A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
Answer: D. ![6^{30}](https://tex.z-dn.net/?f=6%5E%7B30%7D)
Step-by-step explanation:
Using exponent rules an exponent to the power of a number will multiply by each other.
So the -4 and -9 will multiply.
The 6 in the numerator will now have a positive exponent of 36.
![\frac{6^{36}}{6^6}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E%7B36%7D%7D%7B6%5E6%7D)
Now we can divide and when we do so the exponents will subtract from each other.
So 36 - 6 = 30
And the base of 6 does not change.
The simplified form is ![6^{30}](https://tex.z-dn.net/?f=6%5E%7B30%7D)
Answer:
h = 5.318 m
Step-by-step explanation:
6.5/11 = h/9
0.5909 = h/9
h = 5.318