Which of the following rational functions is graphed below?
10
- 10
10
- 10+
O A. F(x) =
X-2
*(x+5)
B. F(x) =
(x + 5)(x-2)
C. F(x) =
(x+5)(- 2)
х
х
D. F(x) =
(x + 5)(x - 2)
Answers
The rational function is:
f(x) = x/ (x - 2)(x + 5).
The correct option is D.
What are the asymptotes?As the function approaches a certain value—typically infinity or negative infinity—as the input approaches positive or negative infinity, this is known as a horizontal asymptote.
When the vertical asymptotes are x = 2 and x = -5, this means that the denominator of the rational expression must contain the factors (x - 2) and (x + 5), but not (x - a) or (x + b) for any other values of a and b.
When the horizontal asymptote is x = 0, this means that the degree of the numerator and denominator must be the same, and the leading coefficients must be equal.
Let's start by setting up the denominator:
denominator = (x - 2)(x + 5)
To satisfy the horizontal asymptote at x = 0, the numerator must also have a factor of x, so we can write:
numerator = kx
where k is a constant to be determined.
To ensure that the rational expression has the desired vertical asymptotes, we need to add any necessary linear or quadratic factors to the numerator.
Since the denominator already has linear factors, we only need to add a quadratic factor.
We can choose any quadratic factor that doesn't affect the horizontal asymptote or the other vertical asymptote.
For example, we can choose:
numerator = kx(x + 7)
Putting it all together, the rational expression is:
f(x) = kx / (x - 2)(x + 5)
To determine the value of k, we can use the fact that the leading coefficients of the numerator and denominator must be equal. The leading term of the numerator is kx², and the leading term of the denominator is x².
Therefore:
k = 1
So the final rational expression is:
f(x) = x / (x - 2)(x + 5)
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Related Questions
A is the point (0, 8) and R is the point (5, 6). Find the point Con the y-axis such that angle ABC is 90°
Answers
Answer:
(0, -13/2) or (0, -6.5)
Step-by-step explanation:
a point on the y-axis means x=0.
so, the solution is a point (0, y).
and I assume (5, 6) is not R but is B.
for the angle at B being 90 degrees, we are looking at a right-angled triangle, and basic Pythagoras has to be true :
c² = a² + b²
with c being the Hypotenuse (the line opposite of the angle with the 90 degrees).
in our case, this c is the connection from A to C.
and a and b are the connections AB and BC.
so,
AC² = AB² + BC²
the distance between two points is again calculated via Pythagoras, where the differences in x and y directions are the sides, and the distance itself is the Hypotenuse.
so, we get
(0-0)² + (8-y)² = (0-5)² + (8-6)² + (5-0)² + (6-y)²
(8-y)² = -5² + 2² + 5² + (6-y)²
64 - 16y + y² = 25 + 4 + 25 + 36 - 12y + y²
64 - 16y + y² = 90 - 12y + y²
64 - 16y = 90 - 12y
-26 = 4y
y = -26/4 = -13/2 = -6.5
solve the equation:
|x+3| >2x-1
Answers
Answer:
x < 4
Step-by-step explanation:
|x+3| >2x-1 [|a| is the absolute value of a]
x+3 > 2x-1
4 > x
Therefore,
x < 4
The negative case doesn't have equal RHS and LHS so, it isn't valid.
Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Select three options.
Answers
Answer:
A. Angle Y is a right angle.
B. The measure of angle Z is 45°.
E. The perpendicular bisector of creates two smaller isosceles triangles.
Step-by-step explanation:
Let x represent the measures of base angles X and Z. 2x is the measure of vertex angle Y.
x + x + 2x = 180°
x = 45°
2x = m∠Y = 90°
The triangle is an isosceles right triangle which has base angles of 45°.
The perpendicular bisector of line XZ creates two smaller isosceles triangles with acute angles of 45°
Answer:
The answers are A B E
Step-by-step explanation:
The graph of a line is shown below. What is the equation of the line, in slope-intercept form, that is parallel to this line and has a y-intercept of 1?
Answers
Answer:
[tex]y = - \frac{3}{2} x + 1[/tex]
Step-by-step explanation:
Slope -intercept form: y= mx +c, where m is the slope and c is the y-intercept.
Parallel lines have the same slope. Let's find the slope of the given line.
Given points: (-2, 0) and (0, -3)
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
slope of given line
[tex] = \frac{0 - ( - 3)}{ - 2 - 0} [/tex]
[tex] = \frac{0 + 3}{ - 2} [/tex]
[tex] = - \frac{3}{2} [/tex]
[tex]y = - \frac{3}{2} x + c[/tex]
Given that the y- intercept is 1, c= 1.
[tex]y = - \frac{3}{2} x + 1[/tex]
calculate the price with VAT of the following case.
MP=Rs.400000
profit=Rs.20000
Discount=10%
VAT=13%
Answers
Answer: $427140
Step-by-step explanation:
Firstly, we'll add MP to the profit and this will be:
= Rs 400000 + Rs 20000
= Rs 420000
Since there is a discount of 10%, this will then be:
= 420000 - (10% × 420000)
= 420000 - 42000
= $378000
With a VAT of 13%, then the final price will be:
= $378000 + (13% × $378000)
= $378000 + (0.13 × $378000)
= $378000 + $49140
= $427140
Given that line a is parallel to line b and that line c isparallel to line d, if m<13 = (12x – 22)° and m<14 = (9x – 29)°, find m<2
Answers
Answer:
∠ 2 = 70°
Step-by-step explanation:
∠ 13 and ∠ 14 are adjacent angles and sum to 180° , then
12x - 22 + 9x - 29 = 180
21x - 51 = 180 ( add 51 to both sides )
21x = 231 ( divide both sides by 21 )
x = 11
Then
∠ 14 = 9x - 29 = 9(11) - 29 = 99 - 29 = 70°
∠ 7 = ∠ 14 = 70° ( Alternate angles )
∠ 2 = ∠ 7 = 70° ( Alternate angles )
find the measure of the missing angles in the kite
Answers
Answer:
Step-by-step explanation:
In a kite, the angles between the two non- congruent side have the same degree.
x = 114 degrees
In a quadrilateral the sum of the inner angles is 360 degrees
88 + (114 * 2) + y = 360
88 + 228 + y = 360
316 + y = 360
y = (360 - 316)
y = 44 degrees
a map of an amusement park is shown on a coordinate plane, where each square of the grid represents 1 square meter. The water ride is at (-17,12), the roller coaster is at (26,-8), and the Ferris wheel is at (2,20). Find each distance to the nearest tenth of a meter.
* what is the distance between the water ride and the roller coaster?
*What is the midpoint between the roller coaster and the ferris wheel? what is the distance from the midpoint to the ferris wheel
Answers
Answer:
Step-by-step explanation:
What is the answer when you evaluate m + p - p2 ÷ 6; use m = 5 and p = 6 ?
Answers
Answer:
5
Step-by-step explanation:
m + p - p^2 ÷ 6
Let m = 5 and p=6
5 + 6 - 6^2 ÷ 6
Exponents first
5 + 6 - 36 ÷ 6
Then divide
5 + 6 - 6
Then add and subtract from left to right
11-6
5
14 A curve has equation y=x2 - 6x² + 16. Find the coordinates of the two turning points.
Answers
Step-by-step explanation:
there is something wrong with your problem description.
you really mean x² - 6x² + 16 ?
or is it 2x - 6x² + 16 ?
in any case this would be a squared equation, which does not have 2 turning points.
we would need an equation with x³.
for that we would create the 1st deviation, which would be then a squared equation with 2 solutions, which would be the 2 turning points of the initial equation.
(06.01)
Write the following expression in exponential form:
1.6 × 1.6 × 1.6 × 1.6
41.6
1.64
1.6 × 4
1.6 + 4
Answers
Answer:
[tex]1.6^{4}[/tex]
Step-by-step explanation:
1.6 is multiplied by itself 4 times. This is represented in exponential form as
[tex]1.6^{4}[/tex]
Stuart needs to run by the store on his way to school. He begins at home, which on a coordinate plane is represented by the point (0,4). He walks to the store, which is the equivalent of walking 2 units right and 4 units down. After grabbing something to eat for lunch, he walks 3 units to the left and 5 units up to school. What point represents the school
Answers
Someone explain what this means ?
Answers
Answer:
20 P 9 means selecting 9 objects (order matters) out of 20 objects.
So in this case, the eight choice of a line up of 9 has 13 options.
For example, think about it this way. The first choice has 20 options, 2nd has 19, and so on...
So the answer is 13
Let me know if this helps!
Anna and Damien still haven't finished inventory for their pet store. They just received a shipment of 4 chinchillas. They already had 3 cages with 4 chinchillas in each. What expression shows Anna and Damien how many chinchillas they have now?
Answers
Answer:
16!
Step-by-step explanation:
4 x 3 = 12 + 4 = 16
twice n
Algebraic expression
Answers
Answer and Step-by-step explanation:
2n is the algebraic expression for twice n.
#teamtrees #PAW (Plant And Water)
5(^ 1/5 +-4) 2(-4)(-0.8)^ 2
Answers
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} \frac{5(\frac{1}{5}+(-4) )}{2\cdot(-4) \cdot (0-0,8)^2} =\frac{^1 \ 5^{ }\!\!\!\!\diagup\cdot \frac{1}{5\!\!\!\!\diagup}-20 }{-8 \cdot 0,64 } = \\\\\\ \frac{-20+1}{-5,12} =\frac{-19}{-5,12} \cdot \frac{25}{25} =\frac{475}{128} =\boxed{\pmb{3\frac{91}{128} }}[/tex]
What is the image of (-3,6) when reflected in the x-axis?
A. (6,-3)
B. (-3, -6)
C. (3,-6)
D. (3, 6)
Answers
The new coordinates are ( -3 , -6) , Option B is the answer.
What is meaning of Reflection ?Reflection means to create a mirror image of an object along any axis .
The shape and size of the object remains constant while reflection.
An object of coordinate ( -3 ,6) is given
This is reflected in the x axis .
When an object is reflected along any axis , the coordinate of that axis remains the same while the coordinate of the other changes to its additive inverse .
object ( -3 ,6) is reflected along x axis ,
( x, y) ----> ( x , -y)
The new coordinates are ( -3 , -6)
Therefore Option B is the answer.
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Marking brainliest
If a job interview says “tell me about yourself” what do u say
Answers
Answer:
I start to say from my name,age,family,qualifications and etc.
Answer:
In your response, do the following:
1. Mention past experiences and proven successes as they relate to the position.Begin by rereading the job description. Take note of the required skills that you have, and identify recent stories that demonstrate them . Ideally, you should draw primarily from recent professional experience; however, volunteer work can also support your narrative while demonstrating a commitment to your community.
2. Consider how your current job relates to the job you’re applying for.Is it a more senior role? If so, explain how you are taking on more responsibilities in your current position. If you are making a lateral transition to a role with different skills, describe how your current skills translate into the new position.
3. Focus on strengths and abilities that you can support with examples.When you start building the script of each example, focus on details and outcomes that you can quantify if possible. For example, stating that you “improved customer service” is less impactful than “increased customer service response rates each quarter by 10–15%.” If you don’t have the exact information, estimate a realistic value.
4. Highlight your personality to break the ice.Since the “Tell me about yourself” interview question is about getting to know you, it’s a good idea to share your personality with your interviewer—but not personal details. You may want to briefly mention hobbies that demonstrate intellectual development and/or community engagement (e.g., reading, music, sports league, volunteering) or those that showcase personal discipline and achievement (e.g., learning a new skill, training for a half marathon). Discussing personal interests is a good way to wrap up your response while maintaining a professional tone.
5. Format your response.For your response to be clear and concise, you’ll want to make sure you organize your answer following a format or formula. There are two common formulas you may consider:
Present, Past, FuturePast, Present, FutureBoth of these formulas work for your response, but you may choose one over the other based on the roles from your experience that are most relevant to the position you're interviewing for. For example, if your most recent role highlights many of the skills and qualifications that are required for the role you’re interviewing with, you may want to lead with the present. However, if you're making a career transition and your past experience is more closely related to the role than your current position, you may want to lead with your past.
Find the total surface area. rectangular prism 4 A. 700 m² B. 3,040 m² C. 135 m² D. 1,308 m²
Answers
Answer:
D
Step-by-step explanation:
The opposite faces of the prism are congruent , then
SA = areas of (top/bottom + front/ back + 2 sides )
= 2(19 × 16) + 2(19 × 10) + 2(16 × 10)
= 2(304) + 2(190) + 2(160)
= 608 + 380 + 320
= 1308 m² → D
The total Surface Area is 1308 m²
What is total Surface area?The total area occupied by the surfaces of an object is called its surface area. In geometry, different 3D shapes have different surface areas which can be easily calculated using the formulas that we will be learning in this article. The surface area is classified into two categories:
Lateral surface area or Curved surface areaTotal surface areaThe total surface area of a prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area = (2 × Base Area) + (Base perimeter × height).
SA = areas of (top/bottom + front/ back + 2 sides )
= 2(19 × 16) + 2(19 × 10) + 2(16 × 10)
= 2(304) + 2(190) + 2(160)
= 608 + 380 + 320
= 1308 m²
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Start from number 11 and keep adding 2 till you get to 201. how many times did you have to add 2 till you got to 201
Answers
Answer:
95 times
Step-by-step explanation:
201=11+(n)*2, 190=(n)*2, n=95
(2x2 + 1) + 3/2x2=1=4
Answers
Answer:
3(2×2+1)+3×(2×2)/3=1×3=4×3
36+3+4=3=12
36+3+4-3-12
43-15
28
Challenge: For a particular job, the Amax Employment Agency charges a fee that is equal to 15% of the first
month's pay. If the job pays X dollars annually, express the agency fee algebraically.
Answers
Answer:
0.0125x or x/80
Step-by-step explanation:
Salary: x dollars per year
To find the pay per month, we divide the annual pay by 12.
The monthly pay is x/12
15% of the first month's salary is
15% of x/12 = 0.15 * x/12 = 0.0125x = x/80
Answer: 0.0125x
Help please! Need this answered quick!
Answers
Answer:
3.6
Step-by-step explanation:
the ratio of AB to AD is 3/5 so the ratio of BC to DE is also 3/5, therefore BC=3/5 DE= (3/5)6= 3.6
How to solve this question pls help asap
Answers
Answer:
answered by g a u t h m a t h
Step-by-step explanation:
The sales tax in a certain city is 2%. A man buys a camera and pays a sales tax of $3.20. What was the cause of the camera, exclusive of the sales tax?
Answers
Answer:
The base cost of the camera, exclusive of sales tax, is $160.
Step-by-step explanation:
Set up this equation and solve for x, which is the cost of the camera:
$3.20 = $0.02x [0.02 = 2%]
Solve the equation by dividing $3.20 by 0.02. The answer is $160.
Answer: $160 for the camera
Step-by-step explanation:
0.2x160=3.2
$160
PLEASE HELP!! Important test!! Option 1 isn't coming up so if you could try to solve others that would be great!
Answers
Answer:
4
Step-by-step explanation:
Func 2 is -2
Func 3 is 1
Func 4 is 8
Func 1 is unknown
the temperature of fridge compartment of a refrigerator is set at 8 °C . the fridge compartment is set at -10°C . what is difference between these temprature sittings
Answers
Answer:
I don't understand the question, but I think its 18°
Step-by-step explanation:
In the opposite figuret triangle OAB has an area of 72 cm2 and. Triangle ODC has an area of 288 Cm2 Then XandY equal
Answers
area of OAB = 72 = (1/2) sin (AOB) * OA * OB solve the above for sin(AOB) to find sin(AOB) = 1/2 area of ODC = 288 = (1/2) sin (DOC) * OD * OD Note that sin(DOC) = sin(AOB) = 1/2, OD = 18 + y and OC = 16 + x and substitute in the above to obtain the first equation in x and y 1152 = (18 + y)(16 + x)...
HOPE SO IT HELPS YOU
15. What is the length of segment FG
Answers
Answer:
10.49
Step-by-step explanation:
FG= squareroot(10)(11) =10.49 took quiz too
what is the answer? I need help!! please and thank you
Answers
Answer:
B
Step-by-step explanation:
27%=0.27 and sqrt(2)<2.75
