Answer:
![\frac{4^{21}}{5^6}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5E%7B21%7D%7D%7B5%5E6%7D)
Step-by-step explanation:
![\left(\frac{4^7}{5^2}\right)^3](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B4%5E7%7D%7B5%5E2%7D%5Cright%29%5E3)
![=\frac{\left(4^7\right)^3}{\left(5^2\right)^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cleft%284%5E7%5Cright%29%5E3%7D%7B%5Cleft%285%5E2%5Cright%29%5E3%7D)
![\left(4^7\right)^3](https://tex.z-dn.net/?f=%5Cleft%284%5E7%5Cright%29%5E3)
![=4^{21}](https://tex.z-dn.net/?f=%3D4%5E%7B21%7D)
![=\frac{4^{21}}{\left(5^2\right)^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E%7B21%7D%7D%7B%5Cleft%285%5E2%5Cright%29%5E3%7D)
![\left(5^2\right)^3](https://tex.z-dn.net/?f=%5Cleft%285%5E2%5Cright%29%5E3)
![5^6](https://tex.z-dn.net/?f=5%5E6)
![=\frac{4^{21}}{5^6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E%7B21%7D%7D%7B5%5E6%7D)
Is this simultaneous equations?
if yes then the first step is
make one of the unknown as the subject
Answer:
The next number selected should be between 2 and 3 .
Step-by-step explanation:
x. x f(x) g(x)
0 10 17
1 11 19
2 14 21
3 19 23
4 26 25
3.5 22.25 24
<u>2.5 16.25 22</u>
1.5 12.25 20
0.5 10.25 18
We see the pattern that it is increasing with only a unit. The last given data is mid of the last two values that is 3 and 4.
So the next value would be the mid of the next last two values that is 2 and 3 and will be 2.5
Now it is moving in the reverse direction in the same pattern with a difference of a unit.
Answer:
Let's define the high temperature as T.
We know that:
"four times T, was more than 2*T plus 66°C"
(i assume that the temperature is in °C)
We can write this inequality as:
4*T > 2*T + 66°C
Now we just need to solve this for T.
subtracting 2*T in both sides, we get:
4*T - 2*T > 2*T + 66°C - 2*T
2*T > 66°C
Now we can divide both sides by 2:
2*T/2 > 66°C/2
T > 33°C
So T was larger than 33°C
Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.
Then the range of possible temperatures is:
(33°C, ...)
Where we do not have an upper limit, so we could write this as:
(33°C, ∞°C)
(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)
Answer:
![-\frac13](https://tex.z-dn.net/?f=-%5Cfrac13)
Step-by-step explanation:
Just the slope, so we can simply apply the definition, as variation in y over the variation in x
![m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cfrac%7B1-4%7D%7B2-%28-7%29%7D%20%3D%20%5Cfrac%20%7B-3%7D%7B9%7D%20%3D%20-%5Cfrac13)