Answer:
1/6
Step-by-step explanation:
The product will only be of the required form if the two chosen factors are of the form (x +by) and (x -by).
For the factor (x+y), there is also a factor (x-y) on the list. For the factor (x+5y), there is no factor (x-5y) available.
So, of the (4·3)/2 = 6 possible ways to choose two expressions from the four given expressions, only one pair of the 6 will have a product of the required form.
The probability is 1/6.
For similar triangles, the ratio of the corresponding sides are equal. To determine the common ratio, we take the square root of the ratio of the given areas.
ratio = sqrt (384 / 1057)
ratio = 384/1057
Then, for the volume, we have to cube the ratio calculated above. If we let x be the value of the volume of the smaller solid.
(384/1057)^3 = x/1795
x = 86 yd
Thus, the volume of the smaller figure is 86 yd³.
72 divides by 9 is 8 so 2 times 8 is sixteen so that would be the answer
4.) The lateral area of a figure is the area of the figure with the exception of the bases.
Given a prism with right triangle bases, the lateral area of the prism is the sum of the areas of the rectangles making up the prism.
This is given by
Lateral area = (8.94)(41) + (4)(41) + (8)(41) = 366.54 + 164 + 328 = 858.54 ≈ 859 m^2
The surface area is the sum of the bases plus the lateral area. The area of a rectangle is given by half base times height.
Surface area = 1/2 x 8 x 4 + 1/2 x 8 x 4 + 859 = 16 + 16 + 859 = 891 m^2
5.) The surface area of a cylinder is given by pi r^2h where r is the radius = 12 inches and h is the height = 17 inches.
Surface area = π x (12)^2 x 17 = 2,448π = 7,690.62 in^2 ≈ 7,691 in^2
