Answer:
B. 8x - 3
C. 8x + 12
Step-by-step explanation:
64 is a perfect square, meaning it has two factors that are identical (8), and 36 is also a perfect square, but in this case, you don't see two 6's in the answer choices.
12 and -3 give you a product of -36, so your answer choices would be:
(8x - 3) (8x + 12)
If you're unsure, you can multiply them together to check if they come out to the unfactorized expression.
There are 4 possibilities out of the 36 ways the dice can land:
... (3, 3), (3, 6), (6, 3), (6, 6)
Hence, the probability of an outcome in this set is 4/36 = 1/9.
Answer:
The length of the sloping section of the ramp is 20.12 m
Step-by-step explanation:
Given;
the total height of the bank, h = 2.8 m
The slope of the ramp must be 8° to the horizontal, i.e, θ = 8°
Let the length of the sloping section = L
let the horizontal distance between the height of the bank and sloping section = b
Thus, h, L and b forms three sides of a right angled-triangle, with L as the hypotenuse side, h (height of the triangle) as the opposite side and b (base of the triangle) as the adjacent side.
We determine L by applying the following formula;
Sinθ = opposite / hypotenuse
Sin θ = h / L
L = h / Sin θ
L = 2.8 / Sin 8
L = 2.8 / 0.13917
L = 20.12 m
Therefore, the length of the sloping section of the ramp is 20.12 m
So... let's say the smaller regular octagon has sides of "x" long, then the larger octagon will have sides of 5x.
![\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bratio%20relations%7D%0A%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccllll%7D%0A%26Sides%26Area%26Volume%5C%5C%0A%26-----%26-----%26-----%5C%5C%0A%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%26%5Ccfrac%7Bs%7D%7Bs%7D%26%5Ccfrac%7Bs%5E2%7D%7Bs%5E2%7D%26%5Ccfrac%7Bs%5E3%7D%7Bs%5E3%7D%0A%5Cend%7Barray%7D%20%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
