Answer:
Step-by-step explanation:
- A. 36 × 6 × 6 × 6 = 6²⁺¹⁺¹⁺¹ = 6⁵ incorrect
- B. 125 × 125 = 5³ × 5³ = 5³⁺³= 5⁶ correct
- C. 6 × 5 incorrect
- D. 25 × 5 × 5 × 5 = 5² × 5 × 5 × 5 = 5²⁺¹⁺¹⁺¹ = 5⁵ incorrect
Answer:
equation: 2.75 g/cm^3 * 1 m *3 m* (100 cm/1 m)^2 *4 cm * (1 kg/1000 g)
Step-by-step explanation:
countertop mass, m =?
density, ρ = 2.75 g/cm^3
wide, w = 1 m
long, l = 3 m
thick, t = 4 cm
countertop volume, V = w*l*t = 1 m *3 m*4 cm* (100 cm/1 m)^2
Isolating mass from density definition gives
ρ = m/V
m = ρ*V
m = 2.75 g/cm^3 * 1 m *3 m* (100 cm/1 m)^2 *4 cm * (1 kg/1000 g)
Answer: infinite solutions
Step-by-step explanation:
(−3) (4) + (−3) (−3x) = 9x + −12
−12 + 9x = 9x + −12
9x − 12 = 9x − 12
9x − 12 − 9x = 9x − 12 − 9x
−12 = −12
−12 + 12 = −12 + 12
0 = 0
Answer with Step-by-step explanation:
We are given that two matrices A and B are square matrices of the same size.
We have to prove that
Tr(C(A+B)=C(Tr(A)+Tr(B))
Where C is constant
We know that tr A=Sum of diagonal elements of A
Therefore,
Tr(A)=Sum of diagonal elements of A
Tr(B)=Sum of diagonal elements of B
C(Tr(A))=
Sum of diagonal elements of A
C(Tr(B))= Sum of diagonal elements of B
Tr(C(A+B)=Sum of diagonal elements of (C(A+B))
Suppose ,A=![\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
B=![\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
Tr(A)=1+1=2
Tr(B)=1+1=2
C(Tr(A)+Tr(B))=C(2+2)=4C
A+B=![\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]+\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
A+B=![\left[\begin{array}{ccc}2&1\\2&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C2%262%5Cend%7Barray%7D%5Cright%5D)
C(A+B)=![\left[\begin{array}{ccc}2C&C\\2C&2C\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2C%26C%5C%5C2C%262C%5Cend%7Barray%7D%5Cright%5D)
Tr(C(A+B))=2C+2C=4C
Hence, Tr(C(A+B)=C(Tr(A)+Tr(B))
Hence, proved.
