Answer:
right side
Step-by-step explanation:
The range of the equation is ![y>2](https://tex.z-dn.net/?f=y%3E2)
Explanation:
The given equation is ![y=2(4)^{x+3}+2](https://tex.z-dn.net/?f=y%3D2%284%29%5E%7Bx%2B3%7D%2B2)
We need to determine the range of the equation.
<u>Range:</u>
The range of the function is the set of all dependent y - values for which the function is well defined.
Let us simplify the equation.
Thus, we have;
![y=2 \cdot 4^{x+3}+2](https://tex.z-dn.net/?f=y%3D2%20%5Ccdot%204%5E%7Bx%2B3%7D%2B2)
This can be written as ![y=2^{1+2(x+3)}+2](https://tex.z-dn.net/?f=y%3D2%5E%7B1%2B2%28x%2B3%29%7D%2B2)
Now, we shall determine the range.
Let us interchange the variables x and y.
Thus, we have;
![x=2^{1+2(y+3)}+2](https://tex.z-dn.net/?f=x%3D2%5E%7B1%2B2%28y%2B3%29%7D%2B2)
Solving for y, we get;
![x-2=2^{1+2(y+3)}](https://tex.z-dn.net/?f=x-2%3D2%5E%7B1%2B2%28y%2B3%29%7D)
Applying the log rule, if f(x) = g(x) then
, then, we get;
![\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%282%5E%7B1%2B2%28y%2B3%29%7D%5Cright%29%3D%5Cln%20%28x-2%29)
Simplifying, we get;
![(1+2(y+3)) \ln (2)=\ln (x-2)](https://tex.z-dn.net/?f=%281%2B2%28y%2B3%29%29%20%5Cln%20%282%29%3D%5Cln%20%28x-2%29)
Dividing both sides by
, we have;
![2 y+7=\frac{\ln (x-2)}{\ln (2)}](https://tex.z-dn.net/?f=2%20y%2B7%3D%5Cfrac%7B%5Cln%20%28x-2%29%7D%7B%5Cln%20%282%29%7D)
Subtracting 7 from both sides of the equation, we have;
![2 y=\frac{\ln (x-2)}{\ln (2)}-7](https://tex.z-dn.net/?f=2%20y%3D%5Cfrac%7B%5Cln%20%28x-2%29%7D%7B%5Cln%20%282%29%7D-7)
Dividing both sides by 2, we get;
![y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cln%20%28x-2%29-7%20%5Cln%20%282%29%7D%7B2%20%5Cln%20%282%29%7D)
Let us find the positive values for logs.
Thus, we have,;
![x-2>0](https://tex.z-dn.net/?f=x-2%3E0)
![x>2](https://tex.z-dn.net/?f=x%3E2)
The function domain is ![x>2](https://tex.z-dn.net/?f=x%3E2)
By combining the intervals, the range becomes ![y>2](https://tex.z-dn.net/?f=y%3E2)
Hence, the range of the equation is ![y>2](https://tex.z-dn.net/?f=y%3E2)
B is true
Step-by-step explanation:
because no number with them to lines can be a negative
If they pay $28 for 16 jerseys then the total they’d have to play is $448
28 x 16 = 448
Hope this helps :)
Answer:
Split the number into the whole number component and fraction component.
5 8/25= 5+8/25.
For the denominator, recognize that
25×4=100.
Multiple =4.
Multiply the numerator and the denominator by the multiple 4.
8×4/ 25×4.
Simplify.
32/100=0.32
Combine the whole number component with the decimal.
5+0.32=5.32
<h3>I hope this helps</h3>