1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kupik [55]
2 years ago
13

Which statement describes the vertical asymptotes of the graph of f(x)=x^2-64/8x-64

Mathematics
1 answer:
g100num [7]2 years ago
4 0
<h3>Answer:  Choice A</h3>

The graph has <u>no</u> vertical asymptote

===========================================================

Explanation:

Let's simplify the function by factoring each piece.

f(x) = \frac{x^2-64}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8(x-8)}\\\\f(x) = \frac{x+8}{8}\\\\

In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.

The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph <u>has no vertical asymptotes.</u>

However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.

The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.

You might be interested in
A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2, and
Free_Kalibri [48]

Answer:

Step-by-step explanation:

When A, B,C are equally likely to be assigned to any one of the stations 1,2 or 3

we find that each one assigned to one station has probability 1/3

Also each person is independent of the other.

Probability that

a) All three family members are assigned to the same station

= P(ABC) to same station

= P(ABC) to 1+P(ABC) to 2 +P(ABC) to 3

=3*P(A)P(B)P(C) since independent

=3*(\frac{1}{3} )^3\\=\frac{1}{9}

b) This would be equivalent to 1- all 3 to the same station

= 1-\frac{1}{9} \\=\frac{8}{9}

c) Every member to a different station

A has 3 choices while B has remaining 2 and C has 1

Hence prob = \frac{3*2*1}{3*3*3} =\frac{2}{9}

7 0
3 years ago
Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is imp
Allushta [10]

Answer:

(a) Null Hypothesis (H₀) = Mean of x₁ > Mean of x₂

Alternative Hypothesis (H₁) = Mean of x₁ ≠ Mean of x₂

(b) We will use here t-test for two sample means which is given by,

[tex]t = \frac{\bar_{x_{1}}-\bar_{x_{2}}}{\sqrt{s^2(\frac{1}{n_{1}}+\frac{1}{n_{2}}  )}}[/tex]

Putting all values we get, t = 17.5 with 20 degree of freedom

At α = 0.05

p-value = 95% Confidence Interval for the Difference ( 6.6068 , 8.3932 )

8 0
3 years ago
How can I do two way tables
Irina18 [472]

Answer: You have to think and show your work

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
PLEASE ANSWER NUMBER 2 HELP WILL GIVE BRAINLIEST
german

Answer:

The measure of each angle remains the same after each transformation. The reason is because when you undergo a reflection, a rotation, or a translation, the triangle remains the same size and shape (congruent), therefore there is no change to the angles. The only thing changing is the position of the shape.

Step-by-step explanation:

4 0
4 years ago
PLEASE HELP ME SOLVE BOTH<br><br> 30 POINTS!!!
balu736 [363]

Answer:

1) x = 4

2) a square root cannot be equal to a negative value

Step-by-step explanation:

1) add 1 to each side

2) square each side

(√2x + 1)² = 3²

2x + 1 = 9

2x = 8

x = 4

2) subtract 4 from each side

√2x + 1 ≠ -5

8 0
4 years ago
Other questions:
  • Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the righ
    5·2 answers
  • Harriet needs to ship a small vase. The box she will use has a volume of 216 inches. If the side lengths are all the same what i
    6·1 answer
  • If the roots of a quadratic equation are real,irrational,and unequal,the discriminant could have a value of
    11·2 answers
  • Find the m∠2 90° 67° 157° 57°
    12·1 answer
  • A group of astronomers observed light coming from a star located a distance of 331,000,000,000,000,000,000,000,000 light-years f
    7·2 answers
  • How do I do this? I don't get it
    8·2 answers
  • An automatic filling machine in a factory fills bottles of ketchup with a mean of 17.6 oz and a standard deviation of 0.05 oz wi
    11·1 answer
  • HELP I NEED THIS ASAP PLEASE AND THANK YOU!!!!! (4)
    13·1 answer
  • Kevin has a checking account. This month he deposits three paychecks. Each paycheck is for $225.75. He also makes two payments f
    7·2 answers
  • Help me find the media, mode and the mean look at the photo and solve the puzzle
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!