12. the change in temperature is -1 C. -3 C + -1 C= -4 C
13. The net gain. Lin gained 14 yards, then loss 7 yards, and lastly gained 9 yards
14 + (-7) + 9= 16 yards
14. Pythagoras was born 582 BC. Newton 1643 AD
1643-582= 1,061 years
15. Sonny has $75 but he needs to buy something costs $93
he needs to borrow $18.
93-75= $18
Answer:
$28
Step-by-step explanation:
The markup was 0.40×$20 = $8, so the new price is ...
$20 +8 = $28
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 LCD of 24 and 23 is 552, so 276/552 - 240/552 = 36. After simplifying 36/552, you get 3/46 and that is your answer.
The answer is 412,987
I hope this helps :)
