In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
Answer:
The length of line segment FG is equal to the length of F'G'
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
Step-by-step explanation:
Given
CDEFG and C'D'E'F'G
Translation: 7 units up and 5 units left
Solving (a): Segment FG and F'G'
When a shape is translated, the resulting image will have the same lengths as the original image (i.e, translation does not change measurements)
Hence:

Solving (b): Perimeter CDEFG and C'D'EF'G'
In (a), we established that lengths do not change during translation;
Hence:
The perimeter of the CDEFG and C'D'EF'G' will remain the same
15)
20/8 = x / 6
x = 20 * 6 / 8
x = 15
16)
18/54 = (x+4)/75
1/3 = (x+4) / 75
3(x+4) = 75
3x + 12 = 75
3x = 63
x = 21
SF = 54/18
SF = 3
17)
complement angles sum = 90
90 /18 = 5
so
5 x 11 = 55
5 x 7 = 35
smaller angle = 35 degrees
18)
ratio 4:5:9
4+5+9 = 18
sum of interior angles of a triangle = 180
180 / 18 = 10
largest angle = 10 x 9 = 90
answer
largest angle = 90 degrees
The answer is a because i said so.
Answer: 7.5
Step-by-step explanation: i hope this helps have a nice day god bless