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
An article fills 5/8 of a magazine page. A related photo takes 1/4 of the article. How much of the page is taken up by the photo?
Answers
Answer:
2/8
Step-by-step explanation:
Hayley is considering two gym membership plans. The plans are detailed here. Plan One: $40 for a monthly pass plus $4 for each gym visit Plan Two: $12 for each gym visit. Which equation expresses the situation in the form of y=mx+b where x is the number of gym visits per year and y is the total cost per month for Plan One?
y=40x+4
y=4x+40
y=12x
y=3x+50
please help
Answers
Answer:
Plan One: y=4x+40
Plan Two: y=12x
Step-by-step explanation:
Travel back in time to the year 2008, when text messages were charged per text. Some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that. Today, most packages include unlimited text and data but cost closer to $100 a month.
Write and solve an equation to determine the range of text messages you can send with the 2008 plan without spending more than $100.
If you have a phone, look at your data summary. Is this range your average daily number, weekly number, or monthly number of texts? Determine how much you would have paid for the month if you had the 2008 text plan? Write this as an equation and solve It.
80 POINTS!!!!
Answers
Answer:
You can send 405 texts in 2008 without going over 100$
Step-by-step explanation:
Equation for 2008:
59$ for 200 texts + .20 dollars per text after that < or = $100
So minus $59 dollars
.20 * (number of txts) < 100 - 59
.20 * (number of txts) < 41
divide both sides by .2
number of txts < or = 205
so therefore you can send exactly 405 texts without going over $100
Then to find how much you would pay plug into this equation
If total number of texts is lower than 200 texts, then you would be paying $59, but if it is more then plug into the following equation
(Total number of texts - 200) * .20 + 59 = Total $ spent for a 2008 text plan per month.
The total number of texts that can be sent is 405 texts in 2008 without going over 100$. The amount will be $99.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The equation for 2008:
59$ for 200 texts + 0.20 dollars per text after that < or = $100 and minus $59 dollars
0.20 x (number of texts) < 100 - 59
0.20 x (number of texts) < 41
Divide both sides by 0.2
number of texts < or = 205
405 texts can be sent without going over $100
If the total number of texts is lower than 200 texts, then you would be paying $59, but if it is more then plug into the following equation
(Total number of texts - 200) x 0.20 + 59 = Total $ spent for a 2008 text plan per month.
( 405 - 200 ) x 0.2 + 59 = $99
Therefore, the total number of texts that can be sent is 405 texts in 2008 without going over 100$. The amount will be $99.
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1/8+1/4=? do you know what it could be!?
Answers
Answer:0.375
Step-by-step explanation:
1/8 + 1/4 = 3/ 8=0.375
The Circumference of Taylor’s bike tire is 72 inches what is the diameter of the tire used 3.14 for and round to the nearest whole number
Answers
Answer:
Step-by-step explanation:
Circumference=72
pi=3.14
Radius=C /2π
72/6.28=11.4649681529
Rounded to the whole would be 11
=11
Kanica wants to earn at least $750 this week in commission. What is the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells? Round your answer to the nearest dollar if necessary.
Answers
Answer:
Total earning Kanica wants to make is at least $750
The commission she gets is 7.5 % Therefore to find the sales she should make we use :
(Total earnings * 100% )/ Commission
= (100 * 750) / 7.5
=75000/7.5
= $ 10,000
The minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Kanica wants to earn at least $750 this week in commission.
Let x be the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells.
The value of x can be found as follows:
x = 750/(7.5%)
x = (750/7.5)x100
x = $10,000
Thus, the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.
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I need help on these functions questions
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Substitute x = - 1 into f(x)
f(- 1) = 6 - 2(- 1) = 6 + 2 = 8
(b)
Substitute x = [tex]\frac{1}{3}[/tex] into g(x)
g([tex]\frac{1}{3}[/tex] ) = [tex]\frac{9}{\frac{1}{3} }[/tex] = 9 × 3 = 27
(c)
Substitute x = f(x) into h(x)
h(6 - 2x)
= 6 + (6 - 2x)² ← expand using FOIL
= 6 + 36 - 24x + 4x² ← collect like terms
= 4x² - 24x + 42
(d)
Substitute x = f(x) into g(x)
g(6 - 2x)
= [tex]\frac{9}{6-2x}[/tex]
(e)
Evaluate g(12) then substitute value obtained into f(x)
g(12) = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] , then
f([tex]\frac{3}{4}[/tex] ) = 6 - (2 × [tex]\frac{3}{4}[/tex] ) = 6 - [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
(f)
Evaluate f(- 9) then substitute the value obtained into h(x)
f(- 9) = 6 - 2(- 9) = 6 + 18 = 24 , then
h(24) = 6 + 24² = 6 + 576 = 582
Which of the following statements about the image below is true?
Answers
Answer:
d. Line UR and Line VW are parallel
Step-by-step explanation:
If they were to continue going straight, they would not touch, making them parallel.
I hope this helps!
66=3x
simplify your anwser as much as possible
Answers
Answer:
x =22
Step-by-step explanation:
66/3 =22
pls give me brainlies
-
Which polynomial has a factor of (x - 5)?
A x² + 4x - 5
B x + 5x + 4
C x² – 2x - 15
D 2x + 11x + 5
-
Answers
Answer:
The correct answer is C
x² - 2x -15
What is the molarity of a solution
made by dissolving 67.3 g of lithium
chloride (LiCl) in enough water to
make 2.37 L of solution?
Molar Mass Li: 6.94 g/mol
Molar Mass Cl: 35.45 g/mol
Answers
Answer:
0.670. M
Step-by-step explanation:
Molarity can be expressed like this:
molarity = number of moles /volume (L)
We know the volume, which is 2.37 L , but we need to find the number of moles. We can do this by dividing 67.3 g by the molar mass of L i C l :
number of moles = mass of sample /molar mass
number of moles = 67.3 g /(6.94 + 35.45) g/mol = 67.3 g /42.39 g/mol
number of moles = 1.59 mol
molarity = 1.59 mol /2.37 L = 0.670. M
20 giraffes were introduced to a certain safari and it is expected to double its population every 5 years. How many giraffes will exist after 2 years? How long it would take to increase their population to 60?
Answers
It would take 7.9 years to increase their population to 60.
An exponential function is in the form:
y = abˣ
where a is the initial value of y and b is the multiplier.
Let y represent the number of giraffes after x years.
From the question:
a = 20, b = 2, hence
[tex]y=20(2)^\frac{x}{5} \\\\for\ x=2:\\\\y=20(2)^\frac{2}{5} =26\\\\For\ y=60:\\\\60=20(2)^\frac{x}{5} \\\\2^\frac{x}{5} =3\\\\x=7.9\ years[/tex]
It would take 7.9 years to increase their population to 60.
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $70. For one performance, 25 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was $2050. What was the price of each kind of ticket?
Answers
Answer:
You can use the method of substitution.
Let the advance and same-day tickets be x and y respectively.
x + y = $70 ---> (1)
25x + 35y = $2050 ---> (2)
From Statement (1):
Let (1) × 25
25x + 25y = $1750
10y = $2050 - $1750
= $300
y = $300 ÷ 10
= $30 ---> (3)
From Statement (3):
Substitute (3) into (1)
x + $30 = $70
x = $70 - $30
= $40
Advance ticket: $40
Same-day ticket: $30
a shirt is on sale for 20% off the original price. if the original price is 25.00, what will be the sale price of the shirt
Answers
Answer:
$20 is the sale price
Step-by-step explanation:
20% of $25 is (0.2*25)=$5
$25 -$5 = $20
Keith bought 4 new baseball trading cards to add to his collection. The next day his dog at half of his collection. There is now 25 cards left. How many cards did Keith start with?
Answers
Answer:
46 cards
Step-by-step explanation:
We can use a variable to represent the starting amount of cards: (x)
Keith bought 4 new cards: (+4)
His dog ate half of the collection: (x/2)
There are now 25 cards: (=25)
So we can use this expression to find the starting amount: (x+4)/2=25
Start by multiplying both sides by 2 to get rid of the (x/2).
Now subtract 4 from both sides to get rid of the (+4).
Finally, we know x= 46
Thus, Keith started with 46 cards.
For her phone service, Kala pays a monthly fee of $24, and she pays an additional $0.07 per minute of use. The least she has been charged in a month is $118.64.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answers
Answer:
m=1352
Step-by-step explanation:
(118.64-24)/0.07=m
If the sum of squares for a sample containing 51 items equals 200, what is the standard deviation?
A) 1.98
B) 2.00
C) 3.92
D) 4.00
Answers
The standard deviation is 1.98. Option A is correct.
The standard deviation formula is given as
[tex]\sigma = \sqrt{\frac{SS}{n} }[/tex]where:
SS is the sum of squares = 200n is the sample size = 51Substitute the given parameters into the formula to have:
[tex]\sigma = \sqrt{\frac{200}{51} }\\\sigma = \sqrt{3.922}\\\sigma = 1.980[/tex]
Hence the standard deviation is 1.98
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What is the length of LN in the right triangle below?
Answers
Answer:
D 280
Step-by-step explanation:
Pythagoras theorem
Answer:
a
Step-by-step explanation:
LN=√19＾2 - 9＾2
=√361 - 81
=√280
pls help me in this question
a . If 3x,2x and (x+12) are supplymentary angles find the sizes of unknown angles
Answers
Answer:
x=28°
Step-by-step explanation:
supplementary angles equal 180°
So:
3x+2x+x+12=180°
6x+12=180
6x=168
x=28°
Therefore:
3x:
3(28)=84°
2x:
2(28)=26°
x+12:
28+12=40°
The figure shown is to be painted on a road sign. Which of the following best describes the two polygons that form the figure?
A. A rectangle and an isosceles trapezoid
B. A rectangle and a rhombus
C. A rectangle and a parallelogram
D. A rectangle and an isosceles triangle
Answers
Answer:
D: A rectangle and an isosceles triangle
Step-by-step explanation:
A recangle for the base of the arrow, and an isosceles triangle to form the full arrow.
The answer will be option D which is a rectangle and an isosceles triangle.
What is an isosceles triangle?The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.
As we can see in the figure there are one isosceles triangle and a rectangle are joined together to form an arrow.
Thus the answer will be option D which is a rectangle and an isosceles triangle.
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What is the value of the expression 2z ÷ [z – (z – 4)] when z = 8?
Answers
2z ÷ [z – (z – 4)]
Sub z=8 into the expression
2(8) ÷ [8 – (8 – 4)] = 16 ÷ 4
= 4
Solve 3x-5 + x= 31.
09
0-12
O 12
Answers
[tex]3x-5 +x = 31\\\\\implies 4x -5 = 31\\\\\implies 4x = 31 +5\\\\\implies 4x = 36 \\\\\implies x =\dfrac{36}4\\\\\implies x = 9[/tex]
مل
Amy is adding two numbers. She got the answer
which is 2003 However she copied the question wrong.
The one's column of the first number should be 7. she
wrote it to I. The hundred's column
of
the second number
should be 2. she wrote it to 3. What is the correct ansuel
if she copied it correctly?
Answers
Answer:
2999
Step-by-step explanation:
There's a lot of possibilities bc it didn't mention any tens columns.
Estimate 4 1/3 x 2 3/4
Answers
Answer:
11 11/12
Step-by-step explanation:
Answer:
≈ 12
Step-by-step explanation:
To estimate, we'll round these mixed numbers to the nearest whole number, then multiply. Let's start with 4 1/3. 4 1/3 is closest to 4, since 1/3 is smaller than 1/2. Then, we can look at 2 3/4. This mixed number is closest to 3, since 3/4 is greater than 1/2.
Now, the two numbers we have are 4 and 3. What is 4 × 3? Well, that's pretty simple - the answer is 12. So, 4 1/3 × 2 3/4 ≈ 12. Hopefully that's helpful! :)
Which sizes can he display? Choose all that apply.
linch
4
0.5 inch
3 inch
8
1 inch
1.5 inch
Answers
Step-by-step explanation:
He can choose the dispay boxes that are 0.5 in, 1/4 in, and 3/8 in
Hope this helps
May I get braineist pls?
The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!
Answers
Step-by-step explanation:
standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation
Help help math math math
Answers
Answer:
pushin p
Step-by-step explanation:
pushin p
please need help with this Calculus question
Answers
I need help with this
Answers
240 because i am smart and also nice pencil
Step-by-step explanation:
Find the value of n
Plz help me fast and send the answer
Answers
Answer:
n is 113
Step-by-step explanation:
Is an isosceles triangle so the base angles are equal
therefor angles sum up to 180
46 + x + x = 180
46 + 2x = 180
2x = 180 - 46
2x = 134
x = 67
now to find n
the sum of angles on a straight line equals 180
n + x = 180
n + 67 = 180
n = 180 - 67
n= 113
Answer:
the base angle of an isosceles triangle are equal
let the base angle be y°
46° + y° + y° = 180°(sum of angles in a ∆)
46° + 2y° = 180°
2y° = 180° - 46°
2y° = 134°
y° = 134/2
y°=67°
n+y=180°[sum of angles on a straight line]
n+67=180°
n=180-67
n=113°