The constant term of this polynomial function with real coefficients will be - 240.
We are given the zeroes of the equation as:
16 and 1 - 2i
Now, we know that, the imaginary root are always in a pair, so the third root will be:
1 + 2i
This means that the factors of the cubic polynomial will be:
(x - 16)
(x - [1 - 2i])
(x - [1 + 2i])
The leading coefficient is 3, so the polynomial function will be:
y = 3 (x - 16) (x - [1 - 2i]) (x - [1 + 2i])
Now, the constant term will be:
3 (- 16) (1 + 2i) (1 - 2i)
( - 48) (1 - 4i²)
= ( - 48) (5)
= - 240
Therefore, the constant term of this polynomial function with real coefficients will be - 240.
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A rectangle with length 10 inches and width 5 inches. A triangle sits on top of the rectangle. The triangle has a base of 10 inches and height of 3 inches.
What is the area of the figure shown?
in²
which produces a rational number when multiplied by 0.5
Answer:
A
Step-by-step explanation:
1/3 x 0.5 = 1/6 which is a rational number
I think you should look up the meaning of rational number to know what is the correct answer
what are the best anime jobs that use math?
Answer:
Possibly Design and 3d printing
Step-by-step explanation:
3D printing and design requires precise measurements and angles. Maybe you can look into jobs with these requirements?
Hope this helped :)
Answer:
Careers that involve math
Step-by-step explanation:
.................................
Answer:
identify my own strengths
interests and challenge
help pleaseee this is due tomorrow
Answer:
4.67
Step-by-step explanation:
You deposit $500 in a savings account for 8 years. How much interest will you earn if the account earns 7% simple interest annually?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (500)(0.07)(8) \implies I = 280[/tex]
Answer:
$280
Step-by-step explanation:
500x7%=35
35x8=280
I need the answer for this, thanks
PLEASE HELP ME WITH MATH
I AM GOING TO FAIL!!
Will give 17 points!!!!
a. Han wrote (1/2, 0) as x-intercept of the line instead of (2, 0).
b. The x-intercept: (2, 0)
The y-intercept: (0, 5)
What is the X-intercept and Y-intercept of a Line?The y-intercept of a line is the corresponding value of y when the value of x is equal to zero.
On the other hand, the x-intercept of a line is the corresponding value of x when the value of y is equal to zero.
Y-intercept is (0, b), while x-intercept is (b, 0), where b is the value of the point on the axis that is being intercepted.
In slope-intercept form, y = mx + b or y = b + mx, the y-intercept is represented as b, which is (0, b).
Given the equation in slope-intercept form as y = 5 - 10/4x, the y-intercept, b = 5. Therefore, is expressed as (0, 5).
To find the x-intercept, substitute y = 0 into y = 5 - 10/4x:
0 = 5 - 10/4x
Solve for x
-5 = -10/4x
-20 = -10x
-20/-10 = x
x = 2
The x-intercept is (2, 0), while the y-intercept is (0, 5).
Therefore:
a. The Han got the x-intercept wrong, it should be (2, 0), not (1/2, 0).
b. The x-intercept is (2, 0), while the y-intercept is (0, 5).
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how do you find the radius of a circle when given the central angle and arc length
arc length = 82 central angle = 135 degrees
The radius of a circle is determined as 27.95 units.
What is relation between arc and radius of circle?The arc length formula for a circle is times the radius of a circle. The arc length formula in radians is as follows: arc length = θ × r, where is in radian.Now the formula for the arc length when the central angle is given in the degrees;
arc length = (θ/360°)×(2πr)
Where, r is the radius of the circle and π = 3.14.
Write the formula for r;
r = (arc length/2π)×(360°/θ)
For the given values in question;
arc length = 82 central angle = 135 degrees.
r = (82/2×3.14)×(360°/135°)
r = (13.05)×(2.67)
r = 27.95
Therefore, the radius of the circle is found as 27.95 units.
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Write a function that gives the length of the hypotenuse of an isosceles right triangle with side length s. Evaluate the inverse of the function to find the side length of an isosceles right triangle with a hypotenuse of 6 in.
A function that gives the length of the hypotenuse of an isosceles right triangle with side length s is given by h(s)=s√2 and the length of the side of the triangle is approximately 4.24 inches.
The hypotenuse of a right angled triangle is defined as the longest side of the triangle. The hypotenuse is also located opposite the right angle.
From the Pythagorean Theorem we know that for a right angled triangle, the sum of the square of the legs of the triangle is equal to the square of the hypotenuse.
Given legs of the right triangle is s. Let us consider a function h(s) for the hypotenuse.
Therefore we can define the function h(s) as
h(s)=s√2
The inverse of the function can be written as
y=s√2
or, s=y²/2
Hence the inverse function is:
h⁻¹(s)=s²/2
Now for hypotenuse = 6 inches.
Each side can be calculated using the inverse function h⁻¹(s)=s²/2.
s=6÷√2
or, s=4.242...
Hence the length of the side of the triangle is approximately 4.24 inches.
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all of them please i need help with it its hw
The correct algebra properties are listed below:
EDHAIFCBGWhat properties are used in each case of algebraic operations?
In this problem we find nine cases of mathematical operations with real numbers, each case has to be defined by defining the appropriate property according to real algebra. Now we proceed to define each case:
11 + 0 = 11 Modulative property of addition (Correct choice: E)x · (y · z) = (x · y) · z Associative property of multiplication (Correct choice: D)8 + (- 8) = 0 Existence of additive inverse (Correct choice: H)14 + 20 = 20 + 14 Commutative property of addition (Correct choice: A)2 × (1 / 2) = 1 Existence of multiplicative inverse (Correct choice: I)22 × 1 = 22 Modulative property of multiplication (Correct choice: F)(19 + 12) + 8 = 19 + (12 + 8) Associative property of addition (Correct choice: C)a × 9 = 9 × a Commutative property of multiplication (Correct choice: B)7 · (4 + 11) = 7 · 4 + 7 · 11 Distributive property (Correct choice: G)To learn more on algebra properties: https://brainly.com/question/1448147
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Does every function have an inverse which is a function? Does every relation have an inverse which is a relation?
No, all functions do not have an inverse functions. Those that do exists named invertible.
What is meant by inverse function?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
In mathematics, an inverse function (or anti-function) exists as a function that "reverses" another function: if the function f used to an input x gives a result of y, then using its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y.For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y. This property ensures that a function g: Y → X exists with the necessary relationship with f.No, all functions do not have an inverse functions. Those that do are called invertible.
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Set up an equation and use it to solve for x.
50
(4x + 2)
Answer:
x = 12
Step-by-step explanation:
Vertical angles are congruent
50 = 4x + 2 Subtract 2 from both sides
48 = 4x Divide both sides by 4
12 = x
5 of 105 of 10 Items 34:04 Skip to resources Question The Community Center has exercise classes on Monday and Friday. The Monday class is 1 3 hours and the Friday class is 1 1 hours. 4 2Patrick attended both exercise classes last week and this week. How many hours did Patrick spend in exercise classes last week and this week? Responses A 6 1 hours 26 1 hours 2 B 3 1 hours 43 1 hours 4 C 6 1 hours 46 1 hours 4 D 8 1 hours 2
Answer:
Monday class is 1 3 hours and the Friday class is 1 1 hours. 4 2Patrick attended both exe
Step-by-step explanation:
Which equation below is graphed? Question 6 options: y = 3x+2 y =-3x +2 y = 3x - 2 y = -3x - 2
The linear function that contains the points (0,3) and (-1,5) is given by:
y = -2x + 3.
What is the missing information?
The graph is not given and I couldn't find the problem on a search engine, hence I am going to suppose that two points on the graph are (0,3) and (-1,5).
You can select the value of y when the function crosses the y-axes(y-intercept) and another point and follow the same procedure I am going to do here.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that when x = 0, y = 3, hence the slope is of b = 3. When x = -1, y = 5, hence the slope(change in y divided by change in x) is given by:
(3 - 5)/(0 - (-1)) = -2.
Hence the function is:
y = -2x + 3.
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Write an equation in slope-intercept form of the line that bisects the angle formed by BA and BC
B
v=D
y = -x +2 an equation in slope-intercept form of the line that bisects the angle.
What exactly does slope intercept mean?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.Given:
Angled formed by ray BA and ray BC is 90 degrees.
To find:
The equation of line that bisects the angle formed by ray BA and ray BC.
If a line bisects the angle formed by ray BA and ray BC, then it must be passes through point B and makes angles of 45 degrees with ray BA and ray BC.
It is possible if the line passes though point B(-1,3) and other point (-2,4).
Equation of line is
y - y₁ = y₂ - y₁/x₂ - x₁ ( x - x₁)
y - 3 = 4 - 3 / - 2 - ( -1) ( x - ( -1)
y - 3 = 1/-1 ( x + 1 )
y - 3 = -x -1
Add 3 on both sides
y = -x -1 + 3
y = -x +2
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Brandi jogged for 2/1:2 mikes in 30 minutes sharana jogged 3/1:2 miles in 3:4hours who jogged at a slower rate
Based on the information provided, neither Brandi nor Sharana jogged at a slower rate.
What is rate?Rate can be defined as the speed at which an event happens or an object moves over a particular period of time.
It is also known as the ratio at which two or more term, quantities or objects with different units are compared.
The formula for rate is expressed as;
Rate = distance/ time
From the information given, we have that;
Brandi jogged a distance = 2/1 : 2 = 2 × 1/ 2 = 1 mile in 30 minutesSharana jogged a distance = 3/1 : 2 = 3/ 2 = 1. 5 miles in 3/ 4 × 60 minutes = 45 minutesSubstitute the values
Brandi's rate = 1/ 30 = 0. 03
Sharana's rate = 1. 5/ 45 = 0. 33
From the values gotten, we can see that neither Brandi nor Sharana jogged at a slower rate.
Thus, neither Brandi nor Sharana jogged at a slower rate.
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Kumi is 16 years old. His father is 44 years old. How many years ago was Kumi's father five times as old as KUMI
Answer:
9
Step-by-step explanation:
4-x = 5(16-x)
44-x = 80-5x
4x = 36
x = 9
Find the sum of all decent fractions whose denominator is equal to 20
a) 10
b) 20
c) 9.5
d) 8
Answer:
B,A
Step-by-step explanation:
hope that's right
The sum of all decent fractions with a denominator of 20 is 4.
Thus, option (d) is correct.
To find the sum of all decent fractions whose denominator is equal to 20, consider fractions with numerators that are coprime to 20 (i.e., the numerator and 20 have no common factors other than 1).
The decent fractions with a denominator of 20 can be written as:
1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, and 19/20.
To find the sum, add up these fractions:
Sum = 1/20 + 3/20 + 7/20 + 9/20 + 11/20 + 13/20 + 17/20 + 19/20
Sum = (1 + 3 + 7 + 9 + 11 + 13 + 17 + 19) / 20
Sum = 80 / 20
Sum = 4
Therefore, the sum of all decent fractions with a denominator of 20 is 4.
Thus, option (d) is correct.
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How do you write five hundred thousandths in number?
Answer: the answer is: 500,000
Simplify the expression. Write the answer in scientific notation.(6 x 10^-4)(6 x 10^-6)
An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . The simplified expression of (6 x 10⁻⁴)(6 x10⁻⁶) is 36 x10⁻¹⁰.
What is Expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
(6 x 10⁻⁴)(6 x10⁻⁶) is the given expression
Now multiply 6 with 6 and 10⁻⁴ with 10⁻⁶
36 x 10⁻⁴x 10⁻⁶
We need to add the powers of same base.
36 x10⁻⁴⁻⁶
36 x10⁻¹⁰
Therefore the simplified expression of (6 x 10⁻⁴)(6 x 10⁻⁶) is 36 x10⁻¹⁰.
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Determine whether each function is an example of exponential growth or decay. Then find the y -intercept.
y=7/8(18)x
The function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.
An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.
We are given a function:
y = 7 / 8 ( 18 ) ˣ
We need to tell whether is is a exponential growth or decay function.
We can see that the value of a ˣ = (18) ˣ
So, the value of a = 18.
Since, it is an integer and not a fraction, its value will increase with the increase in exponent x.
So, it will be a exponential growth function.
Therefore, we get that, the function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.
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kate and jean paint a house together in 6 days
Answer:
Okay? whats the question
Step-by-step explanation:
Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. the 600 residents in this study is an example of a(n) _____
Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The 600 residents in this study is an example of a sample.
Those people who make up a sample are taken from a broader population. Sampling is the process of deciding which group you will use to gather data for your study.
In order for a sample to be representative of the population we are interested in investigating, each participant must have an equal chance of being randomly chosen for the study.
For example, you could interview a sample of 100 students if you were examining the attitudes of students at your university.
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5. A shark is swimming 60 feet below the surface of
the ocean. There is a fish that is 25 feet deeper
in the water. Use the expression (-60) + (-25) to
describe the fish's location relative to the surface
of the ocean.
Answer:
-60x+(-85y)
Step-by-step explanation:
Solve the equation b over 27 equals negative 3 for b.
Answer:
b= -81
Step-by-step explanation:
b/27 = -3
Multiply both sides by 27 and simplify
NEED HELP WITH GEOMENTRY ASAP
Answer:
86????
Step-by-step explanation:
I am not certain, but wouldn't it be 86?
Given the function, calculate the following values
Answer:
6, 2, 14
Step-by-step explanation:
[tex]x=-2 \implies x<1 \implies f(-2)=2(-2)^2-2=6 \\ \\ x=1 \implies 1 \leq x<2 \implies f(1)=2 \\ \\ x=2 \implies x \geq 1 \implies f(2)=4(2)^2-2=14[/tex]
Round to the nearest ten, then estimate the product. 35 x 99 = ___
a. 2,700
b. 3,000
c. 3,600
d. 4,000
Answer:
The answer is 4,000.
Step-by-step explanation:
The closest to 35xn= 3,465
Answer:
Step-by-step explanation:
35 to the nearest 10 is 40 and 99 to the nearest 10 is 100 so 4 times 100 is 4,000 so your answer should be d. 4,000
The sum of two numbers is 14. One number is two less than three times the other. Write an equation to represent the situation
using as a variable.
Answer:
Number 1 is 4
Number 2 is 10
Step-by-step explanation:
Number 1 is x
Number 2 is 3x - 2
so x + (3x - 2) = 14
x + 3x - 2 = 14
4x = 14 + 2
4x = 16
x = 4
so
Number 1 is 4
Number 2 is 3(4) - 2 = 10