2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and .
Review Andrew’s work, identify the error and correct all work from that point forward that is affected by this error. Include at least one sentence explaining his error. Use proper mathematical vocabulary, appropriately
(x-3)(x+2+2i)(x+2-2i)=0
(x-3)(x^2+4x+8)=0
x^3+x^2-4x-24=0)
Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the roots are given as follows:
[tex]x_1 = 3[/tex].[tex]x_2 = 2 + 2i[/tex].[tex]x_3 = 2 - 2i[/tex].Hence the polynomial is given as follows, considering leading coefficient a = 1:
[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]
His error was at the application of the minus signal to the complex roots.
Then:
f(x) = (x - 3)[(x - 2)² - (2i)²]
f(x) = (x - 3)(x² - 4x + 4 + 4)
f(x) = (x - 3)(x² - 4x + 8)
f(x) = x³ - 7x² + 20x - 24.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 5) and (3,-7)
Answer: 15
Step-by-step explanation:
Distance formula: a^2+b^2=c^2 where c is the distance.
a^2=
(-6-3)^2=
(-9)^2=81
b^2=
(5-(-7))^2=
(5+7)^2=
12^2=144
c^2=81+144=225
If c^2=225, then what's c?
c=15
total u.s. land area is 3.537 million square miles. what percentage of u.s. land is national park system land ?
The percentage of u.s. land is national park system land is approximately 41.8%
PercentageConvert acres to square miles
945,000,000 acres = 1476562.5 square milesPercentage of u.s. land is national park system land = national park system land / Total U.S. land area × 100
= 1476562.5 square miles / 3,537,000 square miles × 100
= 0.417461832061068 × 100
= 41.74618320610687%
Approximately,
41.8%
Therefore, the percentage of u.s. land is national park system land is approximately 41.8%
Complete question:
Total U.S. land area is 3.537 million square miles. Total U.S. national park system land occupies 954 million acres. What percentage of U.S. national park system land?
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Write the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 1 5x
Answer:
It's really hard to really solve cause I'm a student in learning.
fractional mathematics
Answer:
the numerator (the top number)/ Denominator (bottom number)
Step-by-step explanation:
you should know this
Answer:
Fractional mathematics have to do with dealing with certain amounts of a number and mathematical proportions. Fractions are amounts out of a whole number.
See attachments!
Paolo wrote the following equation for the perimeter of a rectangle.
Which equation is equivalent to the equation Paolo wrote?
Answer:
p = 2 + l w
Step-by-step explanation:
On a map where each unit represents 100 miles, two airports are located at P(1,17) and Q(12,10). What is the distance, to the nearest whole mile, between the two airports? A. 1,800 miles B. 1,304 miles C. 1,122 miles D. 900 miles
Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
How to Apply the Distance Formula?The distance formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following locations:
P(1,17) = (x1, y1)
Q(12,10) = (x2, y2)
Use the distance formula to find the PQ:
PQ = √[(12−1)² + (10−17)²]
PQ = √[(11)² + (−7)²]
PQ = √170
PQ ≈ 13.04 units
1 unit = 100 miles
PQ = 13.04 × 100
PQ = 1,304 mils
Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
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Answer: B. 1,304 miles.
NEED HELP
Which of the following is and isn't a function? ( There may be more than one answer ). Explain Clearly
Using the function concept, we have that:
Items, a, and d are functions.Item b and c are not functions.When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.
For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.
In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.
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The probability a d-link network server is down is 0.10. if you have three independent servers, what is the probability that at least one of them is operational?
The probability that at least one of them is operational is 0.999
Probability:
Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.
Given,
The probability a D-Link network server is down is 0.10.
Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.
Let D be an event that a D-Link network server is down.
It is given that the probability that a D-Link network server is down is
=> P(D) = 0.10
The number of independent servers
=> (n) = 3
The probability that none of the servers is working is
=>P(None) = P(D) x P(D) x P(D)
=> P(None) = 0.10 x 0.10 x 0.10
=> P(None) = 0.001
The probability that at least one of them is operational is given as
=> 1 - P(None)
=> 1 - 0.001
=> 0.999
Therefore, the probability that at least one of them is operational is 0.999.
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25 points plus brainliest
Answer:
i think b
Step-by-step explanation:
Answer:
B. y = 2x + 8
Step-by-step explanation:
14x - 7y = 1
7y = 14x - 1
y = 2x - 1/7
If two lines are parallel, their slopes are equal.
With m = 2, x = -2, y = 4
y = mx + b
4 = 2(-2) + b
4 = -4 + b
b = 8
so y = 2x + 8
44. the total cost for tuition plus room and board at state university is 2,584 dollars. tuition costs 704 dollars more than room and board. what is the tuition fee?
If total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
Given,
The total cost for tuition plus room and board = 2584 dollars
Consider the cost for room and board as x
Tuition costs 704 dollars more than room and board.
Therefore the tuition fees = 704+x
Then the total cost = Cost for tuition fees+ Cost for room and board
2584 = (704+x)+x
2584= 704+2x
2x= 1880
x= 940 dollars
Then the tuition fees = 704+x
=704+940
=1644 dollars
Hence, if total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
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Write the number 86,360,000 using the number word "million" and then round to one decimal place.
million
M
The number 86,360,000 using the number word "million" and then round to one decimal place is Eighty-six million three hundred sixty thousand.
The writing style used to express numbers in India is known as the Indian numeral system. In this case, numbers are divided into several time periods or groupings. This numbering scheme uses ten distinct symbols, including the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The order of the digits when using the Indian number system is one, ten, hundreds, thousands, ten thousand, lakhs, lakhs, crores, and crores. The era and locations are shown in the table below according to the amount of digits in a number.
Given number: 86,360,000
Eighty-six million three hundred sixty thousand in numbers
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In a set of geometric figures the mass of 4 pyramids and 2 cubes is 40 grams and the mass of 6 pyramids and 4 cubes is 68 grams
The mass of pyramid is 6 grams and the cube is 8 grams
Let's assume the mass of a pyramid is x gram and mass of a cube is y gram .
So, algebraic mass of 6 and 4 pyramids is 6x grams and 4x grams. and algebraic mass of 2 cubes and 4 cubes is 2y grams and 4y grams .
Total algebraic mass of 4 pyramids and 2 cubes are , 4x + 2y = 40 ;(equation 1)
and Total algebraic mass 6 pyramids and 4 cubes are , 6x + 4y = 68 ;(equation 2)
Now we have to use adoption method to solve this problem ,
we have to multiply equation (1) with 4 and equation (2) with 2 , and we will get ,
16x + 8y = 160 ; ( equation 3 )
12x + 8y = 136 ; ( equation 4 )
Now , we will substract equation ( 3 ) from equation ( 4 )
4x = 24 and x = 24/4 = 6
Let's put the value of x in equation ( 1 )
24 + 2y = 40 or, 2y = 16 or, y = 8
Here we can conclude , mass of pyramid is 6 grams and the cube is 8 grams.
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the air quality index, or aqi, measures how polluted the air is in your city and assigns a number based on the quality of the air. over 100 is "unhealthy".the following quadratic regression equation gives us an estimate of n, which is the number of days the aqi exceeded 100 a particular year. we will use this equation to estimate the number of days the aqi was over 100 in the year 1995.n
Final answer:
The estimated number of days the aqi was over 100 in the year 1995 is calculated as 135 days.
Is linear regression quadratic regression ?
Simple linear regression is expanded upon in quadratic regression. While quadratic regression has the drawback of requiring more data points to ensure that your data falls into the "U" shape, linear regression can be carried out with as few as two points (i.e., enough points to draw a straight line).
In situations where the second differences are constant, a quadratic model is adequate. We can ascertain the degree of the model for the data by identifying variations between the dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.
Explanation:
The air quality index, or aqi, calculates a number depending on how clean or dirty the air. Then it is estimate n, the number of days the aqi exceeded 100 in a specific year is evaluated and calculated as it is actually as 135 days on edge.
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Heyy! Could you guys possibly help with the answer to this question? I’m stuck.
The codes of the countries are 34, 35 and 36
How to determine the codes of the countries?The given parameters are
Sum of codes = 105
Where the numbers are consecutive numbers
This means that
B = A + 1
C = A + 2
So, we have
A +A + 1 + A + 2 = 105
Evaluate the like terms
3A = 102
Divide through by 3
A = 34
So, we have
B = A + 1 = 34 + 1 = 35
C = A + 2 = 34 + 2 = 36
Hence, the codes of the countries are 34, 35 and 36
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Which number appears farther to the right on the number line?
a) -53/2
b) -1
c) -100
Answer:
-1
Step-by-step explanation:
-1 has the greatest value
Matt had 6 books to read. Each book has 11 pages. He has already read 60 pages. How many pages does he have left to read? The answer
find the area and circumference of each circle. Use pi in your answer (example: radius = 8, or diameter = 14).
The area of the circle is 64π square unit and the circumference is 16π units
Calculating area and circumference of a circleFrom the question, we are to find the area and circumference of the circle
The area of a circle is given by the formula,
A = πr²
Where A is the area
and r is the radius
Using the parameter, radius = 8
Then,
A = π × 8²
A = 64π square unit
Calculating the circumference
The circumference of a circle is given by the formula
C = 2πr
Where C is the circumference
and r is the radius
Thus,
C = 2 × π × 8
C = 16π units
Hence, the area of the circle is 64π square unit and the circumference is 16π units
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I need help I need it in 1 min please help 13 and 14
i) 9⁻⁴=1/6561
ii1/2⁻⁶=64
Positive exponent: An exponent defines the number of times a number is multiplied by itself. For example, 32. It means that the number 3 has to be multiplied twice. Here, the number 3 is a base number and 2 is an exponent. The exponent can be positive or negative.
Nagative exponent: We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3-2.
Thus, x-2 is written as (1/x²).
i)Rewrite expression using a positive exponent 9⁻⁴
We know that positive exponent.
9⁻⁴=1/94
9⁻⁴=1/6561.
ii)Rewrite expression using a positive exponent 1/2⁻⁶
1/2⁻⁶=26
⇒1/2⁻⁶=64.
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Georgia is on the prom committee. She wants to hang a dozen congruent triangles from the ceiling so that they are parallel to the floor. She sketched out one triangle on a coordinate plane with coordinates (0,4),(3,8) , and (6,0) . If each triangle is to be hung by one chain, what are the coordinates of the point where the chain should attach to the triangle?
The coordinates of the point where the chain should attach to the triangle are (3, 4).
Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).
We need to find the coordinates of the point where the chain should attach to the triangle.
What is the centroid of the triangle?The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).
Now, centroid = ((0+3+6)/3, (4+8+0)/4)
=(3, 4)
Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).
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Use the graph of each function to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
f(x)=x^3-x^2-2x+3
It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.
To check if this is correct, we will find the relative extrema of the function,
f(x) = x³-x²-2x+3
Find it derivative f'(x) = 3x²-2x-2
f'(x) = 0
⇒ x = 2 ± √(4+24)/3
= 3.77 , -1.1
Find the second derivative f''(x) = 6x -2
f''(3.77) = 20.62>0
So the function has a relative minimum at x = 3.77.
f''(-1.1) = -8.6<0
So the function has a relative maximum at x = -1.1
Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.
i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]
So the interval in which the function is decreasing is between the relative maximum and minimum. i.e., the interval (-1, 3.5)
The function is nowhere constant.
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1/3 ÷ 8 =
what s the answer
Answer:
0.0416¯
Step-by-step explanation:
after the 1 six is being repeated. Hope this helps! :)
Simplify an expression for the perimeter of the rectangle shown.
8.6x + 3
5.2
4
Write your answer with NO spaces:
The perimeter of the rectangle is P = (17.2x₊16.4).
Given that,
Length, l = 8.6x₊3
Width, b = 5.2
In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.
We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :
P=2(l₊b)
Putting values of l and b in the above formula:
p = 2(8.6x ₊ 3 ₊ 5.2)
= 2(8.6x ₊ 8.2)
= 2(8.6x) ₊ 2(8.2)
= 17.2x ₊ 16.4
So, the required perimeter of the rectangle is 17.2x₊16.4.
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Find the LCM of
[tex]8 {a}^{2} {b}^{3} {f}^{4} [/tex]
and
[tex]3abg[/tex]
The LCM of 8a²b³f⁴ and 3abg is 24a²b³f⁴g.
What is defined by the term LCM?LCM is an abbreviation for "Least Common Multiple." The smallest multiple which two or even more numbers have in common is defined as the least common multiple.
Consider the following two integers: 2 and 3.2 multiples: 2, 4, 6, 8, 10, 12, 14....Multiples of three: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on.The numbers 6, 12, and 18 are all common multiples of 2 and 3. The smallest number is six. As a result, the least common multiple of 2 and 3 is 6.The smallest number divisible both by numbers is the LCM of two numbers.Figuring the lowest common denominator (LCD) of 2 or even more fractions is a common application of LCM.
It is useful for adding, subtracting, as well as compare different or more fractions.
For the given question, the two numbers are given as; 8a²b³f⁴ and 3abg.
The least common multiple which will divide both the numbers are; all the values with their highest power.
LCM = 24a²b³f⁴g.
Thus, the LCM is found as 24a²b³f⁴g.
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from a sample of 550 items, 52 were found to be defective. the point estimate of the population proportion defective will be:
The point estimate of the population proportion defective will be 0.0945
What is point estimateThe formula for calculating the point estimate is expressed as;
p = x/n,
where p is the proportion of successes in the sample
n is the total sample
Given the following
n = 550 items
x = 52
Substitute
p = 52/550
p = 0.0945
Hence the point estimate of the population proportion defective will be 0.0945
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W
Which graph represents the solution of the system
{x² + y² = 4
x-y = 1
The graph is plotted in the following figure .
To plot a graph we need 2 pts .
First eqn is of a circle ( [tex]x^{2}[/tex] ) + ( [tex]y^{2}[/tex] ) = 4
Second eqn is of a line x - y = 1
The center of circle is ( 0 , 0 )
The circle passes through ( 2 , 0 ) , ( 0 , 2 ) , ( - 2 , 0 ) , ( 0 , - 2 ) .
The line passes through ( 0 , 1 ) , ( 0 , - 1 ) .
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A road sign in Canada gives the distance to Toronto as 140 kilometers. What is this distance to the nearest mile?
Converting 140 kilometers to miles, the distance from a road sign in Canada to Toronto is 87 miles.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
From the problem, we must convert the distance of 140 kilometers into miles.
Converting kilometers to miles, we must use the conversion
1 kilometer = 0.621371 mile
140 kilometers = 140 (0.621371 mile)
140 kilometers = 86.992 miles
Rounding off to the nearest mile,
140 kilometers = 86.992 miles = 87 miles
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Imagine that you are a teacher grading your students’ assignments. The following questions were turned in with incorrect answers. Trace through the process of solving them to discover where your students made a mistake in their order of operations. Which step of PEMDAS did they do out of order? Explain.
(6-2)^2+12-3^2
The correct answer is 19
student answer 97
The student did the subtraction step of PEMDAS out of order.
What is PEMDAS?PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.
Parenthesis.Exponents.Multiplication/Division.Addition/Subtraction.In this problem, the expression is:
(6 - 2)² + 12 - 3².
The student reached an answer of 97 as follows:
(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.
The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.
The correct solution is:
(6 - 2)² + 12 - 3² -> Solve the Parenthesis.
4² + 12 - 3² -> Solve the Exponents.
16 + 12 - 9 -> Solve the Addition and Subtraction.
19.
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What is the slope of the line that contains the points (-2, 2) and (3, 4)?
A. -5/2
B. 5/2
C. 2/5
D. - 2/5
The sum of Sharon's and John's ages is 70 . John is 4 times as old as Sharon.
If you let Sharon's age and John's age, then the problem can be represented by a system of equations. Which of the following shows a graph of this system and the solution to this problem?
Answer:
Graph A shows the system and solution to the system. Option A is correct.
The sum of Sharon's and John's ages is 70. Sharon is times as old as John. The system of equations regarding the problem is determined.
What is the equation?
The equation is the values of two expressions that are equal.
Let the age of Sharon's be x and Jhon's be y.
The sum of Sharon's and John's ages is 70.
x + y = 70 - - - - (1)
Sharon is times as old as John.
x = 4 y
Now put x = 4y in equation 1
4y + y = 70
5y = 70
y = 70/5
y = 14
Now put y = 14 in x = 4y
x = 4*14
x = 56
The solution of a system of equations is (14, 56) shown in graph 1.
Thus, graph A shows the system and solution to the system. Option A is correct.
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Step-by-step explanation:
Sharon is 14 years old and John is 56 years old.
The graph of the system of equations is given below where the solution is (14, 56).
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Let x be Sharon's age and y be John's age.
From the first sentence, we know that:
x + y = 70
From the second sentence, we know that:
y = 4x
Substituting y = 4x into the first equation, we get:
x + 4x = 70
5x = 70
x = 14
Substituting x = 14 into y = 4x, we get:
y = 4(14) = 56
The graph of the system of equations is given below where the solution is (14, 56).
Therefore,
Sharon is 14 years old and John is 56 years old.
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