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
Find the measure of AB
A. 20
B. 21
C. 22
D. 14
Answers
Answer:
[tex]CB.CA=CD .CK[/tex]
[tex]9(9+2x+5)=10(10+2x+1)[/tex]
[tex]9(2x+14)=10(2x+11)[/tex]
[tex]18x+126=20x+110[/tex]
[tex]126-110=20x-18x[/tex]
[tex]16=2x->x=8[/tex]
[tex]AB=2(18)+5[/tex]
[tex]=21[/tex]
So, your answer is B) 21
hope it helps...
Pat was shopping and found a
jacket with the original price of
$120 on sale for $12. What was
the percent decrease in the
cost? %
Hint: Change over original
Answers
Answer:
91.7%
hope I helped
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
O A. y=3x+4
OB. y= 3x - 14
O cy=3x-4
OD. y= 3x+12
Answers
Answer:
y = 3x + 4
Step-by-step explanation:
Given:
Coordinates
(-3 , -5)
Slope m = 3
Find;
Equation of slope
Computation:
Given, x1 = -3 and y1 = -5
Equation of slope = y - y1 = m(x - x1)
Equation of slope = y - (-5) = 3(x + 3)
Equation of slope = y + 5 = 3x + 9
Equation of slope = y = 3x + 9 - 5
Equation of slope = y = 3x + 4
y = 3x + 4
Which equation has the same solution as x^2 – 8x + 19 = -10?
(x +4)^2 = -45
(x – 4)^2 = -13
(x – 4)^2= – 45
(x + 4)^2 = = -13
Answers
A, B & C lie on a straight line. BD = CD. ∠ BCD = 70° and ∠ BAD = 10°. Work out x
Answers
Answer:
x= 100
Step-by-step explanation:
straight line = 180⁰
180-(70+10)= 100
What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer.
-12-1
-3
-11
2
2
-1
2
х
-1
DO
o
-13
من ال۔
ला
Answers
==================================================
Explanation:
Think of a whole cake or pizza. Now slice it into 4 equal pieces. This represents 1 is the same as 4/4.
Adding on another quarter slice gets us 4/4+1/4 = 5/4
In other words, the mixed number 1 & 1/4 is the same as the improper fraction 5/4.
So 1 & 1/4 = 5/4
This then means -1 & 1/4 = -5/4 because we multiply both sides by -1.
Now we'll add on 1/2, which is the same as 2/4, like so
(-1 & 1/4) + 1/2
-(1 & 1/4) + 2/4
-(1 + 1/4) + 2/4
-1 - 1/4 + 2/4
-1 + (-1/4 + 2/4)
-1 + 1/4
-4/4 + 1/4
-3/4
which points us to choice C as our final answer
Notice how if we started at -5/4, and moved to the right 2 tickmarks, we arrive at -3/4. Each tickmark represents 1/4 of a unit, so two of them is 2/4 = 1/2.
Side note: -3/4 converts to the decimal -0.75
What is the volume of this Sphere?
8 pi cm3
16 pi cm3
27 pi cm2
36 pi cm2
Answers
Answer:
V = 36 pi cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3 where 4 is the radius
V = 4/3 pi(3)^3
V = 36 pi cm^3
Find the distance from point P to RQ
Answers
Answer:
option A : about 2.8 units
Step-by-step explanation:
To find the distance from P to RQ , Find the distance from ( 1 , 1) to (3 , 3).
[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]= \sqrt{(3-1)^2 + (3-1)^2}\\\\= \sqrt{2^2 + 2^2 }\\\\= \sqrt{4 + 4 }\\\\= \sqrt{8}\\\\=2\sqrt{2}[/tex]
= 2.83 units
Answer:
A
Step-by-step explanation:
Remark
The distance you want is the point P to the (3,3). Then two lines meet as these two do, the shortest distance is the right angle distance. And that is how distance is defined.
Formula
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Givens
x2 = 1
x1 = 3
y2 = 1
y1 = 3
Solution
d = sqrt( (1 - 3)^2 + (1 - 3)^2 )
d = sqrt( (-2)^2 + (-2)^2 )
d = sqrt ( 4 + 4)
d = sqrt(8)
d = 2√2
d = 2.8
Describe each transformation that must be applied to f(x)=x² to get the function g(x)=1/2(x+2)² (30 POINTS)
Answers
Answer:
translate 2 units to the left and compress by 1/2 in the y direction
Step-by-step explanation:
f(x)=x²
y = f(x + C) C > 0 moves it left
We add 2 to move it 2 units to the left
h(x) = (x+2)^2
y = Cf(x) 0 < C < 1 compresses it in the y direction
g(x) = 1/2 (x+2)^2
Use the given area of the base and the height to find the
volume of the right rectangular prism, in cubic units.
Answers
How many fl oz are in 4 table spoons
Answers
Answer:
2 fl oz
Step-by-step explanation:
2 tbsp = 1 fl oz. Simply double.
if GJ = 11a and IJ = a + 10, find the value of a that makes quadrilateral FGHI a parallelogram
Answers
Note: Consider J is the intersection point of diagonals of quadrilateral FGHI.
Given:
[tex]GJ=11a[/tex]
[tex]IJ=a+10[/tex]
To find:
The value of a that makes quadrilateral FGHI a parallelogram.
Solution:
We know that the diagonals of a parallelogram bisect each other.
If FGHI is a parallelogram and J is the intersection point of diagonals, then
[tex]GJ=IJ[/tex]
[tex]11a=a+10[/tex]
[tex]11a-a=10[/tex]
[tex]10a=10[/tex]
Divide both sides by 10.
[tex]a=\dfrac{10}{10}[/tex]
[tex]a=1[/tex]
Therefore, the required value of a is 1 units.
A system of linear equations in two variables is the collection of two linear equations in two variables considered simultaneously. B. A system of linear equations in two variables must have at least one solution. C. It is possible for a system of linear equations in two variables to have infinitely many solutions. D. The solution to a system of equations in two variables is the set of all ordered pairs for which both equations are true.
Answers
Complete Question:
Which of the following statements is not true?
Choose the incorrect statement below.
Answer:
B. A system of linear equations in two variables must have at least one solution.
Step-by-step explanation:
A linear function has a positive relationship and as such an increase in one variable (input variable) causes an increase in the other variable (output variable) i.e the variables are directly proportional. Thus, the graph of a linear function is a straight-line and its slope is always constant.
Similarly, a linear equation is an algebraic equation of the first order with two variables and each of its term having an exponent of one.
Generally, a system of linear equations in two variables must have at least two solution.
For example, y = 2x + 1 is a linear equation.
a. To find the value of y;
When x = 0
y = 2(0) + 1
y = 2 + 1
y = 3
b. To find the value of x;
When y = 0
0 = 2x + 1
2x = -1
x = -½
10% divided by 24% divided by 49%
Answers
Answer:
[tex]\frac{125}{147}[/tex]
Step-by-step explanation:
10% ÷ 24% ÷ 49%
1/10 ÷ 6/25 ÷ 49/100
5/12 ÷ 49/100
[tex]\frac{125}{147}[/tex]
Please help me with this. Method included please
Answers
Answer:
a) 9.135
b) 392.79
Step-by-step explanation:
Hope my answers are helpful
Find measure of angles B, E, D and C and the length of BC.
Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.
Answers
Answer:
BC = 16 B=85 E=85 D=30 C=65
Step-by-step explanation:
Step-by-step explanation:
< B = 180-30-65=85°
< E = 85°
< D = 30°
< C = 65°
BC = 20/35 × 28 = 16
Find the output, d, when the input, t, is 11.
d= -20 + 1lt
d=
Answers
Answer:
d = -9
Step-by-step explanation:
d = -20 + (1 x 11)
=-20 + 11
=-9
view what's attached
Answers
Step-by-step explanation:
when numbers are negative, the bigger the number looks the smaller it is therefore
-6 is smaller than -5
but 6 is bigger than 5
however, the numbers are;
-5.99, -3, -6, -5.9, -1, -5.999, -5 ,2
Phillipa says that ( 27 − 9 ) × 3 ÷ 9 + 18 = 42 . Is she correct? If not, what is the correct answer? A. She is correct. B. She is not correct. The correct answer is 2. C. She is not correct. The correct answer is 24. D. She is not correct. The correct answer is 26.
Answers
(27-9) x 3 / 9 + 18 = 42
Follow order of operations: parentheses first:
18 x 3 / 9 + 18 = 42
Next is multiplication and division in order from left to right:
18 x 3 = 54
54/9 = 6
Now you have 6 + 18 = 24
24 does not equal 42 so Phillipa is not correct.
The answer is C. She is not correct. The correct answer is 24
Answer:
answer=she is not correct
Step-by-step explanation:
(27-9)*3÷9+18
18*3÷9+18
18*1/3+18
18/3+13
6+13
19
use BODMAS rule (Bracket Of Division Multiplication Addition And Subtraction)
Plane W and Plane B intersect at which following?
Answer Choices:
A. Line a
B. Line t
C. They do not appear to intersect
D. Line p
Answers
Answer:
the answer is (d)!! hope this helps
Step-by-step explanation:
How much total money will Kiara have to pay back at the end of the 9 years?
Answers
Answer:
a= $29,505. it. is useful answer
For each parabola, a) Write the equation of the function; b) Give the minimum or maximum value of the function; c) Find the domain and range.
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the complete question in the attached file.
For question 5:
For point a:
[tex]\to y=x^2[/tex]
For point b:
[tex]Maximum (0,0)[/tex]
For point c:
[tex]Domain: (-\infty,+ \infty)\\\\Range: (-\infty, 0)[/tex]
For question 6:
For point a:
[tex]\to y=-x^2[/tex] (the negative sign is used to change the direction of the parabola)
For point b:
[tex]Maximum (0,0)[/tex]
For point c:
[tex]Domain: (-\infty,+ \infty)\\\\Range: (0,+\infty)[/tex]
Please answer fully and explain
Answers
Answer:
Step-by-step explanation:
Hope this helps u !!
102=(1/3)πr²h
102×3÷π÷(4.96)²=h
h=3.96cm
What is the slope of the line
Answers
Answer:
Slope = 3
Step-by-step explanation:
Take two points and find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{3-0}{-1-(-2)}\\\\m=\frac{3}{1}=3[/tex]
What are the values of AB and DE in parallelogram
ABCD?
AB=?
PLEASE HELP
Answers
Answer:
AB=12
ED=6
Step-by-step explanation:
AB=CD=12
BC=AD=26
ED=26-20=6
Which is the product of (1 +41+3x) (2 - 7x–9x)?
Answers
Answer:
-48x^2 -666x+84
Step-by-step explanation:
Exponet is ^2.
Multiply is •
Use Distributed Property. Multiply the second parathesis by each term from the first parathesis.
Any expression multiplied by 1 remains the same. Distribute 41 through the parathesis. 41(2-7x-9x).
Distribute 3x through the parathesis 3x • (2-7x-9x).
You will have these numbers left: (Slide 2)
Add the numbers, 2 and 82 to get 84. Add -7x -9x + -287x -369x + 6x to get -666x. Add -21x^2 - 27x^2 to get 48x^2.
Use the communitative property to reorder the terms. And then your answer is -48x^2 -666x+84.
4x - 2y + 2x =
I don't know the answer
Answers
Answer:
6x -2y
Step-by-step explanation:
4x - 2y + 2x
Combine like terms
4x +2x - 2y
6x -2y
Answer:
6x - 2y
Step-by-step explanation:
Add 4x and 2x
6x - 2y
Hope this helps!
If you need more help with these types of equations, don't be afraid to reach out!
Tarea 9 (Expresiones algebraicas) entrega 31/5/2021 Copiar en el cuaderno de clase y plantear la ecuación Plantea una ecuación para cada situación Juan compró 2 panchos y 3 hamburguesas y le cobraron $ 330 Realizo un pago de la factura de luz, agua y cable en total me cobran $ 3890 Un padre reparte un dinero X que recibió entre su esposa y su hijo, a su esposa le da el doble que al hijo. En el salón de clase hay 27 alumnos entre mujeres y varones.
Answers
Answer:
1-
2X + 3Y = 330
2-
X + Y + Z = 3890
3-
1/3X + 2/3X = X
4-
X + Y = 27
Step-by-step explanation:
Para plantear ecuaciones para las siguientes situaciones se deben realizar los siguientes razonamientos lógicos:
1- Juan compró 2 panchos y 3 hamburguesas y le cobraron $330.
Panchos = X
Hamburguesas = Y
2X + 3Y = 330
2- Realizo un pago de la factura de luz, agua y cable en total me cobran $3890.
Luz = X
Agua = Y
Cable = Z
X + Y + Z = 3890
3- Un padre reparte un dinero X que recibió entre su esposa y su hijo, a su esposa le da el doble que al hijo.
Esposa = 2/3X
Hijo = 1/3X
1/3X + 2/3X = X
4- En el salón de clase hay 27 alumnos entre mujeres y varones.
Mujeres = X
Varones = Y
X + Y = 27
SJSKSJSKSJ d help :p
Answers
Answer:
Below
Step-by-step explanation:
Discount: 40% of $159 = $63.60
Price you pay: $159 - $63.60 = $95.40
fazer scores 43% in a spelling test, what percentage did he get wrong???
Answers
Answer:
57
Step-by-step explanation:
100 - 43 =
57
Answer:
He got 57% wrong
Step-by-step explanation:
If he got 43% correct, there is 100 percent on the assignment
100 -43 = 57
He got 57% wrong