write the equation of a polynomial of least degree in standard form that has zeros at x=2i & x=3 what is the constant form?
The equation of a polynomial that has zeros at x = 2i and x = 3 is given as follows:
x³ - 3x² + 4x - 12.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros are given as follows:
x = 2i.x = -2i, as if a complex number is a root, then it's conjugate also is.x = 3.Then the polynomial is obtained as the product of it's linear factors, due to the Factor Theorem, as follows:
(x - 2i)(x + 2i)(x - 3)
(x² + 4)(x - 3)
x³ - 3x² + 4x - 12.
(as the base complex number relation is i² = -1).
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PLEASE HELLP MEEEEEE
Answer: angle EHF = 31 degrees
Step-by-step explanation:
Complementary angles mean either of two angles whose sum is 90°.
So the equation is 6x-1+3x+1=90
combine like terms
9x=90
x=10
Substitute in 10 to EHF or 3x+1
3(10)+1
angle EHF = 31
Compare 0. 3 and 0. 8 uing >,=, or <. Draw a model or number line to upport your olution
On solving the provided question, we got that - 0.8 > 0.3, 0.8 is greater as , it is more closer to 1 than 0.3.
What is Number Line?The term "number line" refers to a horizontal line with numbers placed equally apart. Depending on the numbers present, you can choose how to respond to the numbers on the line. The corresponding question dictates how to use numbers. B. When arranging the points.
From the provided question,
we have to compare between 0.3 and 0.8.
Here,
Obviously, 0.8 is greater than 0.3.
as on number 0.8 is closer to 1 than 0.3,
and 0.3 is more closer to 0 than 0.8.
Therefore,
0.8 > 0.3.
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The first few terms of a geometric
sequence are given by 2, 4, 8, 16... What is
the value of the 28th term divided by the
26th term?
Answer:
4
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{2}[/tex] = 2
then
a₂₈ = 2 [tex](2)^{27}[/tex]
a₂₆ = 2 [tex](2)^{25}[/tex]
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{a_{28} }{a_{26} }[/tex]
= [tex]\frac{2(2)^{27} }{2(2)^{25} }[/tex] ( cancel 2 on numerator/ denominator )
= [tex]\frac{2^{27} }{2^{25} }[/tex]
= [tex]2^{(27-25)}[/tex]
= 2²
= 4
3. Amara was given the formula for the volume of a half-cylinder, V=h, and asked to sok
the formula for h, the length of the half-cylinder.
Which equation below is a correct rearrangement of the formula Amara was given?
The equation for the length, h is h= ( 2V ) / ( πr² )
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.
Volume of a half-cylinder:
V= (1/2)πr²h
Move 2 to the left
=> 2V= πr²h
Solve for h
=> 2V/πr² = h
=> h= ( 2V ) / ( πr² )
Thus, the equation for h is h= ( 2V ) / ( πr² )
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Draw all the lines of symmetry for this shape.
Line 1
Answer:
Line down the middle
Step-by-step explanation:
There is only one line of symmetry in this shape because there is no rotational symmetry. Its a line down the middle.
A 6th grade cla did a weekend fitne challenge. Each tudent et a goal of `75` minute of fitne. Amanda exercied for `78` minute. What percent of the goal did he achieve?
Answer: 104%
Step-by-step explanation:
75/78=1.04
b) 4 machines of a factory can finish the required amount of production in 6 days. If one machine had machinery defect and stopped functioning, in how many days would the remaining machines finish the same quantity of production at the same rate of production?
Answer:
Answer = 8 days
Step-by-step explanation:
Step 1: Find how long one machine takes to finish
1. 6 ∙ 4 = 24 days
Step 2: Divide 24 by 3 to get the rate of speed of 3 machines
2. 24 / 3 = 8 days
JP Sports sold football boots on its first day of release. SoccerWorld sold 3 as many boots as JP Sports. DirectSportz sold 5 more boots than JP Sports. Each pair of football boots costs £70 The amount of sales from this particular boot totalled £7000
Work out how many pairs were sold by SoccerWorld.
The total number of pairs sold by SoccerWorld is 57
How to determine the total number of pairs sold by SoccerWorld?From the question, we have the following parameters that can be used in our computation:
SoccerWorld sold 3 as many boots as JP SportsDirectSportz sold 5 more boots than JP Sports. Cost of each pair = £70 Amount in sales = £7000The above parameters means that
s = 3j
d = 5 + j
70(s + d + j) = 7000
Where
j = JP Sports
s = SoccerWorld
d = DirectSportz
Divide both sides of 70(s + d + j) = 7000 by 70
s + d + j = 100
Substitute s = 3j and d = 5 + j
3j + 5 + j + j = 100
Evaluate the like terms
5j = 95
Divide by 5
j = 19
Substitute j = 19 in s = 3j
s = 3 * 19
So, we have
s = 57
Hence, the number of pairs is 57
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If your annual pay is $36,010, what is your biweekly pay based on 26 biweekly paychecks? what is your hourly rate of pay if you work 160 hours per month? what is your overtime rate?.
The biweekly pay is $1,385, the hourly rate of pay for 160 hours of work per month is $17.31, and the overtime rate of pay is $25.96.
Calculation:It is given that, the annual pay is $36,010.
There are 52 weeks in a year. So, there are 26 biweeks in a year.
Then, the biweekly pay = (Annual pay)/the number of biweeks in a year
⇒ biweekly pay = (36,010)/26 = $1,385
There are 160 working hours in a month.
So, biweekly working hours = 160/2 = 80 (for two weeks in a month)
Then, the hourly rate of pay is calculated by
hourly rate of pay = biweekly pay/biweekly working hours
⇒ hourly rate of pay = 1,385/80 = $17.31
To calculate the overtime rate of pay, we need to know the number of overtime working hours and the multiplier.
Here we are finding the overtime rate per hour. So, we can find the overtime rate of pay by
overtime rate of pay = hourly rate of pay × multiplier
We have the overtime multiplier per hour as 1.5.
Then,
Overtime rate of pay = 17.31 × 1.5 = $25.96
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(05.01)
The graph below shows a system of equations:
y=x+4
3y = -2x + 2
The x-coordinate of the solution to the system of equations is
Answer:
x= -2
Step-by-step explanation:
since we know what y equals we fill it into the second equation
3(x+4)= -2x+2
3x+12=-2x+2
-12. -12
3x=-2x-10
+2x +2x
5x=-10
/5. /5
x= -2
hopes this helps please mark brainliest
One-year treasury bills currently earn 3. 25 percent. You expect that one year from now, one-year treasury bill rates will increase to 3. 45 percent and that two years from now, one-year treasury bill rates will increase to 3. 95 percent. The liquidity premium on two-year securities is 0. 05 percent and on three-year securities is 0. 15 percent. If the liquidity theory is correct, what should the current rate be on three-year treasury securities?.
3-year treasury securities as calculated from the data will now have a rate of 3.70%.
Current interest rate is calculated as Current Interest Rate + Liquidity Premium.
Average interest for 3 Year = (3.45% + 3.95% +3.25%)/3 = 3.55
3 year security liquidity premium = 0.15%
3 year Treasury security's current rate is 3.55% +0.15%.
= 3.70%
Therefore, The current rate be on 3-year treasury securities is 3.70%.
Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is often reported as an annual percentage rate, interest expense or revenue is sometimes expressed as a dollar figure (APR).
The compensation a lender or financial organisation receives for giving out money is called interest. The percentage of a stockholder's ownership in a corporation that is also referred to as interest.
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How far must the outfielder throw the ball to return it to the pitcher? round to the nearest foot.
Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.
What are the laws of cosines?The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.
So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.
27° east of the pitcher's mound is the angle at which a ball is struck.
Before an outfielder catches the ball, it travels 162 feet.
Using the law of cosines, we may now:
a² = b² + c² - 2bcosA
When b=43, c=162, and A=27° are entered, we get:
a² = 43² + 162² - 2(43)(162)cos27°
a² = 1849 + 26244 - 12413.4
a² = 15679.6
a = 125.21
a = 125ft
Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.
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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
Please Help with this.
i need answers and explanations for the stuff in the picture
Point= (1, -1)
Hence, this is not the solution of the desired answer.
What is inequality?inequality is defined as declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or the algebraic expressions. Either queries or the declarations of fact in the form of theorems can be used to formulate and solve inequality problems.
Shaded Region represents y<2x-3
Given Point= (1, -1)
Hence, this is not the solution of the desired answer,
As it not defines the equality part.
As for example (2,-2) is the solution of the desired inequality and it satisfies the condition y<2x-3.
And given point (1, -1) is not the solution of the desired equation as it does not satisfy the inequality portion.
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A group of cubes are arranged in a pattern with the same number of cubes in each row and column. There are 225 cubes in the shape. How many cubes are in one row?.
Using square roots, we know that there are (A) 15 cubes in a row.
What is square root?The value that a number produces when it is multiplied by itself is known as the square root of the number.
The square root is denoted by the radical sign. For instance, √16 = 4.
The root symbol or surds is another name for the radical symbol.
So, let x be the total number of cubes in a row.
The number of cubes in each row and column is equal because they are organized in a pattern with the same number of cubes in each.
Now,
Total cubes = x * x
Total cubes = x²
We know that the total number of cubes is 225.
So, we got:
x² = 225
Taking square roots:
x² = 225
x = √225
x = 15
Therefore, using square roots, we know that there are (A) 15 cubes in a row.
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Complete question:
A group of cubes is arranged in a pattern with the same number of cubes in each row and column. There are 225
cubes in the shape. How many cubes are in one row?
A) 15
B) 25
C) 56
D) 75
Mrs. Joyce calculated the class mean on her latest test. 18 students took it and the mean was 81. 2. Three days later the four absent kids made it up and scored 77, 85, 68, and 80. To the nearest tenth, what is the new mean?.
The new mean for the given data would be 80.
What is the mean of the numbers?
The average (mean) is equal to the sum of all the data values divided by the number of values in the data set.
Mean = Sum / Count
Firstly 18 students took the test and the mean was 81.
By using the definition of mean we can write
Mean = sum of scores/number of students
81 = sum of scores / 18
Sum of scores = 81 * 18
= 1458
Now later the four absent kids made it up and scored 77, 85, 68, and 80.
Now new sum of the scores would be = 1458 + 77 + 85 + 68 + 80
= 1768
And the total number of students will be = 18 + 4 = 22
New mean = new score/number of students
= 1768/22
= 80.36
≈ 80
Hence, the new mean for the given data would be 80.
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For each of the following questions solve for the variable.
supposed to questions
Step-by-step explanation:
people say the climate is changing
For positive angles A and B, it is known that tan A = 5/12 and sin B = 3/5. Find the value of cos(A-B) in simplest form.
This question has me stumped. can anyone help?
The value of the cos(A - B) in simplest form would be 273/100.
What are the trigonometric angles?
Trigonometry angles are the angles given by the ratios of the trigonometric functions. Trigonometry deals with the study of the relationship between angles and the sides of a triangle. The angle value ranges from 0-360 degrees. The important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°.
sin B = 3/5
tan A = 5/12
We have find cos(A - B)
first, let’s hope these are both all-integer triangles:
In a 3-4-5 Right triangle,
sinB = 3/5, cos B = 4/5
For tanA = 5/12 the hypotenuse turned out to be 13.
sin A = 5/12
cos A = 12/13
So now we just use the identity for cos ( A + B )
cos(A - B) = cosAcosB + sinAsinB
= (12/13)(4/5) + (5/12)(3/5)
= (60 + 52/65) + (25 + 36/60)
= (112/65) + (61/60)
= 273/100
Hence, the value of the cos(A - B) in simplest form would be 273/100.
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Nolan is going to a carnival that has games and rides. Each game costs $2.50
and each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and
rides. Write a system of equations that could be used to determine the
number of games Nolan played and the number of rides Nolan went on.
Define the variables that you use to write the system.
Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].
What is the system of equation?
A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions.
Here given that,
Nolan is going to a carnival that has games and rides. Each game costs $[tex]2.50[/tex] and each ride costs $[tex]3.50[/tex]. Nolan spent $[tex]52.50[/tex] altogether on [tex]17[/tex] games and rides.
So, let us assume that the number of games are [tex]x[/tex] and the number of rides are [tex]y[/tex].
So, the equation is of the form
[tex]2.5x+3.5y=52.50 ........(1)[/tex]
And Noaln spent altogether $[tex]52.50[/tex] on [tex]17[/tex] games and rides.
So,
[tex]x+y=17[/tex]
Then,
[tex]2.5x+2.5y=2.5(x+y)\\As,\\x+y=17\\So,\\=2.5(17)\\\\=42.5.....(2)[/tex]
Now, subtract equation [tex](2)[/tex] from equation [tex](1)[/tex], we get
[tex]x=52.5-42.5\\\\x=10[/tex]
[tex]y=17-10\\y=7[/tex]
So the equation is of the form
[tex]2.5(7)+3.5(10)=52.50\\17.5+35=52.50\\52.50=52.50[/tex]
Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].
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if f (x) = 4x - 1, what is f (-2)
PLEASE HELP!
Answer: -9
Step-by-step explanation: If you subtitutie -2 in for x, ask yourself , what is 4*-2 which is -8 which is then subtracted by 1 which gets you -9 so, this means f (-2)=-9
Hope this helped!
15PTS HELP ASAP PLEASE! A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 160 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
Answer:
Step-by-step explanation:
68 Ounces B - 61.2
92.4 Ounces A - 60.06
70% of 160 = 112
A+B estimated 112
Expand and simplify:
y(2y³ - 4y² + 8) − 3y²
Who ever is reading these and trying to solve this thank you so much (extra points for you) you helped me so much in my examination I love you.
Answer:
2y4−4y3−3y2+8y :)
Anthony and joan have $10 to buy apples and oranges at the market. They will buy a total of 25 pieces of fruit. Apples cost 50 cents each and oranges cost 25 cents each. Which of these systems best represents this situation?.
The system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Total money Anthony and Joan have to buy apples and oranges = $10
Total pieces of fruit the Anthony and Joan buy is = 25 pieces of fruit
Each Apple's cost = 50 cents
Each orange's cost = 25 cents
Let, x = be the apples
and, y = be the oranges
The equation applied for the number of pieces of fruit they will buy,
x + y = 25
And, the equation applied for cost is,
0.50x + 0.25y = 10.00 (Keep everything in same decimal places)
Hence, the system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10
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The equation of the graphed line is x+2y=5. What is the x-intercept of the graph?
Answer:
(5,0)
Step-by-step explanation:
When graphed the x-intercept meaning the line touching x
is 5 so then your answer is (5,0) because the x-value comes first so then you'd put the 5 in front.
What is the hcf of 315 and 42
Answer: 21
the hcf of 315 and 42 is 21.
Answer:
HCF of 315 and 42:
Your answer is 21 !
vy = a sin( k ( x - d)) + c and y = a cos( k ( x - d)) + c
The equation Vy = a sin(k(x - d)) + c is an equation for a sine wave. A sine wave is a periodic function that describes a periodic oscillation or vibration. It is commonly used to model periodic phenomena in many fields, such as sound, light, and electricity.
In this equation, Vy is the vertical position of the sine wave at a given point in time (x), a is the amplitude of the sine wave (the maximum distance from the midline), k is the wave number (the number of complete cycles per unit distance), x is the horizontal position (time or distance), d is the phase shift (the horizontal shift of the wave), and c is the vertical offset (the distance from the midline).
The equation y = a cos(k(x - d)) + c is similar to the equation for a sine wave, but it describes a cosine wave instead. A cosine wave is also a periodic function, but it is shifted by 90 degrees in phase compared to a sine wave.
Like a sine wave, a cosine wave can be used to model periodic phenomena and is commonly used in many fields. In this equation, y is the vertical position of the cosine wave at a given point in time (x), a is the amplitude of the cosine wave, k is the wave number, x is the horizontal position, d is the phase shift, and c is the vertical offset.
What is sin and cosine sum?
sin(x) + cos(x) = √2 * sin(x + 45°)
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In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister.
The probability that a randomly selected student has a brother given they have a sister is 8/30.
What is the probability calculation formula?We have provided that.
A class of 30 pupils has 13 brothers, 8 sisters, and 3 students who have both brothers and sisters.
The probability of an occurrence is calculated by dividing the total number of outcomes in the sample space by the proportion of favorable events.
Considering that there are 30 pupils overall and that 8 of them have both a brother and a sister,
The probability of a student having a brother given that they have a sister would then be 8/30 (8 out of the 30 students).
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GEOMETRY! Someone help!
By ASA property
What is congruent triangle?Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.
We are asked that will property will show that Δ NKL ≅Δ LMN
It is given that NL bisect KNM and KLM
∠ KNL≅ ∠ MNL (by bisect property) (angle)
∠ KLN ≅∠MNL (by bisect property) (angle)
line NL (common)
Thus by ASA property we can say that Δ NKL ≅ΔLMN
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Please help with these
The values would be
sin2x = -3/5
cos2x = -4/5
tan2x = 3/4
What are double angles in trigonometry?
The double angle formulas are used to find the values of double angles of trigonometric functions using their single angle values. For example, the value of cos 30° can be used to find the value of cos 60°. Also, the double-angle formulas can be used to derive the triple-angle formulas.
Given: tanx = -3
Now as we know,
[tex]sin2x=\frac{2tanx}{1+tan^2x}\\\\sin2x=\frac{2(-3)}{1+(-3)^2}\\\\sin2x=\frac{-6}{10}\\\\sin2x=\frac{-3}{5}[/tex]
Now
[tex]cos2x=\frac{1-tan^2x}{1+tan^2x}\\\\cos2x=\frac{1-(-3)^2}{1+(-3)^2}\\\\cos2x=\frac{1-9}{1+9}\\\\cos2x=\frac{-8}{10}\\\\cos2x=\frac{-4}{5}[/tex]
And similarly, we can find the value of tan2x, as
tan2x = sin2x/cos2x
= (-3/5)/(-4/5)
= 3/4
Hence,
The values would be
sin2x = -3/5
cos2x = -4/5
tan2x = 3/4
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A boat can travel 302.9 miles on 23.3 gallons of gasoline. How far can it travel on 13.7 gallons?
Answer:
178.7 miles
Step-by-step explanation:
First, determine the miles per gallon:
[tex]\frac{302.9\ miles}{23.3\ gallons}\\13.0\frac{miles}{gallon}[/tex]
Then, use that value to find miles traveled on 13.7 gallons:
[tex]13.7\ gallons(\frac{13\ miles}{1\ gallon})\\178.7\ miles[/tex]