Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
1. 7, 1+i
2.
The polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros 7, 1 + i, and 1 - i is f(x) = x^3 - 9x^2 + 21x - 14.
Explanation:In mathematics, zeros are the x-values where a function touches or crosses the x-axis, or the values where f(x) = 0. When a polynomial has rational coefficients and you have a complex zero (a + bi), the conjugate of that zero (a - bi) also needs to be a zero of the polynomial. This is based on the Complex Conjugate Root Theorem. Hence, in this case, the other zero will be 1 - i.
Since you are given zeroes of 7, 1 + i, and 1 - i, the polynomial function of least degree is obtained by employing the Factor Theorem, which states that if k is a zero of a polynomial, then (x - k) is a factor of the polynomial.
Therefore, f(x) = (x - 7)(x - (1 + i))(x - (1 - i)) = (x - 7)(x^2 - 2x + 2). So, f(x) = x^3 - 9x^2 + 21x - 14 is the polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros.
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A polygon has 10 sides. What is the measure of the interior angles of the polygon?
144 degrees is the measure of the interior angles of the polygon.
What is a polygon?In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:
• Triangle
• Quadrilateral
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:
α = 360/n
The sum of the measures of the interior angles of an n-sided polygon is given by the formula:
S = (n - 2) × 180 degrees
So, for a 10-sided polygon, we have:
S = (10 - 2) × 180 = 8 × 180 = 1440 degrees
To find the measure of each interior angle, we divide the sum by the number of angles (which is the same as the number of sides for a polygon):
m = S/n = 1440/10 = 144 degrees
Therefore, each interior angle of a 10-sided polygon has a measure of 144 degrees.
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The community center has a pottery class each month. Each student pays $15 for the class and $27 for materials. This month the pottery class brought in a total of $714. How many students are in the class this month?
please answerrrrrr
Answer:
[tex]17[/tex]
Step-by-step explanation:
Let the number of students in pottery class be [tex]x[/tex]
Price each student pays for the class = [tex]\$15[/tex]
Price each student pays for the material = [tex]\$27[/tex]
Total earning of pottery class = [tex]\$714[/tex]
We can write this in expression as-
[tex]15x + 27x = 714[/tex]
Solving the expression we get[tex]15x + 27x = 714\\42x = 714\\x = \frac{714}{42} \\x = 17[/tex]
There are total [tex]17[/tex] students in the class this month
what is completely factored form of x^4+8x^2-9
Answer: B would be the correct answer on edg. (X+1)(x-1)(x^2+9)
Rolando had $120,000 in a CD at Big Bucks Bank, which just failed. If the FDIC insurance limit per depositor, per bank, is $250,000, how much will Rolando get back?
the answer will be 120,000
PLEASE HELP ME ASAP !!!!!!
A squirrel is traveling at a rate of 12 miles per hour. Write the rate in miles per minute.
1 hour = 60 minutes
12/60 = 0.2 miles per minute
The length of a rectangle is 10 feet more than the width. if the perimeter of the rectangle is 180 feet, find the length and the width of the rectangle
10 An important aspect of ____________ is assigning people to various tasks and jobs?
Jean has $20 and is going shopping to buy 3 scarves and as many pairs of earrings as possible. How many pairs of earrings can she buy if scarves cost $2.55 each and earrings cost $2.99 a pair? Jean can buy at least 4 pairs of earrings. Jean can buy more than 4 pairs of earrings. Jean can buy less than 4 pairs of earrings. Jean can buy at most 4 pairs of earrings.
Calculate the speed of a dog running through a yard covering 24m in 52s
The speed of the dog is 4.8m/s
Data;
Distance = 24mTime = 52 secondsSpeedThis is calculated as the ratio between the distance covered to the time taken.
The formula is given as
[tex]speed = \frac{distance }{time taken}[/tex]
Let's plug in our values and solve
[tex]speed = \frac{24}{5}\\ speed = 4.8m/s[/tex]
The speed of the dog is 4.8m/s
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Final answer:
To find the speed of a dog that covers 24 meters in 52 seconds, divide the distance by the time to get an average speed of approximately 0.4615 meters per second (m/s).
Explanation:
To calculate the speed of a dog running through a yard that covers a distance of 24 meters in 52 seconds, you would use the formula for speed, which is:
Speed = Distance ÷ Time
In this case, the dog covers a distance (Distance) of 24 meters in a time (Time) of 52 seconds. Substituting these values into the formula we get:
Speed = 24 m ÷ 52 s
Now, we perform the division to find the speed:
Speed = 0.4615 meters per second (m/s)
Therefore, the dog is running at an average speed of approximately 0.4615 m/s.
at a local pizza parlor, patrons have 2 choices of cheese and 14 choices of topping. in how many different ways can a patron choose 1 type of cheese and 1 type of topping?
30
28
16
2
What geometric term does the flight path of a plane on radar represent?
A line B plane C angle D point
the answer is A. Line
The Geometric Term that best approximates this reality is option A (A line).
Planes usually travel in a straight Line at constant Speed, Flight Path represents the Trajectory taken by the Plane and shown on radar, which can be either a Line or a Curve.
Hence, the Geometric Term that best approximates this reality is option A (A line).
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Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. apples cost $.24 each and oranges cost $.80 each. she has $12 to spend and would like to purchase at least 20 pieces of fruit total
The system of linear inequalities that represent the situation are
$0.24x + $0.80y ≤ $12 and x + y ≥ 20
Here is the complete question:
Write a system of linear inequalities to represent this situation.
Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. Apples cost $0.24 each and oranges cost $0.80 each. She has $12 to spend and would like to purchase at least 20 pieces of fruit total.
To write a system of linear inequalities to represent the situation, we will consider the statements one after the other.
Let x represent the number of apples and y represent the number of oranges.
From the second statement,
"Apples cost $0.24 each and oranges cost $0.80 each"; and
From the next statement,
"She has $12 to spend"
That means, she can either spend $12 or less than $12.
Therefore, we can write that
$0.24x + $0.80y ≤ $12
Also, from the following statement
"and would like to purchase at least 20 pieces of fruit total"
That means, she will either purchase 20 pieces of fruit or greater than 20 pieces of fruit.
Then we can write that
x + y ≥ 20
Hence, the system of linear inequalities that represent the situation are
$0.24x + $0.80y ≤ $12 and x + y ≥ 20
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The lengths of the sides of a triangle are 8, 15, and 17. if the longest side of a similar triangle is 51, what is the length of the shortest side?
he length of the shortest side is 32
Similar triangles and scale factorsGiven the length if the sides of the triangle to be 8, 15 and 17. If the longest side of a similar triangle is 51, then the scale factor will be expressed as:
Scale factor = 51/17
Scale factor = 4
For the shortest side;
Length = 8 * scale factor
Length = 8 * 4
Length = 32
Hence the length of the shortest side is 32
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fine the distance between 8 and 32
Eric is hanging a rectangle mirror that has a diagonal of 47 inches with an angle of depression of 60°. How many square inches is the mirror?
Answer:
A) 956.5 in^2
Step-by-step explanation:
took the test
A stock market analyst observes the following for the price of two stocks that he owns, one of which is increasing at an exponential rate (geometric) and the other is increasing in a linear fashion (arithmetic).
Stock A: Equation: an = 15n + 130, where an is the value of the stock and n is the number of years.
Year Price
1 $145.00
2 $160.00
3 $175.00
4 $190.00
5 $205.00
Stock B: Equation: an = 36(1.09)n − 1, where an is the value of the stock and n is the number of years.
Year Price
1 $36.00
2 $39.24
3 $42.77
4 $46.61
5 $50.82
Assuming these stock values continue to increase in the same manner until retirement, which stock option is worth more in 50 years and how much more is this stock worth per share?
OPTIONS:
A) Stock B is worth more in 50 years, $1,575.84 more per share
B) Stock A is worth more in 50 years, $1,364.08 more per share
C) Stock B is worth more in 50 years, $1,796.87 more per share
D) Stock A is worth more in 50 years, $880.00 more per share
Stock B is worth more in 50 years, $1,575.84 more per share.
Explanation:To determine which stock option is worth more in 50 years, we need to find the value of each stock after 50 years.
For Stock A, we have the equation: an = 15n + 130. Plugging in n = 50, we get a50 = 15(50) + 130 = $880.
For Stock B, we have the equation: an = 36(1.09)n - 1, where n is the number of years. Plugging in n = 50, we get a50 = 36(1.09)^50 - 1 = $2,455.84.
Therefore, Stock B is worth more in 50 years, $1,575.84 more per share.
Given the statement "If Jack’s pet is a pig, then Jack’s pet cannot fly,” which statement represents the converse?
q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly~q → ~p, where p = Jack’s pet cannot fly and q = Jack’s pet is a pig p → q, where p = Jack’s pet is a pig and q = Jack’s pet cannot flyq → p, where p = Jack’s pet is not a pig and q = Jack’s pet is a pig
the answer is A just had the practice quiz
Converse statement of "If Jack’s pet is a pig, then Jack’s pet cannot fly,” is given by " q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly."
What is converse statement?" Converse statement is defined as when the hypothesis and conclusion of a statement interchange or reversed."
According to the question,
Given,
p → q
Hypothesis of a statement 'p': If Jack’s pet is a pig
Conclusion of a statement 'q' : then Jack’s pet cannot fly
Converse of a statement is given by reversing hypothesis and conclusion we get,
q → p
Hypothesis of a statement 'q' : If Jack’s pet cannot fly
Conclusion of a statement 'p': then Jack’s pet is a pig
Hence, converse statement is given by q → p, where p = Jack’s pet is a pig and q = Jack’s pet cannot fly.
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Given that 56 square equals 3,136 find the square of112
The petting zoo is not closed and the animals are not being fed by people.
write the statement that is logically equivalent to the statement
De Morgan's laws of distributing negation over disjunction and conjunction states that
Which is a correct expansion of (2x+3)(2x^2-5)
A. 2x•2x^2+2x•(-5)+3•2x+3•(-5)
B. 2x•2x^2+2x•(-5)+3•2x^2+3•(-5)
C. 2x•2x^2+3•2x^2+2x^2•(-5)+3•(-5)
Answer: B
2X.2X^2+2X.(-5)+3.2X^2+3.(-5)
Step-by-step explanation:
(2X+3) (2X^2-5)
Cross multiply (2X+3) by (2X^2-5)
2X*2X^2+
2X*(-5)+
3*2X^2+
3*(-5)
= 2X*2X^2+2X*(-5)+3*2X^2+3*(-5)
You roll a six-sided number cube. Which events are mutually exclusive?
A) rolling a multiple of 2 and a multiple of 4
B) rolling a multiple of 3 and a multiple of 6
C) rolling an even number and an odd number
D) rolling a prime number and an even number
Answer:
C) Rolling an even number and an odd number.
Step-by-step explanation:
We are asked to choose the correct option that represents two mutually exclusive events.
Since we know that mutually exclusive events are those events, who can not happen at the same time. As we cannot have both heads and tails in one toss, either we will get heads or we will get tails.
Let us check our given choices one by one.
A) Rolling a multiple of 2 and a multiple of 4.
Multiples of 2: 2, 4, 6,..
Since 4 is a multiple of 2, so both events are not mutually exclusive and option A is not a correct choice.
B) Rolling a multiple of 3 and a multiple of 6.
Multiples of 3: 3, 6, 9,...
Since 6 is a multiple of 3, so both events are not mutually exclusive and option B is not a correct choice.
C) Rolling an even number and an odd number.
Odd numbers on a cube: 1, 3, 5.
Even numbers on a cube: 2, 4, 6.
Since on one roll of dice we can either have an odd or an even number, both events are not possible with a single roll, therefore, option C is the correct choice.
D) Rolling a prime number and an even number.
Prime number on a cube: 2, 3, 5.
Even numbers on a cube: 2, 4, 6.
We can clearly see that 2 is a prime number and it is even as well, therefore, option D is not a correct choice.
Bob runs 5 miles in 38 minutes. at the same rate, how many miles would he run in 57 minutes?
Si vendo los 7/4 de lo que no vendí, ¿que parte del total no vendí?
The part of the total that is not sold is 1/4.
If you sell 7/4 of the lot, the part of the total that is not sold is 1 - 7/4 = 1/4.
Another way to think about it is that if you have 4 slices of pie and you sell 7 of them, you have 1 slice left. Therefore, 1/4 of the pie is not sold.
Suppose you have a lot that is 100 square meters in size. If you sell 7/4 of the lot, you will sell 7/4 * 100 square meters = 175 square meters. This means that you will have 100 square meters - 175 square meters = 25 square meters left.
Therefore, the part of the total that is not sold is 25 square meters / 100 square meters = 1/4.
In general, if you sell a fraction of a total, the part of the total that is not sold is 1 - (fraction sold).
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Write an equivalent expression for 5x + 2y + 3x
The equivalent expression is 8x + 2y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
5x + 2y + 3x
Add like terms.
8x + 2y
Thus,
The final expression is 8x + 2y.
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k + k divided by 2 when k = 20
A survey at your school found that 792 in 1,220 students have a cell phone. what percent of the students in school has a cell phone? round to the nearest hundredth where necessary.
64.84% of the students in the school have a cell phone.
To find the percentage of students with cell phones, divide the number of students with cell phones by the total number of students, then multiply by 100.
Find the fraction of students with cell phones: [tex]\( \frac{792}{1220} \)[/tex].
Divide to get the decimal: [tex]\( \frac{792}{1220} = 0.6484 \)[/tex].
Multiply by 100 to get the percentage: [tex]\( 0.6484 \times 100 = 64.84\% \)[/tex].
If you came home from a trip with 150 south african rand, 350 kuwaiti dinars and 200 japanese yen, how much would you have in u.s. dollars?
We know that:
1 south African rand = 0.075 usd
1 kuwaiti dinar = 3.31 usd
1 japanese yen = 0.0089 usd
Therefore the total money in usd is:
total usd = 150 rand * (0.075 usd / 1 rand) + 350 dinar * (3.31 usd / 1 dinar) + 200 yen * (0.0089 usd / 1 yen)
total usd = 1,171.53 us dollars
What is the circumference of the circle shown below, given that the length of ED (the minor Arc) is 6?