Answer:
Step-by-step explanation:
If we expand 4(3+x), we get (4*3)+(4*x).
Then we do 4*3 to get 12 and 4*x to get 4x
(3+3+3+3) is the same thing as 4*3, because we are adding 3 together 4 times. (3+3+3+3) gives us 12 as well, since they are the same thing.
(x+x+x+x) is the same thing because we are adding x together 4 times, which is the same thing as (4*x). (x+x+x+x) gives us 4x as well.
Hope this helps.
Step-by-step explanation:
![\huge \: 2 \sqrt{x} .4 {x}^{ - \frac{5}{2} } \\ \\ \huge \: = 2.4 {x}^{ \frac{1}{2} } . {x}^{ - \frac{5}{2} } \\ \\ \huge \: = 8 {x}^{ \frac{1}{2} - \frac{5}{2} } \\ \\ \huge \: = 8 {x}^{ \frac{1 - 5}{2} } \\ \\ \huge \: = 8 {x}^{ - \frac{4}{2} } \\ \\ \huge \: = 8. {x}^{ - 2} \\](https://tex.z-dn.net/?f=%20%5Chuge%20%5C%3A%202%20%5Csqrt%7Bx%7D%20.4%20%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B5%7D%7B2%7D%20%7D%20%5C%5C%20%20%5C%5C%20%20%20%5Chuge%20%5C%3A%20%3D%202.4%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20.%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B5%7D%7B2%7D%20%7D%20%5C%5C%20%20%5C%5C%20%5Chuge%20%5C%3A%20%20%20%3D%208%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%20-%20%20%5Cfrac%7B5%7D%7B2%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%20%5Chuge%20%5C%3A%20%3D%208%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%20-%205%7D%7B2%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%5Chuge%20%5C%3A%20%20%20%3D%208%20%7Bx%7D%5E%7B%20-%20%20%5Cfrac%7B4%7D%7B2%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%5Chuge%20%5C%3A%20%20%20%3D%208.%20%7Bx%7D%5E%7B%20-%202%7D%20%20%5C%5C%20)
Find where the equation is undefined ( when the denominator is equal to 0.
Since they say x = 5, replace x in the equation see which ones equal o:
5-5 = 0
So we know the denominator has to be (x-5), this now narrows it down to the first two answers.
To find the horizontal asymptote, we need to look at an equation for a rational function: R(x) = ax^n / bx^m, where n is the degree of the numerator and m is the degree of the denominator.
In the equations given neither the numerator or denominators have an exponent ( neither are raised to a power)
so the degrees would be equal.
Since they are equal the horizontal asymptote is the y-intercept, which is given as -2.
This makes the first choice the correct answer.