The correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:
OB. f(x) = x³ - 5x² - 7x + 35
What is polynomial?
A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.
The polynomial function of lowest degree with only real coefficients and having the given zeros can be obtained by multiplying the factors (x - √7), (x + √7), and (x - 5) since the zeros are √7, -√7, and 5.
Expanding the product, we get:
(x - √7)(x + √7)(x - 5) = (x² - 7)(x - 5) = x³ - 5x² - 7x + 35
Therefore, the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:
OB. f(x) = x³ - 5x² - 7x + 35
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a private student loan at 4.25%, but the rate for such a loan could be 12.59%. Under the same circumstances as Self Check 2 ($10,000 principal, no interest paid while in school) and a rate of 12.59%, what would the principal be when you make your first payment 51 months later? What are some recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations.?
The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
What is the principal?To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.
Using the formula:
Interest = Principal x Rate x Time
where Principal = $10,000,
Rate = 12.59% per year,
Time = 51/12 years (since the interest is compounded monthly):
Interest = $10,000 x 0.1259 x (51/12)
= $5,307.13
So the total amount owed after 51 months would be:
Total amount owed = Principal + Interest
= $10,000 + $5,307.13
= $15,307.13
Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States. Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.
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Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
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Explain how to find the length of XY
The length of XY uisng the midpoint theorem is 40 units
Finding the length of XYThe midpoint theorem states that if a line segment is drawn connecting the midpoints of two sides of a triangle, then that line segment is parallel to the third side of the triangle, and its length is half the length of the third side.
In this case, we have a triangle XYZ, and points A, B, C are the midpoints of sides XY, YZ, and ZX respectively.
By the midpoint theorem, we know that AB is parallel to ZX and has a length of half of ZX.
Similarly, BC is parallel to XY and has a length of half of XY, and AC is parallel to YZ and has a length of half of YZ.
We are given that BC has a length of 20, and we want to find the length of XY.
Using the midpoint theorem, we know that
XY is twice the length of BC
So
XY = 2 * BC = 2 * 20 = 40.
Therefore, the length XY is 40 units
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Which choice is NOT equal to the others? Responses A −[[2/5]]−[[2/5]] B [[2/−5]][[2/−5]] C [[−2/5]][[−2/5]] D [[2/5]]
Answer:
B is the answer
Step-by-step explanation:
The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
1. The radius of the circle is 3 units
2. The standard form of the equation is (x-1)^2+y^2=3
3. The center of the circle lies on X-axis
4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9
The given equation is: x^2+y^2-2x-8=0
The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle
The given equation in standard form can be written as
(x^2-2x+1)+y^2-9=0
(x-1)^2+y^2=3^2
Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.
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In a survey, 150 shoppers were asked whether they have access to a computer at home and if they have a personal e-mail account. Their responses are summarized in the following table. E-Mail account No e-mail account Computer access at home 44 22 No computer access at home 7 77 (a) What percentage of the shoppers have an e-mail account? (b) What percentage of the shoppers do not have computer access at home?
In linear equation, 44% of the shoppers have an e-mail account and 56% of the shoppers do not have computer access at home.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Total number of the shoppers who were surveyed = 150
a). Number of shoppers who have an e-mail account = Shoppers who have email accounts and computer access at home + Shoppers who have email accounts but no computer access at home
= 44 + 22
= 66
Percentage of the shoppers having an e-mail account = 66/150 * 100
= 44%
b). Total number of shoppers who do not have computer access at home
= 7 + 77
= 84
Percentage of the shoppers having computer access at home
= 84/150 * 100 = 56%
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What is the perimeter of the trapezoid?
can u slove ASAP please
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
How many different possible outcomes are there if you roll two fair six-sided dice in the shape of a cube?
Answer: 36
Step-by-step explanation:
Write this in System of Equations from Context
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70 liters of real fruit juice to make 3 times as many liters of Drink A as liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
Let's define the variables as follows:
Let x be the number of liters of Drink B produced.
Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.
Now, let's write the system of equations:
The total amount of real fruit juice used is 70 liters, so we can write:
[tex]0.1x + 0.2y = 70[/tex]
Substituting y = 3x into the above equation, we get:
[tex]0.1x + 0.2(3x) = 70[/tex]
Simplifying the equation:
[tex]0.1x + 0.6x = 70[/tex]
[tex]0.7x = 70[/tex]
[tex]x = 100[/tex]
So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
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question attached
A. 5
B. 16
C. function is not defined for this value
D. 9
F(4)=9 is the value for this function.
What is piecewise function?A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.
The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.
x=4 is bigger than or equal to 0 because it.
we use the third function definition
F(x)=x+5.
Therefore, F(4)=4+5=9.
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Each of forty-nine moviegoers was asked, "What is your favorite movie type?"
Here are the results.
12 men and 10 women chose "Drama".
. 14 men and 13 women chose "Action".
Construct a two-way frequency table for the data.
The numbers in each cell represent the frequency of people who chose that combination of gender and movie type.
What is the frequency?
The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.
To construct a two-way frequency table for the data, we need to organize the responses by gender and movie type. The table is in the attached image.
The rows represent the gender of the moviegoers, and the columns represent the movie type.
The numbers in each cell represent the frequency of moviegoers who chose that combination of gender and movie type.
For example, there are 12 men who chose Drama as their favorite movie type, and there are 13 women who chose Action as their favorite movie type.
The total number of moviegoers who chose Drama is 22, and the total number who chose Action is 27. The total number of moviegoers is 49.
Hence, The numbers in each cell represent the frequency of people who chose that combination of gender and movie type. For example, 12 men chose Drama as their favorite movie type.
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All the students in the sixth grade either purchased their lunch or bought their lunch from home on Monday. 24% of the students purchased their lunch. 190 students bought their lunch from home. How many students are in the sixth grade?
There are 250 students in the sixth grade.
How to find number of students?First, let's define some variables:
The total number of sixth-grade students is called "x."
The number of students who purchased their lunches will be referred to as "p."
The number of students who brought their lunch from home will be referred to as "h."
We know that from the problem statement that
p + h = x (since all students either purchased their lunch or brought their lunch from home)
p = 0.24x (since 24% of the students purchased their lunch)
h = 190 (since 190 students brought their lunch from home)
We can use these equations to solve for x:
p + h = x
0.24x + 190 = x (substituting in the value of p and h from the other equations)
0.76x = 190 (subtracting 0.24x from both sides)
x = 250 (dividing both sides by 0.76)
Therefore, there are 250 students in the sixth grade.
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass.
Starting with 155 grams of radioactive isotope, how much will be left after 5 half-lives?
Use the calculator provided and round your answer to the nearest gram.
After 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in a variety of forms, such as the natural numbers, real numbers, and complex numbers. Numbers can be used to describe physical quantities, such as volume, mass, and time, as well as abstract quantities, such as sets, functions, and abstract objects. Numbers are also used to represent concepts such as truth, beauty, and goodness.
To calculate this, we can use the formula:
Final Mass = Initial Mass * (1/2)Number of Half Lives
In this case, the Initial Mass is 155 g, and the Number of Half Lives is 5. Therefore, the equation to use is:
Final Mass = 155 g * (1/2)⁵
Plugging the numbers into the equation, we get:
Final Mass = 155 g * (1/2)⁵
Final Mass = 155 g * (1/32)
Final Mass = 3.9 g
Therefore, after 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain. This is due to the fact that the half-life of a radioactive isotope is the amount of time it takes for the isotope to be reduced to half its original mass. As the number of half-lives increases, the amount of the isotope left decreases exponentially.
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A bag contains 41 U.S. quarters and nine Canadian quarters. (The coins are identical in size.) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.
%
Answer:
The coins are picked without replacement.
The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:
[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]
[tex] = 1 - .28296 = .71704[/tex]
So the probability of picking at least one Canadian quarter is about 71.7%.
50 Points! Multiple choice algebra question. Shen is simplifying the expression (3x^4+4x^2) (x^3-2x^2-1). Which of the following shows the correct product. Photo attached. Thank you!
So, multiple choice algebra questions. the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2[/tex].
To simplify the given expression [tex](3x^4+4x^2) (x^3-2x^2-1)[/tex], we can use the distributive property of multiplication to multiply each term of the first expression by each term of the second expression. This gives us:
[tex](3x^4+4x^2) (x^3-2x^2-1) \\= 3x^4(x^3) + 3x^4(-2x^2) + 3x^4(-1) + 4x^2(x^3) - 4x^2(2x^2) - 4x^2(1)[/tex]
Simplifying each term, we get:
[tex]= 3x^7 - 6x^6 - 3x^4 + 4x^5 - 8x^4 - 4x^2[/tex]
So, the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2.[/tex]
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Find the Volume of this shape.
Therefore, the volume of the prism is 60 cubic feet.
What is volume?Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.
Here,
The volume of a prism is given by the formula:
V = Bh
where B is the area of the base and h is the height of the prism.
Substituting the given values:
V = (20 ft)(3 ft)
V = 60 cubic feet
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nvrm i got it i am him
Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone
For all x, P(x) (using universal quantifier ∀) and It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
1. For all x in S, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
For all x, P(x) (using universal quantifier ∀)
It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
For all x in S, P(x) (using universal quantifier ∀)
It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
1. For all x, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
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Use circle K for problems 11-13
After calculation we get
11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees
12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.
13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees
What is quadrilateral?A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.
According to the given information:
a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.
b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.
c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.
d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.
a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.
b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.
a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.
b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.
c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.
d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.
e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.
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please help me in this question
Answer:
step by step explanation:
All you have to do is expand and reduce the expressions
then evaluate -2 being a root of the expressions
To do that you need to substitute -2 into the simplified expressions
if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.
Example 1.
simplify (-5x-2)(7x-4)-2x+3
if you substitute f(x) as f(-2)
then substitute x with -2
when you simply and evaluate the expression you will get that the expression is equal to -137
which means -2 isn't a root since the expression must be equal to 0
-2 is not a root
do the same for the other expressions
What is the domain of the function graphed at right?
Answer:
d. x > 2 or x < -2
Step-by-step explanation:
Domain describes the range of x-values in a function.
Domain
The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.
By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.
Included Values
We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.
Given this equation what is the value of y at the indicated point?
Answer: y=2
Step-by-step explanation:
We're given x=1 so we can plug this in 3x - y =1 and isolate to solve for y.
[tex]3(1)-y=1\\3-y=1\\-y=-2\\y=2[/tex]
State any domain restrictions for the expression below from least to greatest (for example: -2,-1,0,1,2), by using one answer box for each domain restriction, then simplify the expression in the last answer box. (81-x²) (x² + 2x − 63) 2x² - 6x 3x2 30x + 63 3x 81x² ÷
The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9
From the question, we have the following function that can be used in our computation:
[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]
Next, we set the denominator to 0 and solve for x
So, we have
81 - x²: x = ±9
2x² - 6x: x = 0 and x = 3
x² + 2x - 6x: x = 0 and x = 4
Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9
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in row 2, write the standard form equation of a circle whose diameter endpoints are shown here (-3,4) (2,1)
The standard form equation of a circle whose diameter endpoints are (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
What is the general form of equation of a circle?The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.
The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:
[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)
And radius of the circle is half of the diameter, which is:
[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]
Therefore, the circle equation is:
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
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A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality-control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, 5 were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference.
The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).
How can you figure up a confidence interval for the proportional difference?Define the populations of interest and the characteristic you want to compare (e.g., proportion of success or failure).Collect random samples from each population and record the number of occurrences of the characteristic of interest in each sample.Calculate the sample proportions ([tex]p_1 \;and \;p_2[/tex]) by dividing the number of occurrences by the sample size for each population.Calculate the standard error (SE) of the difference in proportions using the sample proportions, sample sizes, and appropriate formula (SE = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex], where[tex]p_1 \;and \;p_2[/tex] are the sample proportions and[tex]n_1 \;and \;n_2[/tex] are the sample sizes for the two populations, respectively).Determine the appropriate critical value from the probability distribution (e.g., standard normal distribution for large sample sizes or t-distribution for small sample sizes) based on the desired confidence level.Calculate the margin of error (ME) by multiplying the standard error by the critical value (ME = critical value * SE).Construct the confidence interval by adding and subtracting the margin of error from the sample statistic (e.g., the difference in sample proportions, or the ratio of sample proportions).Interpret the confidence interval, stating that we can be [confidence level]% confident that the true population parameter falls within the calculated interval.Given:
Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285
Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2
Sample size from machine A ([tex]n_1[/tex]) = 35
Sample size from machine B ([tex]n_2[/tex]) = 35
Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]
= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]
= 0.07058061453775912 (rounded to 11 decimal places)
Margin of error (ME) = Critical value * Standard error
= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)
= 0.18765117789861733 (rounded to 11 decimal places)
Confidence interval (CI) = Sample statistic ± Margin of error
= [tex](p_1 - p_2) \pm ME[/tex]
= (0.14285714285714285 - 0.2) ± 0.18765117789861733
= -0.05714285714285715 ± 0.18765117789861733
The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).
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If f(x)={x+4 if x≤−2
-x if x>−2,
what is f(−4)?
A. -2
B. 4
C. -4
D. 0
Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,
f(-4) = (-4) + 4 = 0.
So, the answer is D. 0.
PLEASE HELP ASAP DUE TODAY
Question 4(Multiple Choice Worth 1 points)
(08.07 MC)
The quadratic function f(x) has roots of 3 and 7, and it passes through the point (1, 12). What is the vertex form of the equation of f(x)?
f(x) = −(x + 5)2 − 4
f(x) = −(x − 5)2 − 4
f(x) = (x + 5)2 − 4
f(x) = (x − 5)2 − 4
As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
what is quadratic equation ?A quadratic function is a sort of second-degree polynomial equation, meaning it has at least two squared element. A quadratic equation's generic form is: [tex]ax^2 + bx + c = 0[/tex] where the variable x and the constants a, b, and c. If the coefficient a were zero, the expression would be linear rather than quadratic. Several ways to solve a quadratic equation, including factoring, squaring the square, and utilising the quadratic formula. The negative numbers or roots of the quadratic equation are the values of x which it make the equation true and are the solutions to the quadratic equation.
given
The factored form of the quadratic function f(x), which has roots of 3 and 7, is as follows:
f(x) = a(x - 3)(x - 7) (x - 7) where "a" stands for a fixed coefficient.
We can utilise the point (1, 12) through which the function passes to determine the value of "a"
12 = a(1 - 3) (1 - 3)(1 - 7)
12 = -24a
a = -1/2
Inputting the value of "a" into the factored form yields the following results:
[tex]f(x) = -1/2(x - 3)(x - 7) (x - 7)[/tex]
By extending this phrase, we get:
[tex]f(x) = -1/2(x^2 - 10x + 21)[/tex]
We need to finish the square before we can transform this into vertex form. To achieve this, add and remove the square of the coefficient of x's half:
[tex]f(x) = -1/2(x^2 - 10x + 25 - 4)[/tex]
If we condense this phrase, we get:
[tex]f(x) = -1/2[(x - 5)^2 - 4][/tex]
As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
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If the the a is greater than 1, compared to the parent function the C. Stretched vertically.
How to find the comparison ?The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.
If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".
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What is the circumference of the circle? Use 3.14 for π
. Round your answer to the nearest hundredth. please help 100 points
Answer:
b)
Step-by-step explanation: