Determine the equations of the vertical and horizontal asymptotes, if any, for
Answers
Given:
The function is:
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
To find:
The vertical and horizontal asymptotes of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
For vertical asymptotes, equate the denominator and 0.
[tex]x+4=0[/tex]
[tex]x+4-4=0-4[/tex]
[tex]x=-4[/tex]
So, the vertical asymptote of the given function is [tex]x=-4[/tex].
The degree of the numerator is 1 and the degree of the denominator is also 1.
Since the degrees of numerator and denominator are equal, therefore the horizontal asymptote is:
[tex]y=\dfrac{a}{b}[/tex]
Where, a is the leading coefficient of numerator and b is the leading coefficient of denominator.
Leading coefficient of numerator is 2 and the leading coefficient of denominator is 1, so the horizontal asymptote is:
[tex]y=\dfrac{2}{1}[/tex]
[tex]y=2[/tex]
Therefore, the correct option is C.
Related Questions
Cual de las siguientes expreciones permite a fatima obtener t que es la cantidad de palitos nesesaria para armar una figura n
Answers
Answer:
T(n) = 4 + 12*n
Step-by-step explanation:
La pregunta completa se puede ver en la imagen de abajo.
En ella, podemos ver que:
La primera figura tiene: 16 palitos
la segunda figura, con n = 2, se añaden 3 palitos en cada extremo, por lo que tendremos 16 palitos + 4*3 palitos = (16 + 12) palitos
De manera similar, en la tercera figura se vuelven a añadir 3 palitos en cada extremo de la cruz, entonces esta figura tendrá:
(16 + 12) palitos + 4*3 palitos = (16 + 12 + 12) palitos.
Así, tenemos la relación:
T(1) = 16
T(2) = 16 + 12
T(3) = 16 + 12 + 12
Podemos asumir que la forma general será:
T(n) = 16 + 12*(n - 1)
podemos reescribir esto como:
T(n) = (12 + 4) + 12*(n - 1)
= 4 + 12 + 12*(n - 1)
= 4 + 12*n
La opción correcta es la primera.
Write down the nth term of the following sequence
the following pattern are made using small squares
Answers
Answer:
a) [tex]n = 4 + 7\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex], b) [tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
Step-by-step explanation:
a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:
[tex]n = n_{o} + r\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex] (1)
Where:
[tex]n_{o}[/tex] - Initial element.
[tex]r[/tex] - Difference between two consecutive elements.
[tex]i[/tex] - Index.
If we know that [tex]n_{o} = 4[/tex] and [tex]r = 7[/tex], then the expression for the n-th term of the sequence is:
[tex]n = 4 + 7\cdot i[/tex], [tex]\forall \,i\in\mathbb{N}_{O}[/tex]
b) In this case, we have a geometric sequence described by the following equation:
[tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex] (2)
The constant element ([tex]2[/tex]) represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle ([tex](i+1)^{2}[/tex]) and emulates the area formula of the square.
Answer:
Step-by-step explanation:
?
The solution of this equation has an error. Which of the following steps has an error?
Step 1: -2x + 8 - 3x = 7
Step2:–5x+8=7
Step3:-5x = 15
Step4:
x = -3
O Step 2
O Step 1
O Step 3
Answers
3rd step
Solution:-
[tex]\\ \sf\longmapsto -2x+8-3x=7[/tex]
[tex]\\ \sf\longmapsto -2x-3x+8=7[/tex]
[tex]\\ \sf\longmapsto -5x+8=7[/tex]
[tex]\\ \sf\longmapsto -5x=7-8[/tex]
[tex]\\ \sf\longmapsto -5x=-1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-1}{-5}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{1}{5}[/tex]
help me with this question: Find y
Answers
Answer:
y = 4
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 45
Hypothenus = 4√2
Adjacent = y =?
The value of y can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 45 = y / 4√2
Cross multiply
y = 4√2 × Cos 45
Recall
Cos 45 = 1 / √2
Therefore,
y = 4√2 × 1/√2
y = 4
Factor out the greatest common factor from 4x4 + 12x2 + 8x.
4(x4 + 3x2 + 2x)
2x(2x3 + 6x + 4)
4x(x3 + 3x + 2)
2(2x4 + 6x2 + 4x)
Answers
Answer:
4x( x^3 +3x+2)
Step-by-step explanation:
4x^4 + 12x^2 + 8x
Factor out 4x
4x( x^3 +3x+2)
Someone Please help‼️‼️‼️
Answers
Hi there!
[tex]\large\boxed{m = 2}[/tex]
Since the line is increasing (the y-values are increasing as x increases), we can automatically eliminate any answer choice containing a negative slope.
Thus, the only correct answer choice would be m = 2.
We could also solve using the slope formula:
m = y2-y1/x2-x1
Plug in given points:
m = 3-1 / 0 - (-1)
m = 2 / 1 = 2
Nick drew a rectangular political cartoon that measures 2 inches by 4 inches. He wants to enlarge the cartoon by a scale factor of 3 for a poster presentation. The area of the original cartoon will be what fraction of the area of the enlarged cartoon?
Answers
Answer:
I believ the answer is 6/12 or 1/2
Step-by-step explanation:
2x3 = 6 and 4x3 = 12 and 6/12 simplified would be 1/2
Answer:
I believe the answer is 6/12 or 1/2
Step-by-step explanation:
I just need the numbers can anyone help me with this ??
Answers
Step-by-step explanation:
Hello!
In order to graph this, a point would have to go through (-6, 1). Then, since it says it needs a slope of 5 (or, to make things a bit easer, we could see it as 5/1) we'd need the next point to be 5 up and 1 across.
One possible solution:
(-6, 1) -> (-5, 6)
EXPLAIN:
Answer the following questions using 125 words or more:
Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do differently?
What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What would you do differently?
Answers
Answer:
Step-by-step explanation:
The enlargement of a comic will be very similar to the original. Everything is larger but in the same proportion. The difference is if the original is enlarged so much that the individual pixel in the original comic becomes visible; causing the enlargement to be "pixelated."
If a comic is drawn using a grid, that may reduce pixelation because you can line up things with the grid.
If the comic's size is reduced, then again it will look similar but everything is smaller and in the same proportion. There will not be any pixelation effect.
I WILL GIVE BRAINLIEST!! NO LINKS PLZ
4) Simplify.
Answers
Answer: [tex]\frac{\sqrt{5}}{6}[/tex]
==================================================
Work Shown:
[tex]\frac{\sqrt{10}}{3\sqrt{8}}\\\\\frac{\sqrt{10}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}}\\\\\frac{\sqrt{10*8}}{3\sqrt{8*8}}\\\\\frac{\sqrt{80}}{3\sqrt{64}}\\\\\frac{\sqrt{80}}{3*8}\\\\\frac{\sqrt{16*5}}{24}\\\\\frac{\sqrt{16}*\sqrt{5}}{24}\\\\\frac{4*\sqrt{5}}{24}\\\\\frac{\sqrt{5}}{6}\\\\[/tex]
Note: In the second step, I multiplied top and bottom by [tex]\sqrt{8}[/tex] to rationalize the denominator.
Answer:
square root of 5 over 6 or 0.37267799…
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Find the sum of the first 40 terms of an arithmetic series whose first term is 7 and 40th term is 115. Type answer as an integer (no decimals)
arithmetic sum formula:
Sn = (a1 +
+ an)
geometric sum formula:
az (1 - p)
S =
1-r
Answer:
Answers
Answer:
2440
Step-by-step explanation:
an=115
a=7
Sn=n/2(a+an) [Where n is no. of terms]
= 40/2(7+115)
= 20(122)
= 2440
For each pair of equations, write the letter of the equation that expresses an equal value.
1. a. L = 1 dm3 b. 1 L = 1 cm3
2. a. 1 mL = 1 cm3 b. 1 cm3 = 1 L
3. a. 0°C = –273 K b. 0 K = −273°C
4. a. 1 kg = 100 g b. 1,000 g = 1 kg
5. a. 400 cm = 4.0 m b. 400 cm = 0.40 m
6. a. 1 dm = 10 m b. 1 dm = 0.10 m
7. a. 100°C = 373 K b. 373 K = 10°C
Answers
We must understand that certain standards has been layed down for the conversions of measuring units. A summary of such standards are discussed below:
1. Option A. 1 L = 1 dm³
2. Option A. 1 mL = 1 cm³
3. Option B. 0 K = −273 °C
4. Option B. 1000 g = 1 kg
5. Option A. 400 cm = 4.0 m
6. Option B. 1 dm = 0.10 m
7. Option A. 100°C = 373 K
1. Option A. 1 L = 1 dm³
Option B. 1 L = 1 cm³
From standard measurement,
1 L = 1 dm³
1 L = 1000 cm³
From the measuring standard, we can see that 1 L ≠ 1 cm³.
Hence, option A gives the correct answer.
2. Option A. 1 mL = 1 cm³
Option B. 1 cm³ = 1 L
Hence, option A gives the correct answer.
From standard measurement,
1 mL = 1 cm³
1000 cm³ = 1 L
Thus, option A gives the correct answer.
3. Option A. 0°C = –273 K
Option B. 0 K = −273 °C
Recall:
T (K) = T(°C) + 273
T (K) = Temperature in Kelvin
T(°C) = Temperature in decree celcius
Next, we shall convert 0°C to K
T(°C) = 0°C
T (K) = T(°C) + 273
T (K) = 0 + 273
T (K) = 273 K
Thus, 0°C is equivalent to 273 K
Next, we shall convert 0 K to °C
T(K) = 0
T (K) = T(°C) + 273
0 = T(°C) + 273
Collect like terms
0 – 273 = T(°C)
T(°C) = –273°C
Thus, 0 K is equivalent to –273°C
Therefore, option B gives the correct answer.
4. Option A. 1 kg = 100 g
Option B. 1000 g = 1 kg
From standard measurement,
1 Kg = 1000 g
1000 g = 1 Kg
Hence, Option B gives the right answer
5. Option A. 400 cm = 4.0 m
Option B. 400 cm = 0.40 m
From standard measurement,
100 cm = 1 m
Converting 400 cm to m, we have:
[tex]400 cm = 1 m\\400 cm = \frac{400 cm * 1 m }{100 cm}\\400 cm = 4 m[/tex]
Thus, option A gives the correct answer.
6. Option A. 1 dm = 10 m
Option B. 1 dm = 0.10 m
From standard measurement,
10 dm = 1 m
Thus,
[tex]1 dm = \frac{1 dm * 1 m}{10 dm}\\1 dm = 0.1 m[/tex]
Therefore, option B gives the correct answer.
7. Option A. 100°C = 373 K
Option B. 373 K = 10°C
Recall:
T (K) = T(°C) + 273
T (K) = Temperature in Kelvin
T(°C) = Temperature in decree celcius
Next, we shall convert 100°C to K
T(°C) = 100°C
T (K) = T(°C) + 273
T (K) = 100 + 273
T (K) = 373 K
Thus, 100°C is equivalent to 373 K
Next, we shall convert 373 K to °C
T(K) = 373
T (K) = T(°C) + 273
373 = T(°C) + 273
Collect like terms
373 – 273 = T(°C)
T(°C) = 100°C
Thus, 373 K is equivalent to 100°C
Therefore, option A gives the correct answer.
SUMMARY:
1. Option A. 1 L = 1 dm³
2. Option A. 1 mL = 1 cm³
3. Option B. 0 K = −273 °C
4. Option B. 1000 g = 1 kg
5. Option A. 400 cm = 4.0 m
6. Option B. 1 dm = 0.10 m
7. Option A. 100°C = 373 K
Learn more:
https://brainly.com/question/11650994
https://brainly.com/question/12088003
What is the value of x in the equation -2 =5x + 3
Answers
5x = 3 + 2
5x = 5
x = 1
Step-by-step explanation:
hope it helps you and please mark it brainliest answer
please answer this!!
Answers
both sides are equal so both sides are 51
51+51=102
180-102=78
Please Help!!
The scale on the map is stated as 1 : 200000. A main road connects two towns which are 34 kilometres apart. How far will it be on the map, in centimetres, between the two towns along the main road
WILL GIVE BRAINLIEST!!
Answers
Answer:
34 : 6800000
Step-by-step explanation:
1 : 20000034km : ?34km : 34km × 20000034km : 6800000km34 : 6800000Helpppp Please! Please!
Answers
∠B＝∠D
CA＝AC
△DCA≌△BCA (AAS)
NO＝NQ
OP＝QP
NP＝PN
△NOP≌△NQP (SSS)
∠FOW＝∠KIB
∠OFW＝∠IKB
FW＝KB
△FOW≌△KIB (AAS)
Hope my answer helped u :)
What is the value of the expression below when y = 8 y=8? 2 y + 7 2y+7
Answers
Answer:
23
Step-by-step explanation:
[tex]2 y + 7[/tex]
Replace y with 8
[tex]= 2 (8) + 7\\= 16+ 7\\= 23[/tex]
Therefore, the value of the expression when y=8 is 23.
I hope this helps!
The volume of a sphere is 3,000π m3. What is the radius of the sphere to the nearest meter?
Answers
Answer:
13m
Step-by-step explanation:
volume of sphere = [tex]\frac{4}{3} * pi * r^{3}[/tex] = 3000π
4r^3/3 = 3000
r^3 =2250
r = ∛2250 = 13.10370 = 13
Answer:
Radius of the sphere is 13.1 m.
Step-by-step explanation:
Volume:
[tex]{ \boxed{ \pmb{volume = { \bf{ \frac{4}{3}\pi {r}^{3} }}}}}[/tex]
Substitute:
[tex]{ \tt{3000\pi = \frac{4}{3} \times \pi \times {( {r}^{3}) } }} \\ \\ { \tt{ {r}^{3} = \frac{3000 \times 3}{4} }} \\ \\ { \tt{r = \sqrt[3]{ \frac{3000 \times 3}{4} } }} \\ { \tt{r = 13.1 \: m}}[/tex]
Help please, I need with the question
Answers
Answer: [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
tangent of ∠PLM = [tex]\frac{opposite}{adjacent} =\frac{4}{3}[/tex]
Answer:
PLM=4/3
Step-by-step explanation:
Given that the point (-2,8) is on the graph of an equation that is symmetric with respect to the x-axis, what other point is on the graph?
(Type an ordered pair)
Answers
The step function f(x) is graphed
What is the value of ( -1)?
3
4
0 1
3
0 0
2
1
1
.
-4-3-2
1
2
3
4
5 6
X
-2
Answers
-4-3-2
1
2
3
4
5 6
x
-2gbhdfcjfghu
what is the answer to this equation?
Answers
Answer:
4i
Step-by-step explanation:
apply (a+b)^2 formula
Hope this helps
what is the rule for the reflection
Answers
Step-by-step explanation:
We reflect We triangle across both axis so the x and y values will both switch.
Our triangle is originally in the second quadrant but then go to the 4the after we reflect it.
Second Quadrant are
^;8+1—](
please answer this
simplify it too
Answers
Answer:
x^2 +3x
Step-by-step explanation:
The outer rectangle has an area of
A = l*w = (4x)*(x+2) = 4x^2 +8x
The inner rectangle has an area of
A = (3x+5)*x = 3x^2 +5x
Subtract the inner rectangle from the outer rectangle
Shaded area = 4x^2 +8x - ( 3x^2 +5x)
Distribute the minus sign
=4x^2 +8x - 3x^2 -5x
Combine like terms
= x^2 +3x
if the hypotenuse of an isosceles right triangle has a length of 5 centimeters what is the length of one of the legs
Answers
Answer:
a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} = 5 ^{2}[/tex]
a = b
[tex]2a^{2} = 5 ^{2}[/tex]
[tex]2a^{2} = 25\\[/tex]
[tex]a^{2} = \frac{25}{5}[/tex]
a = [tex]\frac{5}{\sqrt{5} }[/tex]
must rationalize...
a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]
Simultaneous equation 2x-Y= -1 x-2y=4
Answers
Answer:
x + y = -5
Step-by-step explanation:
2x - x - y + 2y = -1 - 4
x + y = -5
which expression is equivalent to \root(3)(x^(5)y)
Answers
Answer:
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{x^{5}y}[/tex]
Required
The equivalent expression
We have:
[tex]\sqrt[3]{x^{5}y}[/tex]
Rewrite as an exponent
[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]
Open bracket
[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
f(x) = x2 – 12x – 29
f(3) = (x+ ?)+ ?
Answers
Answer:
-6 and - 65
Step-by-step explanation:
X-12x-29, by completing the square we get (x-6)^2-65
Find the following products :-
( -7 x² ) × 2 y
please give answer immediately
and give it correct
please don't write incorrect answer
Answers
Answer:
- 14x²y
Step-by-step explanation:
Given
- 7x² × 2y
= - 7 × 2 × x² × y
= - 14x²y
X^2 x y = x^2y
Therefore (-7x^2) x 2y = 14x^2y
Please help a-e I will rate and like response. Thank u
Answers
Answer:
VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3
VOLUME OF SPHERE: ≈523.6cm^3
