This work is faster rate than grading 36 assignments in 30 minutes because :
25 ÷ 20 = 1.25
1.25 hw assignment per minute
36 ÷ 30 = 1.2
1.2 hw assignments per minute
Option C:
is the value of a and b
Explanation:
Given that the expression ![\sqrt{648}=\sqrt{2^a\times3^b}](https://tex.z-dn.net/?f=%5Csqrt%7B648%7D%3D%5Csqrt%7B2%5Ea%5Ctimes3%5Eb%7D)
We need to determine the value of a and b
Let us consider the term
and take the prime factorization of the term 648
Thus, we have,
648 divides by 2,
![648=2 \cdot 324](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%20324)
324 divides by 2,
![648=2 \cdot 2 \cdot 162](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%202%20%5Ccdot%20162)
162 divides by 2,
![648=2 \cdot 2 \cdot 2 \cdot 81](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%2081)
81 divides by 3,
![648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%203%20%5Ccdot%2027)
27 divides by 3,
![648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%209)
9 divides by 3,
![648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3](https://tex.z-dn.net/?f=648%3D2%20%5Ccdot%202%20%5Ccdot%202%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203%20%5Ccdot%203)
Thus, we have,
![\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}](https://tex.z-dn.net/?f=%5Csqrt%7B648%7D%3D%5Csqrt%7B2%5E%7B3%7D%20%5Ccdot%203%5E%7B4%7D%7D)
Therefore, equating the powers of 2 and 3, we get,
![a=3, b=4](https://tex.z-dn.net/?f=a%3D3%2C%20b%3D4)
Hence, the value of a and b is 3 and 4
Thus, Option C is the correct answer.
Answer:
$167.03
Step-by-step explanation:
ok
When put in matrix form, the coefficients of
... 3x -2y = 7
... x + 4y = 2
look like
![\left[\begin{array}{cc}3&-2\\1&4\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26-2%5C%5C1%264%5Cend%7Barray%7D%5Cright%5D%20%20)
The determinant is 3×4 - 1×(-2) = 14.
3bx3bx3b
27xbxbxb
hope this helps