Consider the function f (x) = (2x - a)(x - b)/5(x - b)(x - c). Determine where the following features of its graph
are located in terms of a, b, and/or c. Explain your reasoning for each situation.
a. the x-intercepts
b. the y-intercepts
c. any vertical asymptotes
d. any horizontal asymptotes
e. any “holes” in the graph

Answers

Answer 1

a) The function simplifies to
.. f(x) = (2x -a)/(5(x -c)) . . . . . . x ≠ b
The x-intercept will be located where f(x) = 0, at x = a/2.

b) The y-intercept is located where x = 0, at f(0) = a/(5c)

c) The vertical asymptote is where the denominator is zero, at x = c

d) The horizontal asymptote is the value that results when x gets large, y = 2/5.

e) There is a "hole" in the graph at x=b, where the function is undefined.

Related Questions

The population of trout in a certain pond doubles every year. The current population of the pond is 275 trout.

Answers

this year the population is 275 if it continues at the same rate in 2019 it will be 550 in 2020 it will be 1100 in 2021 it will be 2200 and soo on...

Situation: A 15 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1405. N Noe No initial mass (at time 0) N mass at time t k a positive constant that depends on the substance itself and on the units used to measure time t time, in days

Answers

Your answer is 4.9.
Your welcome

Answer: 4.9

Step-by-step explanation:

Hope this helps

What is the area of a sector with a central angle of 10pi/7 radians and a radius of 18.4 m? Enter your answer as a decimal.

Answers

A = (1/2)r^2*θ
.. = (1/2)*(18.4 m)^2*(10π/7)
.. = 759.73 m^2

which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5

Answers

Answer:

Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}}[/tex]

[tex]\sqrt[4]{(\frac{24}{128})\times (\frac{x^{6}}{x^{4}})\times (\frac{y}{y^{5}})}[/tex]

= [tex]\sqrt[4]{(\frac{3}{16})\times {(x)^{6-4}}\times{(y)^{1-5}}}[/tex]

= [tex]\sqrt[4]{(\frac{3}{16})\times x^{2}y^{-4}}[/tex]

= [tex]\sqrt[4]{\frac{3}{(2)^{4}}\times x\times y^{-4}}[/tex]

= [tex]\sqrt[4]{(3\times x^{2)\times (\frac{y^{-1}}{2})^{4}}}[/tex]

= [tex]\frac{y^{-1}}{2}\sqrt[4]{3x^{2}}[/tex]

= [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]

Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex] is the correct answer.

What is the area of this figure?

Answers

The answer should be 35, because:
5 x 5 = 25
4 x 2.5 = 10
25 + 10 = 35.
Hope this helps!:)

If you worked for 6 days for a total of 67.8 hours. If I worked the same number of hours each day, how many hours did I work in a day?

Answers

Hi there!

To solve this problem, we need to divide 67.8 by 6 to find the amount of hours each day.

67.8 / 6 = 11.3

You worked 11.3 hours each day.

Hope this helps!

7 is greater than or equal to w, and - 1 is less than w

Answers

This written as an expression is 7 >= w > -1

Hope this helps!

helpppppppppppppppppppppppppppp

Answers

For this case we can rewrite the function using properties of neperian and exponential logarithms.
We then have to rewrite:
x*x ^ 2 = 64
Rewriting:
x ^ 3- 64 = 0
x = 4
Answer:
x = 4
option 2

A model ship is built to a scale of 1 cm: 4 m. The length of the model is 40 cm. What is the length of the actual ship? a. 160 m c. 40 m b. 50 m d. 15 m Please select the best answer from the choices provided A B C D

Answers

A. 160m.

You can get this answer by multiplying the scale by the length of the model

4. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
165units
170units
97units
169 units
is the answer A?

Answers

The distance formula for two points in a plane is
D=sqrt( (x1-x2)^2 + (y1-y2)^2 )
From T to U
D= sqrt((80-20)^2 + (20-60)^2) = 72.11
Then flying from U to V
D= sqrt((20-110)^2 + (60-85)^2) = 93.4
So T to U to V = 72.11+93.4 = 165.5
BUT checking also T to V to U
From T to V
D= sqrt((80-110)^2 + (20-85)^2) = 71.6
Then from V to U
D= sqrt((110-20)^2 + (85-60)^2) = 93.4
So from T to V to U = 165
Pretty much the same both directions
So yes the answer is A

Your friend has prepared his monthly budget and asks you if he has overlooked anything in this planning. Which of the following questions points out his most serious omission?
a. What if your income from stocks is lost? b. What if you need to go to the doctor? c. What if the electric bill increases? d. What if you need to replace the furnace?

Answers

d. the question implies the fact the furnace is in bad shape. It would cause readers to infer it needs replaced. So he needs to replace the furnace. hope im right

Which of the economic goals correlates with the explanation "the ability of people to make choices"?
A. equity
B. innovation
C. efficiency
D. freedom

I got D as my answer, is that correct?,

Answers

The correct answer is D, freedom. This is because equity only refers to everything being equal, innovation refers to the a new idea, and efficiency refers to being able to do something with ease. Only freedom makes sense in regards to people being able to make their own choices.

Assume that there are 2 trials.

X = 2 where X represents the number of successes.

Which probability matches the probability histogram?

Round the answer to one decimal place.

P(success)=0.3

P(success)=0.4

P(success)=0.6

P(success)=0.7

Answers

Answer: The p(success) = 0.6

Your question is a little unclear, but I believe you are asking about the probability that at least one of the trials in the experiment were successful.

If that is the case, you simply have to add the probability of 1 success with the probability of 2 successes.

That is 0.48 + 0.16 = 0.64

Rounding our answer to one decimal place gives us 0.6.

The correct answer on the test was

P(success)=0.4

sales: Ye has his own business he checks sales receipts three times a day One day his afternoon sales were $50 more than his morning sales and his evening sales were three times this afternoon so if his total sales for the day were $1000 what were his evening service

Answers

Call the morning sales x.

This means:
- The afternoon sales are x + 50.
- The evening sales are 3(x + 50) = 3x + 150

Now we can calculate x knowing the total sales:
Total sales = morning + afternoon + evening
1000 = x + x + 50 + 3x + 150
800 = 5x
x = 160

We are asked for evening sales, so let's plug are value for x into the evening expression:

evening = 3x + 150 = 3(160) + 150 = $630

Divide the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x.
(4x^2 - 10x -24) / (2x + 3)

Answers

After dividing the polynomials, the answer is 2x-8

Answer:

2x-8

Step-by-step explanation:

Which polynomial is a perfect square trinomial?
A. x^2 +5y + 25
B. x^2 +10y+25
C.x^2+5y+100
D. x^2+10y-25

Answers

the definition of a perfect square trinomial:
When a square of a number (3*3=9) can also add up to another number in the trinomial (3+3=6)

In my example here the equation, in order to be a perfect square trinomial, would be: X^2+6y+9

Now to look at the problem. We can instantly single out C because 10*10 is 100 but 10+10 is not five.
If we look at A we can find the root of 25 (5) but 5+5 is 10 not five. So A is incorrect
Using our previous calculation we know that 5 is our magic number. Leaving us with B and D. If we look at D we can conclude that -5*5 would be -25 but -5+5 is zero. So, it is not D
Using power of elimination we can easily conclude that B is the correct answer. If you wish to check: (5+5=10) (5*5=25)

Answer: B

Hope this helped!

A research firm conducts a sample survey and discovers that, of all the new watchers of three-dimensional tv, 77% have not reported any side effects such as vertigo, headache, or undue eyestrain compared with watching regular television. if this sample questionnaire had 2,100 respondents, what is the margin of error (me), rounded to the nearest thousandth? hint: me equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over n end fraction end square root comma where p hat is the yes proportion in the sample and n is the sample size. me = ±0.009 me = ±0.017 me = ±0.018 me = ±1.837

Answers

Answer: +/- 0.018

All you have to do is plug the known values into the equation and evaluate it.

First, do the work under the square root sign. 0.77(1-0.77) / 2100 gives you a very small number. If you take the square root of that, you will have 0.0091.

The last step is to just multiply that by 2 and you will have 0.018

a poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. if 10 voters are selected at random, wht is the probability that exactly five of them will vote in favor of the initiative?,

Answers

5.1% This is Binomial with n=10 and p=0.76 P(X = 5) = 10C5 (0.76^5) (1-0.76)^5 = 0.0509

Lesson 8: Binomial Distributions

1. a. 91%

2. a. 5.1%

3. c. s^5-25s^4v+250s^3v^2-1250s^2v^3+3125sv^4-3125v^5

4. d. 55.8%

A vacant lot is in the shape of an isosceles triangle. It is between two streets that intersect at an 85.9degree angle. Each of the sides of the lot that face these streets is 150 ft. Long. Find the perimeter of the lot to the nearest foot.

Answers

1. An isosceles triangle has two equal sides and you have the length of these sides (a=105 feet), but you need the other one: "b". So, if you a draw a segment that bisects the angle of 85.9°,you will obtain two equal right triangles, as you can see in the figure attached. Now, you have to find the value of "x" and the side "b" will be 2x:

Sin(α)=Opposite/Hypotenuse

α=89.5°/2=42.95°
Opposite=x
Hypotenuse=105

Sin(42.95°)=x/105
x=(105)(Sin(42.95°))
x=71.54 feet

2. Then the other side of the isosceles triangle (b), is:

b=2x
b=2x71.54 feet
b=143.08 feet

3. The perimeter of the isosceles triangle, is:

P=2a+b
P=2(105 feet)+143.08 feet
P=210 feet+143.08 feet
P=353 feet

. Classify the triangle according to side length and angle measurement.

(1 point)
isosceles; right
equilateral; obtuse
scalene; acute
scalene; right

Answers

Final answer:

The question requests the classification of a triangle by both its side length and angle measurement. An isosceles triangle has two equal sides, and if it also includes a right angle, it is classified as isosceles; right. This understanding combines the concepts of triangle classification by sides and angles.

Explanation:

The question asks to classify a triangle according to side length and angle measurement. When classifying triangles by side lengths, we have three categories: isosceles, scalene, and equilateral. An isosceles triangle has two sides of equal length, a scalene triangle has all sides of different lengths, and an equilateral triangle has all sides of equal length. In terms of angle measurements, triangles can be classified as right (one 90-degree angle), acute (all angles less than 90 degrees), or obtuse (one angle greater than 90 degrees).

According to the information provided and referencing the 4th Theorem, in an isosceles triangle, the angles opposite to the equal sides are equal. This property helps in classifying a triangle when given its angles or side lengths. Furthermore, for a triangle to be a right triangle, it must include a 90-degree angle. This is crucial when identifying a triangle as isosceles; right, which means it is an isosceles triangle with a right angle, typically resulting in the two equal sides being adjacent to the right angle.

What is the value of x?
x=23
x=35
x=58
x=93

Answers

I think is this x=58 hope this helped.

The sum of the remote interior angles of a triangle equals the value of the exterior angle. Therefore, 35+58=93 (last choice).

PLEASE HELP ME!! 25 points
Anna has a 10-foot long ladder that she is going to rest against a vertical wall along the bottom of a window-sill that is 8.5 feet above the ground. The safety code recommends that the angle the ladder makes with the ground be no greater than 65°. Will the ladder be safe resting on the window sill?
please help with too -->Draw a diagram, and show work to support your answer.

Answers

given that the ladder is 10 ft long and the height of the wall is 8.5 ft, to find whether the ladder is safe resting on the window sill we use the formula:
sin x=opposite/hypotenuse
opposite=8.5 ft
hypotenuse=10 ft
thus
sin x=8.5/10
sin x=0.85
x=arcsin 0.85
x=58.21°
Since 58.21°<65° the we conclude that the ladder is very safe.

A tree on a hillside casts a shadow c = 230 ft down the hill. if the angle of inclination of the hillside is b = 19° to the horizontal and the angle of elevation of the sun is a = 49°, find the height of the tree. (round your answer to the nearest foot.)

Answers

From a point A draw a line 19° to the horizontal representing the hill. On the hill, 230 ft from the point A, draw a vertical line.h, representing the height of the tree. From the point A, draw another line 49° to the horizontal to the top of the tree. Lastly, from the bottom of the tree, extend a vertical line (y) down to a point on the horizontal.
let x be the distance from point A to when y intersects the horizonal.
x/230=cos 19
x=230 cos 19=217.5

y/x=tan 19
y=xtan19
y=217.5 tan 19=74.88
(h+y)/x=tan 49
h+y=xtan 49=217.5tan49=250.205
hence
h=250.205-74.88=175.325 ft

the answer is:
height of the tree ~ 175 ft

your boss is impressed with your work and gives you a 3% raise.if the inflation rate is 3% you are
A) making more money in today's dollars
B) making about the same amount in today's dollars
C) making less money in today's dollars
D) seeing no change in your paycheck

Answers

B) making about the same amount in today's dollars

Answer: The answer is (B) making about the same amount in today's dollars.

Step-by-step explanation: Given that our boss is impressed with our work and give us a 3% raise.

We are to select the correct statement if there is an inflation of 3%.

Since the raise of 3% and inflation rate of 3% occur simultaneously, so there will not be much change in the amount of money we are making in dollars.

Thus, (B) is the correct option.

Refer to Explorations in Literature for a complete version of this passage.

Which quotations from “Here Is New York” develop the author’s viewpoint that commuters do not truly experience New York City?

Select each correct answer.

A "About 400,000 men and women come charging on to the Island each week-day morning, out of the mouths of tubes and tunnels."

B "Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night."

C "The commuter dies with tremendous mileage to his credit, but he is no rover."

D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."

Answers

I'm not positive about this one.

C "The commuter dies with tremendous mileage to his credit, but he is no rover."

D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."

Final answer:

The quotations that develop the author's viewpoint about commuters not truly experiencing New York City are highlighted.

Explanation:

The quotations from “Here Is New York” that develop the author’s viewpoint that commuters do not truly experience New York City are:

“Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night.”

“The commuter dies with tremendous mileage to his credit, but he is no rover.”

“Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the seawall.”

These quotes highlight the idea that commuters only see a limited and narrow part of the city, and they do not take the time to truly explore and experience all that New York has to offer.

what triangle congruence theorem is needed?

Answers

side side side
**************************************************************

simplify 4x+2 - x^2 +x-12 / x-3

a) 3x-2
b)3x+4
c)5x-4
d)5x+4

Answers

Answer:

3x-2

Step-by-step explanation:

on edge

How much will be left after 105 Days?

Answers

102 grams would be remaining after a total of 3 half lifes occur in 105 days

There will be 102 grams left.

Since the half-life is 35 days, to figure out how many half-lives to go through, you diving 105 (the number of days total), by 35 (the number of days in a half-life). This gives us 3.

Now, you divide the base number (816 grams) in half. You do this the number of times we got earlier (in this case, three times.)

And that leaves us with 102 grams.

I hope this helps!

a cupcake recipe calls for 1/6 cups of milk and you have 5/8 cups of milk in the refrigerator how many cups of milk will you have remaining after baking the cupcakes

Answers

1/6 = 4/24 5/8 = 15/24
15 - 4 = 11 11/24 cups of milk left

Hope this helps

Answer: 1/8

Step-by-step explanation:

A particular computer takes 13 minutes to download a 39-minute TV show. How long will it take the computer to download a 2-hour movie?

Answers

Final answer:

It will take the computer 40 minutes to download a 2-hour movie based on its current download speed, which is 3 minutes of video per minute of download time.

Explanation:

To answer this question, we first need to establish the download speed of the computer. This can be done by dividing the length of the TV show by the time it takes to download it. In this case, the computer can download 39 minutes of video in 13 minutes, so its download speed is 39/13 = 3 minutes of video per minute of download time.

To find out how long it will take to download a 2-hour movie, we first need to convert the length of the movie to minutes, because our speed is in minutes of video per minute of download time. Two hours is equal to 2*60 = 120 minutes. Therefore to download a 120-minute video, it will take 120/3 = 40 minutes.

Learn more about Download Time here:

https://brainly.com/question/31000914

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