We found that translations have the following three properties: line segments are taken to line segments of the same length;
angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.
Properties of Translations
- Distance Where the lengths of the segments stay the same.
-Angle Measures These remain the same.
-Parallelism Where the parallel lines will stay parallel.
-Collinearity The points will stay on the same line.
-Orientation The order of the letters will stay the same.
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Peter owns a total of one hundred and forty four prized baseball cards. If he were to add 7 more American League players and three more national league players, his collection of American to national would be in a ratio of nine five. Find out how many cards of each league he has currently.
Answer:
24
Step-by-step explanation:
explanation with steps
Answer:
x = 40° , y = 140° z = 10°
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , then
x + 60° + 80° = 180°
x + 140° = 180° ( subtract 140° from both sides )
x = 40°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
y is an exterior angle of the triangle , then
y = 60° + 80° = 140°
x is also an exterior angle , then
30° + z = x
30° + z = 40° ( subtract 30° from both sides )
z = 10°
What is the product of 2x 3y )( 2x 3y )? *?
The product of (2x-3y)(2x+3y) is 4x^2-9y^2
Product= (2x-3y)(2x+3y)
Let the product of (2x-3y)(2x+3y) be P
P=2x(2x+3y)-3y(2x+3y)
P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}
This property states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.
P= 4x^2 +6xy - 6xy -9y^2
solving 6xy-6xy=0
P= 4x^2 - 9y^2
4x^2-9y^2 is the product of (2x-3y)(2x+3y).
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HELP I DONT UNDERSTAND
The of the function a remainderre 3, 2,1,0
What is substitution?You should understand that substitution means replacing figures in a variable to get a value
the given function is
y=-x/3 +2
The given parameter or table to be completed is
x -6 -3 0 3 6
y 4 3 2 1 0
The table above was completed in the following ways
1) y= 6/3 +2 = 2+2 4
2) y = 3/3 + 2 = 1+2 = 3
3) 0/2 + 2 = 2
4) -3/3 +2 = -1+2 = 1
5) y = -6/3+2 = -2+2 = 0
Therefore the table has values descending from 4 to 0
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In the diagram below, PQ is parallel to MN. If PQ, is 22 more than MP, PO=12, and MN=12, find the length of MP. Figures are not necessarily drawn to scale. State your answer in the simplest radical form, if necessary.
The measure of the length MP is equal to 6.
What are similar triangles?Two triangles are similar triangles if they have the same corresponding angle measures and proportional side lengths.
Given is a triangle ΔOMN.
Now, ΔOMN and ΔOPQ are similar. This means that the side lengths are proportional to each other. We can write -
OP/OM = PQ/MN
12/OM = PQ/MN
12/(OP + PM) = PQ/MN
It is given that -
PQ = MP + 2
12/(OP + PM) = (MP + 2)/MN
12MN = (MP + 2)(OP + PM)
12 x 12 = (MP + 2)(MP + 12)
(MP)² + 12MP + 2MP + 24 = 144
(MP)² + 14(MP) - 120 = 0
Let MP = x, then we can write -
x² + 14x - 120 = 0
(x + 20)(x - 6) = 0
(x + 20) = 0 and (x - 6) = 0
x = - 20 and x = 6
x = 6 {Lengths cannot be negative}
Therefore, the measure of the length MP is equal to 6.
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Solve the following problems using completing the Square
Martha and Miguel volunteered in a Tree Planting Program offered by the school. They also donated packs of seeds for the program. The number of Martha's seeds is represented as 2x-3 packs while Miguel's seeds is twice the number of Martha's seeds. If the product of Martha and Miguel's Pack of seed is 50, how many packs of seeds Martha and Miguel donated?
[Write it on paper please ]
Using factorization method to solve the quadratic equation, the number of seed Martha and Miguel donated are 5 and 10 respectively
What is Quadratic EquationA quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and x is an unknown variable. The solution to such an equation is a value of x that will make the equation true.
To determine the number of seeds they donated, we have to write two equations and solve.
data;
Martha = 2x - 3Miguel = 2[2x - 3] = 4x - 6The product of the seeds is (2x - 3)(4x - 6) = 8x² - 24x + 18
This can be written as
8x² - 24x + 18 = 50
Solving the quadratic equation;
8x² - 24x + 18 - 50 = 0
8x² - 24x - 32 = 0
Using factorization method;
8(x - 4)(x + 1) = 0
x - 4 = 0, x = 4
x + 1 = 0, x = -1
x = 4, x = -1
The number of packs Martha donated is
Martha = 2x - 3 = 2(4) - 3 = 5
The number of packs Miguel donated is
Miguel = 2 * 5 = 10
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Here is a piece of cake each piece of cake has the same number of candles how old is rongopai
Rongopai's age is equal to the total number of candles on the cake, thus I need to determine what that is.
How to estimate Rongopai's age?What I need to figure out because I am aware that Rongopai's age is equal to the total number of candles on the cake.
The number of pieces the cake was sliced into must first be determined. A quarter has a specific appearance to me. This is how it would seem (the teacher traces a quarter shape on the circle). There must have been more than four pieces since this one seems a little smaller.
Each cut's location may be identified using my finger. Given that all the pieces must be the same size, I'm predicting the locations of each line using the first piece as a reference.
Here would be the approximate location of the first line, followed by here and here (the teacher draws a line with her finger) (tracing two more lines). the third line. In my mind, the lines and parts are somewhat "visible." Four "invisible" pieces plus the one drawn in are present when I count backward.
The complete question is:
A teacher wants a student to see how visualising the size of a share (in this case, a piece of cake) can be used to work out how many shares are needed to make a whole:
“Here is a piece of Rongopai’s birthday cake. Each piece of cake has the same number of candles. How old is Rongopai?”
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Age of Rongopai is 20 years.
What means one fifth of a circle?One fifth of a circle means if a circle can be divided into five equal parts, then one fifth is one of them.
How old is Rongopai?
As per the figure given, there is shown a 1 fifth of a circular birthday cake.
As all the piece of cake is equal in size so the total number of cake piece is five.
the number of candles in each piece is four.
the total number of candles present in the whole cake is = 5 × 4
the total number of candles = 20
Therefore, Rongopai is 20 years old.
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Type the correct answer in the box. Round your answer to the nearest tenth. The population of Cuba is 1.3 million. The country's population is expected to grow at a rate of 4% each year. The population of Cuba will be million in 10 years.
The population of Cuba in 10 years will be 1.9243 million.
What is meant by exponential growth?A process called exponential growth sees a rise in quantity over time. It happens when a quantity changes at an instantaneous rate that is proportionate to the quantity itself with respect to time.
Data patterns that exhibit exponential growth exhibit quicker rate of expansion over time. Compounding produces exponential returns in the financial world. Savings accounts with a compound interest rate have the potential to expand exponentially.
The population growth will be modeled using exponential growth:
f(x) = a(b[tex])^t[/tex]
where:
a be the initial value
b be the growth rate
Substitute the values in the above equation, we get
f(x) = 1.3(1.04[tex])^t[/tex]
The population after 10 years will be:
f(x) = 1.3(1.04[tex])^{10[/tex]
simplifying the equation, we get
f(x) = 1.9243
Therefore, the population in 10 years will be 1.9243 million.
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The population of Cuba in 10 years will be 1.9243 million, if the population is expected to grow at a rate of 4% each year.
What is meant by exponential growth?Quantities increase over time through a process known as exponential growth. It occurs when a quantity shifts at a pace that is proportional to the quantity's own rate of change with regard to time.
Data patterns that show exponential growth expand more quickly over time. In the world of finance, compounding generates exponential profits. Compound interest savings accounts have the potential to grow tremendously.
The population growth will be modeled using exponential growth:
f(x) = a(b)[tex]^{t}[/tex]
where:
a be the initial value
b be the growth rate
Substitute the values in the above equation, we get
f(x) = 1.3(1.04
The population after 10 years will be:
f(x) = 1.3(1.04
simplifying the equation, we get
f(x) = 1.9243
Therefore, the population in 10 years will be 1.9243 million.
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Identify the inverse function of f(x)=√x - 2 + 3.
A) f-¹(x) = (x + 2)² - 3
B) f-1(x) = (x - 3)² + 2
C) f-¹(x) = √x + 2 - 3
D) ƒ-1(x) = √x + 3 − 2
Questi
The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.
What is the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x)=√x - 2 + 3.
The inverse function can be found as shown below,
f⁻(x) = √(y - 2) + 3 (Replace x by y)
x = √(y - 2) + 3
solve the equation as shown below,
x - 3 = √(y - 2)
Squaring both sides,
(x - 3)² = [√(y - 2)]²
x² + 9 - 6x = y - 2
x² + 9 - 6x + 2 = y
y = x² - 6x + 11 or y = (x - 3)² + 2
Thus, the inverse of the function is (x - 3)² + 2.
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Which is the product of 15 [tex]\frac{5}{12}[/tex]
( 100 POINTS )
Answer:
[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]
[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]
Hence, the product is 6.25.
Help i got some more math
x = 5
AB = 6
BC = 13
What is a line?A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.
Given,
AB = 2x - 4
BC = 3x - 2
AC = 19
By the figure
AB + BC = AC
2x - 4 + 3x - 2 = 19
5x - 6 = 19
5x = 25
x = 5
AB = 2 × 5 - 4 = 10 - 4 = 6
BC = 3 × 5 - 2 = 15 - 2 = 13
Hence the value of x, AB and BC is 5, 6, 13 respectively.
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Are 6x - x + 5 and 6+5 equivalent?
Answer:
no
Step-by-step explanation:
the one equation has variables and numbers go in for the variable and the other equation just equals 11
The average age of a university student was found to be 24 with a standard
deviation of 2. What age group is within 2 standard deviations of the mean?
The age group that falls between two standard deviations is 20 to 28.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.
Given, The average age of a university student was found to be 24 with a standard deviation of 2.
Therefore, age group is within 2 standard deviations of the mean is,
24 + 2×2 = 24 + 4 = 28,
And 24 - 2×2 = 24 - 4 = 20.
So, The age group between 20 to 28 falls within 2 standard deviations of the mean.
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Can 30 60 and 90 be the angles of a triangle?
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
The sum of the angles of a triangle must always add up to 180 degrees. To determine if a set of angles can form a triangle, add the angles together. If the sum is 180, the angles can form a triangle. In this case, 30 + 60 + 90 = 180, which does not equal 180. Therefore, these angles cannot form a triangle.
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
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253 x 804 =
Solve by using standard algorithms
Answer:
203412
Step-by-step explanation:
253
*804
___
16
40
32
20
12
______
203412
This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.
ALGEBRA 2 - Exponential and Logarithmic Functions
April invests $500 in an account that is compounded continuously at an annual interest rate of 5%. Approximately how many years will it take for April’s money to double?
Answer:
It will take approximately 14.2 years for April’s money to double.
Step-by-step explanation:
PLEASE I NEED HELP ASAPPPP!!!!!
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October: A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0. 51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
What is a Scatter Plot?A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.
Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.
Part A:
The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.
Part B:
The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.
Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
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The point N(-2,-3) is rotated 270° clockwise about the origin. What are the coordinates of N'?
A. (-3,-2)
B. (-3,2)
C. (3,-2)
The coordinate of N' is (2, -3)
Now, According to the question:
We have the point n (-2, -3) and we need to rotate it 270 degrees clockwise about the origin.
When rotating 270 clockwise about the origin you switch the x and y coordinate and use the opposite sign of the original y coordinate.
A(x, y) becomes A' (-y, x)
This means that point N becomes:
N (-2, -3) => N'(-(-2), (-3))
=> N'(2,- 3)
Hence, The coordinate of N' is (2, -3)
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Please HURRY!!!
Which of the following must be true
The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 12°F. What was the lowest temperature overnight in that city?
Answer:-14°F
Step-by-step explanation:
-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it
How many dimes are in 4.72
Answer:
There are 47 dimes and 2 pennies.
Step-by-step explanation:
10¢ = 1 dime
$4.70 = 470 ¢
470 dimes = 47 dimes
and 2 pennies
Find the volume of the cylinder. Round your answer to the nearest tenth if necessary. Use 3. 14 for pi.
A can of juice has a radius of 5 inches and a height of 6 inches. What is the volume of the can?
The volume of the can based on mentioned radius and height of can is 471 inches³.
Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.
Use the below mentioned formula to calculate the volume -
V = πr²h, where V is volume, r is radius and h is height.
Keep the values in formula to find the value of volume of cylinder
V = 3.14×5²×6
Next step is to perform multiplication on Right Hand Side of the equation
V = 471 inches³
The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.
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Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Who has the greater test average and who has the most consistent test scores?
Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Jamal has a greater test average than Natalia. Natalia has more consistent test scores than Jamal.
To find the test average, you add up all the test scores and divide by the number of test scores.
Jamal's average: (84+88+92+94) / 4 = 89.50
Natalia's average: (86+88+90+92) / 4 = 89
Jamal has a greater test average.
To find the consistency of test scores, you can use the range, which is the difference between the highest and lowest scores.
Jamal's range: 94-84=10
Natalia's range: 92-86 = 6
Natalia has the most consistent test scores, as the range of her scores is smaller than Jamal's.
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Order the set of numbers from least to greatest: 5, -19, -25, 7, 22, -4, -15
Answer:
-25, -19, -15, -4, 5, 7, 22
Step-by-step explanation:
-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest
The bigger the negative number, the smaller it is; that is why the order is
-25, -19, -15, -4, 5, 7, 22
Simplify (with steps please:))
√((x+c)^2 + y^2) = x*a/c + a
On solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as follows -
√{(x + c)² + y²} = x (a/c) + a
√{(x + c)² + y²} = xa/c + a
√{(x + c)² + y²} = a{x/c + 1}
√{x² + c² + 2xc + y²} = a{x/c + 1}
{x² + c² + 2xc + y²} = ± (a{x/c + 1})²
Now, we can write -
{x² + c² + 2xc + y²} = (a{x/c + 1})² ...... (1)
and
{x² + c² + 2xc + y²} = - (a{x/c + 1})² ......... (2)
Solving (1) as -
{x² + c² + 2xc + y²} = (a{x/c + 1})²
{x² + c² + 2xc + y²} = a²(x/c + 1)²
{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)
{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)
y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}
Solving (2) as -
{x² + c² + 2xc + y²} = - (a{x/c + 1})²
y² = - (a{x/c + 1})² - (x² + c² + 2xc)
y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}
y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}
Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -
y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)} -- Real
y = i√{(a{x/c + 1})² + (x² + c² + 2xc)} -- Complex
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geometry stuff pls help
Answer:
Step-by-step explanation:
SQR-PRQ-SRP
SP/RP=RP/PQ
QP/QR=RQ/SQ
4. What function represents an absolute value that has a vertex at (-7,-10)?
a. |y-7|-10 3
b. |y+7|+10
c. |y+7|-10
d. -|y+7|+10
More than one applies to the slope.
How is the absolute value function calculated?The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.
The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)
The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.
m = 3
It is steeper than one.
As a result, a scale factor other than 1 has been used to dilate the graph.
The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.
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The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards, how much fencing does the city need to surround the park?
The length of the fencing that the city needs to surround the park will be 380.50 yards.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,
8925 = L × 84
L = 106.25 years
Then the length of the fencing that the city needs to surround the park will be given as,
P = 2(106.25 + 84)
P = 2 × 190.25
P = 380.5 yards
The length of the fencing that the city needs to surround the park will be 380.50 yards.
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Five people of different heights will be photographed
standing in a single row. Given that the tallest person
must stand in the middle, how many different
arrangements of the 5 people are possible?
Since the tallest man is a lone individual, he can only take a seat in the center. The four other men can sit in 4! = 24 different positions.
What is the difference of five peopleWe'll take pictures of five people standing in a row, all of varying heights. The tallest individual must be in the middle, so. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The likelihood that an event will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely alternatives that result in a given occurrence. Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. If we throw a coin into the air,
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Is an absolute value graph increasing or decreasing?
The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).
Explain the nature of absolute value graph?When x< 0, you can see on the graph that there is a "open circle" at (0, 0).
This is owing to the fact that the points on y = x approach (0, 0) as that of the x-values reach 0, as we have already shown. Instead, the open circle was drawn since x must strictly be smaller than zero on just this stretch.A point at (0, 0) is filled in when x ≥ 0, which essentially "plugs" the hole represented either by open circle. Thus, we obtain:The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).The absolute minimum value of f is 0, and its relative minimum value is the same (0, 0). The relative maximum value of F is zero.Thus, due to the graph's indefinitely high y values, there is likewise no absolute maximum value for f.
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