The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.
We have,
A rational function is a function that can be expressed as the ratio of two polynomials.
It can have vertical asymptotes and/or holes in its graph, depending on the behavior of the denominator polynomial.
To construct a rational function with no vertical asymptotes and no holes, we need to ensure that the denominator polynomial does not have any real roots.
This means that the denominator polynomial should either have no roots or only complex roots.
One way to achieve this is to use a quadratic polynomial in the denominator that has no real roots.
For example, consider the function:
f(x) = (x² + 1)/(x² + 2x + 2)
The denominator polynomial x² + 2x + 2 has no real roots because its discriminant, 2² - 4(1)(2) = -4, is negative.
This means that the function f(x) has no vertical asymptotes.
To check if the function has any holes, we need to simplify the function by canceling out any common factors between the numerator and denominator.
However, since the numerator x² + 1 has no common factors with the denominator, there are no terms to cancel out.
Therefore, the function f(x) has no holes either.
Thus,
The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.
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The equation P = 24+2.94w represents Barrington's
water bill, where:
P is the price per month, and w is the amount of water they
use in one month, in thousands of gallons.
Answer the below questions. Round any decimals to two
places.
dollars when they use 0
dollars for every one-thousand
1. Barrington pays … type your answer…
gallons of water.
2. They pay type your answer....
gallons of water used.
3. Barrington paid type your answer...
thousand gallons last month.
dollars when they used 11-
Barrington pays 24 for 0 gallons of water and Barrington pays 55.9 for 11 gallons of water
Calculating the amount paid for gallons usedGiven that we have
P = 24 + 2.9w
When they used 0 gallons, we have
P = 24 + 2.9(0)
P = 24
When they used 11 gallons, we have
P = 24 + 2.9(11)
P = 55.9
Hence, the amount paid for 11 gallons is 55.9
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HELP PLS ASAPPP
I don't want to restart this entire thing so someone pls help
Answer:y=4/3x-14/3
Step-by-step explanation:
1. Find the slope of the original line
3/4x-y=7/2
-y=-3/4+7/2
y=3/4x-7/2
2. Using this find the negative reciprocal
3/4 -------- -4/3
3. Now insert -2,-2 in the equation y=-4/3x
-2=-4/3(-2)
-2=8/3
4. Find the needed intercept to make true.
-2=8/3-14/3
Therefore, y=-4/3x-14/3
What is the height of the cylinder?
Answer: 6.996
Step-by-step explanation:
As given in the problem, V = πr²h
We are given V and r, so all we must do is plug them in and solve for h
[tex]351.68=\pi (4)^2h\\351.68=\pi 16h\\h=6.996[/tex]
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
The new coordinates of the vertices of the translated triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). (option 2)
A triangle is a three-sided polygon with three vertices. In this problem, we are given a triangle ABC with vertices A(−3, 3), B(0, 7), and C(−3, 0). The coordinates of the vertices represent the location of each vertex in the coordinate plane.
Using this method, we can determine the new coordinates of the vertices of the translated triangle. The options given for the new coordinates of the vertices are:
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
We can check each option by adding 3 to the y-coordinate of each vertex in the original triangle.
In the first option, the new coordinates of vertex A are (−3, 3+3) = (−3, 6), which matches the coordinates given in option 2.
Therefore, the correct answer is option 2.
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Select the graph of the equation below.
A.
B.
C.
D.
y= 1/2x^2 + 2x -6
The graph of the equation above include the following: D. graph D.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y= 1/2x² + 2x -6 is positive 1/2, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -8.
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A wheel has 5 equally sized slices numbered from 1 to 5.
Some are grey and some are white.
The slice numbered 1 is grey.
The slices numbered 2, 3, 4, and 5 are white.
The wheel is spun and stops on a slice at random.
Let X' be the event that the wheel stops on a white slice, and let P(X) be the
probability of X
Let not X' be the event that the wheel stops on a slice that is not white, and let
P (not X) be the probability of not X.
Event
X
not X
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter
the probability of the event.
(b) Subtract.
Outcomes
12345
0
0
O
1- P(not X) -
0
O
O
Probability
00000 P(not X) -
P(X) -
010
8
X
(c) Select the answer that makes the sentence true.
1-P (not X) is the same as (Choose one)
8
X
5 1
X
4
3
2
The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1
What is the explanation for this?Total numbers on wheel = total possible outcomes
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Grey colored portion = {3}
White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}
X = Event that wheel stops on a white slice
P(X) = number of white slices ÷ total number of slices
P(X) = 9 / 10 = 0.9
P(not X) = 1 - P(X)
P(not X) = 1 - 0.9 = 0.1
Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1
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i would like help finding the inverse
The inverse of the given function include the following: A. G⁻¹(x) = (x + 2)/5
What is an inverse function?In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
g(x) = y = 5x - 2
x = 5y - 2
5y = x + 2
By dividing all through by 5, we have;
G⁻¹(x) = y⁻¹ = (x + 2)/5
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solve for 8v = 3v + 25
Answer:
v = 5
Step-by-step explanation:
Collect like-terms:
[tex]8v = 3v + 25[/tex]
[tex]8v - 3v = 25[/tex]
[tex]5v = 25[/tex]
Divide both sides by 5 to make v the subject:
[tex]v = 5[/tex]
Solve the following simultaneous equation using algebra
6x+3y=45
The solution to the simultaneous equation is x = 6 and y = 3.
To solve this system of equations, we can use the method of elimination. First, we want to eliminate one of the variables, either x or y. In this case, it is easiest to eliminate y. To do so, we can multiply the second equation by 3, which gives us:
6x + 3y = 45
6x - 6y = 18
Now, we can subtract the second equation from the first:
6x + 3y - (6x - 6y) = 45 - 18
Simplifying this expression, we get:
9y = 27
Dividing both sides by 9, we get:
y = 3
Now that we know the value of y, we can substitute it into either equation to find the value of x. Let's use the first equation:
6x + 3y = 45
6x + 3(3) = 45
6x + 9 = 45
Subtracting 9 from both sides, we get:
6x = 36
Dividing both sides by 6, we get:
x = 6
Correct Question :
Solve the following simultaneous equation using algebra
6x+3y=45
2x-2y=6
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PLEASE HELP!! THIS IS URGENT!!
Michelle works for 33 hours this
week. She earns $10 per hour.
Her pay after taxes is $277.11.
How much does she pay in
payroll tax?
This week, Michelle works 33 hours. She is paid $10 per hour. Her take-home pay is $277.11 after taxes. She pays $ 52.89 in payroll tax.
We know that Michelle works for 33 hours this week and her pay for one hour is $10. So, firstly we will calculate her total pay for this week.
Total pay for week = pay for one hour × hours worked
= 10 × 33
= $ 330
Now, after taxes her pay is $277.11. So,
Tax = Pay before tax - pay after tax
= 330 - 277.11
= $ 52.89
A payroll tax is a tax paid by both employees and employers on wages, tips, and salaries. Employers withhold taxes from employees' paychecks and pay them to the government.
Federal, state, and municipal income taxes, as well as the employee's contribution of Social Security and Medicare taxes (FICA), are all included.
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Find the surface area of the prism shown below. You can assume that this prism has all faces, including the bottom.
Show all formulas, work, and drawings that you made to answer the question, and do not forget to include appropriate units.
The surface area of the prism including rectangles and triangles is equal to 13920 square units.
Prism has,
Two rectangles with side length 20 and 120.
Area of rectangle = length × width
= 20 × 120
= 2400
2400 × 2 = 4800
Two rectangles with side length 20 and 30.
Area of rectangle = length × width
= 20 × 30
= 600
600 × 2 = 1200
Two rectangles with side length 17 and 120.
Area of rectangle = length × width
= 17 × 120
= 2040
2040 × 2 = 4080
One rectangle with side length 120 and 30
Area of rectangle = length × width
= 30 × 120
= 3600
Two triangles with base 30 and height 8.
area of triangle = ( 1/2) × 30 × 8
= 120
120 × 2 = 240
Surface area of the prism
= Area of all rectangles + Area of two triangles.
= 4800 + 1200 + 4080 + 3600 + 240
= 13920
Therefore, the surface area of the prism is equal to 13920 square units.
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Find the mode of these numbers:4,2,4,2,3,0,1,2,4,1,3,4,2
Answer:
2 and 4
Step-by-step explanation:
Answer: 4,2
Step-by-step explanation:
Mode: Number that repeats itself more
If there are 2 or more numbers that repeat themself the same amount you put both.
4,2,4,2,3,0,1,2,4,1,3,4,2
4: 4 times
2: 4 times
3: 2 times
0: 1 time
1: 2 times
whats the interests going to be for a mortgage thats 245,000 with a down payment of 44,000 & making a payment of
1205.11 monthly
Answer:
The mathematical equation for calculating the monthly interest is
I = P * (r / n)
where:
I is the monthly interest
P is the loan amount minus the down payment (i.e., $245,000 - $44,000 = $201,000 in this case)
r is the annual interest rate (i.e., 3.5%)
n is the number of payments per year (i.e., 12 for monthly payments)
then I = $201,000 * (0.035 / 12) = $711.06
Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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24. Brittany is making lemonade from
a mix. The instructions say to mix
8 scoops of powder per gallon, but
she is only making a quart. How
many scoops should Brittany use?
A. 1
B. 2
C. 4
D. 16
Answer:
B 2
Step-by-step explanation:because a quart is 0.25 of a gallon
Given the geometric sequence an with the following information, find a10.
a2=-36 a7=128/27
The 10th term of the sequence is 1024/729
Finding the 10th term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
a2 = 36
a7 = 128/27
The nth term of a geometric sequence is
an = a1 * r^(n -1)
So, we have
a2 = a1 * r = 36
a7 = a1 * r^6 = 128/27
Divide the equations
r^5 = (128)/(27 * 36)
This gives
r = [(128)/(972)]^1/5
So, we have
r = [(32)/(243)]^1/5
r = 2/5
Also, we have
a1 = 128/(27r^6)
The 10th term of the sequence is
a10 = a1 * r^9
So, we have
a10 = 128/(27r^6) * r^9
This gives
a10 = 128/(27) * r^3
This gives
a10 = 128/(27) * [2/3]^3
Evaluate
a10 = 128/27 * 8/27
This gives
a10 = 1024/729
Hence, the 10th term is 1024/729
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Shandin looks at the prices of 5 skateboards. The prices are $65, $79, $95, $80, and $175. These prices contain one extreme value ($175). Which measure of center should Shandin use to describe the prices? A. Mean absolute deviation (MAD) OB. Mean O C. Range O D. Median
Answer:
Shandin should use the median to describe the prices since it is a more robust measure of center that is not affected by extreme values. In this case, the median is $80, which represents the middle value when the prices are arranged in ascending order: $65, $79, $80, $95, and $175. The mean and range can be affected by the extreme value of $175, and the MAD is a measure of dispersion rather than center.
Answer:
D
Step-by-step explanation:
Help me please find EC
The length of segment EC is 24 in the given triangle
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
3x=2(x+4)
Apply distributive property on RHS
3x=2x+8
Subtract 2x from both sides
x=8
The segment EC =3x
=3(8)
=24
Hence, the length of EC is 24 in the given triangle
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Question 5 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. More than 1 solution
OB. x=-8, y = 2
OC. No solution
D. x = 12, y=3
3y-12x = 18
2y-8x=12
Answer:
.................D
Step-by-step explanation:
I took the test
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 3 yards by 5 yards by six and one-half yard.
What is the volume of the prism?
195 yd3
ninety seven and one half yd3
forty eight and three fourths yd3
thirty five and one half yd3
The volume of the rectangular prism is 97.5 cubic yards. (option b).
In this case, the rectangular prism has dimensions of 3 yards by 5 yards by 6 and one-half yard. To find its volume, we need to multiply these three dimensions together.
First, we need to convert the height of the prism to yards, as the other two dimensions are already given in yards. We know that 1 yard is equal to 3 feet, so 6 and one-half yards is equal to (6 x 3) + (1/2 x 3) = 18 + 1.5 = 19.5 feet. We then convert this to yards by dividing by 3, which gives us 6.5 yards.
Now, we can find the volume of the rectangular prism by multiplying the three dimensions together:
Volume = length x width x height
Volume = 3 yards x 5 yards x 6.5 yards
Volume = 97.5 cubic yards
Hence the correct option is (b).
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Bernice made 950 ml of gravy to go with her 5 kg turkey. The capacity of the gravy dish is 540 ml. How much gravy will be left in the pot after Bernice fills up the gravy dish?
After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.
We have,
Determine the amount of gravy needed to cover the turkey:
We know that Bernice made 950 ml of gravy to go with a 5 kg turkey.
There are different ways to estimate how much gravy is needed to cover a turkey, but a common rule of thumb is to allow for about 1/2 cup (or 120 ml) of gravy per serving.
Assuming that the turkey will be served to about 8 people, we can estimate that Bernice will need:
We can write it as an expression:
= 120 ml/serving x 8 servings
= 960 ml of gravy
This means that Bernice made just enough gravy to cover the turkey and have a little bit left over.
Calculate how much gravy will be left in the pot:
We know that the capacity of the gravy dish is 540 ml.
If Bernice fills up the gravy dish with gravy, she will have.
= 950 ml - 540 ml
= 410 ml of gravy left in the pot.
Therefore,
After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.
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Slope! answer the questions below please i need help! and i need a good grade!!!
The equation of a line for the given graph is y=2x+5.
From the given graph, the coordinate points are (0, 5) and (1, 7)
Part A:
Slope = (7-5)/(1-0)
= 2
Part B:
The slope mean for the relationship between the number of races and the number of track meets 2 races per track
Part C:
Substitute m=2 and (x, y)=(0, 5) in y=mx+c, we get
5=2(0)+c
c=5
Part D:
Substitute m=2 and c=5 in y=mx+c, we get
y=2x+5
Therefore, the equation of a line for the given graph is y=2x+5.
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the voltage V in a circuit is given by V=\sprt(PR) where P is the power and R is the resistance in ohms. a. if the voltage circuit is 120 volts and the circuit produces 1500 watts of power, what is the resistance in the circuit?
The resistance in the circuit is 9.6 Ohms.
What is the resistance in the circuit?Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.
Given that:
V = √(PR)
Where P is the power and R is the resistance in ohms.
Make the resistance R, the subject of the formula.
V = √(PR)
V² = (√(PR) )²
V² = PR
PR = V²
R = V²/P
Plug in Voltage V = 120V and Power P = 1500 watts
R = V²/P
R = (120)² / 1500
R = 14400 / 1500
R = 9.6 Ω
Therefore, the resistance is 9.6 Ω.
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Which distribution is positively skewed?
The distribution that is positively skewed is Option C.
What is a positive skew ?A positive skew is a statistical pattern, in which the majority of the data points are concentrated at one end within the range and wherein the tail is longer on the right side of the graph.
This phenomenon is also identified as a "right-skewed distribution," oppositely to its counterpart: the negative skew or "left-skewed distribution."
In conclusion, the distribution that is positively skewed is the third distribution or Option C.
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c) The NY Knicks won 35 games out of 65 games. What is the probability that they win the next game?
d) Find the experimental probability of a player on the New York Liberty being over 73 inches.
Answer:
c
Step-by-step explanation:
That's all because it makes more sense and uses a explanation
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).
The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.
To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.
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5. You and some friends are going on a recreation hike and need to hire a guide. Your
friends want you to pick the best guide to hire for the hike.
Larry charges an initial fee of $50 plus $15 per mile on the hike.
Connie charges a flat rate of $200 for an entire hike.
● Teo charges $20 per mile on the hike.
a. Write an equation to represent the total cost C, for m miles on the hike for eac
guide.
Larry -
Connie -
Teo -
The equations to represent the total cost C, for m miles on the hike for each guide are C(m) = 50 + 15m, C(m) = 200 and C(m) = 20m
Writing an equation to represent the total cost C, for m milesFrom the question, we have the following parameters that can be used in our computation:
Larry
Initial fee = 50
Rate = 15 per mile
Connie
Initial fee = 200
Teo
Rate = 20 per mile
Represent the number of miles with m
So, we have
Larry
Initial fee = 50
Rate = 15 per mile
C(m) = 50 + 15m
Connie
Initial fee = 200
C(m) = 200
Teo
Rate = 20 per mile
C(m) = 20m
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Khalil's dining room is 3 meters wide and 7 meters long. Khalil wants to install a new wood floor. It will cost $7.84 per square meter. How much will Khalil's new floor cost?
The total cost to install new wood floor in a room is $164.64.
Given that, Khalil's dining room is 3 meters wide and 7 meters long.
We know that, area of a rectangle is Area = Length×Width
Area of a room = 7×3
= 21 square meters
Total cost = Total area × Cost of per square meter
= 21×7.84
= $164.64
Therefore, the total cost to install new wood floor in a room is $164.64.
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John has 6 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?
There are 6 different ways can the flags be arranged in a row.
We have,
Total number of flags = 6
So, to find the number of ways to arranged n object = n!
Then, the number of ways to arrange the flag
= 6!
= 6 x 5 x 4 x 3 x 2 x 1
=120 x 6
= 720 ways
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