Answer:
10 and 12
Step-by-step explanation:
let the consecutive even integers be n and n + 2 , then
n² - 64 = 3(n + 2) ← distribute parenthesis
n² - 64 = 3n + 6 ( subtract 3n + 6 from both sides )
n² - 3n - 70 = 0 ← in standard form
(n - 10)(n + 7) = 0 ← in factored form
Equate each factor to zero and solve for n
n - 10 = 0 ⇒ n = 10
n + 7 = 0 ⇒ n = - 7
Since n must be a positive even integer then n = 10 and n + 2 = 10 + 2 = 12
The 2 numbers are 10 and 12
Answer:
Charlie should use a stopwatch with minutes and seconds
Step-by-step explanation:
charlie should not count in his head as it is not accurate, he could count too fast or slow
Charlie should not look at that clock and the seconds will affect the 25 minutes, whether it be less or more
Charlie should not use an hourglass as he might flip it over too soon or quick and it's not very accurate
therefore using the stopwatch allows him to accurately and fairly keep track of the exact time
16 times 4 equals to 64. 64 is simply 4 sets of 16 added together.
Other factors of 64 include, 1,2,4,8,16,32, and 64.
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.
Answer:
The answer would be X=24
Step-by-step explanation:
Y is multiplied by 3 to get the answer 30. Because they are varied directly you have to multiply the 8 by 3 to get your answer!
-Hope this helps-
~Bai~
