Answer:
The value of the new volume 'x' would be equal to 40.5 cm³.
Step-by-step explanation:
Given
- Dilation by a factor scale of 3/2.
We can determine the volume of the original prism by multiplying the area of the base by the height,
volume = (3 cm²)(4 cm) = 12 cm³
Dilation by a factor of 3/2 means that the dimensions of the new prism is 3/2 times that of the original object.
let 'x' be the volume of the new solid,
![\frac{x}{12}=\left(\frac{3}{2}\right)^3](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B12%7D%3D%5Cleft%28%5Cfrac%7B3%7D%7B2%7D%5Cright%29%5E3)
![\frac{x}{12}=\frac{27}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B12%7D%3D%5Cfrac%7B27%7D%7B8%7D)
Multiply both sides by 12
![\frac{12x}{12}=\frac{27\cdot \:12}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B12%7D%3D%5Cfrac%7B27%5Ccdot%20%5C%3A12%7D%7B8%7D)
![x=\frac{81}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B81%7D%7B2%7D)
cm³
Therefore, the value of the new volume 'x' would be equal to 40.5 cm³.
Answer:
m=-5
Step-by-step explanation:
You first do distributive property:
(-m*-1)+(-1*-7)+(-3*4m)+(-3*-3)=71
that simplifies to:
16-11m=71
Next subtract 16 on both sides and you get:
-11m=55
Then divide by -11,
m=-5
Look at the attachment. Hope it helps!
Answer:
Step-by-step explanation:
Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.