Given:
The function is:
![f(x)=\dfrac{2x}{x+4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%7D%7Bx%2B4%7D)
To find:
The vertical and horizontal asymptotes of the given function.
Solution:
We have,
![f(x)=\dfrac{2x}{x+4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%7D%7Bx%2B4%7D)
For vertical asymptotes, equate the denominator and 0.
![x+4=0](https://tex.z-dn.net/?f=x%2B4%3D0)
![x+4-4=0-4](https://tex.z-dn.net/?f=x%2B4-4%3D0-4)
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
So, the vertical asymptote of the given function is
.
The degree of the numerator is 1 and the degree of the denominator is also 1.
Since the degrees of numerator and denominator are equal, therefore the horizontal asymptote is:
![y=\dfrac{a}{b}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Ba%7D%7Bb%7D)
Where, a is the leading coefficient of numerator and b is the leading coefficient of denominator.
Leading coefficient of numerator is 2 and the leading coefficient of denominator is 1, so the horizontal asymptote is:
![y=\dfrac{2}{1}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B2%7D%7B1%7D)
![y=2](https://tex.z-dn.net/?f=y%3D2)
Therefore, the correct option is C.
x = 160 gal
y = 80 gal
160 gallons of water and 80 gallons of premium antifreeze solution must be mixed.
Answer: The sign is positive.
Step-by-step explanation:
a > 0 and b < 0
So, a·b < 0
⇒ -4·a·b > 0
⇒ -4·a·b - 4·a·b > 0
Hence, the sign will be positive
Answer:
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
<em>Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake.
</em>
<em>How much space does Lacey's mom cover in frosting?
</em>
My answer:
As we know that the surface area of the the cake is made up of rectangles. The formula for find the area of a rectangle is A = lw
- The area of rectangle ABCD: 4*2 = 8
- The area of rectangle ADFE : 12*2 = 24
- The area of rectangle TJVS : 4*2 = 8
- The area of rectangle ESFV :9*2 = 18
- The area of rectangle HTJG: 5*2 = 10
- The area of rectangle CBHG: 2*8 = 16
The area of CDEVGJ = ABHTFS
= 4*12 + 4*5
= 68
So the total area is: 68 +68 +16+10+18+8+24+8 = 220
Hope it will find you well