Determine the horizontal asymptote for the rational function.
Answer choices:
A.) y= 1
B.) y= -5
C.) y= 1
D.) y= -1
Answers
Answer:
[tex]\text{C) } y=1[/tex]
Step-by-step explanation:
A asymptote represents a control for a function where the function will never touch. We see that as the [tex]y[/tex] approaches 1, [tex]x[/tex] approaches infinity, from either direction. However, the function never touches nor crosses the line [tex]y=1[/tex], and never will. Thus, the horizontal asymptote is located at [tex]y=1[/tex].
y=0 is correct answer but is not in the selection.
Step-by-step explanation:
SOLUTION
For these solutions, we will use \displaystyle f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}, q\left(x\right)\ne 0f(x)=
q(x)
p(x)
,q(x)≠0.
\displaystyle g\left(x\right)=\frac{6{x}^{3}-10x}{2{x}^{3}+5{x}^{2}}g(x)=
2x
3
+5x
2
6x
3
−10x
: The degree of \displaystyle p=\text{degree of } q=3p=degree of q=3, so we can find the horizontal asymptote by taking the ratio of the leading terms. There is a horizontal asymptote at \displaystyle y=\frac{6}{2}y=
2
6
or \displaystyle y=3y=3.
\displaystyle h\left(x\right)=\frac{{x}^{2}-4x+1}{x+2}h(x)=
x+2
x
2
−4x+1
: The degree of \displaystyle p=2p=2 and degree of \displaystyle q=1q=1. Since \displaystyle p>qp>q by 1, there is a slant asymptote found at \displaystyle \frac{{x}^{2}-4x+1}{x+2}
x+2
x
2
−4x+1
.
Synthetic division of the polynomial x^2-4x+1 by x+2 in which it only contains the coefficients of each polynomial.
The quotient is \displaystyle x - 6x−6 and the remainder is 13. There is a slant asymptote at \displaystyle y=x - 6y=x−6.
\displaystyle k\left(x\right)=\frac{{x}^{2}+4x}{{x}^{3}-8}k(x)=
x
3
−8
x
2
+4x
: The degree of \displaystyle p=2\text{ }<p=2 < degree of \displaystyle q=3q=3, so there is a horizontal asymptote y = 0.
Related Questions
What is the value of the following expression? 5.5(k+7), when k= -7
Answers
Answer:
0
Step-by-step explanation:
5.5(-7+7)
5.5(0)
0
Answer:
0
Step-by-step explanation:
putting k = -7
=> 5.5. ( -7 × 7)
=> 5.5 × 0
=> 0
since any number we multiplied by zero is zero
in Lisa’s school, 53% of students take a bus to school, 38% go the bus riders were late one snowy morning. 25% of students who don’t take a bus to school were not late that morning. What percent of students who do not take the bus was late that morning?
Answers
Answer:
I got 53% but I'm not sure
Step-by-step explanation:
if 53% of students take the bus, then 47% of students DON'T.
25% (the percent of non-riding students who were late) of 47 is about 53%
Does anyone know this???
Answers
Answer:
a) 40 is the interquartile range
descriptive statistics, the interquartile range, also called the midspread, middle 50%, or H‑spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q₃ − Q₁.
b).
The first thing you always need to do before estimating fractions is to round each fraction either to the nearest 0, 1/2, or 1. Example #1. Estimate 3/7 + 5/9. Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2. Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.
Kelvin made 12 blueberry muffins for the bake sale he puts 6 muffins in the box how boxes does kelvin math
Answers
Answer:
2 your welcome and I play overwatch
A family of 5 bought airline tickets. In addition to their ticket,each person had to pay $39 to check their bag. They spent a total of $1640.
Find the price of each airline ticket
Answers
Answer:
289
Step-by-step explanation:
5 people pay 39 each for their bag, so, 5*39 is 195
now you have to subtract the cost of the baggage(195) from 1640 to be able to get the total cost of tickets- 1640-195 is 1445
the last thing you do is divide the total cost of tickets by the number of people- 1445/5 is 289
I got it wrong because I’m not too good in math but help a girl out, please
Answers
Answer:
24 is right
Step-by-step explanation:
Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
David gasta el 20% de su salario en el pago de los servicios básicos de su casa del resto gasta el 50% en alimentación si al final se queda con 2000 Córdoba cuanto gana David
Answers
Answer:
Gana 6666,67 Córdoba de los cuales
gasta 3333,33 en alimentos y 1333,33 en servicios.
Step-by-step explanation:
Se queda 2000 Córdoba
Gasta el 20% de su salario para pagar los servicios básicos de su casa.
Gasta el 50% de su salario en comida.
Suponga que gana x cantidad
luego
x = 0,2x + 0,5x + 2000
x = 0,7x + 2000
x-0,7x = 2000
0,3 veces = 2000
x = 2000 / 0,3
x = 6666,67
Gana 6666,67 Córdoba de los cuales
gasta 3333,33 en alimentos y 1333,33 en servicios.
He keeps 2000 Córdoba
He spends 20% of his salary to pay for the basic services of his hous.
He spends 50% of his salary to pay on food.
Suppose he earns x amount
then
x= 0.2x+0.5x+2000
x= 0.7x+2000
x-0.7x=2000
0.3x= 2000
x= 2000/0.3
x= 6666.67
English
He earns 6666.67 Córdoba out of which
he spends 3333.33 on food and 1333.33 on services .
A pole that is 3.4 m tall casts a shadow that is 1.61 m long. At the same time, a nearby building casts a shadow that is 36.75 m long. How tall is the building?
Round your answer to the nearest meter.
Answers
Answer:
Step-by-step explanation:
Set this up as a proportion with pole/building height on the top and shadow length on the bottom, using x for the unknown, which is the height of the building:
[tex]\frac{pole/building}{shadow}:\frac{3.4}{1.61}=\frac{x}{36.75}[/tex] and cross multiply to solve:
1.61x = 124.95 so
x = 78 m
PLEASE HELP According to the stem-and-leaf plot above, how many students scored a
grade lower than 80?
Answers
Answer:
17
Step-by-step explanation:
Do you even know what a stem-leaf plot is?
The scores lower than 80% are:
70, 70, 71, 78, 62, 62, 63, 68, 69, 69, 57, 57, 58, 49, 49, 30, and 21 percent according to the data given. That is 17 scores less than 80 percent.
10 cm
12 cm
20 cm
12 + x
G
12 cm
A
X
Answers
Answer:
x = 12 cm and y = 24 cm
Step-by-step explanation:
Three sides of the first triangle are 10 cm, 12 cm and 12 cm.
Three sides of second triangle are 20 cm, 12+x cm and y cm.
As these two triangles are similar, it means,
[tex]\dfrac{10}{20}=\dfrac{12}{12+x}=\dfrac{12}{y}\\\\\dfrac{1}{2}=\dfrac{12}{12+x}=\dfrac{12}{y}\\\\\dfrac{1}{2}=\dfrac{12}{y}\ \text{and}\ \dfrac{1}{2}=\dfrac{12}{12+x}\\\\y=24\ cm\ \text{and}\ 24=12+x,x=12 cm[/tex]
So, the value of x is 12 cm and that of y is 24 cm.
Pleaseeeee help me!!!
Answers
Answer:
a = -1 b=0 and c=1
Step-by-step explanation:
-x^2 +0x+1
This is in the form
ax^2 +bx+c
a = -1 b=0 and c=1
What is the value of x?
26°
オー
X=
[?]
Enter
Answers
Answer:
154 degrees
Step-by-step explanation:
A quadrilateral has the sum of the interior angles that is 360 degrees
for the tangent theorem we know that the angles where the lines intercept the circumference have a value of 90 degrees
x + 90 + 90 + 26 = 360
x + 206 = 360
x = 360 - 206
x = 154 degrees
A car uses 6 litres of petrol when travelling 66 Km. Calculate the number of litres of petrol used when travelling 165 Km?
Answers
Answer:
15L
Step-by-step explanation:
divide the number of km's you will travel(165) by the number you are given originally(66)- 165/66 is 2.5
then multiply 2.5 by the amount of litres it takes for the original 66 km (6L)- 2.5*6 is 15L
The sixth graders at Kingston Middle School voted for their favorite sport. The results are in the circle graph below. Favorite sports 3/20 Football 1/2 Basketball 1/2 Golf Baseball 1/10 If the 180 students in sixth grade get to choose a sport to play for a special reward, how many of these students will choose basketball?
Answers
Answer:
90 Students.
Step-by-step explanation:
1/2 (Half) of 180 is 90.
Answer:
90 students will choose basketball
Step-by-step explanation:
half (1/2) choose basketball and half of 180 is 90
can someone pls help for brainlest
Answers
Answer:
144
Step-by-step explanation:
PLEASE HELP! BRAINLIEST! AND EXTRA POINTS
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars
Answers
Answer:
The discount is $0.8d.
Step-by-step explanation:
Given that,
The original cost of Tamara's purchase is d dollars.
Tamara uses a coupon to save 20% off her purchase at the bookstore.
Discount = 20%
Discount is applied to the original cost.
Discount = d-(20/100)d
Discount = 0.8 d
Hence, the discount is $0.8d.
what is 2/3 of 4 hours and 30 minutes?
Answers
PLEASE HELP! Translate the following phrase into a variable expression. Use the letter d to name the variable.
…10 times as deep..
A. d + 10
B. 10d
C. d/10
D. d - 1
Answers
Answer:
B. 10d
Step-by-step explanation:
10 times d = 10d
Hope its right
find the points on the y-axis, each of which is at a distance of 13 units from the point (-5,7)
Answers
Answer:
The answer is (0,19) or (0,-5).
By distance formula,
after squaring on both sides we and solving we get,
so, y=19 or -5
Step-by-step explanation:
you get the idea, but i don't think this is the answer yet?
Help, please, what is the answer??
Answers
Answer:
18.0
Step-by-step explanation:
The three lines form a right triangle where 10 and 15 are the two legs of the triangle. You can use the pythagorean theorem to solve for the length of x.
x = [tex]\sqrt{15^{2} + 10^{2} }[/tex]
x = 18.028 (approximately 18)
If the pentagon below is to be reflected over the line y=x, what are the new coordinates of the vertices?
Answers
Answer:
K' (-2, -2)
L' (3, -2)
G' (4,0)
H' (3,2)
J' (-2, 2)
Step-by-step explanation:
list all the coordinates of the image, and apply the y=x rule of reflection. The line y=x states that the previous y is now in the x and vice versa.
K(-2, -2)
L(-2, 3)
G(0,4)
H(2,3)
J(2, -2)
Simplify cot x - cos to the power 3 x csc x
Answers
I hope it will helpful for u
Solve the equation. 6g = 48 what does g equal?
Answers
Answer:
8
Step-by-step explanation:
First we need to figure out what g equals
Since 6 x 8 = 48 your answer would be 8
6 x 8 = 48
~ LadyBrain
The value of g that satisfies the equation is 8.
To solve the equation 6g = 48 and find the value of g, we can isolate the variable g by dividing both sides of the equation by 6:
6g / 6 = 48 / 6
This simplifies to:
g = 8
Therefore, g equals 8. By dividing both sides of the equation by 6, we find that when g is multiplied by 6, it results in 48. Hence, the value of g that satisfies the equation is 8.
To know more about equation:
https://brainly.com/question/10724260
#SPJ6
What is the sum of 4.2 × 10^5 and 5.3 × 10^5
Answers
Answer:
4.2 x 10^5 = 420,000
5.3 x 10^5 = 530.000
Step-by-step explanation:
How much growth or decay is 50(1.05)^t<100
Answers
Answer:
5% growth.
Step-by-step explanation:
1.05 = 1 + 0.05 = 1 + 5%
It is 5% growth.
What is an equation of the line passing between(4, -6) and (12, -8)?*
Answers
Answer:
y= -1/4x - 5
Step-by-step explanation:
first you need to find the slope.
to do this you can use the equation: change in y/change in x which is also y2 - y1/x2-x1
-8 - (-6)/12-4
-2/8
-1/4 = slope
since the line's equation is y = mx + b, we still need to find the y-intercept. we can do this by just plugging in one of the points
-6 = -1/4(4) + b
-6 = -1 + b
-5 = b
so the final equation is y= -1/4x - 5
What is the area of the right triangle shown below?
Answers
Answer:
60 units²
Step-by-step explanation:
Find the other side length:
8² + x² = 17²
64 + x² = 289
x² = 225
x = 15
Find the Area:
1/2(8 x 15) = Area
1/2(120) = Area
Area = 60
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Solve for x. Assume that lines which appear tangent are tangent. X=
Answers
Answer:
x = 32
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+18) * 18 = 30^2
(x+18) * 18 = 900
Divide each side by 18
(x+18) * 18/18 = 900/18
(x+18) = 50
Subtract 18 from each side
x+18-18 = 50-18
x=32
Answer:
50
Step-by-step explanation:
tangent-secant theorem
Question 16. Use the Triangle Inequality Theorems to determine if a triangle can exist with the given side lengths. (HINT: A triangle with sides a, b and c
exists if and only if the sum of any two sides of the triangle is greater than
the third side.) *
7,16, 6
Answers
Answer:
no
Step-by-step explanation:
7 squared plus 6 squared is 85 while 16 squared is 256
