The polynomial satisfying the given conditions is given as 2x⁴ + 10x² + 8.
What is a polynomial?The polynomial is an algebraic expression in which no any terms has the power other than a whole number.
The degree of a polynomial is the highest power of one of its terms.
Given that,
The degree of polynomial is n = 4.
The zeros of the polynomial are i and 2i.
And, f(-1) = 20
Since, a polynomial with real coefficients have either real zeros or complex conjugate zeros.
Here, the given zeros of the polynomial are imaginary which implies that the remaining two zeros are the conjugate of the given two zeros.
Thus, the zeros of the given polynomial are i, 2i, -i and -2i.
The general form of a 4th degree polynomial is given as,
ax⁴ + bx³ + cx² + dx + e
Use the factor theorem to get,
ax⁴ + bx³ + cx² + dx + e = K(x - i) (x - (-i)) (x - 2i) (x- (-2i)) (1)
⇒ ax⁴ + bx³ + cx² + dx + e = K(x² + 1) (x² + 4) (2)
Now, f(-1) = 20 which gives,
K((-1)² + 1) ((-1)² + 4) = 20
⇒ k = 2
Substitute K =2 in equation (2) to get,
ax⁴ + bx³ + cx² + dx + e = 2(x² + 1) (x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2(x⁴ + 5x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2x⁴ + 10x² + 8
Hence, the nth-degree polynomial function with real coefficients satisfying n = 4 and zeros i and 2i is 2x⁴ + 10x² + 8.
To know more about polynomial click on,
https://brainly.com/question/11536910
#SPJ1
A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
please help?!
The angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
What is described as the trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship here between angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.The ramp is the hypotenuse of a right angle triangle formed by the doorway, the ground, and the ramp.
The ramp's elevation angle is the angle Ф it makes with the ground.
Apply the tan function;
Tan Ф = length of doorway/ distance along ramp of building
Tan Ф = 1/5
Ф = 11°
Thus, the angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
To know more about the trigonometric functions, here
https://brainly.com/question/25618616
#SPJ13
mass
density
volume
2.23 kg of oxygen gas has a volume of 1.56 x 106 cm³.
Calculate the density of the oxygen gas in g/cm³.
Give your answer in standard form to 3 significant figures.
Answer:
density = 1.43 × 10⁻³ g/cm³
Step-by-step explanation:
We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.
To do this we have to first convert the mass, which is given in kg, to g:
mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]
= 2230 g
Next, we can find the density of the gas using the following formula:
[tex]\boxed{density = \frac{mass}{volume}}[/tex]
⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]
= 1.43 × 10⁻³ g/cm³
Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.
In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 10 A (amperes), the resistance is 13 ohms. What is the resistance when the current is 26 A?
Answer:
33.8ohms
Step-by-step explanation:
10A : 13ohm
26A : 33.8ohm
Describe a real life siuation for each problem
1. -3 + (-4)
2. -3 (+2)
Answer:
1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.
2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.
Step-by-step explanation:
-Hope this helped
The monthly output at the Olek Carpet Mill is
Q(x) = 15,000 + 2x2 units, (40 ≤ x ≤ 60)
where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).
Q'(46) =
The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.
What is the instantaneous rate of change?The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.
In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.
Taking the derivate of the given function, we have:
Q(x) = 15,000 + 2x²
Q'(x) = d/dx(15,000) + d/dx(2x²)
Q'(x) = 0 + 2x(2)
Q'(x) = 4x.
At x = 46, we have:
Q'(x) = 4(46)
Q'(x) = 184.
Read more on instantaneous rate of change here: https://brainly.com/question/15579867
#SPJ1
Complete Question:
The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).
Q'(46) =
What is the slope of the line that passes through the points (-6, -7) and (-3, -2)?
If the random variable Zhas a standard normal distribution, then P(1.17 S ZS 2.26) is
The value of P(1.17 <= Z <= 2.26 ) is 0.1091
From the question, we have
Z value for 1.17 is 0.8790
Z value for 2.26 is 0.9881
P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
To learn more about probability visit: https://brainly.com/question/11234923
#SPJ9
Write the equation of a line with slope m = -6 and y-intercept (0, -4), in standard form.
The equation in standard form
Equation of the line in standard form is 6x + y + 4 = 0.
Slope-intercept form of equation -> y = mx + c
Given in question,
Slope = m = -6
y-intercept = c = -4
Putting values of m and c in Slope-intercept form of equation,
y = -6x - 4
Standard form :
6x + y + 4 = 0
To learn more about standard form here:
https://brainly.com/question/17264364
#SPJ1
The annual average price per square foot for office space in a city was $30.18 in 2004, and it was $66.85 in 2015.
(a) Find an exponential function of the form f(t)=y0b^t to model these data in which t=0 corresponds to 2004.
The exponential model of the given data is f(t) = 30.18 × 1.06^t.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
Given that,
The average price for office space in 2004 is $30.18.
The average price for office space in 2015 is $66.85.
Suppose the average price in 2004 is taken as y₀.
The given situation can be represented in the form of exponential function f(t) = y₀b^t as,
Take t = 0 for 2004
Then, f(0) = y₀b^0
⇒ f(0) = y₀ = $30.18.
Then, at 2015, t = 12. Substitute the respective values to get,
f(12) = 30.18 × b^12
⇒ 66.85 = 30.18 × b^12
⇒ b^12 = 66.85 / 30.18
⇒ b = 1.06
Thus in exponential form the given situation can be written as,
f(t) =30.18 × 1.06^t
Hence, the given data can be modeled in exponential function as f(t) =30.18 × 1.06^t.
To know more about exponents click on,
https://brainly.com/question/5497425
#SPJ1
Please Help
Find (f-g)(x) if f(x)--3x2+2x-3 and(x)=2x2-3x+4
The function operation (f - g)(x) of the functions f(x) = -3x² + 2x - 3 and g(x) = 2x² - 3x + 4 is -5x² + 5x - 7.
What is the function operation (f - g)(x) of the given functions?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = -3x² + 2x - 3g(x) = 2x² - 3x + 4(f - g)(x) = ?To determine the function operation (f - g)(x), replace the function designators with the real functions and simplify.
(f - g)(x) = f(x) - g(x)
(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )
Apply distributive property to eliminate the parenthesis.
(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )
(f - g)(x) = -3x² + 2x - 3 - 2x² + 3x - 4
Collect and add like terms
(f - g)(x) = -3x² - 2x² + 2x + 3x - 3 - 4
(f - g)(x) = -5x² + 5x - 7
Therefore, the function operation (f - g)(x) is -5x² + 5x - 7.
Option A is the correct answer.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
If f(x)= (x+3)(3x-5)-4, what is the value of f(3)-f(-2)? Type your answer in the box
If function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35
The function is
f(x) = (x+3)(3x-5) - 4
We have to find the value of f(3) - f(-2) ,to find that find the value of f(3) and f(-2) separately.
The function is
f(x) = (x+3)(3x-5) - 4
Substitute the values in the equation
f(3) = (3+3)(3×3 - 5) - 4
= (6) × (9-5) - 4
= 6 × 4 -4
= 24 - 4
= 20
The value of f(3) = 20
f(-2) = (-2+3)(3×-2 - 5) - 4
= 1 × (-6-5) -4
= 1 × (-11) - 4
= -11 - 4
= -15
The value of f(-2) = -15
Then,
f(3) - f(-2) = 20 - (-15)
= 20 + 15
= 35
Hence, if function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35
Learn more about function here
brainly.com/question/9554035
#SPJ1
Classify the following number: 5√2. Choose all that apply.
Answer:
Real, Irrational
Step-by-step explanation:
5sqrt2 is NOT:
Natural (1,2,3...)
Whole (0,1,2,3...)
Integer (...-3,-2,-1,0,1,2,3...)
Rational (can be written like a ratio)
Imaginary (have the number i in it.)
It IS Irrational, will have neverending decimal with no repeating pattern.
5sqrt2 = 7.0710678119...
It IS REAL and IRRATIONAL.
4x/3 -x=x/15-12/5 x =??????????
Given: ST=3x+3 and TU= 2x+9
What is the value of TU?
The value of TU is 21
From the question, we have
ST=3x+3 and TU=2x+9
ST = TU
3x + 3 = 2x + 9
3x - 2x = 9 - 3
x = 6
substituting the value, we get
TU = 2x + 9
= 2 (6) + 9
= 12 + 9
TU = 21
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
To learn more about addition visit: https://brainly.com/question/680614
#SPJ9
35 lbs of bananas
cost $280. How
much would 42 lbs
cost?
Answer:
$336
Step-by-step explanation:
[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]
need help with this asap first answer will get brainliest
Answer:
x° = 34°
Step-by-step explanation:
First, find the interior angle supplementary to the given exterior angle 124°.
I will label it y.
124° + y° = 180°
y° = 180° - 124°
y° = 56°
Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.
x° + y° + 90° = 180°
x° + y° = 90°
x° + 56° = 90°
x° = 90° - 56°
x° = 34°
Answer:
x = 34---------------------------
Exterior angle in the triangle is the sum of remote interior angles124 = x + 90x = 124 - 90x = 34rajesh is working out the are of the cirle with radius 10 he writes area=3.142x20 explain why rajesh is wrong
Answer:
100π = 314.1592654
Step-by-step explanation:
area of a circle πr²
π×10²
10×10 =100
100×π
Based on problems 1-3, what can you conclude about
triangle ABC's orthocenter if x is less than 90°?
What happens to the orthocenter as x increases towards 90°?
What happens to the orthocenter as x reaches 90°?
What happens to the orthocenter as x increases to larger than 90°?
Answer:
Step-by-step explanation:
smaller
larger
bigger
larger
A cuboid box has a square base and a height of 0.8 m, as shown in the diagram below. If
the volume of the box is 0.288 m3
, calculate the total surface area of the box.
Answer:
c
Step-by-step explanation:
because the explanation its just c
Help Need ASAP
Paula makes purses. The materials cost $2.25 per purse. She sells them for $5.00 each. Paula wants to invest $5000 for some new equipment. Which of these could be used to determine x, the number of purses Paula must sell to pay for the new equipment?
Responses
5.00x - 2.25x = 5000
5.00x + 2.25x = 5000
5.00x = 5000
2.25x = 5000
The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Paula makes purses and the materials cost $2.25 per purse.
She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.
Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.
The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.
learn more about functions here :
https://brainly.com/question/12431044
#SPJ1
Answer: 5.00x - 2.25x = 5000
Step-by-step explanation:
If the area to the left of x in a normal distribution is 0.193, what is the area to the right of x?
The area to the right of x in the normal distribution is 0.807
What is the normal distribution?The normal distribution is the probability distribution that helps to find the probability for continuous variables.
For a probability x, for a normal distribution, we have that
P(X ≤ x) + P(X ≥ x) = 1
How to find the area to the right of x?Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.
Since P(X ≤ x) + P(X ≥ x) = 1 where
P(X ≤ x) = area to the left of x P(X ≥ x) = area to the right of xMaking P(X ≥ x) subject of the formula, we have that
P(X ≥ x) = 1 - P(X ≤ x)
Given that P(X ≤ x) = 0.193
Substituting this into the equation, we have
P(X ≥ x) = 1 - P(X ≤ x)
P(X ≥ x) = 1 - 0.193
P(X ≥ x) = 0.807
So, the area to the right of x is 0.807
Learn more about normal distribution here:
https://brainly.com/question/28096232
#SPJ1
The digit 7 appears twice in
the product.
Answer:
The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21
(Lesson 22)
P=L(+)
a. Find the monthly payment P on a $75,000 loan with an
annual interest rate of 4% (let r= .9967) and a term of
20 years (n = 240 months). Show your work below and
circle your final answer.
The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
Given that,
We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).
We know that,
Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)
Here,
P is principal amount $75,000
n is number of months 240 months
i is interest rate 4% is 0.04
=P(i(1+i)ⁿ/(1+i)ⁿ-1)
=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)
=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)
=75,000(0.04(12246.20236)/(12245.20236)
=75,000(0.04×1.000081665)
=38455
Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
To learn more about monthly visit: https://brainly.com/question/22891559
#SPJ9
I need help! could someone help me with this? is from Imagine Math
Answer:
1st: One solution
2nd: Infinite many solutions
3rd: No solution
4th: No Solution
5th: One Solution
Step-by-step explanation:
1st:
The solution is (6,9)
x = 6 if a vertical line going though (6,0)
y = 9 is a horizontal line going through (0,9)
The two lines with intersect at (6,9)
2nd:
3y = 15x + 6 If you divide all the way through by 3, you get
y = 5x + 2
This is identical to the first equation given. Since it is the same line, the answer is infinite many solutions.
3rd:
3y = x + 2 Divide all the way through by 3
y = 1/3 x + 2/3
9y = 3x + 7 Divide all the way through by 9
y = 1/3 x + 7/9
Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.
4th:
Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.
5th:
2y = 3x Divide both sides by 2
y = 3/2
-5y = -10 Divide both sides by -5
y = 2x
These equations are proportional so they go through the origin. They both have a y intercept of zero, so they intersect at (0,0). The answer is one solution.
Graph the polygon with the given vertices and its image after a reflection in the line y = -x .
A(2, 0), B(3, 4), C(6, 4), D(5, 0)
As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.
Transformation:
Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Given,
Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.
Now we have to plot the graph with the given vertices and its image after a reflection in the line y = -x .
Here reflection refers flipping of a figure.
Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)
For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:
A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)
The image of the polygon is attached below.
To know more about Transformation here.
https://brainly.com/question/11709244
#SPJ1
You are on a safari and pass by some hippos and birds (the kind
that hang out on top of the hippos). You see a total of 42 animals ane
114 legs. how many of each animal were there?
Answer:
15 hippos27 birdsStep-by-step explanation:
You have a total of 114 legs among hippos and birds, of which there are a total of 42. You want the number of each kind of animal.
SetupLet h represent the number of hippos. Then 42-h is the number of birds, and the total number of legs is ...
4h +2(42 -h) = 114
SolutionSimplifying the equation gives ...
2h +84 = 114
2h = 30 . . . . . . subtract 84
h = 15 . . . . . . . . number of hippos
42 -h = 27 . . . . number of birds
There were 15 hippos and 27 birds.
What is the solution set for 5x−5=15, given the replacement set {0, 1, 2, 3, 4}?
Responses
x = 4
x, = 4
x = 3
x, = 3
x = 2
x, = 2
x = 1
x, = 1
x = 0
The solution to the equation 5x - 5 = 15 in the replacement set is x = 4
How to solve the equations using the replacement sets?From the question, we have the following equation that can be used in our computation:
5x - 5 = 15
The replacement set is given as
{0,1, 2, 3, 4}
So, we replace the variables using the elements in the replacement set
When x = 0, we have
5(0) - 5 = 15
-5 = 15 -- false
When x = 1, we have
5(1) - 5 = 15
0 = 15 -- false
When x = 2, we have
5(2) - 5 = 15
5 = 15 -- false
When x = 3, we have
5(3) - 5 = 15
10 = 15 -- false
When x = 4, we have
5(4) - 5 = 15
15 = 15 -- true
Hence, the value of the equation is x = 4
Read more about equations at:
brainly.com/question/2972832
#SPJ1
Evaluate the algebraic expression for the given values of the variables.
x²-13(x-y), for x = 7 and y=4
When x = 7 and y=4, x² - 13(x - y) =
The answer to the algebraic expession is 10.
What is algebraic expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression.
Main Body:
We have to find the value of x²-13(x-y) at x=7 and y=4
Now substitute the value of x,y in the expression
=(7)²-13(7-4)
= 49-13(3)
= 10
Hence the answer is 10.
to learn more about algebraic expression click on the link below..
https://brainly.com/question/395066
#SPJ13
a man travels xkm at 60 km per hour and ykm at 40 km per hour and takes 11/4 hours for the Journey,if the time taken for 5x km at 40 km per hour and 3y km at 50 km per hour is 11 hours 42 minutes find X and Y
The value of the x is 60 km and the value of the y is 70 km.
Given that a man travels x km at 60 km/h and y km at 40 km/h and the total time traveled is 11/4 i.e 2.75 h.
Let's suppose that the time traveled for the x km is t1, time traveled for the y km is t2 and total time is T ,so by using the speed distance formula t1 & t2 will be :
t1 = x/60 and t2 = y/40 ;
T = t1 + t2;
i.e 2.75 = x/60 + y/40 ;
Multiply both sides with 120,
330 = 2x + 3y ............i
Now given that man traveled 5x km at 40 km/h and 3y km at 50 km/h in total time of 11. 7 hours. Similarly the equation for this situation will be :
T = t1 + t2;
x/8 + 3y/50 = 11.7 ;
Multiply both sides with 200, we will get
25x + 12y = 2340 .........ii
Now by simplifying the equation i and ii we will get the value of x and y which are 60 and 70 respectively.
To know about about more value of x and y https://brainly.com/question/22625679
#SPJ1
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.
How to find Sandy hour wages and commission?Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.
She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.
The amount she will earn in her hourly wages and commission is as follows:
amount earn in commission = 15% of 2046
amount earn in commission = 15 / 100 × 2046
amount earn in commission = 30690 / 100
amount earn in commission = 306.9 dollars
Therefore,
amount earn in hourly wages = 2046 - 306.9
amount earn in hourly wages = 1739.1 dollars.
learn more on commission and wages here: https://brainly.com/question/1153438
#SPJ1
