so we add 5 to the total price
y = 0.95x + 5
We have to find a price where both rides match
1.1x + 2 = 0.95x + 5
Let's move the like terms to one side by subtracting 0.95x from both sides
1.1x + 2 = 0.95x + 5
-0.95x -0.95x
0.15x + 2 = 5
Now, subtract 2 from both sides
0.15x + 2 = 5
- 2 - 2
0.15x = 3
Finally, divide both sides by the coefficient, 0.15, to isolate the variable, x
0.15x/0.15 = 3/0.15
x = 20
This means they traveled 20 miles if they were to pay the same price
The total length of line segment FH = 140
We have a line segment FH and G is its midpoint such that - FG = 14x + 25 and GH = 73 – 2x.
We have to find FH.
<h3>What is Line Segment?</h3>
A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
According to question, we have -
FG = 14x + 25.
GH = 73 – 2x.
Since, G is the midpoint of line FH, therefore -
FG = GH
Now -
FG = GH
14x + 25 = 73 – 2x
14x + 2x = 73 - 25
16x = 48
x = 3
Therefore, the total length of the Line segment is -
FG + GH = 14x + 25 + 73 – 2x
Substitute x = 3, we get -
FH = 14 x 3 + 25 + 73 - 2 x 3 = 73 + 67 = 140
Hence. the total length of line segment FH = 140
To solve more questions on Lines and Lengths, visit the link below -
brainly.com/question/16345328
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