9514 1404 393
Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
__
The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
__
The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Answer:
The coordinates are (50, 103)
Step-by-step explanation:
The three hallways are AB, BC, CD.
The co-ordinate of D is (50, 75).
The school's flagpole is 28 meters right of the point D.
Hence the y-coordinate for the flagpole will be same as D, that is 75.
The x-coordinate will be (28 + 75) = 103.
The location of the school's flagpole will be represented by (50, 103)
No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.
<h3>When are Two Lines Proven to be Parallel to each other?</h3>
Two lines that are cut across by a transversal can be proven to be parallel to each other if:
- The alternate interior angles along the transversal and on the two lines are congruent [alternate interior angles theorem].
- The alternate exterior angles along the transversal and on the two lines are congruent [alternate exterior angles theorem].
- The same-side interior angles along the transversal and on the two lines are supplementary [same-side interior angles theorem].
- The corresponding angles along the transversal and on the two lines are congruent [corresponding angles theorem].
Thus, given the following information:
m∠2 = 115°
m∠15 = 115°
With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.
In summary, we can conclude that:
D. None of the options are correct.
Learn more about the Parallel lines on:
brainly.com/question/16742265
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Answer:
angle bisectors
Step-by-step explanation:
The incentre is where a triangle's three angle bisectors intersect ( an angle bisector is a ray that cuts an angle in half ). The incentre is the centre of a triangle drawn inside the triangle.
Answer:
(-1.5, 3.275)
Step-by-step explanation:
midpoint = ( x1+X2/2 , y1+y2/2)
=(0+(-3)/2, 0.55+6/2)
=( -3/2, 6.55/2)
=( -1.5, 3.275)
