Final answer:
The mean usually has the greatest value among measures of central tendency like the median and mode, particularly in skewed distributions. The range is not a central tendency measure but represents the difference between the highest and lowest values.
Explanation:
When comparing different measures of central tendency, the mean usually has the greatest value in a skewed distribution. The mean is the arithmetic average of all the numbers, while the median is the middle value when the numbers are sorted, and the mode is the number that appears most frequently. Examples given show that in various cases, the mean tends to be larger than the median and mode, especially when the data set is right-skewed, which is when there are values that are significantly higher than the rest. Range, however, represents the difference between the highest and lowest values in the set, and is not a measure of central tendency, but rather a measure of spread.
How much fencing would he need?
The width of the garden would be found by dividing the area by the length.
Width = 324 / 24 = 13.5 feet.
Now you need to find the total perimeter of the garden:
Perimeter = 2 x length + 2 x width
Perimeter = 2 x 24 + 2 x 13.5
Perimeter = 48 + 27
Perimeter = 75 feet.
He will need 75 feet of fence.
Answer:
75 feet of fence
Step-by-step explanation:
324/24=13.5
13.5+13.5+24+24=75
what is the average rate of change for this quadratic function for the interval from x= -4 to x= -2
Answer:
B. 6.
Step-by-step explanation:
We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].
We will use formula [tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(-2)-f(-4)}{-2--4}[/tex]
[tex]\text{Average rate of change}=\frac{6--6}{-2+4}[/tex]
[tex]\text{Average rate of change}=\frac{6+6}{2}[/tex]
[tex]\text{Average rate of change}=\frac{12}{2}[/tex]
[tex]\text{Average rate of change}=6[/tex]
Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.
Answer:
6
Step-by-step explanation:
just took on A P E X
What is the slope of the line that is represented by the equation y−15=−6(x+7)?
Enter your answer as a number, like this: 42
Or, if your answer is a fraction, such as 314, enter it like this: 3/14
Answer:
slope = - 6
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 15 = - 6(x + 7) ← is in point- slope form
with slope m = - 6
The slope of the line that is represented by the equation y-15=-6(x+7) is -6.
The given equation is y-15=-6(x+7).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The standard form of the slope intercept form is y=mx+c.
Where, m=slope and c=y-intercept
Here, y-15=-6(x+7) can be written as y-15=-6x-42
⇒ y=-6x-42+15
⇒ y=-6x-27
So, slope of an equation is -6.
Therefore, the slope of the line that is represented by the equation y-15=-6(x+7) is -6.
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Based on the function F(x)=x^4-3x^2-1 and the graph of G(x) below, which of the following statements is true
Analyzing the given function F(x), we can predict that it is a quartic function with various possible shapes and intersection points with the x-axis. However, a comparison or correlation to function G(x) cannot be accurately made without additional information about graph G(x).
Explanation:Given the function F(x)=x^4-3x^2-1 and the unspecified G(x) graph, it's difficult to make an accurate statement without observing the shape, slope, and specific points on the G(x) graph. However, by understanding the given function F(x), we can still provide some insights. The function F(x) here is a quartic function (as the largest exponent is 4). The graph of a quartic function can have various shapes - it may have zero, one or two extreme points, and it may pass through the x-axis at zero, two or four points. It is essential to look at two-dimensional graphing to properly analyze and correlate F(x) and G(x).
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how to find slope??................................
y2-y1/x2-x1
Y(subscript 2) - Y(subscript 1) / X(subscript 2) - X(subscript 1)
The formula for slope is the difference in y-values divided by the difference in x-values. the slope of a line is its steepness or its rate of change. There are 4 types of slopes positive, negative, zero, and undefined.
find the sum of the geometric series 6Σ3i i=2
[tex]
\sum_{3}^{6}2=\sum_{0}^{3}2=2+2+2=\boxed{6}
[/tex]
Or did you mean:
[tex]
6\times\sum{3i}=6\times\sum{6}=6\times6=\boxed{36}[/tex]
A line passes through the point (0, 2) and has a slope of -1/2. What is the equation of the line?
A) 2x+y=4
B)x-2y=4
C)x+2y=4
Answer:
C) x + 2y = 4Step-by-step explanation:
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept (0, b)
We have (0, 2) → b = 2 and m = -1/2. Substitute:
y = -1/2x + 2 multiply both sides by 2
2y = -x + 4 add x to both sides
x + 2y = 4
PLEASE HELP ME ASAPP !!
Answer:
1. you start with $ 3 and save $1 each month
2. your total savings is 3 times the number of month multiplied by itself
3. you save $3 the first month and then each month the amount triples
Step-by-step explanation:
1.
as y axis represents savings while x axis represents months
the statement "you start with $ 3 and save $1 each month"
is best described by the graph of straight line having slope of 1 and intercept of 3.
2. your total savings is 3 times the number of month multiplied by itself
= 3(x)(x)
= 3x^2
3. as y axis represents savings while x axis represents months
the statement "you save $3 the first month and then each month the amount triples" is best described by the exponential graph starting to rise from point (1,3) which means $3 save at 1 month.
!
Elaina is planning to save enough money to buy laptop computer. She needs $600. She already has $200 in her bank account. She is planning to deposit $40 each week into her bank account. Write an equation to represent Elaina’s plan to save for a laptop computer based on X weeks.
Answer: 200+40x=600
Step-by-step explanation:
200+40x=600
600-200=400
40x=400
40/40= 1 or x
400/ 40=10
x=10
A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
A.) 275 miles
B.) 200 miles
C.) 550 miles
D.) 1,100 miles
Answer:
275 miles
Step-by-step explanation:
3.5 cm = 175 and 2 more centimeters past that is 100 so 175 +100=275
so your answer is a 275 miles
The LCM of three numbers is 48. What are the numbers?
2, 3, 4
6, 16, 24
3, 8, 12
6, 8, 12
Answer:
{6, 16, 24}
Step-by-step explanation:
The least common multiple is the least number that is common to the multiples of two or more numbers.
The LCM of 2,3,4 is 12
The LCM of 6,16,and 24 is 48
The LCM of 3,8, 12 is 24.
The LCM of 6,8, 12 is 24.
The numbers that have the least common multiple of 48 is {6, 16, 24}
[tex]6=2\times 3[/tex]
[tex]16=2^4[/tex]
[tex]24=2^3\times 3[/tex]
The LCM is the product of the highest powers of the common factors
[tex]2^4\times3=48[/tex]
in need help ASAP!! 25 points!
Kami and her mother offer tours of a nearby canyon. They charge a $50 base rate plus $10 per person for a 2.5 hour tour. Which equation represents A, the amount they make to tour p people thorough the canyon?
A. 2.5p+50=10A
B. 10p+50=A
C. 2.5p=50=A
D. 10/p+50=A
Answer:
b
Step-by-step explanation:
becuase 10p which it states in the equation the 10 dollars per person and plus 50 base and 2.5 is not in the equation
4% of 975 is what number
Answer:
39
Step-by-step explanation:
Answer:
4% of 975 is 39
Step-by-step explanation:
4% of 975 = 0.04 x 975 = 39
Answer
4% of 975 is 39
HELP ASAP
H(x)=-6x+8
G(x)=10-2x
H(G(x))
Answer:
H(G(x)) = 12x - 52
Step-by-step explanation:
We are given the following two functions:
[tex] H ( x ) = - 6 x + 8 [/tex]
[tex] G ( x ) = 1 0 - 2 x [/tex]
And we are to find the value of H(G(x)).
For that, we will apply the function of H on the function of G.
[tex]H(G(x))=H(10-2x)[/tex]
[tex] H ( G ( x ) ) = - 6 ( 1 0 - 2 x ) + 8 [/tex]
[tex]H(G(x))=-60+12x+8[/tex]
H(G(x)) = 12x - 52
Which of the following are accurate descriptions of the distribution below?
Choose all answers that apply:
(A)
The distribution has an outlier.
(B)
The distribution has a cluster from 4 to 6 days.
(C)
None of the above
Answer:
both option (A) & (B) is description of given distribution.
Step-by-step explanation:
The outlier is a point which lies differently or far away from rest points in datasets or distribution.
Here we can self-time for one apple on the 10th day is outlier present in the distribution. Thus Option (A) is correct.
We divide the heterogeneous group into many homogeneous groups, these homogeneous group is known as Cluster. It can be seen naturally.
Also, here distribution is divided into many clusters and we can see given distribution has many clusters and one of them is from 4 to 6 days. Thus Option (B) is also a correct option here.
here are my analyses of the possible answer choices based on the image you sent: The distribution clusters around 4-6 days and has a few potential outliers above 8 days.
here are my analyses of the possible answer choices based on the image you sent:
(A) The distribution has an outlier.
There are a few data points that are higher than the rest of the distribution, so in that sense, yes, there are outliers. However, it is important to consider what an outlier is in the context of the data. If the data is normally distributed, then outliers are data points that fall more than two standard deviations away from the mean. In this case, it is difficult to say for sure whether the data is normally distributed, so it is also difficult to say for sure whether there are outliers. However, there are a few data points that are higher than the rest of the distribution.
(B) The distribution has a cluster from 4 to 6 days.
There is a cluster of data points from 4 to 6 days, so yes, this statement is accurate.
In conclusion, the accurate descriptions of the distribution are:
The distribution has a cluster from 4 to 6 days.The distribution has a few outliers.two business partners, Ellen and Bob, invested money in their business at a ratio of 3 to 7. Bob invested the greater amount. the total amount invested was 200 dollars. how much did each partner invest?
Answer:
Ellen invested $60 and Bob invested $140
Step-by-step explanation:
let the two amounts invested by 3x and 7x
(notice 3x : 7x = 3 : 7 )
then 3x + 7x = 200
10x = 200
x = 20
then 3x = 3(20) = 60
and 7x = 7(20) = 140
60+140=200
Ellen invested $60, and Bob invested $140 in their business.
The student's question involves determining how much each business partner invested in their business based on a given ratio and total investment amount. Ellen and Bob invested money at a ratio of 3 to 7 with a total of $200 invested. To solve this, we need to find out what each 'part' of the ratio is worth in dollars.
Let's consider the total number of parts in the ratio, which is 3 (for Ellen) + 7 (for Bob) = 10 parts in total. Since the total amount invested is $200, each part of the ratio is worth $200 divided by 10, which is $20. Therefore:
Ellen invested 3 parts: 3 parts * $20 per part = $60.Bob invested 7 parts: 7 parts * $20 per part = $140.Hence, Ellen invested $60, and Bob invested $140 in their business.
whats the equivalent ratio of 30:24
Answer:
10:8
Step-by-step explanation:
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism is 10in
ANSWER
[tex]211.2 {in}^{2} [/tex]
EXPLANATION
The surface area of a triangular prism is
equal to the area of two triangular faces
plus the area of the three rectangular faces.
The area of the equilateral triangle is calculated using the formula:
[tex] = 2 \times \frac{ \sqrt{3} }{4} {s}^{2} + 3 \times \: bh[/tex]
where s=6 is the length of one side.
and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.
Surface area
[tex]= 2 \times \frac{ \sqrt{3} }{4} \times {6}^{2} + 3 \times \: 6 \times 10[/tex]
[tex]= 18\sqrt{3} + 180[/tex]
=211.2square inches.
A parabola can be represented by the equation y2 = –x. What are the coordinates of the focus and the equation of the directrix?
ANSWER
Focus:
[tex](- \frac{1}{4} ,0)[/tex]
Directrix:
[tex]x=\frac{1}{4} [/tex]
EXPLANATION
The given parabola has equation:
[tex] {y}^{2} = - x[/tex]
We compare this to the general equation,
[tex] {y}^{2} = - 4px[/tex]
Comparing the coefficient of x, we have:
-4p=-1
[tex]p = \frac{1}{4} [/tex]
The focus is (-p,0)
[tex](- \frac{1}{4} ,0)[/tex]
The equation of the directrix is
x=p
[tex]x = \frac{1}{4} [/tex]
Answer:
A
Step-by-step ex
only if youre lazy like me to read it, its A
Use a calculator to find the value of each expression. Round your answer to the nearest hundredth.
11. Arcsin(1/5)
12. Arcsin(-0.34)
13. Arcsin(0.6)
Answer:
Arcsin(1/5) = 0.20
Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.64
Step-by-step explanation:
Using a calculator we can find the value of each expression:
Arcsin(1/5) = 0.20135792079, rounding to the nearest hundredth we have that: Arcsin(1/5) = 0.20.
Arcsin(-0.34) = -0.346916897527, rounding to the nearest hundredth we have that: Arcsin(-0.34) = -0.35
Arcsin(0.6) = 0.643501108793, rounding to the nearest hundredth we have that: Arcsin(0.6) = 0.64
We found the arc-sin (or inverse sine) of three different values using a calculator, rounding to the nearest hundredth decimal place: Arcsin(1/5) is approximately 0.20, Arcsin(-0.34) is -0.34, and Arcsin(0.6) is about 0.64.
Explanation:The student asked to find the arc-sine (inverse sine) of three values and round the answers to the nearest hundredth. You use your calculator to find these values:
Arcsin(1/5): When you input this into your calculator, you'll get a value of approximately 0.201. So, arc-sin of 1/5 is about 0.20,Arcsin(-0.34): Inputting this into your calculator gives an approximate value of -0.344. So, arc-sin of -0.34 is around -0.34,Arcsin(0.6): Inputting this into your calculator gives about 0.643. So, arc-sin of 0.6 is approximately 0.64.Note: Arcsine is a trigonometric function which checks the angle whose sine is a given number.
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what is the midpoint of the segment shown below? (-3,4) (-6,-1)
Answer:
-9/2 , 3/2
Step-by-step explanation:
The coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
What are the coordinates of the midpoint of the line segment AB?Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.
Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,
x = (-3-6)/2 = -9/2 = -4.5
y = (4-1)/2 = 3/2 = 1.5
Hence, the coordinates of the midpoint of the line segment that has endpoints (-3,4) and (-6,-1) are (-4.5, 1.5).
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Waves with an amplitude of 2ft pass a doc every 30 seconds. Write an equation for a cosine model the height of a water particle above and below the mean water line
[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}[/tex]
[tex]\bf \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)[/tex]
with that template in mind, let's see.
[tex]\bf \stackrel{A = 2}{g(x) = 2cos(Bx+C)}\qquad \begin{cases} \stackrel{\textit{period of 30 seconds}}{\cfrac{2\pi }{B}=30}\\\\ \cfrac{2\pi }{30}=B\\\\ \cfrac{\pi }{15}=B \end{cases}\implies g(x)=2cos\left( \frac{\pi }{15}x+C \right)[/tex]
now, since the period is 30, and cos(x) starts off at 1, recall cos(0) = 1, so then le'ts move the starting point over by simply doing a horizontal shift to the right by a quarter of the period, 30/4 = 15/2 units, that way the initial "hump" starts off at 0.
[tex]\bf \stackrel{\textit{horizontal shift of }\frac{15}{2}}{\cfrac{15}{2}=\cfrac{C}{B}}\implies \cfrac{15}{2}=\cfrac{C}{~~\frac{\pi }{15}~~}\implies \cfrac{15}{2}=\cfrac{15C}{\pi }\implies 15\pi =30C \\\\\\ \cfrac{15\pi }{30}=C\implies \cfrac{\pi }{2}=C~\hfill \stackrel{\textit{horizontally to the right}}{-\cfrac{\pi }{2}=C} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=2cos\left(\frac{\pi }{15}x-\frac{\pi }{2} \right)~\hfill[/tex]
Check the picture below.
according to a recipe each batch of pancake mix can make 12 pancakes Kathy is making 3 batches for a brunch party. if each batch needs 7/12 cups of milk how much milk does she need in total?
The answer is 1 and 3/4 because if you divide 21 by 12 you get 1.75 convert the decimal into a fraction and get 1 and 3/4. :)
She will need 1 3/4 cups of milk
Number of batches of pancake to be made = 3 batches
Number of cups of milk needed for each batch = 7/12
Therefore, in order to get the total number of cups of milk needed for the batches will be calculated thus:
= 7/12 × 3
= 21/12
= 1 9/12
= 1 3/4
Therefore, she will need 1 3/4 cups of milk.
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A toy manufacturer uses 90 pints of plastic to make 600 action figures. If they use 810 pints of plastic in an 8 hour shift, how many action figures are made per hour?
Answer:
The number per hour = 5400 ÷ 8 = 675 action figures
Step-by-step explanation:
* Lets explain how to solve the problem
- A toy manufacturer uses 90 pints of plastic to make 600 action figures
- they use 810 pints of plastic in an 8 hour shift
- To find how many action figures are made per hour we must to find
how many action figures in an 8 hour shift and then find the number
of the action figures per hour
∵ The toy manufacture uses 90 pints of plastic to make 600 action
figures
∵ They use 810 pints
- Lets find how many action figures are made by this numbers of pints
∴ 90/600 = 810/x ⇒ x is the number of action figures
- Use the cross multiplication to find x
∴ 90 x = 810 × 600
∴ 90 x = 486000 ⇒ divide both sides by 90
∴ x = 5400
∴ They will use 810 pints to make 5400 action figures
∵ They use 810 pints in an 8 hour shift
∴ They make 5400 action figures in 8 hours
- To find the number of the action figures per hour divide the number
of them in 8 hours by 8
∴ The number per hour = 5400 ÷ 8 = 675 action figures
solve problem - 2 = g -9
Answer:
G=Seven
Step-by-step explanation:
-two=g-nine
two=nine-?
two=nine-seven
-two=seven-nine
A iron worker will cut 2.4 meters of a iron rod into 4 smaller rods. The smaller rods will all be the same length. What should the length of the 4 smaller rods be?
Answer:
.6 meters
Step-by-step explanation:
We need to take the total length and divide it by 4, since that is the number of rods we want and they are all the same length
2.4/4 =.6 meters
Each rod will be .6 meters long
Please help meee I’m bad at math!!!!!
the answer to this question is C
y=2x+6×
What is the perimeter of parallelogram LMNO? 18 cm 22 cm 40 cm 80 cm
Answer:
The correct answer is last option 80 cm
Step-by-step explanation:
From the given figure we can see a parallelogram LMNO
To find the perimeter of parallelogram
Here side length of the parallelogram is 18 cm and 22 cm
Perimeter = sum of side lengths
= 22 + 22 + 18 + 18 = 80 cm
Therefore the perimeter of parallelogram LMNO = 80 cm
The correct answer is last option 80 cm
The perimeter of the parallelogram is P = 80 cm
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The sum of angles of a parallelogram is 360°
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as LMNO
Now , the measure of side MN = 18 cm
The measure of side LM = 22 cm
And , the side MN is parallel and congruent to OL
And , the side LM is parallel and congruent to side ON
So , the perimeter of parallelogram = LM + OL + ON + MN
P = 22 + 18 + 22 + 18
P = 80 cm
Hence , the perimeter is 80 cm
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help me hurry please
Answer:
28x + 8y + 2
Step-by-step explanation:
Combine like-terms within the parentheses, then distribute -2.
Hope this helps! :)
Answer:
B
Step-by-step explanation:
Given
- 2(3x + 12y - 5 - 17x - 16y + 4)
Simplify the parenthesis by collecting like terms
= - 2 (- 14x - 4y - 1) ← distribute the terms in the parenthesis by - 2
= 28x + 8y + 2 → B
according to the rational root theron what are all the potential roots of f(x)=9x^4-2x^2-3x+4
Answer:
Potential roots: [tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
Step-by-step explanation:
Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
Where
a_n is the number before the highest power of the polynomial, and
a_0 is the constant in the polynomial
From the polynomial shown, we have a_n = 9 and a_0 = 4
The factors of 9 are 9, 3, 1
and
The factors of 4 are 4,2,1
So, if there are any rational roots, they would be:
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
± [tex]\frac{9,3,1}{4,2,1}[/tex]
Which is ± 9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1
or
[tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
Using the Rational Root Theorem, the polynomial f(x) = 9x^4 - 2x^2 - 3x + 4 has potential rational roots which are ±4, ±2, ±1, and their counterparts divided by 3. In the complex number system, every nth-order polynomial can be factored into n roots, including imaginary roots for equations that lack real solutions.
Explanation:Rational Root Theorem and Potential Roots
The Rational Root Theorem is a useful tool for identifying all potential rational roots of a polynomial equation. When applying this theorem to the given polynomial f(x) = 9x^4 - 2x^2 - 3x + 4, we note that the potential rational roots are the divisors of the constant term (in this case, 4) divided by the divisors of the leading coefficient (in this case, 9). Therefore, the potential roots are ±4, ±2, ±1, and their counterparts divided by 3, which are ±4/3, ±2/3, and ±1/3. To determine which of these are actual roots, each must be tested in the polynomial equation.
The concept of complex number system further elaborates on polynomials by stating that every nth-order polynomial can have up to n roots, factored into linear factors in accordance with the fundamental theorem of algebra. In the case of second-order polynomials, the real number system may not yield roots for equations like x² + 1, but in the complex number system, such polynomials do have roots and can be factored as (x - i)(x + i), for instance.