please help with this vertical asymptote of rational functions problem
A. x= -5
B. x=0
C. x= -2
D. x= 5
Answers
[tex]f(x)= \frac{5x+10}{ x^{2} +7x+10} \\ \\ f(x)= \frac{5(x+2)}{ x^{2} +2x+5x+10} \\ \\ f(x)= \frac{5(x+2)}{(x+2)(x+5)} [/tex]
x+2 occurs in both numerator and denominator. This means there is a hole at x=-2, this can also be seen from the graph.
So, the vertical asymtptote will occur at the point where:
x+5=0
⇒
x = -5
So, option A gives the correct equation of the vertical asymptote of the function
x=-5
The explanation is shown below:
1.To solve this problem you must apply the proccedure shown below:
2. You must factor the denominator, as following:
f(x)=(5x+10)/(x^2+7x+10)
f((x)=(5x+10)/(x+2)(x+5)
x+5=0
x=-5
Related Questions
Suppose that a jar contains 4 pens: 2 black, 1 blue, and 1 red. three people select a pen at random from the jar, sign a document, and replace the pen in the jar before the next person selects a pen. what is the probability that none of the people use the red pen to sign the document?
Answers
which function is a quadratic function?
Answers
Answer:
y = -2x² - x is quadratic function.
Step-by-step explanation:
Given : Function .
To find : Which function is a quadratic function.
Solution : We have given that functions .
Quadratic function: A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers.
We can see from given options
y = -2x² - x in form of f(x) = ax² + bx + c,
Where, a = -2 , b = -1 c = 0
Therefore, y = -2x² - x is quadratic function.
The coordinate grid shows the plot of four equations. A coordinate plane is shown with four lines graphed. Line A crosses the x axis at negative 3.2 and has a slope of 4. Line B crosses the x axis at 3 and the y axis at 6. Line C crosses the x axis at 1.5 and the y axis at negative 6. Line D crosses the x axis at negative 3 and the y axis at 3. Which set of equations has (2, 2) as its solution? A and D B and D A and C B and C
Answers
m=(y-y)/(x-x) and y=mx+b
Line A
y=4x-3.2
Line B
(3,0) and (0,6)
m= 6/-3= -2
y= -2x+b
0=-2(3)+b
b=6
y= -2x+6
Line C
(1.5,0) and (0,-6)
m=-6/-1.5=4
y=4x+b
0=4(1.5)+b
b = -6
y=4x-6
Line D
(-3,0) and (0,3)
m=3/3=1
y=x+b
0=-3+b
b=3
y=x+3
The equation sin(40o) =b/20 can be used to determine the length of line segment AC. What is the length of AC? Round to the nearest tenth.
Answers
sin (40o) = b / 20
Clearing b we have:
20 * sin (40o) = b
Therefore, the length of the AC segment is given by:
b = 12.9
Answer:
the length of AC is:
b = 12.9
A and B share the cost in a ratio of 3:2. A pays £125 how much does b pay?
Answers
3 + 2 = 5
125 divided by 5 = 25
25 x 3:2 = 2
25 x 2 = 50
To solve this problem, we can set up proportion, which is two equivalent ratios. In this case, we are using the ratio of A to B to figure out the amount that B pays using our value for A. We are allowing x to represent the unknown value for the B payment. This is modeled below:
3/2 = £125/x
To simplify, we can perform cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other and setting it equal to the product of the other numerator and denominator. This is modeled below:
(125)(2) = (3)(x)
Next, we can simplify the equation by performing the multiplication on both sides of the equation.
250 = 3x
Finally, we should divide both sides by 3 to get our unknown variable x alone on the right side of the equation.
x = 83.33
Therefore, B costs £83.33.
Hope this helps!
The ratio of the areas of two similar polygons is 400:25. what is the ratio of their corresponding sides
Answers
A1 / A2 = 400/25 = k ^ 2
Therefore, the relationship of the sides is given by:
L1 / L2 = k
Clearing k we have:
k = root (400/25)
Rewriting we have:
L1 / L2 = k = 20/5
Answer:
The ratio of their corresponding sides is:
20: 5
Answer: 16:1
simplify 400:25 by dividing 400 by 25, which is 16.
The velocity of sound in air is given by the equation
please only answer if you're gonna show work
Answers
[tex]v=20 \sqrt{273+t} \\ \\ 329=20 \sqrt{273+t} \\ \\ 16.45 =\sqrt{273+t} \\ \\ 270.6025=273+t \\ \\ t=-2.3975 [/tex]
This solution can also be seen from graph attached below. The blue horizontal line shows the velocity equal to 329 meter per second.
A system of equations is shown below:
x + y = 3
2x – y = 6
The x-coordinate of the solution to this system of equations is _____.
Answers
1. You have the following system of equations:
x+y = 3
2x–y = 6
2. Then, you must clear the variable y from the first equation and susbtitute it into the second equation, as below:
x+y=3
y=3-x
2x-y=6
2x-(3-x)=6
2x-3+x=6
3x=6+3
3x=9
3. Therefore, the value of x is:
x=9/3
x=3
4. As you can see, the correct answer is:
x=9
Why are jobs at food stands and restaurants good for college students?
Answers
Answer:
The reason a university student is looking for work is that he needs an extra salary income.
Step-by-step explanation:
It is a way to get a salary without overloading tasks.
In addition to that many times, they are given the time to study and work because there are very flexible schedules.
The university student gets used to the need to work for a fixed salary.
In addition, many university students need income to be able to pay the value of the semester or any project necessary for the university.
Keisha is investing her money in an IRA. Initially she will be putting in $775. Using C as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year.
Answers
Monthly investments = $C
Period of investment = 1 year = 12 months
Total monthly investments = Monthly amount*12 = C*12 = 12C
Total investment after 12 months = Initial investment + Total monthly investments = 775 + 12C
An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. (a)
A list of the names and addresses of all customers who bought the new cars is available. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.
Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or 32.5%, reported a problem specifically with the power door locks. (b)
Explain why 0.325 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven. (c)
Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.
Answers
1) Define the sample population: who are the customers you want to contact?
The costumers who bought a new car on a certain year.
2) Define the size of population: how many customers are you going to contact?
Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: how are you going to contact the customers?
You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: what is the time or contact frame to get in touch with your customers?
You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: is yours a qualitative or quantitative research?
In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
= 0.013
Therefore,
N = 0.013 × 30000
= 390
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
Analyzing the situation of the automobile industry it will be important that:
A)build a list that attracts buyers to cars, looking for an interested audience, through emails, nearby residents.
B) 0.013
C)390
If it is necessary to analyze how to attract a corresponding public so that a car sale can take place, a list will be created that takes into account:
A) 1) Define the sample population: The costumers who bought a new car on a certain year.
2) Define the size of population: Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
[tex]P= \frac{13}{1000} = 0.013[/tex]
[tex]N=0.013*30000=390[/tex]
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit. part
a.determine the vertex. what does this calculation mean in the context of the problem? part
b.determine the x-intercepts. what do these values mean in the context of the problem?
Answers
f(x)=-x^2+16x-60
a)a.determine the vertex. what does this calculation mean in the context of the problem?
The vertex form is given by y=(x-h)^2+k, where (h,k) is the vertex:
y=f(x)=-x^2+16x-60
y=x^2-16x+60
c=(-b/2a)^2
b=16
thus
c=(-16/2)^2=64
hence:
y=x^2-16x+64+60-64
y=(x-8)(x-8)-4
y=(x-8)^2-4
hence the vertex form will be:
y=(x-8)^2-4 the vertex is (8,-4)
The vertex represents the highest point of the graph which is the highest daily profits attained.
b] determine the x-intercepts. what do these values mean in the context of the problem?
let y=0 thus
0=−x2 + 16x − 60
factorizing the above we get:
0=x^2-16x+60
0=x^2-6x-10x+60
0=x(x-6)-10(x-6)
thus
x=6 and x=10
thus the x-intercepts are x=6 and x=10, they represent the breakeven point. The minimum number of units they can sell and not make any profit
Graph f(x)=- square root -x
Answers
[tex]x=0\to f(0)=-\sqrt0=0\to(0;\ 0)\\\\x=-0.25\to f(-0.25)=-\sqrt{-(-0.25)}=-\sqrt{0.25}=-0.5\to(-0.25;-0.5)\\\\x=-1\to f(-1)=-\sqrt{-(-1)}=-\sqrt1=-1\to(-1;-1)\\\\x=-4\to f(-4)=-\sqrt{-(-4)}=-\sqrt4=-2\to(-4;-2)[/tex]
The graph of function f (x) = - √- x is shown in image.
We have to given that,
Graph the function,
f (x) = - √- x
Here, Function is defined as,
f (x) = - √- x
At x = 0;
f (x) = - √-0
f (x) = 0
Plot the graph of function f (x) = - √- x.
Hence, The graph of function f (x) = - √- x is shown in image.
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The steepness, or grade, of a highway or railroad is expressed as a percent. In the photo of the cog railway at Pike’s Peak, in Colorado, the grade is 18%. Thus, for every 100 ft of horizontal run, the train rises 18 ft. Find the angle of the inclination of the railway.
Answers
The angle of inclination will be between the hypotenuse of the triangle and the bottom leg. The bottom leg is the 100 ft run. The rise of 18 feet will be the other leg, which is opposite this angle.
This gives us the sides opposite and adjacent the angle we are looking for; opposite/adjacent is the ratio for tangent:
tan x = 18/100
We can solve this using inverse tangent:
tan⁻¹ x = tan ⁻¹(18/100)
x = 10.2°
The negative sign can be read as "the opposite of." true or false
Answers
Answer:
true
Step-by-step explanation:
m 2 = 40°, m 4 = 150°, m 3 =
Answers
First you have to find angle 1
angle 1 and angle 4 are supplementary meaning they add to 180
angle 1 + angle 4 = 180
angle 1 + 150 = 180
angle 1 = 30
The angles in a triangle always add up to 180
angle 1 + angle 2 + angle 3 = 180
30 + 40 + angle 3 = 180
70 + angle 3 = 180
angle 3 = 110
The answer is 110°
Hope this helps!
The answer is 110° Hope this helps!
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 2
B. 12
C. 13
D. 1
Answers
Please, see the attached file.
Thanks.
To convert a distance of 1.25 miles to feet, which ratio could you multiply by? Remember that 1 mile = 5280 feet.
Answers
1 mile is equal to-----------> 5280 feet
1.25 miles------------> x
x=1.25*(5280/1)-----> 6600 ft
ratio=5280 ft/1 mile
the answer is
the ratio is (5280 ft/1 mile)
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0
Answers
Then we see were the graph cuts the x-axis, and these values of x are the real solutions of the given equation:
The real solutions of the given equation are:x = -1, 3, and 7
Answer:
c: x=-1,3,7
Step-by-step explanation:
Find the margin of error for each sample. Then find an interval likely to contain the true population proportion.
a. 15% of 457 teachers
b. 56% of 87 musicians
Full answers please
Answers
a) For n = 457, p = 0.15, mean x = 68.55, standard error = sqrt[p(1-p)/n] = 0.0167. Then the confidence interval is x +/- z*SE, which is68.55 +/- 1.96*0.0167 gives the interval (68.52, 68.58).
b) For n = 87, p = 0.56, man x = np = 48.72, SE = sqrt(0.56*0.44/87) = 0.1043The confidence interval will be 48.72 +/- 1.96*0.1043, which gives (48.52, 48.92).
In the coordinate plane line p had slope 8 and y intercept (0,5). Line r is the result of dilating line p by a factor of 3 with (0,3) what is the slope and y intercept of line r?
Answers
The slope of line r is 24 and the y-intercept is (0, 3).
How to find the slope and y-intercept?
To find the slope and y-intercept of line r, which is the result of dilating line p by a factor of 3 with a center at (0,3), we can use the following steps:
The slope of the dilated line r is the product of the dilation factor and the slope of the original line p.
The y-intercept of the dilated line r is the point where the original line p intersects the line of dilation.
Given that line p has a slope of 8 and a y-intercept of (0,5), the slope of line r is:
8 * 3 = 24.
The y-intercept is (0, 3)
Therefore, the slope of line r is 24 and the y-intercept is (0, 3).
If (x + 1)(x - 3) = 12, then which of the following statements is true?
Answers
A rectangular room has an area of 315 square feet. the length is 6 feet more than the width. find the dimensions of the room.
Answers
Length - (x+6)ft.
x(x+6)=315
x²+6x-315=0
a=1, b=6, c=-315
D=b²-4ac=36+4*1*315=1296, √D=√1296=36
[tex] x = \frac{-b+/- \sqrt{D} }{2a} \\ \\ x= \frac{-6+/-36}{2} \\ \\ x=15, x=-21[/tex]
For the width we can use only positive number.
The width =15 ft.
The length =15+6=21 ft.
Check :
Area =15*21=315 ft²
The room's width is calculated to be 15 feet, and the length, which is 6 feet more than the width, comes to 21 feet. These dimensions satisfy the given area of 315 square feet for the rectangular room.
To find the dimensions of a rectangular room with a known area where one dimension is dependent on the other, we can use algebraic methods to determine the length and width. In this case, the area of the room is given as 315 square feet and it is known that the length is 6 feet more than the width. Let's denote the width of the room as 'w' feet. Therefore, the length will be 'w + 6' feet. The area of a rectangle is calculated by multiplying the length by the width, so we have the following equation:
w imes (w + 6) = 315
Expanding the left side of the equation gives us:
w²+ 6w = 315
To find the value of w, let's move all terms to one side to form a quadratic equation:
w²+6w - 315 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. For this case, factoring is applicable. We look for two numbers that multiply to -315 and add up to 6. The numbers 21 and -15 satisfy this condition. Therefore, we can write the equation as:
(w + 21)(w - 15) = 0
The possible solutions for w are -21 or 15; since a width cannot be negative, we take the positive solution:
w = 15 feet
Having obtained the width, we can now find the length:
Length = w + 6 = 15 feet + 6 feet = 21 feet
Therefore, the dimensions of the room are 15 feet in width and 21 feet in length.
The ratio of gold charms to silver charms is 1:3. Which statement does not describe the relationship?
Answers
The ratio from gold charms to silver charms is 1:3
This means for every gold charm there are 3 silver ones
Choice A says the opposite so this is the answer
The answer is A) For every silver charm, there are 3 gold charms.
Hope this helps!
Answer: A
Step-by-step explanation:
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.
Answers
Answer:
At 10 PM both candles will be same height.
Step-by-step explanation:
Let h represent the number of hours.
We have twelve inch candle and an 18 inch candle are lit at 6pm and the 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns 2 inch every hour.
Height 18 inch candle after h hours, = 18 - 2h
Height 12 inch candle after h hours, = 12 - 0.5h
At same height we have
18 - 2h = 12 - 0.5h
1.5 h = 18 - 12
h = 4 hours.
Time = 6 PM + 4 hours = 10 PM
At 10 PM both candles will be same height.
Answer:
At 10 PM, both the candles will be of same height.
Step-by-step explanation:
Two candles are lit at 6 PM.
The length of candles is 12 inch and 18 inch.
The rate of burning of 12 inch candle is 0.5 inch per hour.
The rate of burning of 18 inch candle is 2 inch per hour.
Let [tex]h[/tex] represents the number of hours of burning.
In [tex]h[/tex] hours, the remaining length of the 12 inch candle will be,
[tex]l_1=12-0.5\times h[/tex]
In [tex]h[/tex] hours, the remaining length of the 18 inch candle will be,
[tex]l_2=18-2\times h[/tex]
Now, it is required to find the time at which the length of both the candles will be same.
So, the time [tex]h[/tex] in hours will be,
[tex]l_1=l_2\\12-0.5h=18-2h\\1.5h=6\\h=4\rm hour[/tex]
So, after 4 hours, both the candles will be of same length.
Therefore, the time will be [tex]6+4=10[/tex] PM. At 10 PM, both the candles will be of same height.
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If using the method of completing the square to solve the quadratic equation x^2+13x-35=0x 2 +13x−35=0, which number would have to be added to "complete the square"?
Answers
Answer:
42.25 or 169/4 on delta math
Step-by-step explanation:
The table below shows the number of hours some college athletes in two states spend on indoor sports each week:
State A 7 9 5 4 25 21 6 6 8
State B 14 12 10 13 15 14 11 15 16
Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)
Part B: Are the box plots symmetric? Justify your answer. (4 points)
Answers
State B: 14 12 10 13 15 14 11 15 16
When arranged in order,
State A: 4 5 6 6 7 8 9 21 25
State B: 10 11 12 13 14 14 15 15 16
Part A:
For state A, Q1 = minimum number = 4, Q2 is the lower quartile = 6, Q3 is the middle number = 7, Q4 is the upper quartile = (9 + 21)/2 = 15, Q5 = maximum number = 25
Interquatile range = upper quatile - lower quatile = 15 - 6 = 9
For state B, Q1 = minimum number = 10, Q2 is the lower quartile = 11.5, Q3 is the middle number = 14, Q4 is the upper quartile = 15, Q5 = maximum number = 16
Interquatile range = upper quatile - lower quatile = 15 - 11.5 = 3.5
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Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree
Answers
The velocity of current = 5 ∠213° = (5 cos 213°) i+ (5 sin 213°) j
So, the resultant velocity = 22 ∠157° + 5 ∠213°
= (22 cos 157°) i+ (22 sin 157°) j + (5 cos 213°) i+ (5 sin 213°) j
= (22 cos 157° + 5 cos 213°) i + (22 sin 157° + 5 sin 213°) j
= -24.444 i + 5.873 j
= 25.14 ∠166.5°
The correct answer is option (1)
1) 25 knots at 166.5 degree
The sum in a half adder can be represented by what boolean expression (assuming a
Answers
If they are both 0, the sum is 0. If they are both 1, the sum is 0 and the carry is 1.
This is the XOR logic gate; either one of the two inputs, but not both. In boolean algebra, XOR can be represented as: ¬AB + A¬B
Danielle built a ramp with a stopping block at the bottom for her scout troop’s pinewood derby. She wants to paint the top and sides of the ramp. Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Did Danielle calculate the area correctly? If not, what was her mistake?
A. Yes, Danielle calculated the area correctly.
B. No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
C. No, Danielle needs to add 1 triangle to the ramp and remove 1 rectangle from the block.
D. No, Danielle needs to remove 1 triangle from the ramp and add 1 rectangle to the block.
Answers
Answer:
Actually its b).
Step-by-step explanation:
She only wants to paint the top and sides of the ramp therefore you will have to take off the bottom parts of the ramps aka b).
No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. The space inside the perimeter or limit of a closed shape is referred to as the "area".
Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Danielle calculated some extra Areas.
As, per the discussion Danielle do not need to calculate the part ramp and block that coincides.
Thus, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
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