Answer: radius = 5.83 cm height = 8.12 cm
<u>Step-by-step explanation:</u>
First, let's find the circumference of the 210° section of the circle.
The circumference of the the cone is . We can use this to find the radius .
When you fold the 210° section into a cone, the slant height is the original radius of 10. We can use the radius and slant height of the cone to form a right triangle with the height. Use the Pythagorean Theorem to find the height.
radius² + height² = slant height²
Answer:
2x − 9 and x + 6
Step-by-step explanation:
2x² + 3x − 54
Factor using the AC method.
2 × -54 = -108
Factors of -108 that add up to 3 are +12 and -9.
Divide by 2 and reduce: 12/2 = 6/1, -9/2 = -9/2.
Therefore, the factors are x + 6 and 2x − 9.
Answer:
24 and 25
Step-by-step explanation:
1/4 of 24 = 6
1/5 of 25 = 5
6 + 5 = 11
Part a.
An angle bisector divides the angle into two congruent angles.
m<FGH = m<HGI
2x - 4 = 3x - 22
Subtract 2x from both sides. Add 22 to both sides.
18 = x
x = 18
Now that we know x = 18,
m<FGH = 2x - 4 = 2(18) - 4 = 36 - 4 = 32
m<FGH = 32
Part b.
m<HGI = 3x - 22 = 3(18) - 22 = 54 - 22 = 32
m<HGI = 32
Part c.
m<FGI = m<FGH + m<HGI = 32 + 32 = 64
m<FGI = 64