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
s344n2d4d5 [400]
3 years ago
11

NEED HELP ASAP 20 PTS PLEASE. The graph of which is the following rational functions has a hole?

Mathematics
1 answer:
Paha777 [63]3 years ago
8 0

Answer:

  see below

Step-by-step explanation:

The denominator quadratic of each of the rational functions has two real roots, so the rational function would ordinarily have two vertical asymptotes. If there is one vertical asymptote, it is because the other one has been canceled by a numerator factor, creating a "hole."

A graph of the first rational function shows it to have only one vertical asymptote, at x=3. The product of zeros of the denominator quadratic is the constant term, -12, so the other denominator zero must be at x=-4. That is where the hole is found. (See the graph in the second attachment.)

_____

Without a graphing calculator, you would determine the zeros of each quadratic, and identify the rational function that had numerator and denominator zeros that were the same.

f(x)=\dfrac{x^2+5x+4}{x^2+x-12}\\\\=\dfrac{(x+4)(x+1)}{(x+4)(x-3)} \qquad\text{has a common factor in numerator and denominator, a hole}

You might be interested in
What is the answer to x+36=4x
rosijanka [135]

The answer is the number that 'x' must be in order for
that equation to be a true statement.  Here's one way
to find out what the number is:

                                         x + 36 = 4x

Subtract 'x' from each side:    36 = 3x

Divide each side by  3 :          12 =  x
 
5 0
4 years ago
A bank is offering a loan to account holders. If they pay the full amount off in fourteen months, they are charged no interest.
lara [203]

Answer:

$464.29

Step-by-step explanation:

Assuming equal payments, $6500/14 months=$464.2857, or round up to $464.29/month.

5 0
3 years ago
Cho tam giác ABC vuông tại A đường cao AH có BH=9 cm, CH= 10 cm. a tính AH. b tính ^B ,^ C
ohaa [14]

Answer:

Could you please put this in english?

Step-by-step explanation:

So sorry I can't help

4 0
3 years ago
Find the measure of angle 1<br><br> 60 degrees<br> 72 degrees<br> 36 degrees<br> 54 degrees
GarryVolchara [31]
The sum of all angles (around the black dot) is 360°

All 5 angles (if you forget the red line) are the same; so each angle is 360°/5 = 72°

So Angle 1 is 72°
3 0
4 years ago
Hot air balloons generally descend at a rate of 200 to 400 feet per minute. Four balloons descend 295 feet per minute for 7 minu
slavikrds [6]

make a proportion

<span>Let x = the amount of feet descended in 3 minutes (thus the total change of altitude of the balloon)

</span><span> 320 (feet per minute) / 1 (minute) = x (feet per minute) / 3 (minutes)

</span><span> 1) Divide: 320/1 = 320.
</span><span> 2) Multiply: 320 x 3= 960.

</span><span> The balloon that descends at a rate of 320 feet/minute (so, every minute, it descends 320 feet) descends a total of 960 feet in 3 minutes.

</span><span> The balloon's total change in altitude is -960 feet. </span>

4 0
4 years ago
Other questions:
  • C=59(F−32)
    10·1 answer
  • Please help i dont understandd
    8·1 answer
  • Please help me with this question!
    14·1 answer
  • Minny has two coupons, but can use one of them. The first one is for $5 off an item; the second coupon is for 20% off an item. T
    10·1 answer
  • 4. Juan is building a fish tank for his fish Juan wants the fish tank to be a cute He knows his fish need 216 cubic inches of wa
    15·1 answer
  • Help me with this please
    15·1 answer
  • There is a boat fleeing the scene of a crime that occurred at the light house. The boat is 250 feet away from the light house. H
    11·1 answer
  • THIS IS FOR MATH
    10·1 answer
  • 1. Find the area of parallelogram ABCD.
    15·1 answer
  • Write an algorithm to solve the problem with long division. Answer in at least 3 complete sentences.​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!