Answer:
![\large\boxed{\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}=-\dfrac{1}{5}a^5b^4=-\dfrac{a^5b^4}{5}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cdfrac%7B-3a%5E%7B-2%7Db%5E3%7D%7B15a%5E%7B-7%7Db%5E%7B-1%7D%7D%3D-%5Cdfrac%7B1%7D%7B5%7Da%5E5b%5E4%3D-%5Cdfrac%7Ba%5E5b%5E4%7D%7B5%7D%7D)
Step-by-step explanation:
![\dfrac{-3a^{-2}b^3}{15a^{-7}b^{-1}}=\dfrac{-3}{15}\cdot \dfrac{a^{-2}}{a^{-7}}\cdot\dfrac{b^3}{b^{-1}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=-\dfrac{3\!\!\!\!\diagup^1}{15\!\!\!\!\!\diagup_5}\cdot a^{-2-(-7)}\cdot b^{3-(-1)}=-\dfrac{1}{5}a^{-2+7}b^{3+1}=-\dfrac{1}{5}a^5b^4](https://tex.z-dn.net/?f=%5Cdfrac%7B-3a%5E%7B-2%7Db%5E3%7D%7B15a%5E%7B-7%7Db%5E%7B-1%7D%7D%3D%5Cdfrac%7B-3%7D%7B15%7D%5Ccdot%20%5Cdfrac%7Ba%5E%7B-2%7D%7D%7Ba%5E%7B-7%7D%7D%5Ccdot%5Cdfrac%7Bb%5E3%7D%7Bb%5E%7B-1%7D%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Cdfrac%7Bx%5En%7D%7Bx%5Em%7D%3Dx%5E%7Bn-m%7D%5C%5C%5C%5C%3D-%5Cdfrac%7B3%5C%21%5C%21%5C%21%5C%21%5Cdiagup%5E1%7D%7B15%5C%21%5C%21%5C%21%5C%21%5C%21%5Cdiagup_5%7D%5Ccdot%20a%5E%7B-2-%28-7%29%7D%5Ccdot%20b%5E%7B3-%28-1%29%7D%3D-%5Cdfrac%7B1%7D%7B5%7Da%5E%7B-2%2B7%7Db%5E%7B3%2B1%7D%3D-%5Cdfrac%7B1%7D%7B5%7Da%5E5b%5E4)
3x+21-12=8x-28
collect the like terms
3x-8x=-28(21-12=9)
-5x=-28-9
-5x=-37
x=7.4
The constant of proportionality will be same as the slope of the line. Let's take two points from the line: (0,0) and (1,2)
The slope for a line that passes through two points
and
is:
![\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute the two points into this formula for slope and we have:
![=\dfrac{2-0}{1-0}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2-0%7D%7B1-0%7D)
After solving and simplifying, we get
![=2](https://tex.z-dn.net/?f=%3D2)
Thus, the slope of the line is 2. This means that the constant of proportionality is 2. Let me know if you need any clarifications, thanks!
~ Padoru
Answer:
Step-by-step explanation:
integer or rational. All rational numbers can be expressed as a fraction. After the division is performed, you get an integer. (-15)
I would answer it is a rational number.
Answer:
Third and fourth statement are true ("There are 7 unit cubes..." and "The volume of the prism can be found by 12x3..."). The rest are untrue.
Step-by-step explanation:
No.Middle layer has (2+3) five cubes, not seven.
No. Bottom layer has (2+3+4) nine cubes, the middle layer has five and the top has two. In total, this is sixteen cubes, not nine.
Yes. You can see 9 cubes and there are 16 total, so yes, seven are hidden from view.
Yes. Volume can also be found by multiplying length by width by depth, which is 4x3x3=12x3=36.
No. The volume of the prism is 36. There are 16 cubes. 16 is not half of 36.