Answer:
<em>The volume of the cube is </em>
<em>cu in.</em>
Step-by-step explanation:
<u>The Volume of a Cube</u>
Let's have a cube of side length a. The volume of the cube is:
![V=a^3](https://tex.z-dn.net/?f=V%3Da%5E3)
The cube of the image has a side length of
![\displaystyle a=\frac{3x^{-3}}{z}\ inches](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Cfrac%7B3x%5E%7B-3%7D%7D%7Bz%7D%5C%20inches)
Simplifying the expression of the base by converting the negative exponent in the numerator to the denominator:
![\displaystyle a=\frac{3}{zx^{3}}\ inches](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Cfrac%7B3%7D%7Bzx%5E%7B3%7D%7D%5C%20inches)
Now find the volume:
![\displaystyle V=\left(\frac{3}{zx^{3}}\ inches\right)^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cleft%28%5Cfrac%7B3%7D%7Bzx%5E%7B3%7D%7D%5C%20inches%5Cright%29%5E3)
Applying the exponents:
![\displaystyle V=\frac{3^3}{z^3x^{9}}\ inches^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B3%5E3%7D%7Bz%5E3x%5E%7B9%7D%7D%5C%20inches%5E3)
![\displaystyle V=\frac{27}{z^3x^{9}}\ inches^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B27%7D%7Bz%5E3x%5E%7B9%7D%7D%5C%20inches%5E3)
The volume of the cube is
cu in.
Answer:
Option A.
Step-by-step explanation:
Properties of the similarity of two polygons,
1). All angles of one polygon will be equal to the angles of the other polygon.
2). Their corresponding sides will be in the same ratio.
If the measures of corresponding angles of KLMN and ABCD are equal, but the lengths of the corresponding sides of ABCD are half those of KLMN,
Then the polygons ABCD and KLMN will be similar.
Option A will be the answer.
![Amy=n](https://tex.z-dn.net/?f=Amy%3Dn)
![Chris=n+18](https://tex.z-dn.net/?f=Chris%3Dn%2B18)
Mean:
![45= \frac{(n)+(n+18)}{2}](https://tex.z-dn.net/?f=45%3D%20%5Cfrac%7B%28n%29%2B%28n%2B18%29%7D%7B2%7D%20)
So,
![45=n+9](https://tex.z-dn.net/?f=45%3Dn%2B9)
Therefore,
![n=36](https://tex.z-dn.net/?f=n%3D36)
![Amy=n=36pounds](https://tex.z-dn.net/?f=Amy%3Dn%3D36pounds)
![Chris=n+18=54pounds](https://tex.z-dn.net/?f=Chris%3Dn%2B18%3D54pounds)
Hope I helped :)
(Sorry I was late for you other question)
Step 1
find the total volume of the fish tank
volume of a rectangular prism=51*39*28----> 55692 cm³
step 2
find the 95% of the volume of the tank fish
95%=55692 cm³*.95-----> 52907.40 cm³
step 3
find the 5% of the volume of the tank fish
5%=55692*0.05----> 2784.6 cm³
or
55692-52907.4=2784.6 cm³
step 4
find the volume of the log
volume of a cylinder=pi*r²*h
r=5 cm
h=44 cm
volume of a cylinder=pi*5²*44-----> 3454 cm³
step 5
<span>water spills out of the tank=volume of the log-volume of the 5% of the tank
</span>water spills out of the tank=3454 cm³-2784.6 cm³-----> 669.40 cm³
the answer is
669.40 cm³
Answer:
#4: -18xy^3z * sqrt(z)
#5: 24xy^3 * sqrt 3(x^2)
Step-by-step explanation:
#4: -2*sqrt(9^2 * x^2 * y^2 * y^2 * y^2 * z^2 * z)
You can cancel if there is a number sqaured
-2 * 9 * x * y * y * y * z * sqrt(z)
-18xy^3z * sqrt(z)
#5: 6 * sqrt 3( 4^3 * x^3 * x^2 * (y^3)^3 )
You can cancel if the number is cubed.
6 * 4 * x * y^3 * sqrt 3( x^2 )
24xy^3 * sqrt 3(x^2)