Answer:
Option C.
Step-by-step explanation:
We start with the expression:
where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers)
We want to find the equivalent expression to this one.
Here, we can do the next two simplifications:
And:
If we apply these two to our initial expression, we can rewrite it as:
Here we can use the second simplification again, to rewrite:
So, concluding, we have:
Then the correct option is C.
Answer:
x=4
Step-by-step explanation:
√x+12=x
x+12=x2(Square both sides)
x+12=x2
x+12−x2=x2−x2(Subtract x^2 from both sides)
−x2+x+12=0
(−x−3)(x−4)=0(Factor left side of equation)
−x−3=0 or x−4=0(Set factors equal to 0)
x=−3 or x=4
x=−3(Doesn't work in original equation)
x=√x+12
Answer:
51.2 ounces.
Step-by-step explanation:
If its 20% of a 64 ounce half gallon, you just need to find the last 80% of the half gallon. Since you know it is 64 ounces you can divide it by 5 which gives you 12.8. 12.8 would be 20% so you just subtract 12.8 from 64 ounces which gives you 51.2.
The main factor when x values are high is the nature of the function. For example, polynomial functions intrinsically grow slower than exponential functions when x is high. Also, the greater the degree of the polynomial, the more the function grows in absolute value as x goes to very large values.
In specific, this means that our 2 exponential functions grow faster than all the other functions (which are polynomial) and thus they take up the last seats. Also, 7^x grows slower than 8^x because the base is lower. Hence, the last is 8^x+3, the second to last is 7^x.
Now, we have that a polynomial of 2nd degree curves upwards faster than a linear polynomial when x is large. Hence, we have that the two 2nd degree polynomials will be growing faster than the 2 linear ones and hence we get that they fill in the middle boxes. Because x^2+4>x^2, we have that x^2+4 is the 4th from the top and x^2 is the 3rd from the top.
Finally, we need to check which of the remaining functions is larger. Now, 5x+3 is larger than 5x, so it goes to the 2nd box. Now we are done.
