Answer:
(3, 3 )
Step-by-step explanation:
Under a translation < 8, 0 > then
A(- 5, - 3 ) → (- 5 + 8, - 3 + 0 ) → (3, - 3 )
The line with equation y = 0 is the x- axis
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
(3, - 3 ) → (3, 3 )
Answer:
0.75 as a decimal for -3/4
I hope this helps
12.5 kilometers per liter
You would multiply the orignial price by (10%) converted to decimal to find the discount:
21 * 0.10
=2.10
Then, you subract the discount from the original price to see how much he paid:
21 - 2.10 = $18.90
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.
