Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.
A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.
To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.
In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:
(x+1)(x+4) = 0
This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:
x+1 = 0 or x+4 = 0
x = -1 or x = -4
These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.
It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.
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Mrs. Flips sold 300 cookies for her bake
sale. She sold two types of cookies: large
chocolate chip and small peanut butter
cookies. She charged $1 for the chocolate
chip and 50-cents for the peanut butter
cookies and collected $270 total. How
many of each type did she sell?
Mrs. Flips sold 240 large chocolate chips.
Mrs. Flips sold 60 small peanut butter cookies.
How to write the required expressions?In order to write the required expressions that models the situation, we would assign variables to the number of large chocolate chips and the number of small peanut butter cookies, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of large chocolate chips.Let the variable y represent the total number of small peanut butter cookies.Since Mrs. Flips charged $1 for the chocolate chip and 50-cents for the peanut butter cookies and collected $270 total, an expression that models the situation is given by:
x + 0.5y = 270
Additionally, she sold a total of 300 cookies:
x + y = 300
270 - 0.5y + y = 300
0.5y = 30
y = 60 small peanut butter cookies.
x = 270 - 0.5(60)
x = 240 large chocolate chips.
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How much is 1 HEROES in USD?
As of 22/02/2023, the value of 1 HERO (cryptocurrency) is $0.01 USD. This means that if you have 1 HERO, it can be exchanged for $0.01 USD.
The value of HERO, like most cryptocurrencies, can fluctuate rapidly due to market demand and supply. As a result, the value of HERO can change significantly over short periods of time. It's important to keep this in mind when buying or investing in cryptocurrencies, as the value can both rise and fall quickly. Investors in cryptocurrencies should do their research and consider the risks associated with investing in a volatile and relatively new asset class.
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SIMPLIFY THE MONOMIAL. YOUR ANSWER SHOULD CONTAIN POSITIVE EXPONENTS ONLY.
Based on the information, the equation can be simplified as follows: 7xy - 2x² - y
How do you simplify an equation?To simplify an equation we must carefully observe all the values that make up the equation. Once we identify the values with the same symbols, (x or y) we can group them. According to this procedure we can group the values of x as shown below:
7xy - 2x² - andIn this case the 2x was added with the 5x to form the 7x. In the case of 2x², it cannot be added with the other values of x because it has an exponent of ².
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What is expression mean in math?
Answer: a type of equation
Step-by-step explanation:
Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour.Compute the probability that no more than 5 cars will arrive in the next half-hour.
Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour, the probability that no more than 5 cars will arrive in the next half-hour is 0.75.
The Poisson distribution can be used to model the number of events that occur in a fixed interval of time. In this case, the average number of cars arriving at the drive-up window of a bank is 6 cars per hour, so we can use the Poisson distribution to calculate the probability of a certain number of cars arriving in a half-hour interval.
To calculate the probability that no more than 5 cars will arrive in the next half-hour, we can use the cumulative Poisson distribution function, which gives the probability that the number of events is less than or equal to a given value.
The cumulative Poisson distribution function can be calculated using the following formula:
P(X <= x) = Σ P(X = i) for i = 0, 1, 2, ..., x
Where X is the number of cars arriving in a half-hour interval, and x is the given value (in this case, x = 5).
The mean number of cars arriving in a half-hour interval is 3 (6 cars per hour / 2), so the cumulative Poisson distribution function can be calculated as follows:
P(X <= 5) = Σ P(X = i) for i = 0, 1, 2, 3, 4, 5
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= (e^-3) * (3^0) / 0! + (e^-3) * (3^1) / 1! + (e^-3) * (3^2) / 2! + (e^-3) * (3^3) / 3! + (e^-3) * (3^4) / 4! + (e^-3) * (3^5) / 5!
= 0.0498 + 0.1494 + 0.224 + 0.224 + 0.1494 + 0.0498
= 0.75
Therefore, the probability that no more than 5 cars will arrive in the next half-hour is approximately 0.75, or 75%.
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the length of a rectangle is 3 times its width. Given that its area is 27 cm, find the length and the width of the rectangle
Answer:
The width is 3 cm and the length is 9 cm.
Step-by-step explanation:
L --> Length
W --> Width
L = 3W
LW = 27
3W(W) = 27
3W^2 = 27
W^2 = 9
W = 3
L = 3(3) = 9
Solve. Please i need help with this.
The value of x and y in the equations are as follows:
x = -8
y = -1
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, let's use elimination method to solve the equation.
Therefore,
8x - 8y = -8
-3x + 4y = -4
multiply equation(ii) by 2
8x - 8y = -8
-6x + 8y = -8
add the equations
2x = -16
x = -16 / 2
x = -8
Let's find y
-8y = -8 - 8x
-8y = -8 - 8(-8)
-8y = -8 + 16
-8y = 8
y = 8 / -8
y = -1
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The amount, in dollars, of Marisa’s savings account can be represented by the expression 5x + 40. Marisa saved the same amount x each month for a period of 5 months. Her mother contributed an additional amount each month to Marisa’s savings account. How much did her mother contribute each month? The amount, in dollars, of Marisa’s savings account can be represented by the expression 5x + 40. Marisa saved the same amount x each month for a period of 5 months. Her mother contributed an additional amount each month to Marisa’s savings account. How much did her mother contribute each month?
The amount of money that the mother contributes each month will be $5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The expression that represents the amount of savings is given as,
Amount of saving = 5x + 40
Where 'x' is the number of months.
The slope is 5 which represents the amount of savings in each month and the y-intercept is 40 which represents the amount already saved.
The amount of money that the mother contributes each month will be $5.
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The process standard deviation is 0. 15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9. 85 or greater than 10. 15 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.
The probability of a defect units is 0.3174 by calculating the z-score of the greater than and less than value.
When the distribution is normal, we use the z-score formula.
Z = (X - μ)/σ
We have σ = 0.15 and units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.
μ = 10.15 - 0.15 = 9.85 + 0.15 = 10
Now, the probability that a unit is defective.
P(X ≥ 10.15)
1 subtracted by the pvalue of Z when X = 10.15
[tex]Z = \frac{10.15-10}{0.15}[/tex]
Z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
P(X ≤ 9.85)
[tex]Z = \frac{9.85-10}{0.15}[/tex]
Z = -1 has a pvalue of 0.1587
P = P(X ≥ 10.15) + P(X ≤ 9.85)
P = 0.1587 + 0.1587
P = 0.3174
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What is the Systematic Approach algorithm?
The Systematic Approach algorithm is a problem-solving methodology that is widely used in many different fields, such as engineering, business, and science.
It is a structured and systematic process that involves identifying a problem, analyzing it, generating possible solutions, evaluating these solutions, and selecting the best one. The algorithm is also known as the "systems engineering process" or "systems analysis and design."
The algorithm is typically divided into several phases, including:
Problem identification: This involves defining the problem, its boundaries, and its scope. This step also involves identifying the objectives and constraints of the problem. Analysis: This step involves gathering data and information related to the problem, and identifying the root cause of the problem. This may involve conducting surveys, interviews, or experiments. Design: In this step, potential solutions are generated, and a conceptual design is created. The design should be flexible enough to allow for the incorporation of new information and changes. Evaluation: The potential solutions are evaluated based on predetermined criteria, and the best solution is selected. Implementation: The selected solution is implemented and monitored to ensure it is working effectively. Any necessary modifications or adjustments are made during this phase.
The Systematic Approach algorithm is a powerful tool for problem-solving as it provides a structured, step-by-step approach to analyzing and solving complex problems. It also allows for a thorough understanding of the problem and its potential solutions, as well as the ability to evaluate and select the best solution based on predefined criteria.
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Lebo buys seven icecreams for R37,65 how much will five icecreams cost?
Answer:
R2689 IS THE CORRECT ANSWER
Sample response: Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them. Which did you include in your answer? Check all that apply
Based on the information, the integer used will be (10 - 4). The difference is 6.
On a number line, there'll be 6 units between the numbers
How to explain the informationTo find the difference between two integers by adding the additive inverse, we can follow these steps:
Subtract the smaller integer from the larger one: (larger integer) - (smaller integer).
Take the absolute value of the result to get the distance between the two integers on a number line.
The distance between two integers is the absolute value of the difference, so we do not include the sign in our answer. The answer will always be a non-negative number.
By plotting the two integers on a number line and counting the units between them, we can visualize the distance between them.
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Alonso has x quarters and y dimes. He has no less than 18 coins worth a maximum of $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.
Answer: A quarter is worth $0.25 and a dime is worth $0.10, so the total amount of money Alonso has can be represented by the expression 0.25x + 0.1y. To find one possible solution to the system of inequalities, we need to find the values of x and y that satisfy both the inequality 0.25x + 0.1y ≥ 3.60 and the inequality y ≥ 0.
The inequality 0.25x + 0.1y ≥ 3.60 represents all points (x, y) that are on or above the line 0.25x + 0.1y = 3.60. The inequality y ≥ 0 represents all points (x, y) that are above or on the x-axis. The intersection of these two regions is the solution set of the system of inequalities, which represents all points (x, y) that satisfy both inequalities.
To graph the solution set, we can start by plotting the line 0.25x + 0.1y = 3.60 and shading the region above the line. Then, we can plot the x-axis and shade the region above the x-axis. The intersection of the two shaded regions is the solution set.
One possible solution to the system of inequalities is the point (14, 4). This means that Alonso has 14 quarters and 4 dimes, which total $3.60. However, there may be other solutions to the system of inequalities that would also satisfy the conditions.
Step-by-step explanation:
I NEED HELP ASAP!!!
Answer:
A. B is correct
B. A is correct
C. B is correct
Step-by-step explanation:
Area of triangle: A = 1/2bh
A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69
Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420
So A is incorrect and B is correct
B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2
Surface area = 4(area of triangle) = 4(111.2) = 444.8
So A is correct and B is incorrect
C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35
Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8
Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6
So A is incorrect and B is correct.
ASAP need help with this question
answer: 204!!!
tn = a + (n-1)d
a is the first value
n is the position
d is the difference
t(50) = 8+(50-1)(4)
t(50)= 204
Jon tossed a standard die several times. He got the number "4" on 5 of the tosses. Based on theoretical probabilities, what is the best estimate of the total number of times he tossed the cube? A) 20 times B) 60 times C) 30 times D) 10 times
Based on theoretical probabilities, the best estimate of the total number of times Jon tossed the cube would be 60 times. The probability of rolling a "4" on a standard die is 1/6. If Jon got "4" on 5 of the tosses, then the total number of tosses would be 5/ (1/6) = 30 tosses. To find the best estimate of the total number of tosses, it is common to round up to the nearest multiple of 10, which in this case would be 60. Therefore, the best estimate would be 60 times (Option B).
Truman's father is designing a toy car ramp for him. His dad determined that the measure of angle x needs to be increased by 200 .
What is the measure of the new angle?
__ °
The measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.
What is the angle measurement?
A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.
If the measure of angle x needs to be increased by 200, we can simply add 200 to the original measure of angle x to find the new angle.
So, if the original measure of angle x is, for example, 30 degrees, the new angle would be:
New angle = 30 degrees + 200 degrees
New angle = 230 degrees
Therefore, if the measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.
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Leah measured a line to be 2.1 inches long. If the actual length of the line is 2.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
Step-by-step explanation:
divide the required value by the total value and multiply by 100.
a/bx100= y
2.2 - 2.1 =0.1 inches
percentage of error=
0.1 / 2.2 x100
4.54 %
Help please…………………………………..
Answer:
-4
Step-by-step explanation:
I hate calc nevertheless, factor the top number, cancel out x+2 and then plug in -2. Its simple once you see the pattern
[tex]\frac{x^2 - 4}{x+2} \\\frac{(x+2)(x-2)}{x+2} \\(x-2)\\-2-2\\-4[/tex]
MTR
728. MODELING REAL LIFE Find the height of the roller
coaster using two different methods. Explain.
x ft
45°
283 ft
The height of the roller coaster is 200.11 feet
How to determine the height of the roller coasterMethod 1
Here, we make use of the cosine rule
So, we have
cos(45) = x/283
So, we have
x = 283 * cos(45)
Evaluate
x = 200.11
Method 2
Here, we make use of the sine rule
The sine can be calculated as
When x + y = 90;
sin(x) = cos(y)
This means that
sin(45) = cos(45)
So, we have
sin(45) = x/283
So, we have
x = 283 * sin(45)
Evaluate
x = 200.11
Hence, the height is 200.11 feet
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6 - Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 −2
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a nonlinear function because there is not a constant rate of change in the input and output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Answer:
The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
Step-by-step explanation:
From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).
The slope of the line is
The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.
Since the rate of change (slope) is same for all points, therefore the table represents a linear function.
If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a linear function.
Twelve miles is approximately equal to 6 km. How many km are equal to 18 miles? How many miles are
equal to 42 km? Draw a tape diagram below to solve.
Answer:
below
Step-by-step explanation:
12m=6km
divide both by 6
2m=1km
how many km is equal to 18m?
18m=9km
how many m are equal to 42km?
42km=64m
never gonna give you up, never gonna let you down
a cone is sliced such that the cross section is perpendicular to its base and the cross section intersects its vertex. what is the shape of the cross section?
The cross section is shaped like a circle.
A cone is a three-dimensional geometric object with a flat base and a smooth transition to the apex or vertex.
If a cone is sliced such that the cross section is perpendicular to its base and intersects its vertex, the cross section will be a circular shape. This is because the cross section cuts through the entire cone at a right angle, producing a circle that is defined by the curved surface of the cone and the slicing plane. The diameter of the circle is equal to the base diameter of the cone, and its center is located at the midpoint of the base.
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A triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
Mark this and return
Which expression represents the possible values of n,
in feet? Express your answer in simplest terms.
O x-1
On = 3x + 5
On=x-1
O 3x+5
Save and Exit
Next
Submit
The possible value of n in the triangle given is, n < 3x+5
What is a triangle?The triangle is a polygon with three side, vertex, and angles.
Given that, a triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
We asked to find the expression that represents the possible values of n.
We know that,
The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Therefore,
2x+2+x+3 = 3x+5
Thus, the possible value of n is,
n < 3x+5
Hence, the possible value of n in the triangle given is, n < 3x+5
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9/16 divided by 7/ 10
Answer: 15/7
Step-by-step explanation:
9/16 / 7/10 = 9/6 * 10/7 multiply by recipricol to find answer
90/42
15/7 simplify
F(x) has zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1 find the degree of polynomial?
The degree of polynomial is 3
How to find the degree of polynomial?From the question, we have the following parameters that can be used in our computation:
zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1
The degree of a polynomial is the sum of the multiplicities
Using the above as a guide, we have the following:
Degree = 2 + 1
Evaluate
Degree = 3
Hence, the degree is 3
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In ΔXYZ, ∠X=17° and ∠Y=82°. ∠XWZ=90° and XY=700. Find the length of XW to the nearest integer.
The length of XW from the given triangle XYZ is 671.16 units.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in ΔXYZ, ∠X=17° and ∠Y=82°. ∠XWZ=90° and XY=700.
By using angle sum property,
∠X+∠Y+∠Z=180°
17°+82°+∠Z=180°
99°+∠Z=180°
∠Z=180°-99°
∠Z=81°
Now, YZ/sinX=XZ/sinY=XY/sinZ
YZ/sin17°=XZ/sin82°=700/sin81°
XZ/0.9902=700/0.9876
XZ/0.9902=708.78
XZ=701.83
Now, cos17°=XW/701.83
0.9563=XW/701.83
XW=0.9563×701.83
XW=671.16
Therefore, the length of XW is 671.16 units.
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Answer:671
Step-by-step explanation:
Y^2 + 6y+8 when y is -3
Ravi buys candy that costs $5 per pound. He will spend at least $45 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Ravi will buy.
Write your answer as an inequality solved for p.
Answer:
90p or 9p
Step-by-step explanation:
if he will spend 5p per pound then do 5x9P=45P
what is the inverted matrix calculator symbol?
The formula D = inv (A) returns the inverse of a symbolic matrix A. The symbol will be [tex]A^{-1}[/tex].
If A is a non-singular square matrix, then [tex]A^{-1}[/tex], often known as the inverse matrix of A, must exist if it is to satisfy the following property:
A[tex]A^{-1}[/tex] =[tex]A^{-1}[/tex]A = I, where I is the identity matrix.
Finding the minors and cofactors of the given matrix's components is one of the most crucial steps in determining its inverse. To comprehend this approach clearly, follow the steps listed below.
The following formula may also be used to find the inverse matrix:
[tex]A^{-1}[/tex]= adj(A)/det (A).
The calculation for the inverted matrix is done.
Hence they are the symbol and methods to find the inverted matrix.
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