Answer:
+ 16
Step-by-step explanation:
x² - 8x = - 10
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + (- 4) = - 10 + (- 4)²
x² - 8x + 16 = - 10 + 16
thus 16 is added to both sides to complete the square
2x - 3y = 7 and -3x + y = 7..multiply Equation 2 by THREE and add to Equation 1
-9x + 3y = 21...........................watch the y's disappear
-7x........ = 28
x = -4
substitute -4 instead of x in either of the ORIGINAL equations
2x - 3y = 7
2(-4) - 3y = 7
-8 -3y = 7..........add 8 to both sides
-3y = 15
y = -5
im not sure
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.
Two solutions exist,
2(x - 1) = 8
2x - 2 = 8
2x = 10
x = 5
&
2(x + 1) = 8
2x + 2 = 8
2x = 6
x = 3
the two solutions are 5 and 3
