Answers
Answer:
f(x) = (3x -12)/(x² -7x +12)
Step-by-step explanation:
The equation for a rational function can be written from the clues offered by the horizontal and vertical asymptotes, the y-intercept, and any "holes" in the function graph. Here, those clues are ...
horizontal asymptote: y = 0vertical asymptote: x = 3hole: (x, y) = (4, 3)y-intercept: (0, -1)__
The horizontal asymptote at y=0 tells you the denominator is of higher degree than the numerator. The vertical asymptote at x=3 tells you (x-3) is a factor of the denominator. The hole at x=4 tells you there is a factor of (x-4) in both numerator and denominator.
At this point, the function is tentatively ...
[tex]f(x)=a\dfrac{x-4}{(x-3)(x-4)}[/tex]
Evaluating this at the y-intercept, x=0, gives ...
f(0) = -1 = a/(0 -3) = -a/3
a = 3 . . . . . multiply by -3
Then our rational function, consistent with all of the features of the graph, is ...
[tex]f(x)=\dfrac{3(x -4)}{(x -3)(x -4)}\\\\\boxed{f(x)=\dfrac{3x-12}{x^2-7x+12}}[/tex]
Related Questions
Veronica wants to convert 108 inches to feet. What does she need to do?
Answers
Answer:
Divide 108 by 12 since there are 12 inches in a foot.
108 ÷ 12 = 9
Veronica needs to divide 108 inches by 12 to get 9 feet.
To convert inches to feet, Veronica needs to divide the number of inches by 12, as there are 12 inches in a foot.
Given that Veronica wants to convert 108 inches to feet, she should perform the following calculation:
108 inches ÷ 12
= 9 feet
Therefore, Veronica needs to divide 108 inches by 12 to get 9 feet.
To learn more on Conversion factor click:
https://brainly.com/question/32020768
#SPJ6
GEOMETRY: VOLUME & SURFACE AREA!! HELP PLEASE WITH ANY ONE OF THEM!!
Answers
Answer:
1) 728
2) 274.89
Step-by-step explanation:
Find the volume and surface formulas for each shape attached.
I'll do a couple for you. For rest just use the formulas and input the values and solve.
1) It is a pyramid.
V = 1/3 * b * h, where b is the area of base, which is a rectangle so,
b = l * w
so,
V = 1/3 * l * w * h
V = 1/3 * 8 * 21 * 13
V = 1/3 * 2184
V = 2184 / 3
V = 728
2) It is a cylinder
[tex]V = \pi *r^2*h[/tex]
V = π * 5^2 * 3.5
V = π * 25 * 3.5
V = 87.5 π
V = 274.89
pls help do today:(!!
Answers
[tex] \qquad\qquad\huge\underline{\boxed{\sf Answer}} [/tex]
The correct way to write the name of a ray is :
[tex] \large \tt Problem\:\: 1 [/tex]
[tex] \sf \overrightarrow{DC}[/tex][tex] \large \tt Problem \:\:2 [/tex]
[tex] \sf \overrightarrow{IG}[/tex][tex] \large \tt Problem \:\:3 [/tex]
The Correct choice is C
Ray has one end point and continues forever on the other side.
The perimeter of a triangle is 7 m. The longest side is twice the length of the shortest side. The sum of the
lengths of the shortest side and the middle side is 1 m more than the length of the longest side. Find the
lengths of the sides.
Answers
Answer:
See below in bold.
Step-by-step explanation:
Let the length of the shortest side be x, then the longest side = 2x.
Also x + y = 2x + 1 where y = length of the middle side,
Simplifying:
2x - x - y = -1
x - y = -1 (A)
Also as the perimeter = 7:
x + 2x + y = 7
3x + y = 7 (B)
Adding (A) and (B):
4x + 0 = 6
x = 6/4 = 1.5
Plug x = 1.5 into equation B:
3(1.5) + y = 7
y = 7 - 4.5 = 2.5.
Answer:
So the shortest side = 1.5, middle = 2.5 and longest = 2*1.5 = 3.
Find the measure of each angle in the isosceles trapezoid.
Answers
Answer:
Step-by-step explanation:
Rosalinda has a circular serving platter in the middle of her circular table.
The radius of the platter is 15 inches less than the radius of the table
The diameter of the table is 4 feet. What is the difference between the
area of the table and the area of the platter? Use 3.14 for 17, and write your
answer in decimal form. 7.G.4
Answers
diameter=4ft=12(4)=48in
Radius of table=48/2=24inRadius of platter=24-15=9inSo
Area of table:-
π(24)^2576πin²Area of platter:-
9²π81π in²Difference:-
576π-81π495π1554.3in²Answer:
1554.3 in²
Step-by-step explanation:
Given information:
The radius of the platter is 15 inches less than the radius of the tableThe diameter of the table is 4 feetπ = 3.141 foot = 12 inches
⇒ 4 ft = 4 × 12 = 48 in
Radius = ¹/₂ diameter
⇒ Radius of table = ¹/₂ × 48 in = 24 in
⇒ Radius of platter = 24 in - 15 in = 9 in
Area of a circle = πr²
⇒ Area of table = 3.14 × 24² = 1808.64 in²
⇒ Area of platter = 3.14 × 9² = 254.34 in²
Difference = area of table - area of platter
= 1808.64 - 254.34
= 1554.3 in²
how can we use a "line of best fit" to make a prediction?
Answers
Step-by-step explanation:
To draw a line of best fit, balance the number of points above the line with the number of points below the line.
There are 9 new books and 5 used books on a shelf.
(a) What is the ratio of all books on the shelf to used books?
(b) What is the ratio of new books to all books on the shelf?
Answers
A.) 14:5
B.) 9:14
Answer:
A- 14:5
B - 9:14
Step-by-step explanation:
Hope this helps!!!
i need help asap this is k 12 and 100 points
Answers
Answer:
6.8
Step-by-step explanation:
Add the numbers and divide by the amount of numbers and get 6.8
Answer: 6.8.
Step-by-step explanation: When finding the mean of a data set, you need to add all the numbers of the set, and then divide the answer by however many numbers you have on the data set. The work is done below:
14 + 7 + 2 8 + 3 = 34.
34 / 5 = 6.8, because there are 5 numbers in the data set.
Have a great day! :)
II. A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming election. A poll of 150 randomly selected voters is taken, and 78 of those selected plan to vote for the incumbent candidate. Construct a 90% confidence interval for the proportion of all voters who plan to vote for the incumbent candidate.
a
(0.02709, 0.09291)
b
(0.4529, 0.5871)
c
(0.02131, 0.09869)
d
(0.0309, 0.0691)
Answers
The function f(x)=(2)(1.0)+x(0.5)2+x models the concentration of pineapple when 2 gallons of pineapple juice are added to x gallons of another juice. Find the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice. Give the answer as a percent but do not include the percent sign (%).
Answers
The concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice is 5.75
Functions and valuesGiven the functions that model the concentration of pineapple when 2 gallons of pineapple juice are added to x gallons of another juice as:
f(x)=(2)(1.0)+x(0.5)²+x
If the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice, then;
f(3) = (2)(1.0)+3(0.5)²+3
f(3) = 2.0 + 3.75
f(3) = 5.75
Hence the concentration of pineapple when 2 gallons of pineapple juice are added to 3 gallons of the other juice is 5.75
Learn more on functions here: https://brainly.com/question/2833285
A fair dice is rolled.
Work out the probability of getting a number less than 6.
Give your answer in its simplest form
Answers
Answer: 5/6
Step-by-step explanation: If its a six sided die with numbers 1 - 6
Given f() = -4x + 3, find f(-3)
Answers
Answer:
The answer is 15
Step-by-step explanation:
f(x) = -4x + 3, f(-3)
f(-3) = -4x + 3
f(-3) = -4(-3) + 3
f(-3) = 12 + 3
f(-3) = 15
Thus, The answer is 15
Answer:
f(-3)=-4(-3)+3
=12+3=15
Step-by-step explanation:replace x with -3
Si un átomo tiene un número atómico de 18 y 22 neutrones, ¿cuál es su masa atómica?
DOY CORONA
Answers
su masa atómica es de 4 creo
A
The bases are the same size and shape and perpendicular to each
other.
B
The bases are a different size and shape and parallel to each other.
с
The bases are a different size and shape and perpendicular to each
other.
D
The bases are the same size and shape and parallel to each other.
Answers
Tiffany had finished 78% of her homework. Write this amount as a decimal.
Could someone please help me!?
Answers
Using only 3,4&5 what equals 11
Answers
(5×3)-4 = 11
hope it helps...!!!
Answer:
(5*3)-4=11
Step-by-step explanation:
because when you multiply 5*3=15, then subtract 4 from it, it gives you 11. There are no other options becuase 5*4-3=17 and 4*3-5=16 and 5*4+3=23 and 4*3+5=17.
How many cars are needed to transport 82 children if each car can take 6 children
Answers
Mai and her sister are planting a garden.They made 2 plant beds.one was 4 feet by 3 feet and the other 5 feet by 5 feet.they want to outline the beds with bricks that are 1foot long.How many bricks will they need to outline both beds?
Answers
Answer:
27 bricks
Step-by-step explanation:
find the perimeter of the first one, 4 x 3 = 12. Then the perimeter of the second one, 5 x 5 = 25. Therefore 12 + 15 = 27. Meaning you need 27 bricks
On a coordinate plane the graph of a line passes
through the origin and the point (9,12) What is
the equation of the line?
Answers
Answer:
y = (4/3)x
Step-by-step explanation:
Two points on the line are the origen (0, 0) and the given (9, 12).
Starting at the origin and moving to (9, 12), we see the change in x being 9 and that in y being 12. Thus, the slope of the line through these two points is m = rise/run = 12/9 = 4/3.
Thus the equation of the line in slope-intercept form is y = (4/3)x + 0, or
just y = (4/3)x
A reciangular pyramid is sliced
horizontally, parallel to its base.
Which figure could represent the
cross section of the pyramid?
A rectangle
Pl triangle
C. cirde
D. hexagon.
Answers
HELP ME OUT PLS!!!!
The radius of a sphere is 7 cm. What is the sphere's volume? Round to the nearest tenth, and use 3.14 for pi.
O 723,2 cm
O 1868.2 cm
O 1436,0 cm
O 2052,5 cm
Answers
⠀
Explanation :
⠀
We know,
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]
⠀
Here,
The radius of the sphere is 7 cm.We will take the value of π as 3.14⠀
Substituting the values in the formula :
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]
⠀
Therefore,
The volume of the sphere is 1436.0 cm³The box-and-wishker plots bellow
Answers
Answer:
H: Plots 1 & 2
Step-by-step explanation:
6. The length of Garden B is 3 more than the length of Garden A. Write, and solve the equation
you can use to find the length of Garden A.
Answers
Answer:
B = A + 3
Step-by-step explanation:
Let B be the length of Garden B and A the length of Garden A.
We are told that B = A + 3
We can use this equation to find the length of Garden B.
Each month, Edward budgets $1860 for fixed expenses, $860 for living expenses
and $250 for annual expenses. His annual net income is $32,508.
Which statement best describes his monthly budget?
Answers
Answer:
His annual net income.
Step-by-step explanation:
Hope it helps.
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 51.6 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Tthe total weight of the liquid in the tank, to the nearest full pound is 13,514 pounds.
What is the total weight of the liquid in the tank?The first step is to determine the volume of the tank.
Volume of a hemisphere = Volume of a hemisphere = (2/3) x (π) x (r³)
π = 22/7r = radius2/3 x 5³ x 22/7 = 261.91 ft³
Weight = 261.91 ft³ x 51.6 = 13,514 punds
To learn more about the volume of a hemisphere, please check: https://brainly.com/question/26840364
I am a solid figure with two congruent
polygons that are bases, connected
with lateral faces that are rectangles.
Answers
THE ANSWER IS PRISM
1.) If the function f(x) = (x – 3)^2+ 2, the minimum value occurs when x is
1)-2
2)2
3)-3-
4) 3
Answers
Answer:
2
Step-by-step explanation:
A garden measures 10 ft by 10 ft.
What is the area of the garden in square inches?
Answers
Answer:
1200 sq. in.
Step-by-step explanation:
(10x10)x12=100x12=1200
Write the expression.
Answers
Answer: 4 (4x + 7)
Step-by-step explanation:
4 ( 4x + 7)
4 is the greatest number divisble by both 16 and 28 so 4 is factored out of the equation