The volume of the dilated cube is 
Explanation:
The volume of the cube is 
It is given that the cube is dilated by a factor of 5.
We need to determine the volume of the dilated cube.
Since, we know that the dilation is a transformation that changes the size of the image but not the shape.
Since, it is given that the volume of the cube is dilated by a factor of 5, the length of the image will be 5 times greater, the width of the image will be 5 times greater and the height of the image will be times greater than the original image.
Thus, the volume of the dilated cube is given by,
Thus, the volume of the dilated cube is
Answer:
The answer to your question is: the last option
Step-by-step explanation:
m² - 6m + 6m -36
Simplify like terms m² - 36
Factor (difference of squares) (m + 6) (m - 6)
X = 3 + bi
|x| = √(3² + b²)
|x| = √(9 + b²) ..............(a)
But from the question |x|² = 13
|x| = √13
Substitute this into equation (a)
|x| = √(9 + b²) ..............(a)
√13 = √(9 + b²)
13 = 9 + b²
9 + b² = 13
b² = 13 - 9
b² = 4
b = √4
b = + or - 2
Possible value of b is +2 or - 2.
Cheers!
Check the picture below.
let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.
running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".
now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.
![\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Ddp~~%20%5Cbegin%7Bcases%7D%20d%3Dapothem%5C%5C%20p%3Dperimeter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20d%3D2%5Csqrt%7B3%7D%5C%5C%20p%3D24%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%282%5Csqrt%7B3%7D%29%2824%29%5Cimplies%20A%3D24%5Csqrt%7B3%7D)
Change = new value - original value
Amount of Change = 21 - 15 = 6
Now, you'd want to divide the change by the original value.
6/15 = 0.4
0.4 = 40%
The percent change is 40% increase.
Hope this helped!
