Final answer:
To form a polynomial with real coefficients, given non-real zeros 4i and 5i, include their conjugates -4i and -5i. Multiply the corresponding factors to get f(x) = (x^2 + 16)(x^2 + 25), which simplifies to f(x) = x^4 + 41x^2 + 400.
Explanation:
To form a polynomial, f(x), with real coefficients having a specified degree and given zeros, you must use the fact that non-real roots of polynomials with real coefficients come in conjugate pairs. Since 4i and 5i are given as zeros of the polynomial, their conjugates, -4i and -5i, must also be zeros of the polynomial.
The factors of the polynomial that correspond to these zeros are (x - 4i), (x + 4i), (x - 5i), and (x + 5i). To find the polynomial, these factors are multiplied together.
Multiplying the factors that come in conjugate pairs first:
Next, multiply these two results to obtain the polynomial:
(x^2 + 16)(x^2 + 25) = x^4 + 25x^2 + 16x^2 + 400 = x^4 + 41x^2 + 400
Therefore, the polynomial with degree 4 and zeros 4i and 5i is f(x) = x^4 + 41x^2 + 400.
To form the polynomial f(x) with real coefficients and given the zeros 4i and 5i, we use the conjugate pairs and multiply the resulting factors to get x⁴ + 41x² + 400.
To form a polynomial f(x) with real coefficients given the degree and zeros, we start by noting that complex roots always come in conjugate pairs when dealing with polynomials that have real coefficients. Hence, for the zeros 4i and 5i, the polynomial must also include the conjugate roots -4i and -5i.
Using these roots, we can form the factors:Thus, the polynomial f(x) is x⁴ + 41x² + 400.
"The graph below shows the population of mice in an ecosystem where the mice are not allowed to enter or leave.
Which best describes the population at point A?
A.The death rate is higher than the birthrate.
B.The population is decreasing.
C.The birthrate is higher than the death rate.
D.It has reached carrying capacity"
The point marked A is the point where the birth rate is higher than the death rate.
What is birth rate/ death rate?The term birth rate refers to the rate at which new organims are introduced into the population and the death rate refers to the rate at which individuals exit in the population.
In this case, when we observe the graph, we can see that the point marked A is the point where the birth rate is higher than the death rate.
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A highway map of Ohio has a coordinate grid superimposed on top of the state. Springfield is at point (1, –4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (One unit = 5.38 miles)
On monday, deborah ran 3 2/5 miles and on tuesday she ran 4 1/5 miles how many miles did she run on these 2 days togehter
Final answer:
Deborah ran a total of 7 3/5 miles combined on Monday and Tuesday. This was determined by adding 3 2/5 miles and 4 1/5 miles together after converting them to improper fractions.
Explanation:
On Monday, Deborah ran 3 2/5 miles and on Tuesday she ran 4 1/5 miles. To find the total distance Deborah ran over these two days, we need to add the two distances together. When working with mixed numbers, it's often easiest to convert them to improper fractions before adding.
3 2/5 miles is the same as (3 × 5 + 2)/5 = 17/5 miles.
4 1/5 miles is the same as (4 × 5 + 1)/5 = 21/5 miles.
Adding these two fractions:
17/5 miles + 21/5 miles = (17 + 21)/5 miles
= 38/5 miles
= 7 3/5 miles
So, Deborah ran a total of 7 3/5 miles on Monday and Tuesday combined.
PRE-ALGEBRA HELPPPP!!
Answer:
yeet
Step-by-step explanation:
If x2 − 8xy + 12y2 = 8 and x − 6y = 3, then x − 2y =
Translate the phrase into a math expression.
Twenty divided by the sum of 4 and 1.
(1+4) ÷ 20
20 ÷ (1+4)
1 + (4÷20)
(20÷4) + 1
Answer:
[tex]\displaystyle 20 \div (1 + 4)[/tex]
Explanation:
It is EXACTLY how it sounds, and of course, you must include grouping symbols to separate both parts of the expression.
I am joyous to assist you anytime.
the area of a rectangle is 15x^2y^5. if the length is 5xy^3, what is the width?
Paco buys a carton of eggs. the carton has 2 rows of eggs. there are 6 eggs in each carton. how many eggs are in the carton
The total number of eggs in the carton is 12, as there are 2 rows with 6 eggs each, and you calculate the total by multiplying these two numbers.
Paco buys a carton with 2 rows of eggs and there are 6 eggs in each row.
To find the total number of eggs in the carton, you multiply the number of rows by the number of eggs in each row: 2 rows× 6 eggs per row equals a total of 12 eggs in the carton.
So, in this case, the number is 12, and the unit is eggs.
oli has a volume of 9000cm3 and a density of 0.8g/cm3
what is the mass of the oil
for tomoz plz help
tan^4x-sec^4x=1-2 sec^2(x)
verify
SOLVE. integration of (1-v) /(1+v^2)
Answer:
[tex]tan^-1( v) - \frac{1}{2} ln(1+{v}^2) +c[/tex] is the answer.
Step-by-step explanation:
∫[tex]\frac{1-v}{1+{v}^2} \\\frac{1}{1+{v}^2}- \frac{v}{1+{v}^2}}[/tex]
∫[tex]\frac{dv}{1+{v}^2}[/tex]-∫[tex]\frac{2v}{1+{v}^2}[/tex]dv
[tex]{tan}^{-1} (v)-\frac{1}{2} ln(1+{v}^2) +c[/tex]
15-28i=3m+4ni find the values of m and n that make this equation true
Final answer:
The values of m and n that satisfy the equation 15 - 28i = 3m + 4ni are m = 5 and n = -7 after equating and solving the real and imaginary parts separately.
Explanation:
To find the values of m and n that make the equation 15 - 28i = 3m + 4ni true, we must equate the real parts and the imaginary parts of both sides of the equation separately. The real part of the left side of the equation is 15, and the imaginary part is -28i. Similarly, for the right side, the real part is 3m, and the imaginary part is 4ni.
Equate the real parts: 15 = 3m
Dividing both sides by 3, we get m = 5.
Equate the imaginary parts: -28i = 4ni
Dividing both sides by 4i, we get n = -7.
Hence, the values that satisfy the equation are m = 5 and n = -7.
In ∆ABC shown below, ∡BAC is congruent to ∡BCA. Given: Base ∡BAC and ∡ACB are congruent.
Prove: ∆ABC is an isosceles triangle.
Construct a perpendicular bisector from point B to line segment AC.
Label the point of intersection between this perpendicular bisector and line segment AC as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the definition of congruent angles. Line segment AD is congruent to line segment DC by _______1________.
∆BAD is congruent to ∆BCD by the _______2________. Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.
options are:
a)1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)
b) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. Angle-Side-Angle (ASA) Postulate
c) 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate
d) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector
Refer to the image attached.
Given: [tex]\angle BAC[/tex] and [tex]\angle BCA[/tex] are congruent.
To Prove: [tex]\Delta ABC[/tex] is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to line segment AC. Label the point of intersection between this perpendicular bisector and line segment AC as point D.
Proof:
Consider [tex]\Delta BDA, \Delta BDC[/tex]
[tex]\angle BDA = \angle BDC= 90^\circ[/tex]
(By the definition of perpendicular bisector)
[tex]AD=DC[/tex] (By the definition of perpendicular bisector)
So, Line segment AD is congruent to DC by the definition of perpendicular bisector.
[tex]\angle BAC[/tex] = [tex]\angle BCA[/tex] (given)
So, [tex]\Delta BDA \cong \Delta BDC[/tex] by ASA congruence postulate.
∆BAD is congruent to ∆BCD by the ASA congruence Postulate.
Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
So, Option C is the correct answer.
How do I find dy/dx of the equation 4x^3-3xy^2+y^3=28 at the point (3,4)?
To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), you can use implicit differentiation and solve for dy/dx.
Explanation:To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), we need to use implicit differentiation. We differentiate both sides of the equation with respect to x, treating y as a function of x. Thus, we get:
12x^2 - 3y^2 - 3x(2y(dy/dx)) + 3y^2(dy/dx) = 0
Now we substitute x = 3 and y = 4 into the equation and solve for dy/dx:
12(3)^2 - 3(4)^2 - 3(3)(2(4)(dy/dx)) + 3(4)^2(dy/dx) = 0
Can someone help me...again?
What is the absolute value or −|9| = −9?
Which of the following best describe perpendicular lines? A.lines that are not in the same plane B. Lines that meet at a 90* angle C. Lines that meet at a 45' angle D. Lines that are coplanar and do not intersect
A line is said to be perpendicular to another line if the two lines intersect at a right angle. An angle is said to be a right angle if its measure is 90 degrees.
The question is asking us to select the option which best describes a perpendicular lines.Among all the options given option B states :Lines that meet at a 90* angle.
Option B is the right answer.
The perpendicular lines are those lines that meet at a 90* angle. That is option B.
Perpendicular linesPerpendicular lines are those lines that meet at an angle of 90°. To further explain the perpendicular lines, a diagram above is used.
Line AB is perpendicular to XY because AB and XY intersect each other at 90°.
Some of the characteristics of perpendicular lines include:
These lines always intersect at right angles.Adjacent sides of a square and a rectangle are always perpendicular to each otherTherefore, perpendicular lines are those lines that meet at a 90* angle.
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Does this set of ordered pairs represent a function? Why or why not?
{(–2, 2), (–1, 2), (3, –1), (3, 1), (4, 11)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Write an equation that models the sequence 400, 200, 100, 50, ...
1. A bag of chips costs $3.79 including tax Mr.Connor wants to purchase chips for his class and has a $15 budget. Write and inequality to solve for the number of bags of chips Mr.Connor can purchase with his budget
A. $15x > $3.79
B.$15x < $3.79
C $3.79 > $15
D. $3.79 < $15
(There is a flat line under all the greater than and less than signs)
2. A cab charges $1.75 for the first mile $0.25 for each additional mile. Write and solve an inequality to determine how many miles eddie can travel if he has $15
A. $1.75 + $0.25x < $15; x < 53 miles
B. $1.75 + $0.25x > $15; x >53 miles
C. $0.25 + $1.75x < $15; x< 8 miles
D.$0.25 + $1.75x > $15; x > 8 miles
jika f(x)= 1/2 x - 1 dan g(x)= 2x 4. Maka nilai (gof)^-1 (10) adalah ...
a. -9
b. -8
c. 8
d. 9
e. 10
The cost of a service call to fix a washing machine can be expressed by the linear function y=45x+35 where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
a-the cost for each hour it takes to repair the machine
b=the cost for coming to look at the machine
c-the total cost for fixing the washing machine
d-the amount of time that it takes to arrive at the home to make the repairs
Answer:
The slope represents the cost for each hour it takes to repair the machine.
Step-by-step explanation:
We are given that the cost of a service call to fix a washing machine can be expressed by the linear function
[tex]y=45x+35[/tex]
Where
y=Total cost of a service to fix the machine.
x=Number of hours takes to fix the machine
We have to find that slope in this function what represents.
General equation of line is given by
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y- intercept
Comparing the general equation with the given function
We get m=45,c=35
m=45 represents the cost for each hour it takes to repair the machine because when number of hours multiplied by 45 then we get total cost of x hours.
Hence, the slope represents the cost for each hour it takes to repair the machine.
Latonya bought flowers for her mother. She spent $45. Each tulip was $1 and each rose was $2. She bought 3 more tulips than roses.
Let t be the number of tulips. Which algebraic sentence would help you figure out how many tulips Latonya bought?
A. t + 2(t + 3) = 45
B. t + 2(t – 3) = 45
C. 2t (t + 3) = 45
D. -3t + 2t = 45
What does 28 tens divided by 4 equal?
You calculate this by first understanding that '28 tens' means 280, and then dividing 280 by 4. So, 28 tens divided by 4 equals 70.
The phrase '28 tens' refers to 28 multiplied by 10, 28 x 10 = 280.
To find the result of dividing this by 4, we calculate 280 ÷ 4 = 70.
Therefore, 28 tens divided by 4 equals 70.
What is the solution to the system of linear equations
A. (-3,0)
B. (-3,3)
C. (0,2)
D. (3,1)
what is the domain of the composite function G ( F ( x ) )
A radio commercial for a loan company states: “You only pay $0.29 a day for
each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you
repay, and what annual interest rate is the company actually charging?
Find equation of the axis of symmetry of Y= -3x^2+12x-7
The number of days between Aug. 9 and Jan. 3 is
What number represents the same amount as 2 hundreds 14 tens 3 ones
The representation of the given number will be given below such that it sum should be 343.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation.
There might simply be two terms, but there might also be 100,000 or a million. Summations exist with an infinite number of parameters.
The summation is to add or subtract any two or more terms by doing the operation.
The representation of 200, 14, and 3 will be
200 hundred
14 tens
+ 3 ones
--------------------
343
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