A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
<h3>What are asymptotes?</h3>
A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.
The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,
![(2x-5)=0\\\\2x=5\\\\x=\dfrac52](https://tex.z-dn.net/?f=%282x-5%29%3D0%5C%5C%5C%5C2x%3D5%5C%5C%5C%5Cx%3D%5Cdfrac52)
![x-5=0\\\\x=5](https://tex.z-dn.net/?f=x-5%3D0%5C%5C%5C%5Cx%3D5)
Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.
![f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7B%287x-1%29%28x-5%29%7D%7B%282x-5%29%28x-5%29%7D%5C%5C%5C%5C%5C%5Cf%285%29%20%3D%20%5Cdfrac%7B%5B7%285%29-1%5D%285-5%29%7D%7B%5B2%285%29-5%5D%285-5%29%7D%5C%5C%5C%5C%5C%5Cf%285%29%20%3D%20%5Cdfrac%7B%2835-1%29%280%29%7D%7B%2810-5%29%280%29%7D%20%3D%200)
Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.
![f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7B%287x-1%29%28x-5%29%7D%7B%282x-5%29%28x-5%29%7D%5C%5C%5C%5C%5C%5Cf%28%5Cfrac52%29%20%3D%20%5Cdfrac%7B%5B7%28%5Cfrac52%29-1%5D%28%5Cfrac52-5%29%7D%7B%5B2%28%5Cfrac52%29-5%5D%28%5Cfrac52-5%29%7D%5C%5C%5C%5C%5C%5Cf%28%5Cfrac52%29%20%3D%20%5Cdfrac%7B%2816.5%29%28-2.5%29%7D%7B%280%29%28-2.5%29%7D%20%3D%20%5Cdfrac%7B%5Cinfty%7D%7B0%7D)
Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
Learn more about Asymptotes:
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Answer:
it Would be easier to answer with a picture but since these Question are normaly the same picture but it is Angle 3 and 7
Step-by-step explanation:
#NO ADDS
Answer:
III
Step-by-step explanation:
it represent the cost of a dog each day and they have about 30 dogs
14/25 , 29/50 , 53/100 , 13/20 and 3/5
<u>Solution:</u>
Put your numbers first in decimal form;
0.56 , 0.58 , 0.53 , 0.65 and 0.60
Then arrange them from the least to greatest;
0.53 , 0.56 , 0.58 , 0.60 and 0.65
Then revert your values to fraction form to give a final answer:
53/100 , 14/25 , 29/50 , 3/5 , 13/20
Answer:
![Solution,\\First=(\frac{-2}{3} +\frac{3}{5} )*\frac{1}{2} \\=-\frac{1}{15} *\frac{1}{2} =-\frac{1}{30} \\Second=(-1/30+3/5)*1/2\\=17/30*1/2=17/60\\Third=(17/60+3/5)*1/2\\=53/60*1/2=53/120\\Fourth=(53/120+3/5)*1/2\\=25/24*1/2=25/48](https://tex.z-dn.net/?f=Solution%2C%5C%5CFirst%3D%28%5Cfrac%7B-2%7D%7B3%7D%20%2B%5Cfrac%7B3%7D%7B5%7D%20%29%2A%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%3D-%5Cfrac%7B1%7D%7B15%7D%20%2A%5Cfrac%7B1%7D%7B2%7D%20%3D-%5Cfrac%7B1%7D%7B30%7D%20%5C%5CSecond%3D%28-1%2F30%2B3%2F5%29%2A1%2F2%5C%5C%3D17%2F30%2A1%2F2%3D17%2F60%5C%5CThird%3D%2817%2F60%2B3%2F5%29%2A1%2F2%5C%5C%3D53%2F60%2A1%2F2%3D53%2F120%5C%5CFourth%3D%2853%2F120%2B3%2F5%29%2A1%2F2%5C%5C%3D25%2F24%2A1%2F2%3D25%2F48)
First number=-1/30
Second number=17/60
Third number=53/120
Fourth number=25/48
Step-by-step explanation: