The given rational function has a vertical asymptote at x = 12, and the
graph has x and y-intercept at the negative x and y-axis.
Response:
(a) The point (5, -2) is not on the graph
(b) f(x) = -1
The point on the graph of f is (-1, 3)(c) If f(x) = 2, x = 30
The point on the graph of f is (30, 2)(d) Domain = (-∞, 12) ∪ (12, ∞)
(e) x-intercept is at x = -6, which is the point (-6, 0)
(f) The y-intercept is at y = -0.5, which is the point (0, -0.5)
(g) A zeros of f, is x = -6
Which method is used to evaluate the rational function?The possible given function is presented as follows;
[tex]f(x) =\mathbf{\dfrac{x + 6}{x - 12}}[/tex]
(a) When x = -2, we have;
[tex]f(-2) = \dfrac{(-2) + 6}{(-2) - 12} = \dfrac{4}{-14} = \mathbf{-\dfrac{2}{7}}[/tex]
Therefore;
The point ([tex]-\frac{2}{7}[/tex], -2) is on the graph, which gives;
The point (5, -2) is not on the graph(b) If x = 3, we have;
[tex]f(3) =\mathbf{ \dfrac{3 + 6}{3 - 12}} = \dfrac{9}{-9} =-1[/tex]
f(3) = -1The point on the graph of f is (-1, 3)(c) If f(x) = 2, we have;
[tex]f(x) =2 = \mathbf{ \dfrac{x + 6}{x - 12}}[/tex]
2·(x - 12) = x + 6
2·x - x = 6 + 2 × 12 = 30
x = 30
If f(x) = 2, x = 30The point on the graph of f is (30, 2)(d) The domain which is the list of possible x-values, which is expressed as follows;
Domain; -∞ < x < 12, and 12 < x < ∞
Which gives;
Domain = (-∞, 12) ∪ (12, ∞)(e) The x-intercepts are;
[tex]0 = \mathbf{ \dfrac{x + 6}{x - 12}}[/tex]
x-intercept is at x = -6, which is (-6, 0)(f) The y-intercept
[tex]At \ the \ y-intercept, \ f(x) = \dfrac{0 + 6}{0 - 12} = -\dfrac{1}{2} = \mathbf{ -0.5}[/tex]
The y-intercept is at y = -0.5, which is (0, -0.5)(g) The zeros of the graph, f, are the points at which the graph crosses the x-axis which at the point x = -6
A zeros of the graph is x = -6Learn more about the graph of functions here:
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What’s the correct answer for this question? Any help would be appreciated
Answer:
28.317 litres
62.8 litres
3x+3x+3x+3x+4x
what is the measure of vertex A
Answer:
16x
Step-by-step explanation:
just sum all of it friend π - π
the awnser is 16x duh that's easy how do u not know
2. In a random sample of 87 college students, the average number of GroupMe messages handled in
one day is 49. The 95% confidence interval for the mean number of messages handled by students
daily is given as 47 to 51.
a. What is the population standard deviation of the sample?
b. If the number of samples were doubled, by what factor would the confidence interval change
(keeping the same confidence level?)
We have that the population standard deviation and confidence interval is mathematically given as
SD=1
W = 2.8284
Standard deviation and the new widtha) Generally, normal distribution 95% of the values lies within 2 standard deviations from the mean.
Therefore, we have here:
2*2SD = 51 - 47
2*2SD
SD=1
Hence, the standard deviation is
SD=1
b)
Where,the margin of error is inversely proportional to the square root of sample size.
1 / sqrt{2}
Hence, the new width is
1 / sqrt{2}[tex]1 \ sqrt{2}[/tex]
W = 2.8284
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Sophie has 60 pencils.
The ratio of sharpened pencils to blunt pencils is 4:1
How many sharpened pencils does Sophie have?
Answer:
30
Step-by-step explanation:
Because of the following statement is not true no.of atoms
Answer:
48
Step-by-step explanation:
4+1=5
60÷5=12
12×4=48
29. Find CD.
30. Find ZV.
Answer:
for cd it's 12 I believe fs
1. integers less than or equal to +5 but greater than -5
2. negative integers greater than -8 but less than +10
[tex] \tt\huge Answer \to[/tex]
5 , 4 , 3 , 2 , 1 , 0 , - 1 , -2 ,-3 , -4-7, -6 , -5, -4 , -3 , -2 , -1look at the photo attached for the question, please help asap!
Answer:
y ≥ - 0.8
Step-by-step explanation:
[tex]\sqrt{25y^2 +40y+16}[/tex] = 5y + 4
[tex]\sqrt{(5y+4)^2}[/tex] = 5y + 4
5y + 4 = 5y + 4 and 5y + 4 ≥ 0 ⇒ y ≥ - 0.8
y ∈ [ - 0.8 , ∞ )
- ( 5y + 4 ) = 5y + 4
10y = - 8
y = - 0.8
The answer is y ≥ - 0.8
- What is the measure of the external angle which is marked in yellow?
A 156 degrees
B 24 degrees
C 145 degrees
D 53 degrees
Answer:
the measure of the external angle which is marked by yellow is 156 degrees
II. UNKNOWN VALUE. Solve for the measure of the unknown angles in parallel lines cut by transversal
I need it asap
Answer it for 10 points
HELP!!
Select the correct answer from each drop-down menu.
Consider triangle ABC
The center of the circumscribed circle of the triangle lies on segment ____ which is ____ of the circle.
Answer:
ca and diameter
Step-by-step explanation:
Answer:
In the image
Hope this helps!
Step-by-step explanation:
1. AC
2. the diameter
Simplify -3(9+2z).Simplify this expression and I will give you virtual points.
Answer:
-27 -6z
Step-by-step explanation:
"Simplify" in this context means "eliminate parentheses." You do that by making use of the distributive property. The factor -3 outside the parentheses multiplies each term inside parentheses.
-3(9 +2z)
= -3(9) +(-3)(2z)
= -27 -6z
Hey there!
-3(9 + 2z)
= -3(9) - 3(2z)
= -27 - 6z
= -6z - 27
Therefore, your answer is: -6z - 27
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A class consists of 15 boys of whom 5 are prefects.
a) How many committees of 8 can be formed if each consists of exactly 2 prefects?
there would only be one committee of eight, because there is only 15 boys if you add it up 7 + 8= 15 you do not have enough boys to form more than one committee there will be seven boys left out three of which are perfect
What is x3+y3+z3? I need help please.
x^3 + y^3 + z^3
Cannot be fully factored because it is already in it's most simplistic form.
But, I can halfway factor it, which is
(x+y+z)^3 - 3( yx^2 + zx^2 + xz^2 + yz^2 + xy^2 + zy^2 + 2xyz )
HELPPPPPPPPPPPPP FAST PLS
Answer:
angle xdq= 90-49= 41
angle uxd= 180-41= 139
Step-by-step explanation:
A right angle equals 90 degrees.
90-49 = angle xdq = 41 degrees
49 + 90 + x = 180
angle x = 41
180-41 = angl uxd = 139
find the coordinates if the midpoint of the line segment whose endpoints have the given coordinates (2,4) and (6 ,8)
Answer:
[tex]m = \frac{y2 - y1}{x2 - x1} \\ \frac{8 - 4}{6 - 2} \\ = \frac{4}{4} \\ m = 1[/tex]
Answer:
if you mean find the coordinates "of" the midpoint then the solution is
Step-by-step explanation:
(x1+x2)/2 and (y1+y2)/2
so
(2+6)/2=8/2=4 and (4+8)/2=12/2=6
so the coordinates of the midpoint of the given segment is
(4,6)
please help worth 100 pts
Answer:
the first one is x=20. the second one is x=31.33 cm.
Step-by-step explanation:
1. x=20
2. x=31.33 cm
Hope this helps!!! :)
Find the value of x.
Answer:
x=56
Step-by-step explanation:
Hope this helps!
Answer:
x = 12.05
using sine rule:
[tex]\boxed{sin(a) = \frac{opposite}{hypotenuse} }[/tex]
Here given the angle is 35° and hypotenuse is 21.
To find x:
→ sin(35) = [tex]\frac{x}{21}[/tex]
→ x = 21 * sin(35)
→ x = 12.04510516
→ x = 12.05 ................rounded to nearest tenth.
make h the subject of formula
[tex]v = \frac{1}{2} lbh[/tex]
Answer:
Step-by-step explanation:
Multiplying both sides of this equation by 2 eliminates the fraction:
2v = lbh
and dividing both sides by lb isolates (solves for) h:
2v
h = ---------
lb
Education researchers are interested in the workload expectations of freshmen at a local university. Which of the
following techniques would give a stratified random sample?
Randomly select 10 freshmen from each of the majors at the university
Randomly select 10 freshmen from the cafeteria on each of the 5 days of the first school week.
Randomly select 1 professor at the university and have them survey all of their freshman students.
Survey the students in some randomly selected freshman seminar classes, since freshmen are randomly put into
those classes
Answer:
A: Randomly select 10 freshmen from each of the majors at the university.
Step-by-step explanation:
This is because stratified random sampling is taking a population and dividing them into subpopulations. So, majors would be the best way to divide up college freshmen into different subsections to survey them about their workloads because each major would have a different answer and result.
The techniques to give a stratified random sample would be A: Randomly select 10 freshmen from each of the majors at the university.
What is simple random sampling?If the sampling is done from the population randomly, without any other rule, then such sampling is called simple random sampling. Items are selected in a fixed size, all randomly.
The best sampling is simple random sampling, as it is randomly picking data values from the population.
Stratified random sampling it is taking a population and dividing them into subpopulations.
The majors would be the best way to divide up college freshmen into different subsections to survey them about their workloads because each major would have a different result.
The techniques to give a stratified random sample would be A: Randomly select 10 freshmen from each of the majors at the university.
Learn more about sampling here:
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if f(x) = 3x^2 express the value of f(2+h)-f(2)/h as a polynomial in terms of h.
A. 3h+12
B. 6h
C. 3h+3
D. 6h+6
Answer:
Step-by-step explanation:
Car A is traveling west at 40 mph and car B is traveling north at 55 mph. Both are departing from the intersection of two roads at the same time. Write a function representing the distance between the two cars in terms of the time , in hours, that has elapsed since the cars left the intersection.
Answer:
[tex]5\sqrt{185}t[/tex]
Step-by-step explanation:
after time t (hr), the distance between A and starting point is 40t
the distance between B and starting point is 55t
These two distances are perpendicular to each other, so
the distance between A and B is
[tex]\sqrt{(40t)^2+(55t)^2}=\sqrt{4625t^2}=5\sqrt{185}t[/tex]
Felicia pours juice from a carton into a glass. Every time she fills the glass, the amount of juice in the carton changes by −0.44 L. She fills her glass 2 3/4 times in all. Bernadette has a different carton of juice that is the same size. Every time she fills her glass, the amount of juice in her carton changes by −0.42 L. She fills her glass 2 2/3 times in all. Who has the greater total change in the amount of juice in their carton? Show your work. Explain your reasoning.
The length of a diagonal of square is 20cm.
a) Find the length of a side of the square.
b) Show that the area of the square is 200cm²
I'll mark you as brainliest
[tex]\bold{\huge{\underline{ Solutions }}}[/tex]
Given :-The length of a diagonal is 20 cmTo Find and prove :We have to find the length of a side of the square We also have to show that the area of square is 200 cm²Solution ( a)We have,
The length of the diagonal of a square is 20 cmWe know that,
[tex]\bold{\red{ d = }}{\bold{\red{\sqrt{2}}}}{\bold{\red{ a }}}[/tex]
Where, a is the length of the side of the square d is the the length of the diagonalSubsitute the required values in the above formula :-
[tex]\sf{ 20 = }{\sf{\sqrt{2}}}{\sf{ a }}[/tex]
Squaring on both the sides :-
[tex]\sf{ 400 = 2a^{2}}[/tex]
[tex]\sf{\dfrac{400}{2}}{\sf{ = a^{2}}}[/tex]
[tex]\sf{ 200 = a^{2}}[/tex]
[tex]\bold{ a = 14.14 cm }[/tex]
Hence, The side of the square is 14.14 cm
Solution ( b) :-Here, we have to prove that,
The area of square is 200 cm²We know that,
Area of square
[tex]\bold{\pink{ = side}}{\bold{\pink{\times{ side}}}}[/tex]
The side of the square is 14.14 cmSubsitute the required values,
[tex]\sf{ = 14.14 }{\sf{\times{ 14.14}}}[/tex]
[tex]\bold{ = 200 cm^{2}}[/tex]
Hence, It is proved that the area of the square is 200 cm².
The Rose garden is formed by joining the rectangle in the semicirculation below the rectangle is 22 ft long and 18 ft wide if the gardener wants to build a fence around the garden how many feet of fences required
First, let's find the area of the rectangle.We know that the area of a rectangle is the length times width, or 20⋅32in this example:20⋅32=640So the area of the rectangle is 640ft2.You may not know the area of a semicircle, but that's fine −we know the area of a circle, or πr2.Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by 2:So the area of a semicircle is πr22.The question asks for πto just be 3.14, so instead the equation is A=3.14r22The picture gives the diameter of the circle.To find the radius, or r, we divide the diameter by 2:202=10Now we can solve for the area of the semicircle:3.14(10)223.14(100)23142157ft2Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:640+157=797ft2
Help PLEASEEE!!!
Given that AC=30, AB=5x-21, BC=3y+4, CD=2x-3, and DA=4x+1, find the indicated variables for each question. Find the value of x, y, z.
Answer:
x = 6
y = 7
z = 23
Step-by-step explanation:
ÀC = z + 7
30 = z + 7
30 - 7 = z
z = 23
2x - 3 = 5x - 21
21 - 3 = 5x -2x
18 = 3x
x = 18÷3
x = 6
4x + 1 = 3y + 4
4(6) + 1 = 3y + 4
25 = 3y + 4
3y = 25 - 4
y = 21 ÷ 3
y = 7
please mark as brainliest i appreciate so much
Tevin leaves school to walk home. His friend, Karen, notices 0.2 hours later that Tevin forgot his phone at the school. So Karen rides her bike to catch up to Tevin and give him the phone. If Tevin walks at 2 mph and Karen rides her bike at 8.2 mph, find how long (in hours) she will have to ride her bike until she catches up to him.
Answer:
Step-by-step explanation:
equation is:
8.2x=0.2x+0.4
if x is time
8.2x-0.2x=0.4
8x=0.4
x=0.05 hours from when Karen starts and 0.45 hours fromt the time tevin started.
can someone pls look at the recent questions on my page.
Answer:
sure I will
Step-by-step explanation:
please give brainiest
Answer:
where is your pic can you post
HELPP! i don’t know this
Answer: A
Step-by-step explanation:
Using the 3D Pythagorean theorem, [tex]AB=\sqrt(6^2 + 4^2 + 1^2)=\sqrt(53)[/tex]
ANSWER FOR 100 POINTS!!! VERY EASY QUESTION, BUT NEED EXPLANATION AS IT's A FREERESPONSE
In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while point E is the point of intersection between segment AG and segment DF.
Prove ΔABC ∼ ΔGEF.
Step-by-step explanation:
We are given that ∠ABC≅∠DEC and ∠GFE≅∠DCE
By Vertical Angles: ∠DEC≅∠GEF and ∠DCE≅∠ACB
By Substitution: ∠ABC≅∠GEF and ∠GFE≅∠ACB
By Angle-Angle Similarity: ΔABC~ΔGEF
Hope this helps! Sorry if I didn't explain well :(
given that sectheta - tantheta =1/4, find sectheta + tantheta
Answer:
4
Step-by-step explanation:
{sec(θ) - tan(θ) = 1/4, sec(θ) + tan(θ)} = tan(θ) + sec(θ) = 4
use subsitution