Write an equation for a rational function with:
Vertical asymptotes of x = 1 and x = 4
x intercepts at (-1,0) and (-6,0)
y intercept at (0,8)
Use y as the output variable. You may leave your answer in factored form.
Answers
Answer:
[tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]
Step-by-step explanation:
Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.
Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.
Now we have [tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex] where we plug in (0,8) to solve for a:
[tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex]
[tex]8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}[/tex]
[tex]8=\frac{6a}{4}[/tex]
[tex]32=6a[/tex]
[tex]\frac{32}{6}=a[/tex]
[tex]\frac{16}{3}=a[/tex]
Therefore, the equation for the rational function is [tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]
Related Questions
What is the answer to this question?
Answers
Answer:
linear = 3x+y = 12, y = x/2 -3, y=x
nonlinear y = 6/x -2, y=3x³+5
In trapezoid DEFG, EG = 24.3 and DH = 9.4. Identify HF.
Answers
Answer:
HF = 14.9
Step-by-step explanation:
It takes cadence 36 hours to read 12 books. Write a unit rate that models the situation.
Answers
Answer:
three hours every 1 book
Step-by-step explanation:
36-12
6-2
3-1
The approximate average distances from the sun to Mars and Mercury are listed
below:
Mars: 2.28 x 108 kilometers
Mercury: 5.79 x 107 kilometers
How many times farther from the sun is Mars? Write your answer in standard
notation, rounding to the nearest tenth.
Answers
Answer:
3.9
Step-by-step explanation:
Your calculator will tell you ...
(2.28×10^8)/(5.79×10^7) ≈ 3.9
Mars is about 3.9 times as far from the sun as Mercury.
What is the quotient of the following division problem?
71= 2 = ?
O A. 37 11
B. 35r1
O C. 35r2
O D. 34 r1
Answers
Answer:
35 remainder 1
Step-by-step explanation:
71 ÷ 2 = 35.5
The 35 is the whole number part of your answer. The .5 part of the answer is .5 of 2, which is 1
OR you can think that
35 × 2 =70. The 1 is the remaining part from 71.
Simplify:
(8)214+(8)(−12)
plz help :(
Answers
1712-96
Your welcome
Determine the slope from the given graph below:
The slope is−17
The slope is 5
The slope is 7
The slope is -5
Answers
Answer:
The slope is positive 7
Step-by-step explanation:
The y-intercept is -5, and the next point going upwards is positive 2. (Sorry I'm bad at explaining)
Answer:
The slope is 7
Step-by-step explanation:
(1,2)(0,-5)
[tex]m=\frac{-5-2}{0-1} ==\frac{-7}{-1} =7[/tex]
Hope this helps
A helicopter starting on the ground is rising directly
into the air at a rate of 25 ft/sec. You are running on the
ground starting directly under the helicopter at a rate of 10
ft/sec. What is the rate at which the distance between you and the helicopter is changing when the helicopter has risen to a height of 60 ft in the air, assuming that, initially, it was 30 ft above you?
I want to understand how any why this is solved. So images/diagrams, detailed step by step breakdowns solutions are VERY much appreciated. Thanks!
Answers
Answer:
Oook, quick setup: pick a cartesian plane, be [tex](0;y(t))[/tex]the position of the helicopter as time passes, and [tex](x(t);0)[/tex] your position as you start running. In my horrible sketch, the green line is the distance when you start running, the red line is the distance you need, in general what you want is to move one end of the segment up, the other right, and stretch it.
That distance is easily found with the formula for the distance between two points in the plane, or [tex]d=\sqrt{(\Delta x)^2+(\Delta y)^2}= \sqrt{x^2(t)+y^2(t)}[/tex] (playing a bit with the squares). At this point we need to write down expressions for both [tex]x(t), y(t)[/tex] and find at what value of t we need to evaluate our distance.
For the sake of semplicity, let's start measuring times the moment you start running. Since speed is constant, both expressions will be of the form [tex]s=vt+s_0[/tex]
The equation for the runner becomes simply [tex]x(t)=10t[/tex], since you haven't moved until the heli is high enough.
The equation of the helicopter is [tex]y=25t+30[/tex] since the heli is 30ft above ground when you start running.
Finally, we need to know how many seconds have passed when the heli is at 60 ft above ground. that happens when [tex]60=25t+30 \rightarrow t=\frac{30}{25} = 1.20s[/tex]. in this time, you are at [tex]x(1.2)=10(1.2)=12ft[/tex] from the origin.
Plugging it in the distance formula you get: [tex]\sqrt{12^2+60^2}= \sqrt{144+3600}=4\sqrt {234}\approx 61.2ft[/tex]
solve systems of equations 6x+2y=1 y=-3x+3 using substition??? Need answers quickly!!!!!
Answers
8. A company makes electronic components for TV's. 95% pass final inspection (and 5% fail and need to be fixed). 120 components are inspected in one day. (10 points) b.What is the variance of the number that pass inspection in one day
Answers
Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.
For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability, and has variance given by:
[tex]V(X) = np(1 - p)[/tex]
In this problem:
95% pass final inspection, hence [tex]p = 0.95[/tex]120 components are inspected in one day, hence [tex]n = 120[/tex].The variance is given by:
[tex]V(X) = np(1 - p) = 120(0.95)(0.05) = 5.7[/tex]
The variance of the number that pass inspection in one day is 5.7.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
Round 523,009.974 to the nearest tenth
Answers
Answer:
Step-by-step explanation:
523,010.0
Translate the sentence into an inequality.
Six times the sum of a number and 20 is greater than 16.
Use the variable c for the unknown number.
Answers
Answer:
6 (20 + c) > 16
Step-by-step explanation:
the sum of the number and 20 is 20 + c. so you multiply that equation by 6 giving you 6 (20 + c)
The volume (V) of a rectangular pyramid can be determined by using the following
formula.
Iwi
V
Where l= the length of the rectangle, w = the width of the rectangle, and h = the heigh
of the pyramid, what is the result of solving this equation for w?
Ow=3V-th
O2 - V +3 - th
V3
th
3V
O w=
Answers
Answer:
[tex]{ \rm{V = \frac{lwh}{3} }} \\ \\ { \rm{3V = lwh}} \\ \\ { \boxed{ \rm{ \: w = \frac{3V}{lh } \: }}}[/tex]
Find an equation in the form y=ax^2+bx+c for the parabola passing through the points.
(3,25) (1,3) (-5,-15)
Thanks for the help! :)
Answers
Answer: [tex]x^2+7.0x-5.0x[/tex]
Step-by-step explanation:
A rectangular garden is 24 feet wide. Its length is 4 feet more than twice the width. What is the area of the garden?
Answers
Answer:
1248
Step-by-step explanation:
w = 24feet
L=2w+4feet that means L= 2*24+4 =52
aera is 24*52=1248
3 2/3 + 2 3/5 + x = 8
Answers
Answer: x= [tex]-\frac {109}{15}[/tex]
How does the value of 2 dimes compare to the value of 2 dollars
Answers
Answer:
The 2 dollars has $1.80 more than the two dimes.
Step-by-step explanation:
2.00-0.20=1.80
Examine the figure. What is the measure of angle b?
Answers
Answer:
b =146
Step-by-step explanation:
34 and b form a straight line so they add to 180
b+34 = 180
b = 180-34
b =146
Please look for the question in the picture.
Answers
Answer:
two negitives equals a positive so C none of the above
Hope This Helps!!!
Answer:
A and B
Step-by-step explanation:
Which of the following is equivalent to [picture]
A) a0 + a1 + a2 + a3 + a4 + a5
B) a1 + a2 + a3 + a4 + a5
C) a0 + a1 + a2 + . . .
D) a1 + a2 + a3 + . . . + a∞
Answers
Answer:
A) a0 + a1 + a2 + a3 + a4 + a5
Step-by-step explanation:
Answer:
A) a0 + a1 + a2 + a3 + a4 + a5
Step-by-step explanation:
2x+7y+7x=18
Find the value of Y
Answers
Answer:
y=−9/7x+18/7
Step-by-step explanation:
2x+7y+7x=18
9x+7y=18
Step 1: Add -9x to both sides.
9x+7y+−9x=18+−9x
7y=−9x+18
Step 2: Divide both sides by 7.
7y/7=−9x+18/7
y=−9/7x+18/7
Given :
2x + 7y + 7x = 18To Find :
The value of ySolution :
[tex]\qquad { \dashrightarrow \: { \sf{2x + 7y + 7x = 18}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{ 7y + 9x = 18}}}[/tex]
Transposing 9y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{ 7y = 18 - 9x}}}[/tex]
Dividing both sides by 7 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{7y}{7} = \dfrac{18 - 9x}{7} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{ y = \dfrac{18 - 9x}{7} }}}[/tex]
⠀
Therefore, the value of y = 18 – 9x/7 .
(d) Given that the fifth and the seventh terms of the G.P form the first two consecutive terms of an arithmetic sequence, calculate the sum of the first 20 terms of the sequence
Answers
Step-by-step explanation:
the answer is shown in the photo
Heheh... uhm, yeah, I don't do best with algebraic questions-
Answers
Answer:it's a for sure I think
How many sides does the regular polygon have if each interior angle measure is four times the (1 point)
measure of each exterior angle measure?
Answers
Answer:
The exterior and interior angles must add up to 180 degrees. Thus, 180 divided by five gives the exterior angle as 36 degrees (and hence the interior angles as 144 degrees).
Answer:
10 Sides
Step-by-step explanation:
Int Angle + Ext Angle = 180
4Ext + Ext = 180
Ext = 36 degrees
-----
360/36 = 10 sides
The area
of this figure
is square inches.
20 in
28 in
30 in.
7 in
25 in.
Answers
Answer:
946 square Inches
Step-by-step explanation:
First, you should split up the shape into parts.
1st part 28x7
2nd part 30x25
We are multplying simply because
Area = Length x Width
Now that we have split up the parts lets multply them and add them togeher.
28 x 7 = 196
30 x 25 = 750
196 +750 = 946
So the area of this figure is 946 square inches.
A rock is 7 feet below the surface of a river. If its position can be recorded as −7 feet, what would the position of 0 represent? (5 points)
Question 3 options:
1)
On the surface of the river
2)
At the bottom of the river
3)
7 feet above the surface of the river
4)
7 feet below the surface of the river
Answers
Answer:
A on the surface of the river
Step-by-step explanation:
100 persent correct
Figure B is a scale image of Figure A, as shown.
7
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this: 42/53
Answers
Explanation:
Divide the side length for B over the corresponding side length for A.
scale factor = B/A = 7/(2.5) = 2.8
Let's now convert this to a fraction
2.8 = 2 + 0.8 = 2 + 8/10 = 20/10 + 8/10 = (20+8)/10 = 28/10
Then reduce that fraction
28/10 = (14*2)/(5*2) = 14/5
Note that 14/5 = 2.8
y-5=2(x-3) slope intercept.
Answers
Answer:
y=2x-1
Step-by-step explanation:
Because this equation is in point-slope form and we need it in slope-intercept form, all we need to do is simplify y-5=2(x-3).
y-5=2x-6 Distribute.
+5 +5 Add 5 to both sides of the equation.
y=2x-1
Hope this helped! Have a great day ♥
Which is equivalent to the following expression? (2x - 1)(x + 3)
Answers
Answer:
2x2+5x−3
Step-by-step explanation:
Expand the polynomial using the FOIL method.
How do we graph y+6=45(x+3)?
Answers
Answer:
.....,....................