Answers
The zeroes of the function f(x) = x⁵ - 8x³ - 9x are x = 0, 3, - 3, i, and - i.
Consider the function,
f(x) = x⁵ - 8x³ - 9x
x⁵ - 8x³ - 9x = x( x⁴ - 8x² - 9 )
Factoring: x⁴ - 8x² - 9
The coefficient of x⁴ is 1, the coefficient of -8x² is - 8, and - 9 is the constant term.
x⁴ - 8x² - 9 = x⁴ - 9x² + x² - 9 = x²( x² - 9 ) + 1( x² - 9 )
x⁴ - 8x² - 9 = ( x² - 9 ) ( x² + 1 )
So,
x⁵ - 8x³ - 9x= 0
x( x⁴ - 8x² - 9 ) = 0
x( x² - 9 ) ( x² + 1 ) = 0
x( x - 3 )( x + 3 ) ( x² + 1 ) = 0
Therefore, the zeroes of the function are:
x = 0, x = 3, x = - 3, and
x² + 1 = 0
x² = - 1
x = ± √( - 1 ) = ± i
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Related Questions
Find the slope of the line.
EAT
(3,1
-8-
O A.
(3-1)
O
What is the slope of the line? Select the correct choice below and, if
necessary, fill in the answer box to complete your choice.
The slope of the line is. (Type an integer or a simplified
fraction.)
B. The slope of the line is undefined.
Answers
Option A. The slope of the line is zero
How is the slope calculated?
First point = [tex](x_1,y_1)=(-3, -1)[/tex]
Second point = [tex](x_2,y_2)= (3,-1)[/tex]
Slope of the line = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m =\frac{-1+1}{3+3} \\\\m = \frac{0}{3} \\\\m= 0[/tex]
Thus the slope of the line is zero.
What is a zero slope?
The slope will be 0 if time passes without any change and is called a zero slope. Here each y point in a horizontal line is identical. This implies that the slope will always be zero because the numerator of the fraction will always equal zero.A vertical line is an undefined slope where the x-points never change as the y-points rise and fall. The zero slope equation, or y = b, is the formula for a line with no slope, also known as a horizontal line.To learn more about zero slope, refer:
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(3.22x10^3)-(2.96x10^3)
Answers
The value of (3.22 - 2.96)×10³ is 0.26×10³.
What is scientific notation?We use scientific notation for writing large numbers in compact form.
Scientific notation is written in base multiplied by 10 raised to some power where 0 ≤base < 10 scientific notation also has an alternative name which is known as engineering notation.
We know when we have numbers in scientific notation with the same exponent value we can do arithmetic operations to the base.
∴ (3.22x10³) - (2.96x10³).
= (3.22 - 2.96)×10³.
= 0.26×10³.
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the table show how many points eduardo scored during each game use mental math to find how many points he scored
Answers
The total points scored by Eduardo in the first three games is 97.
We are given a table that shows the points scored by Eduardo during three games.
In game 1, he scored 52 points.
In game 2, he scored 19 points.
In game 3, he scored 26 points.
In game 4, he scored 10 points.
We need to find the sum of the total points scored by him in the first three games.
A summation, also known as a sum, is the outcome of adding numbers or quantities arithmetically. A summation always has an even number of terms.
The points are 52 + 19 + 26 = 97.
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Please solve with explanation so I can use as reference in the future thank you!
Answers
Answer:
x=24
Step-by-step explanation:
y = x*c
x=2, y=7
2*c=7 => c=7/2
x*7/2 = 84
x = 84*2/7
x = 12*2
x = 24
I hope this helps TwT
Determine whether the statement is always, sometimes, or never true. Complete the explanation.If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greaterthan 1.This statement is (select) true. If line m is parallel to line n, then the lines have (select)slope. Therefore, if the slope of line m is greater than 1, the slope of line m (select) greater than 1.
Answers
The given statement is
If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greater
than 1.
This statement is always true because parallel lines have the same exact slope, otherwise they wouldn't be parallel.
Therefore, the complete statement would be
This statement is always true. If line m is parallel to line n, then the lines have an equal slope. Therefore, if the slope of m is greater than 1, the slope of n is always greater than 1.
The range of the function f(x)= x^2 + 2x - 8 is all real numbers..
Answers
Simplify the expression x^2+2x-8 to obtain the equation as complete square.
[tex]\begin{gathered} x^2+2x-8=x^2+2x+1-1-8 \\ =(x^2+2x+1)-9 \\ =(x+1)^2-9 \end{gathered}[/tex]The value of square terms is 0 or postive, so range of the expression x^2+2x-8 is,
[tex]\lbrack-9,\infty)[/tex]So correct option is B greater than or equal to -9.
A line includes the point (7,5)has a slope of 1.What is its equation in slope intercept form?
Answers
Given:
Point( 7, 5)
x = 7 and y=5
slope(m) = 1
We need to first find the intercept.
Substitute x=7, y=5 and m=1 into y=mx + b and solve for intercept(b)
5 = 1(7) + b
5 = 7 + b
5 - 7 = b
-2 = b
Now, form the equation by substituting the value of the slope and intercept into y=mx + b
y = x - 2
help me please
thank you
Answers
Answer:
is a functiondomain: [-6, 2]range: [-4, 0]Step-by-step explanation:
You want to know if the graph of the semicircle centered at (-2, 0) with radius 4 extending below the x-axis is a function. You also want to know its domain and range.
FunctionThe graph passes the vertical line test. That is, no vertical line intersects the graph in more than one place. That means the relation is a function.
DomainThe domain of the function is the horizontal extent of the graph. The solid dots at the extreme points of (-6, 0) and (2, 0) indicate those points are part of the domain. The domain also includes all x-values between them. In interval notation, the domain -6 ≤ x ≤ 2 is written as ...
[-6, 2]
RangeThe range is the vertical extent of the graph. The semicircle extends from a low point of (-2, -4) to high points on the x-axis. Thus its range is -4 ≤ y ≤ 0, written in interval notation as ...
[-4, 0]
__
Additional comment
The brackets used in interval notation are square brackets if the end points are included in the interval. Otherwise, they are round brackets (parentheses).
I NEED THIS ANSWER SOON!
Rewrite the expression 6a + 21 to demonstrate the distributive property. Describe how the rewritten expression can be verified to be equivalent to 6a + 21.
Answers
Answer:
it can be verified as 2a + 7
16.What is the equation of the vertical asymptote for the function f(x) = x-1,x+4(A) x=1(B) x=-1(C) x=4(D) x=-417.
Answers
The vertical asymptotes is when the denominator is 0
Hence we have
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]X=-4 is the vertical asymptote
The right option is D
i need help asap with these questions please worth 100 of my grades
Answers
Use the rule to complete the input/output table. Rule: the output is t-3•Input t: 17, 20, 22, 24•output r: On the home work it’s set as a table
Answers
Step 1
Write the rule
r = t - 3
Step 2:
Find each output for corresponding input.
When t = 17
r = 17 - 3 = 14
When t = 20
r = 20 - 3 = 17
When t = 22
r = 22 - 3 = 19
When t = 24
r = 24 - 3 = 21
Step 3
Final answer
what is the image point of (-7 6) after a rotation of 270 degrees counterclockwise
Answers
270° counterclockwise about the origin. Check the picture below.
A certain group of women has a 0.97% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answers
The probability that a randomly selected women does not have red/ green color blindness is 0.9903.
The probability of a woman has red/ green color blindness is,
P (Color blindness) = 0.0097.
The probability that a randomly selected women does not have red/ green color blindness is,
P (No Color blindness) = 1 - P (Color blindness)
= 1 - 0.0097
= 0.9903
Thus, the probability that a randomly selected women does not have red/ green color blindness is 0.9903.
Hence the probability that the women does not have red/green color blindness is 0.9903.
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Name the quadrant in which each of the points lies -1, -8
Answers
Given the point ( -1, -8 )
The x-coordinate of the point = -1
The y-coordinate of the point = -8
So, x < 0, y < 0
So, the point lies in the third quadrant
So, the answer will be Quadrant 3
Which polynomial is prime?O 3x²+3x²-2x-2O 3x-2x²+3x-4O4x²+2x²+6x +3O4x³+4x²-3x-3
Answers
Explanation:
Concept:
If the only factors a polynomial are 1 and itself, then that polynomial is prime.
The first polyonial will be factorised below as
[tex][/tex]Zena's Z-score on the chemistry final was 0.65. If the class mean on the final was 78, the the standard deviation was 12, and the distribution was normal, what was Zena's raw score?
Answers
Zena's raw score in the chemistry test is 85.8
How to determine the raw score of the test?From the question, the given parameters are
Mean score of the class = 78Standard deviation of the class = 12z-score of the test = 0.65The z-score of the distribution is calculated using the following z-score formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
So, we have the following equation
0.65 = (Raw score - 78)/12
Cross multiply in the above equation
Raw score - 78 = 7.8
Add 78 to both sides
Raw score = 78 + 7.8
Evaluate
Raw score = 85.8
Hence, the raw score is 85.8
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What is (a)
5(x+1)+4_4
6
Answers
Answer:
x=-1
Step-by-step explanation:
Which of the following is the coordinate of the minimum?O (-9,-4)O (4,-6)0 (0,2)O (9,5)O (1,3)
Answers
In this case the answer is very simple.
The minimums are represented by the valleys.
Analyzing the graph we can say that the minimum would be:
(4 , -6)
That is the solution.
is 0.49 a rational or irrational number? Explain how you know.
Answers
The decimal 0.49 is a rational number.
What is a rational number?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers, can be used to represent a rational number.
A rational number is a number that can be expressed as a fraction where the numerator is a whole number and the denominator is a whole number .
In this case, 0.49 is the same as 0.49 over 1. In other words, it can be seen that 0.49 can be written with a numerator and denominator like 49/100.
Therefore, it's a rational number.
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Kevin needs to rent tables for his party. There will be 26 people at his party. Each table can seat 4 people. How many tables does Kevin need to order? Write a multiplication and division sentence that will help you answer the question. Use n for the unknown. __ x __ =___ ___÷___=____
Answers
Answer:
6.5
Step-by-step explanation:
Well if you do 4 x n=26 26/4=n
Find what X equals [tex]2(x + 7) = - 4x + 14[/tex]
Answers
To solve the expression: 2(x + 7) = - 4x + 14, just follow these steps:
1. Distribute the product on the left side of the equation:
2(x + 7) = - 4x + 14
2*x + 2*7 = - 4x + 14
2x + 14 = -4x + 14
2. subtract 14 on both sides:
2x + 14 - 14 = -4x + 14 - 14
2x = - 4x
3. Add 4x on both sides:
2x + 4x = -4x + 4x
6x = 0
4. Divide both sides by 6:
6x/6 = 0
x*6/6 = 0
x*1 = 0
x=0
Then x equals 0
Joy's investment of $3600 grows to $4800 in 48 weeks. What simple interest did she earn?
Answers
Answer:
answer
down
below
8 294 400
help me please
thank you
Answers
In interval notation, the interval notation has [tex](-\infty, -4)[/tex].
if a (9,18) and b = (1,12) what is the length of ab
Answers
To calculate the lenght of AB we'll use the formula for distance between two points.
Remember that the disnatce between points
[tex]\begin{gathered} (x_1,y_1) \\ \text{and} \\ (x_2,y_2) \end{gathered}[/tex]is:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Using this, and the data given,
[tex]\begin{gathered} AB=\sqrt[]{(1_{}-9)^2+(12-18)^2} \\ \rightarrow AB=\sqrt[]{(-8)^2+(-6)^2} \\ \rightarrow AB=10 \end{gathered}[/tex]This way, the lenght of AB is 10 units
please help i dont have as much time
Answers
Answer:
f(2) = -7
Step-by-step explanation:
f(x) = -2x-3
f(2) = -2(2)-3
f(2) = -4-3
f(2) = -7
Hello I am quite confused by this question may you please help me solve and explain this? thank you:)
Answers
Given the mean score of a group of people in a quiz, the standard deviation of the scores of the people, and the score of a person, we can easily determine the z-score like this:
[tex]z=\frac{x-μ}{σ}[/tex]Where σ is the standard deviation, μ is the mean score and x is the score. By replacing 78 for μ, 4.2 for σ and 80 for x, we get:
[tex]z=\frac{80-78}{4.2}=0.4762[/tex]Then the z-score equals 0.4762. In this case, the score of 80 is a usual value since it is within one standard deviation of the mean.
x+6=4x+1-3xsolve for x
Answers
we place the x's on the same side and the number on the other side
[tex]\begin{gathered} x-4x+3x=1-6 \\ (1-4+3)x=-5 \\ 0x=-5 \\ 0=-5 \end{gathered}[/tex]x is removed, and equality is meaningless, so x has no solution
A group of students are making a flag to represent their team on game day. The students are going to sew together pieces of fabric to make a design and glue it to the center of the flag. The design is made up of a rectangle, triangle, and semicircle. The dimensions of the design are shown in the diagram.
Answers
Explanation:
First we have to find the areas of each piece and then add them up.
The area of a triangle is the length of the base multiplied by its height and divided by 2:
[tex]A_{\text{triangle}}=\frac{12in\times6in}{2}=36in^2[/tex]The area of a rectangle is the product of the lengths of the sides:
[tex]A_{\text{rectangle}}=10in\times12in=120in^2[/tex]The area of a circle is pi times the radius squared. For a semicircle it's half the area of the circle:
[tex]A_{\text{semicircle}}=\frac{\pi r^2}{2}=\frac{\pi\cdot5^2}{2}=\frac{25}{2}\pi\approx40in^2[/tex]The total area of the flag is:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{rectangle}}+A_{\text{semicircle}} \\ A=36in^2+120in^2+40in^2 \\ A=196in^2 \end{gathered}[/tex]Answer:
B. 196 in²
Simplify the expression. 5+8(37)
Answers
Answer:
301
step by step explanation:
5+(8)(37)
=5+296
=301
Answer:
301
Step-by-step explanation:
using pemdas:
5+(8)(37)
=5+296
=301
