Identify the rational function whose graph is given below. Note the x-intercept of the graph is x=4 and the y-intercept of the graph is y=−3. The graph has one vertical asymptote at x=2
Answers
Using the vertical asymptote of the function, it is found that it is given by:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the x-intercept of the graph is x=4, hence the numerator is a(x - 4).
The graph has one vertical asymptote at x=2, hence the denominator is x - 2.
Hence:
[tex]f(x) = \frac{a(x - 4)}{x - 2}[/tex]
The y-intercept of the graph is y=−3, hence:
[tex]-3 = \frac{a(0 - 4)}{0 - 2}[/tex]
[tex]-4a = 6[/tex]
[tex]a = -1.5[/tex]
Thus, the function is:
[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]
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Related Questions
Dante is saving money to buy a game. So far he has saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Answers
Answer:
The game costs 36$ dollars.
Step-by-step explanation:
2/3 of 36 is 24 :p
The total cost of the game Dante wants to buy is 26 dollars.
What is a fraction?A fraction describes some parts of a certain quantity. Fractions are of two types one is a proper fraction and another is an improper fraction. In a proper fraction, the numerator is smaller than the denominator and n improper fraction numerator is greater than the denominator.
Assuming The total cost of the game is x dollars.
Given that 24 dollars is (2/3)rd of the total cost of the game.
So we can write 24 is (2/3)rd of the total cost of the game.
∴ 24 = (2/3)×x.
24 = (2/3)x.
x = 24×(3/2).
x = 12×3.
x = 36 dollars.
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You need 120 pieces of chalk for art day. your teacher gar 6 boxes of chalk. Each box he's 18 pieces of chalk. Is that enough chalk for art day if there is 24 students
Answers
Answer:
No
Step-by-step explanation:
6 time 180 is only 108
108<120
There is not enough chalk.
Which of the following are not polynomials?
Answers
Answer:
D
I really wish is right!!!
Find the hourly wage for a person with an income of $60376, who works 57 hours a week for 44 weeks.
Answers
Answer:
$24.07
Step-by-step explanation:
57×44=2508 hrs
60376÷2508=$24.07 per hr
Looking for good answer on this
Answers
[tex]\dfrac{6x-24}{16-x^2}\\\\=\dfrac{6(x-4)}{4^2 -x^2}\\\\=\dfrac{6(x-4)}{(4+x)(4-x)}\\\\=-\dfrac{6(x-4)}{(x+4)(x-4)}\\\\=-\dfrac{6}{x+4}[/tex]
HELP, i need help!!!!!!!!!!!!!!
Answers
Answer:
t = 7.46, 0.42
Explanation:
h = 126t - 16t² [ "h" is height, "t" is time ]
when height is 50 feet
126t - 16t² = 50-16t² +126t -50 = 016t² -126t +50 = 0==================
[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]
==================
[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]
[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]
[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]
Let's find
h=126t-16t²Put h=50
-16t²+126t=50-16t²+126t-50=0Use quadratic formula
[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]
[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]
All the clocks below show the time in the aftemoon or evening. Write the times below the clocks using 24 hour time. Time is Time is Times Times
Answers
Answer:
1. 15:00
2. 20:10
3. 14:20
4. 14:45
5. 17:45
Step-by-step explanation:
please help me out, simple
Answers
Reason: since the angle adjacent to ATC is 90° we can assume that ATC = 90°. Since ATB is 45° we can subtract this from ATC to get us 45° for BTC.
Answer:
Answer is 45⁰
Step-by-step explanation:
The angle ATB IS 45⁰
Lainey is sliding down a water slide that is 423 feet long at a rate of 47 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
Answers
Answer:
It will take Lainey 9 seconds to travel from top to bottom
Further explanation:
The formula of speed will be used to calculate the time to reach from top to bottom of the slide.
Given
\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}
Distance=d=423 feet
Speed=s=47 feet per second
The formula for speed is:
s=\frac{d}{t}s=
t
d
Putting the values of distance and speed in the formula:
\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}
47=
t
423
t=
47
423
t=9 seconds
It will take Lainey 9 seconds to travel from top to bottom
Keywords: Speed, distance
Learn more about speed
I. Elena wants to estimate what proportion of computers produced at a factory have a certain defect. A random sample of 200 computers shows that 12 computers have the defect. She is willing to assume independence between computers in the sample. Based on this sample, construct a 95% confidence interval for the proportion of computers that have the defect.
a
(0.4529, 0.5871)
b
(0.02709, 0.09291)
c
(0.02131, 0.09869)
d
(0.0309, 0.0691)
Answers
The sum of squares of lengths of the two sides of a rectangular field is 25m2.Their difference is 1m .what is the length of each side of the field
Answers
Answer:
Perimeter of a rectangle = 2×(Length+Breadth)
(i) Length = 16.8 cm
Breadth = 6.2 cm
Perimeter = 2×(Length+Breadth)
= 2×(16.8+6.2) =46 cm
(ii) Length = 2 m 25 cm
=(200+25) cm (1 m = 100 cm )
= 225 cm
Breadth =1 m 50 cm
= (100+50) cm (1 m = 100 cm )
= 150 cm
Perimeter = 2×(Length+Breadth)
= 2×(225+150) =750 cm
(iii) Length = 8 m 5 dm
= (80+5) dm (1 m = 10 dm )
= 85 dm
Breadth = 6 m 8 dm
= (60+8) dm (1 m = 10 dm )
= 68 dm
Perimeter = 2×(Length+Breadth)
= 2×(85+68) =306
8 less than the product of 3 and j
Answers
Answer:
3j - 8
Step-by-step explanation:
8 less than the product of 3 and j
3×j - 8
3j - 8
15 over r - 1 when r= 5
Answers
15 / 4 = 3.75
NEED HELP ASAP!!!
On a coordinate plane, sketch the graphs. y=|x| , y=|x+3| , and y=|x-2|
Answers
Answer:
Step 1. Plot x-intercept
Step 2. Plot y-intercept
Step 3. Connect dots
y = |x|
x-intercept = (0,0)
y-intecept = (0,0)
y = |x + 3|
x-intercept = (-3,0)
y-intecept = (0,3)
y = |x - 2|
x-intercept = (2,0)
y-intecept = (0,2)
BRAINLIEST please if this helped!Given the sequence 1,1,2,3,5,8….,find the 6th term
Answers
Answer:
8 is the ans because it is 8
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56cm. Find the lengths of each side of the rectangle
Answers
Answer:
smaller side: 10 cmlarger side: 18 cmStep-by-step explanation:
The given relationships can be translated to equations using L and W for the length and width of the rectangle. The distance from the center to the short side is L/2, and the distance from the center to the long side is W/2.
SetupP = 2(L +W) . . . . . formula for the perimeter
56 = 2(L +W) . . . . . the perimeter is 56 cm
L/2 = 4 + W/2 . . . . . distance to short side is 4 cm longer
__
SolutionDividing the first equation by 2 gives ...
28 = L +W
Multiplying the second equation by 2 gives ...
L = 8 + W
Substituting for L in the first equation, we have ...
28 = (8 +W) +W . . . . . . use L=8+W
20 = 2W . . . . . . . . .subtract 8
10 = W . . . . . . . . divide by 2
L = 8 +10 = 18 . . . . . find the length
__
The smaller side is 10 cm; the larger side is 18 cm.
how do i do this? im confused
Answers
Answer:
θ ≈ 64.62°
Step-by-step explanation:
In this problem we will use trig: SOH CAH TOA. Since we are given hypotenuse (line AB) and adjacent (line ) to the missing angle θ, we will use cosine.
cosθ = adjacent/hypotenuse
cosθ = 3/7
Now take inverse cosine of both sides to cancel out cosine and find the missing angle:
cos⁻¹(cosθ) = cos⁻¹(3/7)
θ = cos⁻¹(3/7) ----> Plug into calculator
θ ≈ 1.128 radians · 180°/π rad ------>. Convert from radians to degrees
θ ≈ 64.62°
Hope this helps!
Answer: The measure of angle ? is approximately 64.62 degrees.
Step-by-step explanation:
The given value 3 is adjacent to angle ? and 7 is the hypotenuse. Remembering SOH CAH TOA, that means 3/7 = cos(?). To solve, use a calculator to find the inverse cosine of 3/7, which is about 64.62. Look at https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/trig-solve-for-an-angle/a/inverse-trig-functions-intro to get a better understanding if needed.
An employer pays you penny the first day you work and doubles your wages each day after that: Find your total earnings after working 7 days a week for (a) One week (b) Two weeks (c) Three weeks (d) Four weeks
Answers
a) answer is 64 pennies
b) answer is 8 192 pennies
c) answer is 1 048 576 pennies
d) answer is 134 217 728 pennies
Susan has 600 feet of fencing to use in making a yard for her new puppy. The yard she has
planned has a length that is 75 feet less than twice the width. What are the dimensions of the
yard?
Answers
Answer:
Length = 175
Width = 125
Step-by-step explanation:
P=2(L+W)
600ft=2(L+W)
300=L+W
300=2W-75ft+W
375=3W
125=W
L=2W-75
L=2(125)-75
L=250-75
L=175
end
A cruise ship is 1480 feet from a light house off a Caribbean Island.
If the angle of elevation from the cruise ship to the top of the light
house is 4º, what is the height of the lighthouse? Round to the
nearest whole foot.
Answers
Answer:
104 feet
Step-by-step explanation:
To get the height of the lighthouse, we need to take the sine function of the anglesin4° = 0.07sin4° = h/1480⇒ h/1480 = 0.07⇒ h = 1480 x 0.07⇒ h = 103.6⇒ h = 104 feethelp me out guys thank u
Answers
Answer:
[tex] \sf \: a5 = 769[/tex]
Fill in the blanks below with the correct units. (a) Carmen saw an elephant at the zoo. The elephant's mass was about 5000 ? . (b) Deandre drank about 300 ? of juice with lunch. (c) Martina's family went on a hike that was about 9 ? .
Answers
Answer:
a. 5000 kg
b. 300 ml
c. 9 hours
Write the exponential function y = 22(1.35)' in the form y = aekt.
(a) Once you have rewritten the formula, give k accurate to at least four decimal places.
k%3D
help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and
continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing
decay the negative rate is implied).
(b) The annual? rate is
% per year (round to the nearest 0.01%).
Answers
Answer:
y = 22·e^(0.3001t), growingannual rate: 35%continuous rate: 30.01%Step-by-step explanation:
When an exponential function is in the form ...
y = ab^t
the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...
b = 1 +r
In the alternate form, this can be written ...
y = a·e^(kt)
Comparing the forms, we see that ...
b = e^k ⇒ k = ln(b)
__
(a)y = 22·1.35^t
k = ln(1.35) ≈ 0.3001
y = 22·e^(0.3001t)
The growth factor is greater than 1, so the function is growing.
__
(b)The annual growth rate is ...
r = 1.35 -1 = 0.35 = 35.00%
__
(c)The continuous growth rate is ...
k = 0.3001 = 30.01%
I NEED help ASAP!!!!!!!
Answers
Step-by-step explanation:
Step 1: Plot the points
L(1,2)
M(0,-1)
J(1,-2)
K(2,-1)
Step 2: Multiply each point by 5.
and record thise points so we have
L(5,10)
M(0,-5)
J(5,-10)
K(10,-5)
Step 3: Plot those points.
Answer:
Graph attached below.
Step-by-step explanation:
After dilation of 5, the new coordinates follow the rule :
(x, y) ⇒ (5x, 5y)The points are :J' = (1 x 5, -2 x 5) = (5, -10)K' = (2 x 5, -1 x 5) = (10, -5)L' = (1 x 5, 2 x 5) = (5, 10)M' = (0 x 5, -1 x 5) = (0, -5)Line AB contains points A (8, −4) and B (1, −5). The slope of line AB is (1 point) a −7 b negative 1 over 7 c 1 over 7 d 7
Answers
Heya !
Given two points A ( 8 , -4 ) and B ( 1 , - 5 )
To find - slope of line AB
Solution -
[tex] Slope = \frac{y_{2}-y_{1}}{x_{2} - x_{1}} \\ \\ \dashrightarrow \frac{ -5 - (-4 )}{ 1 - 8 } \\ \\ \dashrightarrow \frac{ - 5 + 4 }{ 1 - 8 } \\ \\ \dashrightarrow \frac{-1}{-7} \\ \\ \dashrightarrow \frac{1}{7}[/tex]
Hence ,
Option ( c ) is correct.
Hope helpful ~
Find the distance between the two points in simplest radical form.
(-8,3) and (-2,5)
Answers
Here we would be using distance formula to calculate the distance between those two points.
Points are,
(-8,3) (-2,5)★ Distance Formula :
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]We have :
x1 = -8 x2 = -2 y1 = 3 y2 = -5Substituting the values :
Refer the attachment.Additional Information :Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]what is the unit rate of 36 ounces of 5.79
Answers
A unit ounce is 0.16
If 36 ounces worth 5.79, 1 ounce will be
= 5.79 / 36
= 0.1608
9. Find the value of x. Round your answer to the nearest tenth.
sin Xº = 4/15
Answers
Answer: 15.5 degree
Step-by-step explanation:
A person who can afford a monthly payment of __________ and signed a mortgage with a monthly payment of __________ was most likely the victim of predatory lending.
A. $900; $1000
B. $900; $800
C. $900; $900
D. $900; $700
Answers
Answer:
A . 900-1000
Step-by-step explanation:
Find the value of cos F rounded to the nearest hundredth, if necessary
Answers
Using the trigonometric ratios, the value of cos F in the right angle triangle is 0.28 .
What are right angle triangle?Right angle triangle are triangle that has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore,
cos F = adjacent / hypotenuse
adjacent = FE
hypotenuse = 50
50² - 48² = FE²
FE = √2500 - 2304
FE = √196
FE = 14
Therefore,
cos F = 14 / 50
cos F = 0.28
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