The exact answer would be 167.09 so if you round the closest answer is D. $170
Answer:
Step-by-step explanation:
We have two conditions:
Bella: y = 25x + 60 = 25(10) + 60 = 250 + 60 = 310
Heather: y = 30x + 10 = 30(10) + 10 = 300 + 10 = 310
Answer:
11
Step-by-step explanation:
x+y=8 y=3
x+3=8
-3 -3
x=11
Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
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<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
