Answer:
C(t) = 5t for 0 < t ≤ 3
C(t) = (8t-9) for 3 < t ≤ 6
C(t) = 44 for 6 < t ≤ 10
C is given in thousands of dollars and t is given in months.
Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000
Step-by-step explanation:
We will do a piecewise analysis for this cost function.
How to obtain the total cost changes with each time interval.
In the first 3 months,
C(t) = 5t for 0 < t ≤ 3
Note that C is given in thousands of dollars
In the next 3 months,
C(t) = (8t-9) for 3 < t ≤ 6
- Here, it gets a little complex, we use the upper limit of the previous interval and the lower limit of this new interval to get the constant to be subtracted from the normal 8t that characterizes this interval.
8(3) = 24
5(3) = 15
constant = 24 - 15 = 9
In the last 4 months,
C(t) = 44 for 6 < t ≤ 10
- For the last four months, it is a single sum of $5000 plus the [8(6) - 9] from the previous inteval
C = [8(6) - 9] + 5 = 39 + 5 = 44
So, the cost of parking, tracked month after month gives
T | Cost (in thousands of dollars)
1 | 5
2 | 10
3 | 15
4 | 23
5 | 31
6 | 39
7 | 44
8 | 44
9 | 44
10 | 44
Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000
Hope this Helps!!!
This is not my answer yet is a stollen verrified one.
A basking shark measures 25 feet long. A giant squid measures
33 feet long. How many inches longer is the basking shark than
the giant squid?
ounds and
Answer: 8 feet
Step-by-step explanation:
you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.
Consider your construction of pentagon ABCED. What segments, if any, are perpendicular? Explain how you made your determination
Answer:
Sine AB is perpendicular to sides AE and BC/
Step-by-step explanation:
The slope is the change in y over the change in x.
Line segment AE has a slope of 3/4
(0,4)(4,7)
The y values are 7 and 4.
The x values are 4 and 0.
You find the change by subtracting
[tex]\frac{7-4}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Line segment BC has the same slope
((3,0)(7,3)
The y values are 3 and 0.
The x values are 7 a d 3.
You find the change by subtracting
[tex]\frac{3-0}{7-3}[/tex] = [tex]\frac{3}{4}[/tex]
Since line segments Ae and BC has the same slope. They are parallel.
Line segments that are perpendicular will have opposite reciprocals slopes. In this case the slope should be - [tex]\frac{4}{3}[/tex].
Let's look at line segment AB
(0,4)(3,0)
The y values are 0 and 4.
The x values are 3 and 0.
You find the change by subtracting
[tex]\frac{0-4}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex]
Since the slopes are opposite reciprocals, side AB is perpendicular to sides AE and BC
30PTS 30PTS don’t explain just answer (it’s not 90)
Answer:
20
Step-by-step explanation:
110 -70 = 40 40/2= 20
Answer:
[tex] \sf \: x = {20}^{o} [/tex]
Step-by-step explanation:
Let's take the value of y as,
→ y = 90°
(Because, it is a right angle)
Forming the equation,
→ x + y + 70° = 180°
Now the value of x will be,
→ x + y + 70° = 180°
→ x + 90° + 70° = 180°
→ x + 160° = 180°
→ x = 180° - 160°
→ [ x = 20° ]
Hence, the value of x is 20°.
S(5-4-2) and y (1 7)
Answer:
i do not not the answer of this question
What is the average rate of the function from x =2 to x =4 write as whole number
Answer:The average rate of the function from x = 2 to x = 4 is 6.
Step-by-step explanation:
In ΔEFG, g = 8.4 inches, mm∠G=79° and mm∠E=25°. Find the length of f, to the nearest 10th of an inch.
The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side EG = f is about 8,3 inches.
What is the law of sines?The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.
Mathematically, the law of sines can be presented as follows;
[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]
Where;
a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.
The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;
The length of EF = g = 8.4 inches
Length of EG = f
The angle sum property of a triangle indicates that we get;
∠E + ∠F + ∠G = 180°
∠F = 180° - (∠E + ∠G)
∠F = 180° - (25° + 79°) = 76°
According to the law of sines, we get;
8.4/(sin(79°) = f/(sin(76°))
f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3
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Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.
What is rounding off?Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.
We can use the formula of conditional probability to find the value of P(A n B).
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
So we can substitute this in the first equation:
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
P(An B) = P(A U B) - P(A) - P(B) + P(An B)
Now we can substitute the given values:
P(An B) = 0.366 - 0.32 - 0.2 + P(An B)
P(An B) = 0.346 + P(An B)
To find P(An B) we can subtract 0.346 from both sides of the equation:
P(An B) = P(An B) - 0.346
P(An B) = P(An B) - 0.346
So, P(An B) = 0.346
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why is sin ( 17.5 + pi ) = - 0.3 and not positive 0.3 ?
Answer:
Step-by-step explanation:
Name the property of the real numbers illustrated by the equation
Select the theorem that can be used to prove that RST = VUT
How do you determine area?
Answer:
You multiply one side and then the other. Basically doing hxw
Circle of circumstances
The circumference of the circle is 2πr.
What is circumference of a circle?The circumference of a circle is the distance around the outside of the circle. It is given by the formula C = 2πr, where C is the circumference, π is the mathematical constant approximately equal to 3.14 and r is the radius of the circle. In other words, the circumference is equal to the diameter times pi.
For the given question,
The formula of the circumference of the circle,
C = 2πr
where r is the radius of the circle.
Hence we can conclude that the circumference of the circle is 2πr.
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Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren
By probability, she will not receive a phone call from any of her grandchildren after 146 days
How does probability affect our lives?In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.
There is a [tex]\frac{2}{3}[/tex] chance that the first child won't call, a [tex]\frac{3}{4}[/tex] chance that the second child won't call, and a [tex]\frac{4}{5}[/tex] chance that the third child won't call on any given day. There is a [tex]\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}[/tex] chance that no child calls her on a randomly selected day.
When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in 144.
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How to solve a function?
To solve a function, you must determine the value of the function for a given input. This requires finding the equation for the function and then plugging in the given input to find the output. For example, if the function is f(x) = x2 + 2x - 5, and the given input is 3, then the output of the function is f(3) = 12.
1. Substitute the given input, x = 3, into the equation.
2. Simplify the equation: f(3) = 32 + 2(3) - 5
3. Solve the equation: f(3) = 9 + 6 - 5
4. Simplify the equation: f(3) = 12
5. Therefore, the output of the function is f(3) = 12.
To solve a given function, you must first determine the equation for the function. Then, you must substitute the given input into the equation and solve it. In this example, the given input was 3 and the equation for the function was f(x) = x2 + 2x - 5. After plugging in the input of 3, the equation was simplified to f(3) = 9 + 6 - 5, which was further simplified to f(3) = 12. Therefore, the output of the function is f(3) = 12.
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Answer:
do it
Step-by-step explanation:
a) Complete the prime factor trees for 24 and 40:
24
2
2
6
2
40
2
2
3
b) What is the Lowest Common Multiple of 24 and 40?
2
2
1
5
Submit Answer
Answer:
a)
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 120
Step-by-step explanation:
a)
24 40
/ \ / \
2 12 2 20
/ \ / \
2 6 2 10
/ \ / \
2 3 2 5
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 2³ × 3 × 5
LCM = 120
Suppose that $x$ is directly proportional to $y$. Let $x_1, x_2$ be two values of $x$ such that $\frac{x_1}{x_2} = 4$. Let their corresponding values be
$y_1$, $y_2$ respectively. If at least one of $y_1, y_2$ is nonzero, find $\frac{y_2}{y_1}$.
If at least one of $y_1, y_2$ is nonzero, then $\frac{y_2}{y_1}$ = $\frac{1}{4}$
If x is directly proportional to y, we can write this as x = ky for some constant k.
Since $\frac{x_1}{x_2} = 4$, we can write it as $x_1 = 4x_2$.
Now, substituting the value of $x_1$ in equation x = ky gives
$4x_2 = ky_1$.
Also, since x = ky, we can write $x_2 = ky_2$.
Now, we can substitute the value of $x_2$ in the equation $4x_2 = ky_1$
So, $4ky_2=ky_1$, which gives $\frac{y_2}{y_1} = \frac{1}{4}$
Therefore, $\frac{y_2}{y_1}$ = $\frac{1}{4}$ when x is directly proportional to y and $\frac{x_1}{x_2} = 4$.
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A particle traveled a distance of 9. 0 x 1012 meters at a rate of 1. 8 x 105 meters
per second. If distance = rate x time, how many seconds did it take the particle to
travel the specified distance?
A particle takes 5 × 10^7 sec of time to travel a distance of 9.0 × 10^12 meters at a rate of 1.8 × 10^5 meters.
What is speed?
Speed indicates how quickly something or someone is moving. If one knows how far something has travelled and how long it took to get there, then one can calculate its average speed.
The particle travels at a rate of 1.8 × 10^5 m.
The particle travels a distance of 9.0 × 10^12 m.
Let the time taken for the particle to travel be x.
The formula for calculating the distance traveled by the particle is -
distance = rate × time
time = distance/rate
Plugging in the values in the equation -
x = 9.0 × 10^12/1.8 × 10^5
x = 9.0/1.8 × (10^12-5)
x = 5 × 10^7 sec
Therefore, the time taken by the particle to travel is 5 × 10^7 sec.
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Ana and Darryl answered 80 calls. Ana answered 4 times as many as Darryl. How many calls did ana answer
There were 64 calls that Anna answered in this algebra question,
What is Answered calls?
Total engaged calls, another name for answered calls, is a measurement of all incoming calls that were handled by an agent during regular business hours.
Solution:
If Ana answers more calls than Darryl does, then let D be the number of calls Darryl Answered.
A + D = 80
A = 4D
4D + D = 80
5D = 80
D = 80 / 5
= 16
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According to the algebra, Ana answered 16 calls,
What is algebra, exactly?The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we use numbers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine numbers with variables like x, y, and z.
Solution:
Let D be the number of calls Darryl answered if Ana answers more calls than he does.
A + D = 80
A = 4D
4D + D = 80
5D = 80
D = 80 / 5
= 16
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How do you tell if a graph is linear quadratic or exponential?
A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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Assuming that birthdays are distributed equally throughout the week, what is the probability that two people that have never met passing each other on the street were both born on a Friday is
1/7 2/7 1/49 2/49 4/49
Probability of Two people was born on Friday = 1/49
What is the definition of probability?
Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.
What is the probability that two people were born on a Friday?
Assume that birthdays are equally distributed throughout the week.
probability of one people having birthday on Friday = 1/ 7
probability of another people has birthday on Friday = 1/7
probability of two people was born on Friday = 1/7× 1/7 = 1/ 49
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PLS HELP I WILL GIVE BRAINLIEST TO THE BEST CORRECT ANSWER
Answer:
Step-by-step explanation:80085
Answer:
Graph 1: No
Graph 2: No
Graph 3: No
Graph 4: Yes
Graph 5: No
Graph 6: Yes
Step-by-step explanation: To figure out whether a graph is a function, you need to give each graph a Vertical Line Test. All you need to do is see if more than one point is on the same line whenever a vertical line is placed. If there is more than one point on any vertical line that you drew, it's not a function.
Hope this helps! :)
5. Refer to the figure below. (show work)
Given: UVWX is a parallelogram, m
A. Find m
B. Find UV.
C. Find m
D. Find YW.
Answer:
see explanation
Step-by-step explanation:
A
∠ UVX and ∠ WXV are alternate angles and are congruent , then
∠ UVX = ∠ WXV = 15°
∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°
B
opposite sides of a parallelogram are congruent , then
UV = XW = 36
C
consecutive angles are supplementary , sum to 180° , then
∠ XUV + ∠ WVU = 180° , so
∠ XUV + 39° = 180° ( subtract 39° from both sides )
∠ XUV = 141°
D
diagonals bisect each other , so
YW = UY = 10
What is the x-coordinate of the solution to the system shown?
3x - y = 6
3x + y = 34
The x-coordinate of the solution of the system of equations is x = 20/3
What is the x-coordinate of the solution?Here we have a system of equations below:
3x - y = 6
3x + y = 34
And we want to find the x-cordinate of the solution, so we need to solve this for x.
We can use the elimination method, you can see that if we add both equations we will get:
(3x - y) + (3x + y) = 6 + 34
6x = 40
x = 40/6
We can simplify that fraction to get:
x = 20/3
That is the x-coordinate of the solution.
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I need help with this question, its confusing.
Here are several function rules. Calculate the output for rules 1–5 when you use -6 as the input for each rule. Simplify fractions and express in the form a/b if necessary and use the word pi for π
.
Answer: 13,36,-2,-2,pi
Step-by-step explanation:
You do exactly what it says for the rule to -6 to get your answer.
Find each product. (Please help me on this-i will give you brainlist!)
l think it's answer is this .
You can use your calculator.
decide whether the function is a polynomial function. If so right it in standard form and state it’s degree type in leading coefficient if so write it in standard form and state its degree type in leading coefficient P(x)=-3x^2+10-4x
For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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NEED THIS ASAP!
(picture below)
is it
A
B
C
or D ?
(this is Fractions and Whole Numbers)
(100 Points)
Answer:
C) 4 2/3------------------------------
The product of 7/9 and 6 is:
7/9 × 6 = Simplify by cancelling 37/3 × 2 = Multiply 14/3 = Convert to mixed number4 2/3 AnswerAnswer:
[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]
Step-by-step explanation:
To find the product of two numbers, multiply them.
[tex]\implies \dfrac{7}{9} \times 6[/tex]
To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:
[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]
[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]
Simplify:
[tex]\implies \dfrac{42}{9}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 3:
[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]
[tex]\implies \dfrac{14}{3}[/tex]
Divide the numerator by the denominator:
[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 4\frac{2}{3}[/tex]
Write down the value of angle x, y and z and give a reason for your answers: Angles
The missing angles and their reasons are as follows;
a) x = 65°; Opposite angles
b) y = 71°; Alternate angles
c) z = 44°; sum of angles in a triangle
What are the missing angles of the triangle?a) In triangles or line geometry, we know that the angles that are directly opposite to each other are known as opposite angles. They are also referred to as as vertical angles or even vertically opposite angles in some cases and are always congruent to each other.
We see that x is an opposite angle to 65 and so;
x = 65°
b) Alternate angles are gotten on the opposite sides of a transversal line they always have the same size. In this problem, we see that y is an alternate angle to 71° and as such;
y = 71°
c) The sum of angles in a triangle is 180° and as such;
x + y + z = 180°
Thus;
65 + 71 + z = 180
z = 180 - 136
z = 44°
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3 Write an equation for each function, where x is the
number of months and y is the amount owed.
Mr. Allen's plan:
Mr. Jessup's plan:
rriculum Associates, LLC Copying is not permitted.
In
-L-
ODPPY LINAL
The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the y-intercept of the line represents the value of the loan initially.
From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.
Let 'x' be the number of months and 'y' be the amount owed.
The two points are (0, 560) and (1, 480). Then the equation of the line is given as,
(y - 560) = [(560 - 480) / (0 - 1)](x - 0)
y - 560 = - 80x
y = - 80x + 560
And the equation of the line for Mr. Jessup's plan will be given as,
y = - 40x + 400
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Classify each statement about the function f(x)=2x^3+8 as true or false.
The domain of the function is all real numbers.
The domain of the function is all real numbers.
The range of the function is (0, [infinity]).
The y-intercept is (0, 0).
The center of symmetry is (0, 8)
Statement A,B is true rest all statement are false about the given function.
Given the function: [tex]2x^3+8[/tex]
Statement A:
The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).
It is because the expression inside the function, 2x^3, is defined for all real numbers.
so above statement is true.
Statement B:
statement A and B are same so it's also true.
Statement C:
The range of a function is the set of all possible output values (y-values) that the function can produce.
For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)
It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.
so this statement is false.
Statement D:
The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.
so this statement if false.
Statement E:
A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.
The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.
So this statement is also false.
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