Which of the following rational functions is graphed below?
A. F(x) =1/(x-4)^2
B. F(X) =1/(x + 4)^2
C. F(X) = 1/4x^2
D. F(x) = 4/x^2
Answers
Answer to your question is B. f(x)= 1/(x+4)^2
The equation of the rational function is f(x) = 1/(x + 4)^2
How to determine the graph?From the figure, we have the following property:
Vertical asymptote at;
x = -4
Add 4 to both sides
x + 4 = 0
Square both sides
(x + 4)^2 = 0
The above means that the denominator of the equation of the graph is (x + 4)^2
So, we have:
f(x) = 1/(x + 4)^2
Hence, the equation of the rational function is f(x) = 1/(x + 4)^2
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Related Questions
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 4, 0), (-2, -5, 2), and (-2, 2, 1).
Answers
17 cubic units.
Step-by-step explanation:
The volume (V) of a parallelepiped with one vertex at the origin is given by the absolute value of the scalar vector product of the vectors at the adjacent vertices.
V = |(a x b) · c|
In this case,
a = (1,4,0) = i + 4k + 0j
b = (-2,-5,2) = -2i -5j + 2k
c = (-2,2,1) = -2i + 2j + k
First, let's calculate the cross product of vectors a and b. i.e a x b as follows:
(i) Arrange the vectors in a matrix form
a x b = | i j k |
| 1 4 0 |
| -2 -5 2 |
(ii) Calculate the determinant of the matrix
a x b = i(8 - 0) -j(2-0) + k(-5+8)
a x b = i(8) -j(2) + k(3)
a x b = 8i - 2j + 3k
Secondly, calculate the scalar product of the cross product found above and the vector c as follows;
(a x b) . c = (8i - 2j + 3k) · (-2i + 2j + k)
Multiply like terms
(a x b) . c = (8 * -2)(i.i) + (-2 * 2)(j.j) + (3 * 1)(k.k) [i.i = j.j = k.k = 1]
(a x b) . c = (-16) + (-4) + (3)
(a x b) . c = -16 - 4 + 3
(a x b) . c = -17
Thirdly, find the absolute value of the result found above. i.e
|(a x b) . c| = |-17|
|(a x b) . c| = 17
Therefore, the volume of the parallelepiped is 17 cubic units.
ESTION 1
T1
- Say whether you think each statement is True or False. Motivate your answer.
1 It always makes sense to talk about a certain percentage of a number, for example 1%
Answers
9514 1404 393
Answer:
False
Step-by-step explanation:
"Always" and "never" statements are generally false--especially when they relate to something like a topic of conversation. Even in the context of math and physics, we find exceptions to most "rules."
[tex]f(x)=\sqrt(x) \\ g(x)=\sqrt((4)/(5)x)[/tex]
Identify a horizontal or vertical stretch or compression of the function f(x)=\sqrt(x) by observing the equation of the function g(x)=\sqrt((4)/(5)x)
A. A vertical compression by a factor of 5/4
B. A horizontal compression by a factor of 5/4
C. A horizontal stretch by a factor of 5/4
D. A vertical stretch by a factor of 5/4
Answers
9514 1404 393
Answer:
C. A horizontal stretch by a factor of 5/4
Step-by-step explanation:
Replacing x in f(x) by kx introduces a horizontal compression by a factor of k, or a stretch by a factor of 1/k. Here, we have k=4/5, so the curve is stretched horizontally by a factor of 5/4.
1,4,1,8,1,16,1 what’s next in the sequence?
Answers
Answer:
32
hope this helps
have a good day :)
Step-by-step explanation:
if a student is selected at random, find the probability that the student is 14 year old
Answers
Answer:
If the student is selected at random the answer is if you put 14 years apart of the student selected at random means the answer are not apart.
Step-by-step explanation:
14 years selected the problem is that 14-9 is more then 9 and u add that up to get the right equation for the 14 years apart
The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the domain of f-1(x)?
Answers
====================================================
Explanation:
Plug in the lower bound of the domain, which is x = -3
f(x) = 3x+2
f(-3) = 3(-3)+2
f(-3) = -9+2
f(-3) = -7
If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.
If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.
The range of f(x) is -7 < y < 17
Recall that the domain and range swap places when going from the original function f(x) to the inverse [tex]f^{-1}(x)[/tex]
This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.
-----------------------
In short, we found the range of f(x) is -7 < y < 17.
That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.
The domain of the resulting function exists on all real values that is the domain is -∞ < f-1(x) < ∞
How to find the domain of an inverse function?The domain of a function are the independent values of the function for Which it exists.
Given the function f(x) = 3x + 2
Find its inverse
y = 3x + 2
Replace x with y
x = 3y + 2
Make y the subject of the formula:
3y = x - 2
y = (x-2)/3
The domain of the resulting function exists on all real values that is the domain is -∞ < f-1(x) < ∞
Learn more on domain here: https://brainly.com/question/26098895
Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that the average community pool membership cost consists of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 40.
Identify and interpret the y-intercept in this model.
Answers
Answer:
40
Step-by-step explanation:
You can find y intercept by looking at the end of the equation, that’s what’s added. So +40 is the y intercept
The y intercept in this equation represents the one-time registration fee
What are the domain and range of this function?
Answers
Answer:
first one. domain: all real numbers, range: {y | y ≥ 0}
Answer:
The domain is all real numbers
The range is y ≥ 0
Step-by-step explanation:
The domain is the values that x can take
The domain is all real numbers
The range is the values that y can take
The range is y ≥ 0
Mention any two similarities between rectangle and square.
Answers
The similarities between a rectangle and a square as:
All 4 angles are 90 deg each.
Opposite sides are parallel and equal.
The diagonals bisect each other.
Circles can circumscribe both figures.
The diagonals form the diameter of the circumscribing circle.
The square root of the sum of the squares of adjacent sides is the diagonal.
The area is the product of adjacent sides.
The diagonals bisect the figure into 2 congruent triangles.
Join the midpoints of opposite sides and you get 4 similar figures of 1/4 the area of the original figure.
Join the midpoints of 4 sides in order and you get a rhombus, whose area is half that of the original figure.
A jeweler purchases a necklace for $80. She will increase the cost by 50% to sell in her
store. What will the jeweler charge for the necklace to her customers?
Answers
Answer:
120
Step-by-step explanation:
First find the markup
80 * 50%
80*.5
40
Add this to the original cost
80+40
120
The price will now be 120
The police station has a parking lot that is 72 feet long by 41 feet wide. Each parking spot measures 8 feet wide and 18 feet deep. Each spot has 23 feet behind it Por the cars to back out. How many parking spots can the police station have?
Answers
9514 1404 393
Answer:
9
Step-by-step explanation:
The total depth of a parking space must be (18 ft +23 ft) = 41 ft. The lot is 72 ft by 41 ft, so can have (72 ft)/(8 ft) = 9 parking spaces.
Complete the explanation on why it is a good idea to use multiple samples when making comparative inferences about two populations.
It is a good idea to use multiple random samples to see how statistical measure vary among the ————-(different/same) samples.
Answers
please help! (listing BRAINLIST and giving points)
Answers
Hope it helps : )
PLS HELP ASAP !!! PLSSS !! will mark whoever answers correctly as brainliest !
Answers
Answer:
60° is the answer sure
I hope the above pic explanation helps
I HOPE IT HELPS
HAVE A GREAT DAY
#Liliflim
Answer:
60°
Step-by-step explanation:
....................................
help help please help help
Answers
Answer:
The range is 5.
Step-by-step explanation:
You can deduce this by concluding all other statements are true, or by calculating the range. 10 - 1 = 9
Pls help LOL I WILL MARK U BRAINLIEST‼️‼️‼️‼️
Answers
Answer:
B=17
A=16
Step-by-step explanation:
It is my friend OK if you want say again and I can ans
What value of x will make the triangle congruent
Answers
Answer:
x = 3/5 = 0.6
Step-by-step explanation:
By the ASA Triangle Congruence Theorem, the two given triangles are congruent (vertical angles are congruent). Because we know that corresponding parts of congruent triangles are congruent, we can write the following equation: 7x - 3 = 2x. Now we can solve:
7x - 3 = 2x
-3 = -5x
3/5 = x
In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High School tested athletes at random and Warrenton High School did not. In a confidential survey, 6 of 108 athletes at Wahtonka and 28 of 129 athletes at Warrenton said they were using drugs. Regard these athletes as SRSs from the populations of athletes at similar schools with and without drug testing.
Required:
a. You should not use the large-sample confidence interval. Why not?
b. The plus four method adds two observations, a success and a failure, to each sample. What are the sample sizes and the numbers of drug users after you do this?
Answers
Answer:
b
Step-by-step explanation:
Circle P contains a diameter AB with coordinates A(1, 2) and B(-7, 2).
5a) State the coordinates of the center.
5b) Determine the length of the radius.
5c)Johnny used the above information for the center and radius and come up with the equation below. Do you agree or disagree with his answer? Explain.
PLEASE ANSWER I DONT HAVE MUCH TIME
Answers
Answer:
[tex]centre = ( \frac{1 - 7}{2} , \: \frac{2 + 2}{2} ) \\ = ( - 3, \: 2)[/tex]
[tex]length = \sqrt{ {( - 7 - 1)}^{2} + {(2 - 2)}^{2} } \\ = \sqrt{ { - 8}^{2} } \\ = 8 \: units[/tex]
radius = 8÷2
= 4 units
Johnny was right
fill in the missing digits pls asap
Answers
Answer:
3 8
× 2 7
______
2 6 6
+ 7 6
_______
1 0 2 6
Answer:
38
x 27
266
+ 76_
1026
Simplify the polynomial (4n2 + 3n - 5) - (2n2 + 3n+ 6)
Answers
We keep brackets
(4n^2 + 3n - 5 ) - (2n^2 + 3n + 6)
We change signs and we group
4n^2 - 2n^2 + 3n - 3n - 5-6
We simplify
2m^2 - 11
Answer: = 2.n^2 - 11
The value of (4n^2 + 3n - 5) - (2n^2 + 3n+ 6) is 2n^2 - 11
How to simplify the expression?The polynomial expression is given as;
(4n^2 + 3n - 5) - (2n^2 + 3n+ 6)
Open the bracket
4n^2 + 3n - 5 - 2n^2 - 3n- 6
Evaluate the like terms
2n^2 - 11
Hence, the value of (4n^2 + 3n - 5) - (2n^2 + 3n+ 6) is 2n^2 - 11
Read more about polynomials at:
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Evaluate A= 2
B= 3
C= 5
) A2+B 2+ C2
C2-4A + 2B
Answers
Answers
A : 38
B :23
4 1) Which of the following is the correct way to solve
(i( 11 x 44? 4 X 11 44 (0) (ii) 4 X 44 11 X 44 4 X 44 11 (iii) (iv) 11 X 44
Answers
Answer:
c)4*44 / 11
Step-by-step explanation:
which of the following is the correct way to solve 4/11 * 44
a) 4*11 / 44
= 44/44
= 1
b) 4*44 / 11*44
= 176/484
= 44/121
c)4*44 / 11
= 176/11
= 16
d)11*44 / 4
= 484/4
= 121
Correct way
4/11 * 44
= (4 * 44) / 11
= 16
In rhombus LMNO, diagonals top enclose L N end enclose and top enclose M O end enclose intersect at P. If the measure of angle L P M is represented by 2x + 70. Solve for x.
Answers
9514 1404 393
Answer:
x = 10
Step-by-step explanation:
The diagonals of a rhombus cross at right angles.
2x +70 = 90
2x = 20 . . . . . . . subtract 70
x = 10 . . . . . . . . . divide by 2
Evaluate the expression 53 ÷ (13 − 8) × 2.
Numerical Answers Expected!
Answers
53 ÷5x2
10.6x2
21.2
Hope this helps
Answer:
21.2
Step-by-step explanation:
BODMAS : First bracket, then Division then multiplication.
[tex]53 \div (13-8) \times 2\\53 \div 5 \times 2\\10.6 \times 2\\21.2[/tex]
plz plz guys solve this i will give you brainliest with procedure
Answers
Answer:
5:9
Step-by-step explanation:
1/5kg:360g
kg to g
1kg=1000g
1/5kg=1/5x1000
=200g
200g:360g
200g/360g
200/360
5/9
5:9
Question 3
Simplify
4x² × 2x³
Answers
Step-by-step explanation:
[tex]4 {x}^{2} \times 2 {x}^{3} = 8 {x}^{5} [/tex]
Answer:
Step-by-step explanation:
4x^2 * 2x^3
(2)^2 *x^2 *2*x^3
(2)^2+1 *x^2+3
(2)^3 *x^5
8*x^5
8x^5
another method
4*x^2*2*x^3
multiply 4 and 2
8*x^2+3
8x^5
in multiplication if the bases are same we add their power(exponent).In division if the bases are same we subtract their power(exponent).
Given that tangent squared theta = three-eighths, what is the value of secant theta?
Answers
Answer:
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Step-by-step explanation:
Given
[tex]\tan^2 \theta = \frac{3}{8}[/tex]
Required
[tex]\sec\ \theta[/tex]
We have:
[tex]\sec^2\theta = 1 + \tan^2 \theta[/tex]
This gives:
[tex]\sec^2\theta = 1 + \frac{3}{8}[/tex]
Take lcm and solve
[tex]\sec^2\theta = \frac{9+3}{8}[/tex]
[tex]\sec^2\theta = \frac{11}{8}[/tex]
Take square roots
[tex]\sec \theta = \frac{\sqrt{11}}{\sqrt 8}[/tex]
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}[/tex]
Rationalize
[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]
Answer:
answer is B
Step-by-step explanation:
i got it right on edg
I’m stuck between 51 or 42 HELP!!!
Answers
Answer:
51
Step-by-step explanation:
Have a nice day :)
What is the probability that a randomly chosen person from this group is a
sophomore and attended the jazz band concert?
Round your answer to two decimal places.
A. 0.56
B. 0.52
C. 0.26
D. 0.31
Answers
Answer:
0.26 or C
Step-by-step explanation:
Basically you would do the sophomores that attended the jazz band concert (35) and divide that by the total number of students. (137) - - 35 ➗ 137 = .2554744526 round that to .26 or 0.26
The probability that a randomly chosen person from this group exists a sophomore and attended the jazz band concert is 0.31.
What is probability?Probability exists about calculating or estimating how possible or 'probable' something exists to occur.
Let A be the event that a person exists a sophomore.
B be the event that a person attended volleyball game.
A∩B denote the event that a person exists a sophomore and attend volleyball game.
P be the probability of an event.
We have to estimate the value of P(A∩B),
Given: A∩B = 42
P(A∩B) = 42/137 = 0.3065 approximately equal to 0.31
P(A∩B) = 0.31.
The probability that a randomly chosen person from this group exists a sophomore and attended the jazz band concert is 0.31.
Therefore, the correct answer is option D. 0.31.
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