Answer:
True
Step-by-step explanation:
(6³ * 3³)² = 18⁶
Multiply inside the parenthesis.
(18³)² = 18⁶
When you put powers to powers, they multiply, eg:
(x³)⁴ = x³°⁴ = x¹²
18⁶ = 18⁶
True.
Answer:
2w - 13
Step-by-step explanation:
here we just simplify the expression,
3w - 4 - w - 9
becomes:
2w - 13
Answer:
![\boxed{ \ - \frac{3}{45} }](https://tex.z-dn.net/?f=%20%20%5Cboxed%7B%20%5C%20-%20%20%5Cfrac%7B3%7D%7B45%7D%20%7D)
Step-by-step explanation:
10 3/9 - 10 2/5
we need to convert mixed fractions to improper fractions
![10 \frac{3}{9} = \frac{10 \times 9 + 3}{9} = \frac{93}{9}](https://tex.z-dn.net/?f=10%20%5Cfrac%7B3%7D%7B9%7D%20%20%3D%20%20%5Cfrac%7B10%20%5Ctimes%209%20%2B%203%7D%7B9%7D%20%20%3D%20%20%5Cfrac%7B93%7D%7B9%7D%20)
![10 \frac{2}{5} = \frac{10 \times 5 + 2}{5} = \frac{52}{5}](https://tex.z-dn.net/?f=10%20%5Cfrac%7B2%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B10%20%5Ctimes%205%20%2B%202%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B52%7D%7B5%7D%20)
Now, we have 93/9 - 52/5
We need to equate the denominators, before subtracting them.
![\frac{93}{9} - \frac{52}{5} = \frac{93 \times 5}{45} - \frac{52 \times 9}{45}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B93%7D%7B9%7D%20%20-%20%20%5Cfrac%7B52%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B93%20%5Ctimes%205%7D%7B45%7D%20%20-%20%20%5Cfrac%7B52%20%5Ctimes%209%7D%7B45%7D%20)
![\frac{465}{45} - \frac{468}{45}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B465%7D%7B45%7D%20%20-%20%20%5Cfrac%7B468%7D%7B45%7D%20)
![\frac{ - 3}{45}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B%20-%203%7D%7B45%7D%20)
![\boxed{ - \frac{3}{45} }](https://tex.z-dn.net/?f=%20%20%5Cboxed%7B%20-%20%20%5Cfrac%7B3%7D%7B45%7D%20%7D)
The result of 10 3/9- 10 2/5 is - 3/45
Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if ![\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_1%7D%7Bx_2%7D%3D%20%5Cdfrac%7By_1%7D%7By_2%7D%3D%20%5Cdfrac%7Bz_1%7D%7Bz_2%7D)
here;
![d_1 = (-1, \ 2, \ -3)](https://tex.z-dn.net/?f=d_1%20%3D%20%28-1%2C%20%5C%202%2C%20%5C%20-3%29)
Thus;
![r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%5Cdfrac%7Bx-1%7D%7B-1%7D%20%3D%20%5Cdfrac%7By-3%7D%7B2%7D%3D%5Cdfrac%7Bz-0%7D%7B-3%7D%20%3D%20t)
![d_2 =(2, \ -4, \ +6)](https://tex.z-dn.net/?f=d_2%20%3D%282%2C%20%5C%20-4%2C%20%5C%20%20%2B6%29)
![s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cdfrac%7Bx-0%7D%7B2%7D%20%3D%20%5Cdfrac%7By%2B5%7D%7B-4%7D%3D%5Cdfrac%7Bz-3%7D%7B6%7D%20%3D%20t)
∴
![\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_1%7D%7Bd_2%7D%3D%20%5Cdfrac%7B-1%7D%7B2%7D%20%3D%20%5Cdfrac%7B2%7D%7B-4%7D%3D%20%5Cdfrac%7B-3%7D%7B-6%7D)
Hence, we can conclude that r(t) and s(t) are parallel.
Answer:
4 x 8.5 x 12.5 =425 (multiple hight x width x length)
The volume of the box is ![425in^{3}](https://tex.z-dn.net/?f=425in%5E%7B3%7D)