Answer:
D
Step-by-step explanation: All the numbers have to be less than 7 but greater than -45
Answer:
The answer is −a^4 + 5a^3b + 2a^3c − 4a^2b^2 − 10a^2bc − a^2c^2 + 8ab^2c + 5abc^2 − 4b^2c^2 / −a^4 + 2a^3b + 2a^3c − a^2b^2 − 4a^2bc − a^2c^2 + 2ab^2c + 2abc^2 − b^2c^2
Step-by-step explanation:
This the equation being simplified
<span>the coordinates of vertex A = (1,1)
</span><span>the coordinates of vertex B = (2,3)
</span><span>the coordinates of vertex C = (2,1)
</span>
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.
the answer is c you just have to solve each one
