Option C: -3 is the average rate of change between
and ![x=1](https://tex.z-dn.net/?f=x%3D1)
Explanation:
The formula to determine the average rate of change is given by
Average rate of change = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We need to find the average rate of change between
and ![x=1](https://tex.z-dn.net/?f=x%3D1)
Thus, from the table, we have,
, ![y_1=5](https://tex.z-dn.net/?f=y_1%3D5)
, ![y_2=-1](https://tex.z-dn.net/?f=y_2%3D-1)
Thus, substituting these values in the formula, we get,
Average rate of change = ![\frac{-1-5}{1+1}](https://tex.z-dn.net/?f=%5Cfrac%7B-1-5%7D%7B1%2B1%7D)
![=\frac{-6}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%7D%7B2%7D)
![=-3](https://tex.z-dn.net/?f=%3D-3)
Thus, the average rate of change between
and
is -3.
Hence, Option C is the correct answer.
For this case we must find an expression equivalent to:
![log_ {5} (\frac {x} {4}) ^ 2](https://tex.z-dn.net/?f=log_%20%7B5%7D%20%28%5Cfrac%20%7Bx%7D%20%7B4%7D%29%20%5E%202)
So:
We expanded
by moving 2 out of the logarithm:
![2log_ {5} (\frac {x} {4})](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28%5Cfrac%20%7Bx%7D%20%7B4%7D%29)
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
![log (xy) = log (x) + log (y)](https://tex.z-dn.net/?f=log%20%28xy%29%20%3D%20log%20%28x%29%20%2B%20log%20%28y%29)
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
![log (\frac {x} {y}) = log (x) -log (y)](https://tex.z-dn.net/?f=log%20%28%5Cfrac%20%7Bx%7D%20%7By%7D%29%20%3D%20log%20%28x%29%20-log%20%28y%29)
Then, rewriting the expression:
![2 (log_ {5} (x) -log_ {5} (4))](https://tex.z-dn.net/?f=2%20%28log_%20%7B5%7D%20%28x%29%20-log_%20%7B5%7D%20%284%29%29)
We apply distributive property:
![2log_ {5} (x) -2log_ {5} (4)](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28x%29%20-2log_%20%7B5%7D%20%284%29)
Answer:
An equivalent expression is:
![2log_ {5} (x) -2log_ {5} (4)](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28x%29%20-2log_%20%7B5%7D%20%284%29)
3x - 4 = <span>3(-3) - 4 = -9 - 4 = -13
</span>3x - 4 = <span>3(-1.4) - 4 = -4.2 - 4 = -8.2
answer
range { -13, -8.2}</span>
Mel's Age = xRahfat's Age = x-3Aurelio's Age = 2x 2x + x +x -3 = 574x -3 = 574x = 60x = 15So Mel's age is 15.Hope this helps! :D
Answer:
2x+12
Step-by-step explanation:
We have a square patio, then each side of the patio has the same lengt. As we know the perimeter of a square is the sum of all sides. Then to know the length of the patio we just need to divide by 4 the perimeter.
![\dfrac{(8x+48)}{4}=\dfrac{8x}{4}+\dfrac{48}{4}=2x+12](https://tex.z-dn.net/?f=%5Cdfrac%7B%288x%2B48%29%7D%7B4%7D%3D%5Cdfrac%7B8x%7D%7B4%7D%2B%5Cdfrac%7B48%7D%7B4%7D%3D2x%2B12)
Then each side of the square patio has a length of 2x+12