Okay, so there's a number rounded to the nearest million, in this case 2 million. So this tells me that the number of visitors is between 1,500,000 and 2,499,999. The reason why 1,499,999 doesn't count is because the hundred thousands digit is not 5 or above, so it doesn't count. It would round down to 1 million, not 2 million. The reason why 2,500,000 doesn't count, is because the hundred thousands digit is 5, so that rounds to 3 million, not 2 million. The greatest number of visitors that visited the aquarium has to be 2,499,999, because that's one digit away from 2.5 million, and the hundred thousands digit is a 4, not 5. The answer is 2,499,999
Answer:
![x=2](https://tex.z-dn.net/?f=x%3D2)
Step-by-step explanation:
So we have the equation:
![5^x+5^{x+1}=150](https://tex.z-dn.net/?f=5%5Ex%2B5%5E%7Bx%2B1%7D%3D150)
First, separate the second term:
![5^x+(5\cdot5^x)=150](https://tex.z-dn.net/?f=5%5Ex%2B%285%5Ccdot5%5Ex%29%3D150)
Let u equal 5ˣ. So:
![u+5u=150](https://tex.z-dn.net/?f=u%2B5u%3D150)
Combine like terms:
![6u=150](https://tex.z-dn.net/?f=6u%3D150)
Divide both sides by 6:
![u=25](https://tex.z-dn.net/?f=u%3D25)
Substitute back u:
![5^x=25](https://tex.z-dn.net/?f=5%5Ex%3D25)
Take the base 5 logarithm of both sides:
![\log_5(5^x)=\log_5(25)](https://tex.z-dn.net/?f=%5Clog_5%285%5Ex%29%3D%5Clog_5%2825%29)
The left cancels:
![x=\log_5(25)](https://tex.z-dn.net/?f=x%3D%5Clog_5%2825%29)
Evaluate the right:
![x=2](https://tex.z-dn.net/?f=x%3D2)
So, our answer is 2.
And we're done!
Answer:
Non-linear equations:
![y=x^2 +2x-3](https://tex.z-dn.net/?f=y%3Dx%5E2%20%2B2x-3)
![3y=2^x](https://tex.z-dn.net/?f=3y%3D2%5Ex)
Step-by-step explanation:
Linear equation: y = mx + b
Therefore, a linear equation has 2 variables that have no exponents.
So the non-linear equations are:
(this is a quadratic equation - polynomial with degree 2)
(this is an exponential equation)
Answer:
p(x) = (5x - 1) (x + 3)
Step-by-step explanation:
I apologize if I couldn't answer correctly, the question was a bit hard to understand because of the formatting.
Also I didn't see my answer in the list of answer choices but here it is:
if the polynomial has zeros at 0.2 and -3 the equation would have to be:
p(x)=(x-0.2)(x+3)
This is because plugging either of those numbers into the polynomial would cause it to equal 0.
(x-0.2) can be simplified by multiplying everything in the parenthesis by 5, getting rid of all of the decimals, making the final answer:
p(x) = (5x - 1) (x + 3)