The sequence of functions f_n : a → r, where f_n(x) = nx, demonstrates a collection of linear functions that have an increasing slope with each natural number n.
Te sequence of functions fn : a → r is defined as f(x) = nx, where n is a positive integer and a and r are real numbers. This sequence of functions is a linear sequence, as each function fn is a linear function with slope n.
In terms of the behavior of this sequence of functions, we can say that as n increases, the slope of the linear function also increases, resulting in a steeper and steeper line.
As a result, the sequence of functions becomes increasingly "zoomed in" on the x-axis, with each successive function having a smaller and smaller slope.
In addition,
We can say that this sequence of functions is unbounded, as there is no maximum value that the function can reach.
As n approaches infinity, the slope of the function also approaches infinity, resulting in an increasingly steep line that approaches vertical.
The sequence of functions f_n : a → r is defined by f_n(x) = nx for each n ∈ ℕ (natural numbers).
As n increases, the function becomes a linear function with a steeper slope.
For example, when n = 1, f_1(x) = x, and when n = 2, f_2(x) = 2x.
Each function in the sequence takes an input x from the set a and maps it to a real number r, represented as a point on the coordinate plane. In summary,
Overall, the sequence of functions fn : a → r by f(x) = nx is a linear sequence with increasing slopes and an unbounded behavior.
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Answer:
Step-by-step explanation:
It seems that you have defined a sequence of linear functions, where each function fn maps a real number x to the real number nx, where n is a fixed constant.
We can express this sequence more formally using mathematical notation as follows:
For a fixed constant n, we define the sequence of functions {fn : a → ℝ} by:
fn(x) = nx, for all x in the domain a.
Here, fn(x) represents the value obtained by applying the nth function in the sequence to the input x. In this case, since each function is a linear function with slope n, the graph of each function is a straight line with slope n, passing through the origin.
It is worth noting that the domain a is not specified in your question, and that the properties of the sequence of functions may depend on the choice of domain. For example, if a is a closed interval, then the sequence of functions may or may not converge pointwise or uniformly on a, depending on the specific values of n and a.
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Which expression is equivalent to startfraction 3 x superscript negative 6 baseline y superscript negative 3 baseline over 15 x squared y superscript 10 baseline endfraction? assume x not-equals 0, y not-equals 0.
The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.
Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]
Lets simplify the equation:
[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]
Expression:
An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.
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The area of Marc's square garden is 225 ft².
What are the dimensions of his garden?
F. 5 ft by 45 ft
H. 15 ft by 15 ft
G. 12 ft by 12 ft
J. not given
Answer:
H. 15 ft by 15 ft
Step-by-step explanation:
area of square = side²
225 ft² = side²
side = √(225 ft²)
side = 15 ft
Answer: H. 15 ft by 15 ft
Complete the sentence using the following formula. Enter your answer using digits.
area
The length of a rectangle can be found using the following formula: length width
The length of a rectangle that has a width of 2.5 cm and an area of 20.5 cm² is __ cm.
Answer: 8.2 cm
Step-by-step explanation:
Area of a rectangle = l x w
[tex]A= 25 cm^{2}[/tex]
[tex]l= ?[/tex]
[tex]w= 2.5 cm[/tex]
[tex]25cm^{2} = l(2.5cm)[/tex]
Rearrange the equation to get Length by itself[tex]\frac{25cm^{2} }{2.5cm}= l[/tex]
[tex]8.2 cm=l[/tex]
Which set of numbers is included in the solution set of the compound inequality?
The set of numbers is included in the solution set of the compound inequality is {-7, 5, 18, 24, 32}
Number line and inequalitiesInequalities are expressions not separated by an equal sign.
From the given number line, the equivalent inequality expression are
x > 22 (22 s excluded since it is an open circle) and x≤ 18 (18 is included since the circle is shaded)
Hence the set of numbers is included in the solution set of the compound inequality is {-7, 5, 18, 24, 32}
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The set of numbers that is been included in the solution set of the compound inequality is [tex]{-7, 5, 18, 24, 32}[/tex]
What is inequalities and set of numbers?The inequality can be referred to as the relationship between two values which are not equal and cannot be separated by an equal sign.
From the open circle, Checking the number set, [tex]x > 22[/tex], 22 cannot be involved, from the shaded circle, x≤ 18 , 18 can be included.
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If fish are sold at 10 for $864. what will be the cost to the nearest dollar of 16 fish
If fish are sold at [tex]10[/tex] for $[tex]864[/tex]. the cost to the nearest dollar of [tex]16[/tex]fish is $ [tex]1382[/tex]
How can we find the cost of the [tex]16[/tex] fish ?
The cost of the selling [tex]10[/tex] fish = $[tex]864[/tex]
So the cost of the [tex]1[/tex] fish is
[tex]= \frac{864}{10} \\=86.4[/tex]
So the cost of the selling [tex]16[/tex] fish
[tex]= 16* 86.4\\=1382 $[/tex]
$[tex]1382[/tex] is the selling cost of [tex]16[/tex] fish.
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what is 23,578 times 39,344
Answer:927652832
Step-by-step explanation:
using long multiplication step by step multiply.
1. Find the length of each side of the triangle if its perimeter is 86cm the sides are. 3a-2, 5a+3, 6a+1
Hello,
3a - 2 + 5a + 3 + 6a + 1 = 86
14a + 2 = 86
14a = 86 - 2
14a = 84
a = 84/14
a = 6
lengths :
3a - 2 = 3 × 6 - 2 = 18 - 2 = 16 cm
5a + 3 = 5 × 6 + 3 = 30 + 3 = 33 cm
6a + 1 = 6 × 6 + 1 = 36 + 1 = 37 cm
The table displays The scores of students on the recent exam. Find the mean of the scores to the nearest 10th.
Answer:
80
Step-by-step explanation:
To find the mean we add up all the numbers and then divide that number by the amount of numbers we added up.
So in this case we added up 65, 70, 75, 80, 85, 90 & 95. This gives us 560. Now we divide 560 by 7 as that is the amount of numbers we added up. This gives us 80 which means the answer is 80.
I hope this helped! :)
determine which two of the three given triangles are similar. Find the scale factor for the pair.
Since the ratio of their similar sides are equal hence the triangles are similar
Scale factorsTwo figures are are known to be similar if the ratio of their similar sides are equal to a constant known as the scale factor.
For the triangles given, take the ratio of the sides;
12/2 = 6
30/5 = 6
36/6 = 6
Since the ratio of their similar sides are equal hence the triangles are similar
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pls help me on this one :((
Answer:
The answer is B) b
Step-by-step explanation:
According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.
So d+(a+b)/2=d+b
(a+b)/2=b
a+b=2b
a=b
hope this helps <3
Tom has x bags of apples. he buys 8 times more and sells 12. write the amount he has left as an algebraic expression:
Answer:
Step-by-step explanation:
x times 8 +12
8x+x=9x-12
Answer = 9x-12
how to simplify cos(6x) + 1
Select the correct answer from the drop-down menu.
Compare the steps for constructing a perpendicular line to line ABthrough point C using a reflective device and using paper.
.C
A
When using paper to construct the perpendicular line, the paper is folded so that
line ABwill lie exactly on top of each other.
When using a reflective device to construct a line perpendicular to line AB, set one end of the device to coincide with
then swing the other end of the device so the reflection of line ABcoincides with
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and the two sides of
and
The C is perpendicular to AB
When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.
When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB
The question is incomplete hence the complete question is shown here
Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line through point using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line coincides with.
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Answer:
I toke the test, I think the first one is A and B coincide
Step-by-step explanation:
10 points to you if you help me
and brainlyist
Answer:
Step-by-step explanation:
For the frequency distribution, count the numbers that satisfy each category.
79 to 83: 4 (81, 82, 83, 81)
84 to 88: 3 (87, 88, 86)
89 to 93: 7 (92, 93, 93, 93, 90, 90, 91)
94 to 98: 1 (97)
For the historagram, raise the bars at the bottom of the histogram to the numbers above (4, 3, 7, 1; in this order)
A sector has a radius of 12 centimeters and an angle 65 degrees. find its arc length
If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.
Given a sector has a radius of 12 cm and an angle 65 degrees.
We have to calculate arc's length.
We know that arc's length is equal to Θr where Θ is in radians.
We have been given angle in degrees ,so we have to convert degrees in radians.
Angle=65*π/180=13π/36
length of arc =Θr
Putting the values in the formula above :
length =13π/36*12
=13*3.14/3
=40.82/3
=13.6
Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.
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I need help solving this problem
Answer:
Please see the picture below.
Step-by-step explanation:
SOMEONE PLEASE HELP!!! Find the area of the sector. Round your answer to the nearest tenth.
Answer:
398.2 cm^2
Step-by-step explanation:
[tex]\frac{270}{360}[/tex] * [tex]169\pi[/tex] ≈398.2 cm^2
Tas
The three points marked on the graph are
the vertices (corners) of a parallelogram.
10
9
y
8
7
6
5
4
3
2
1
A
1 2
C
2
B
3 4 5 6 7 8 9
10
What are the coordinates of the fourth
vertex?
Answer: (8,10)
Step-by-step explanation:
To go from A to C, we go right 2 units and up 6 units.
So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.
Therefore, the answer is (8, 10).
The expression 40x²-65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the
interior angles of the pentagon are equal, which expression represents the measure of two angles?
Answer:
[tex]16x^2-26x+20[/tex]
Step-by-step explanation:
Since it represents the sum of interior angles, the angle is essentially: [tex]angle + angle + angle + angle + angle[/tex], and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division): [tex]\frac{40x^2-65x+50}{5} = \frac{40x^2}{5} - \frac{65x}{5} + \frac{50}{5}[/tex] this simplifies to: [tex]8x^2-13x+10[/tex]. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2): [tex]2(8x^2-13x+10) = 16x^2-26x+20[/tex] which is the solution
You want to retire on the equivalent of $50,000 per year in today's money. inflation is expected to be 3%. you will retire in 30 years. you will earn 10% annually on your investments from not till retirement and you will earn 8% during retirement (which is expected to last 20 years). how much do you need to save per month in order to fund this retirement?
$662.18 needs to be saved per month.
$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.
i.e. $218,454 is required in retirement years (for 20 years)
Calculating the PV of these payments at 7% is calculated as below.
FV = 0
1/y = 7%
n=20; PMT = 218454; calculate PV = $2,314,305
Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.
FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT = $662.18
So $662.18 needs to be saved per month.
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PLS HELP ASAP
does anyone know these answers
Answer: i know it
Step-by-step explanation: i know
15 athletes are assigned to one of three teams. Each team will have five athletes. The teams are different, so it matters who gets assigned to which team. How many ways are there to assign the athletes to the teams
Answer:
There is only one way to assign the athletes to the team by giving 5 athletes to each team
"The average speed of a vehicle and the distance it covers in a period " Is this a direct proportion
Answer:
Yes
Step-by-step explanation:
As the Average speed increases, the amount of distance covered will increase. As the average speed decreases, the amount of distance traveled will decrease as well over a certain period.
1. If 8x + 4y = 44, what is the value of 6x + 3y?
The value of the expression 6x+3y is 33
System of equationsSystem of equations consists of two or more equation with unknown variables.
Given the equation below
8x + 4y = 44,
Factor out 4 from the equation to have:
4(2x+y) = 44
Divide both sides by 4
2x+y = 11
Determine the value of 6x+3y
6x+3y = 3(2x+y)
6x+3y = 3(11)
6x+3y =33
Hence the value of the expression 6x+3y is 33
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How many minutes are equal to 2 hours 20 minutes? how many minutes are equal to 2 hours 20 minutes? 100 120 220 240 none of these
Answer:
None of the answers
Step-by-step explanation:
There are 60 minutes in one hour so to find the number of minutes in two hrs we multiply 2 by 60: 2*60 = 120 minutes
We then add the extra 20 minutes: 120+20 = 140 minutes
None of the answers include 140 minutes.
Please i really need help
for both qeutions
100 points
Answer:
7. a) slope = 5
7. b) slope = 1/2
8. slope = 1
Step-by-step explanation:
slope = rise/run
rise is the vertical change, run is the horizontal change
7. a)
Pick any two points on your line. (0,0) and (1,5) are easy to work with.
The vertical change between the two points is 5
The horizontal change between those points is 1
so slope = 5/1 = 5
7. b)
Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.
slope = 4/2 = 1/2
8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...
m = slope = (y2-y1) / (x2-x1)
= (8 - 4) / (5 - 1)
= 4/4
= 1
I hope that helped!
HELP! what is this? what’s the answer?!
D. not continuous at X=0
if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0
One cupcake weighs 3 1/2 ounces how many cupcakes are there in 28 ounce package
Using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.
According to the question,
One cupcake weighs 3 1/2 ounces. In order to find the number of cupcakes are there in 28 ounce package.
1 cupcake = 7/2 ounces
x cupcakes = 28 ounces
28 = 7/2 * x [cross multiplication]
x = (28*2)/7 [Using division]
x = 8
Hence, using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.
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Which of the statements below is true for the following set of numbers?42,10,36,51,70,28
Answer:
statement 1(one)
Step-by-step explanation:
Find the polar coordinates in radians from the given rectangular coordinates (-11, -3).
the polar coordinates are:
(√130, 285.3°)
How to find the polar coordinates?For rectangular coordinates (x, y), the polar coordinates are:
[tex]R = \sqrt{x^2 + y^2}[/tex]
For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:
θ = arctan(y/x) + 270°
In this case, we have:
x = -11
y = -3
Then:
[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]
Then the polar coordinates are:
(√130, 285.3°)
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