No, the system is inconsistent.
Step-by-step explanation:
If the last column is a pivot column, then that row gives an equation that looks something like 0x+0y+0z=1 , meaning , 0=1. Clearly, this is false.
So, the system of linear equations is inconsistent.
Answer:
8
Step-by-step explanation:
Given the equation 1/4 (16 + 12x) = 28, to solve this first we open the bracket using the distributive property. According to this property, given A, B and C then:
A(B+C ) = AB+AC
Step 1:
1/4 (16 + 12x) = 28
= 1/4(16)+1/4(12x) = 28
= 4+3x = 28
Step 2:
We move 4 to the other side to have:
3x = 28-4
3x = 24
Step 3:
Divide both sides by 3 to have,:
3x/3 = 24/3
x = 8
The answer is 8
Answer:
0.54 ounces in each tube
Step-by-step explanation:
Add the amount she used so we can add it in. 1.35+0.27= 1.62. Then divide it by the number of tube and since it was a 3 pack you divide it by 3. 1.62/3=0.54 so there is 0.54 ounces in each tube.
Simplifying –8.3 + 9.2 – 4.4 + 3.7.
Identify and explain any errors in his work or in his reasoning
Original problem 1. −8.3 + 9.2 + 4.4 + 3.7
Additive inverse 2. −8.3 + 4.4 + 9.2 + 3.7 (error, not additive inverse; +3-3=0)
Commutative property 3. −8.3 + (4.4 + 9.2 + 3.7)
Associative property 4. −8.3 + 17.3
Simplify 5. 9
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
