Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
A small circle is centered inside of a larger circle. The large circle has a radius of 10 inches. The small circle has a radius of 3 inches.
Answer: 126in
Step-by-step explanation:
ftc6yhunum8im
huju7kt6r
5+10=24
g5ghykn
1. Two congruent solids 1 and 2 have the property that 1 ∩ 2 is a right
triangular prism with height√3 and a base that is an equilateral triangle of
side length 2. If the volume of 1 ∪ 2 is 25 units
3
, find the volume of 1.
The volume of solid 1 is 14 cubic units calculated through the formula of volume.
What is volume?Volume is the maximum quantity of space that an object can contain. Volume, which is essentially a measurement of an object's size, is the quantity of space a thing occupies. A three-dimensional object's volume, which is calculated in cubic units, is the quantity of space it takes up. For instance, glass has a cylindrical form and can hold a certain volume of water.
Let V1 and V2 be the volumes of the congruent solids 1 and 2, respectively. The volume of their union is given
V1 U V2 = V1+V2-V1∩V2
We know that V1 ∩ V2 is a right triangular prism with height √3 and a base that is an equilateral triangle of side length 2. So, the volume can be calculated with the following formula:
V1 ∩ V2 = (1/2) * base * height * heightbase
where base is the area of the equilateral triangle, which is √3, height is √3, and height base is 2. Plugging in these values, we get:
V1 ∩ V2 = (1/2) * √3 * √3 * 2 = 3
Now we can use the given information to find the volume of 1:
25 = V1 + V2 - V1 ∩ V2
25 = V1 + V2 - 3
We also know that V1 = V2, since the solids are congruent.
Substituting the following value with the above equation, we get:
25 = 2V1 - 3
28 = 2V1
V1 = 14
Therefore, the volume of solid 1 is 14 cubic units.
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FIND THE MISSING SIDES OF THE KITE
Picture for more info!
Thank you.
The required sides of kite are √61, √61, √221 and √221 units.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.
According to question:In ΔAOD
AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔAOB
AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units
In ΔBOC
BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
In ΔDOC
DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units
Thus, required sides of kite are √61, √61, √221 and √221 units.
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Can yall help me out?
the answer is A: 63 square units
Answer:
A (Im not entirely sure if this is correct)
Step-by-step explanation:
how I got this answer is: I found the area of the two triangles which was 12.5 (because the area of a triangle is 1/2(b*h) and the base is 3 and the height is 7 then you divide that by two) and I added them up to get 21. Then you would multiply 3 by two because a triangle is half of a rectangle and you would do b*h for a rectangle area and then multiply that by 7 ot get 42 and you would add taht to 21 to get 63
which postulate or property can be used to prove that kimball is not between scottsbluff and sidney?
The postulate or property that can be used to prove that Kimball is not between Scottsbluff and Sidney is the Segment Addition Postulate.
The Segment Addition Postulate states that for three points A, B, and C, where B is between A and C,
we have AB + BC = AC.
Given that Kimball is not between Scottsbluff and Sidney, this means that Kimball is either to the west of Scottsbluff or to the east of Sidney.
Let's assume that Kimball is to the west of Scottsbluff.
Then, we can draw the line segment as follows:
Scottsbluff ——————— Kimball ——————— Sidney
Let AB represent the distance between Scottsbluff and Kimball, and let BC represent the distance between Kimball and Sidney. According to the Segment Addition Postulate, AB + BC = AC, where AC is the distance between Scottsbluff and Sidney.
However, if we draw the line segment from Scottsbluff to Sidney without Kimball, we can see that the distance between the two points will always be shorter than the sum of the distances from Scottsbluff to Kimball and from Kimball to Sidney.
This implies that if Kimball is not between Scottsbluff and Sidney, then it is not possible for the segment addition postulate to hold true for the three points.
Therefore, we can use the segment addition postulate to prove that Kimball is not between Scottsbluff and Sidney.
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. in a classroom of 30 students, 3 of the students wear wrist watches. (a) if 14 students are selected with replacement, what is the probability that exactly 2 of them wear wrist watches? (b) if 14 students are selected without replacement,
Probability of
=0.0403.
The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.
The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.
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Which of the following equations have x-intercepts at (2,0) and (4,0)? Check all that apply.
what is $510,451 rounded to the nearest 1,000 dolllars?
Answer:
$510,000
Step-by-step explanation:
Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.
Remember, 4 or less, round down. 5 or more, round up.
Since the hundreds digit is 4, we do not need to round.
We only need to change the rest of the digits to 0.
So, our answer would be $510,000.
A plant in my garden is growing 2/3 of a foot every 3/4 of a month. How much does it grow per month?
The plant is growing 0.89 feet per month.
To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.
Since the plant is growing 2/3 of a foot every 3/4 of a month,
we can first convert the fractions of a foot and a month into decimal equivalents.
2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.
We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).
The equation is 0.67 feet / 0.75 months = 0.89 feet per month.
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Maggie is 15 years older than Bobby. How old is Bobby? 1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 15 years older than Bobby. We have to determine Bobby's age.
Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.
1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.
According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.
So, (x + 15) + 3 = (1.5)(x + 3)
Simplifying the above equation, we get
x + 18 = 1.5x + 4
Now, we will solve for
x.x - 1.5x = -14-0.5x = -14x = 28
Therefore, Bobby is 28 years old now.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.
So, x + 25 = (x + 10) + 15x = 15
Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.
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A bag contains 6 red marbles and 1 blue marble. A marble is taken at random, put to one side, and then another marble is taken at random. What is the probability that at least one of the marbles takes was blue?
Give your answer as a fraction in its simplest form
We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7
To understand probability as a concept, pay attention to the steps below.
Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.
Step 2. As there are two separate events in this scenario, double the probabilities of each.
Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.
In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)
The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).
Step 4. Do the same for red next.
Thus the probability of drawing blue marble = 1/7
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Can someone help me with this aleks
I think the best way to do this is by splitting up the trapezoid into two shapes since it is not a regular trapezoid. We can make a split to form a small right triangle on the left and a regular trapezoid on the right.
Small right triangle on the left:
4 inch side length and 6 inch hypotenuse with the Pythagorean theorem will give us the missing side.
missing side = square root of 6^2-4^2 = [tex]2\sqrt{5}[/tex]
Then the area is [tex]\frac{1}{2}*4*2\sqrt{5}=4\sqrt{5}[/tex]
Regular trapezoid on the right:
Area will be [tex]\frac{6+(17-2\sqrt{5})}{2}*4=46-4\sqrt{5}[/tex]
Summing up the two areas to get the total we have [tex]4\sqrt{5}+46-4\sqrt{5}=46[/tex] in^2.
6x6x6x6x6x6x6 devided by 6x6x6x6x6x6 in indext form
The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.
In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:
(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:
6⁽⁷⁻⁶⁾ = 6¹ = 6.
Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.
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original sample: 84, 71, 79, 96, 87. do the values given constitute a possible bootstrap sample from the original sample?
Yes, the given values constitute a possible bootstrap sample from the original sample.
Bootstrap samples are taken with replacement from the original data set. In other words, it means that each sample consists of a random sample of the same size as the original data set taken from the original data set.
Hence, a given set of values can be a bootstrap sample from the original sample as long as the values are randomly selected from the original sample and with replacement.
The sample is said to be a bootstrap sample from the original data set if it satisfies the following properties:
1. The bootstrap sample must be of the same size as the original data set.
2. Each observation from the original data set must have an equal chance of being selected in each bootstrap sample.3. The bootstrap samples must be independent of each other.
In the given problem, the sample consists of 5 values, namely 84, 71, 79, 96, and 87.
These values can be a bootstrap sample from the original sample as long as the values were randomly selected with replacement from the original sample.
Since the problem does not provide any information on how the sample was obtained, it cannot be determined whether or not it is a bootstrap sample.
Therefore, the answer is that the given values constitute a possible bootstrap sample from the original sample.
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the height of a parallelogram is 10 feet more than the length of the base. if the area of the parallelogram is 1200 square feet, find the length of the base and the height.
The length of the base of a parallelogram is 30 feet and the height is 40 feet.
Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.
We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.
Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.
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how to determine if we can apply the existence and uniquness theorem to guarantee that there is exactly one unique soltuion
The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.
To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.
To illustrate, consider the system of equations:
x1 + x2 - x3 = 2
2x1 - x2 + 2x3 = 8
3x1 + 2x2 - 4x3 = 0
= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.
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how would i graph my question when the x and y intercept is (10,140) when the slope is -14
The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
What is point-slope form?When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).
The y value of the y-intercept point is denoted by the symbol b in the formula.
The general form of a linear equation is y-y1=m(x-x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
So, in the given situation:
The point-slope form is: y = mx + b
Then y is y and b is the x value and m is the slope.
Now, insert values as follows:
y = mx + b
140 = -14x + 10
Graph the equation as follows:
(Refer to the graph attached below)
Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
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pls help i need this by today
Answer: 131.95 cm
Step-by-step explanation:
The diameter of the semicircle is 42 cm, which means the radius is half of that:
r = d/2 = 42/2 = 21 cm
The circumference of a full circle with radius "r" is given by the formula:
C = 2πr
Since this is a semicircle, we need to divide the circumference by 2:
C/2 = πr
Substituting the value of "r" we found above, we get:
C/2 = π(21)
Simplifying:
C/2 = 21π
C = 2(21π)
C ≈ 131.95
Rounding to the nearest hundredth, we get:
C ≈ 131.95 cm
Therefore, the circumference of the semicircle is approximately 131.95 cm.
There was a girl named Ashley and her friend ava. They decided to go to the park and ava got apples also Ashley brought . Ashley bought 5 times more than ava how much will it be?
For 10 points Easy!
Answer:
the amswer is five apples
Solve for x,
using the secant lines.
6 cm
3 cm
x = [?] cm
X
15 cm
Remember a b = c d
W
Enter
Answer: 3
Step-by-step explanation:
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
Explain about the secant lines?A straight line connecting two points on such a function is known as a secant line. The average change rate or just the slope across two locations can also be used to describe it.
The slope between two points and the average rate of shift in a function among two points are interchangeable terms.
Given data:
AE = 6 cm, AB = 3 cm, ED = x cm, BC = 15 cm
Now,
AD = AE + ED
AD = 6 + x ...eq 1
AC = AB + BC
AC = 3 + 15
AC = 18 ....2
As the given two chords are intersecting internally,
AC x AB = AD x AE
18 x 3 = (6 + x) x 6
6 + x = 18 x 3 / 6
6 + x = 9
x = 3
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
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Complete question:
Solve for x, using the secant lines.
AE = 6 cm, AB = 3 cm,ED = x = [?] cm, BC = 15 cm
Remember a.b = c.d
The diagram is attached.
Rolling-circle replication of plasmids proceeds Choose one: in one direction from a single fixed origin. O in opposite directions from a single fixed origin. in one direction from multiple origin sites. O in opposite directions from multiple origin sites,
Rolling-circle replication of plasmids proceeds in one direction from a single fixed origin
Explanation:
How does Rolling-circle replication of plasmids proceed?Rolling-circle replication of plasmids is a replication mechanism in which the replication process moves in one direction from a single fixed origin. Rolling-circle replication is a process that is often seen in circular plasmid DNA. It is a process that begins with an initiator protein, which is responsible for the nicking of a single DNA strand.The initiation point allows the helix to begin unwinding in one direction.
As the DNA helix unwinds, replication is carried out in a continuous manner, and the helix is wound up behind it. During the replication process, a new strand is synthesized that is attached to the parent strand's 3' end.
Rolling-circle replication, on the other hand, is utilized to produce new plasmids that have a single strand, which can then be employed in other cells for the production of proteins or for research purposes.
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HELPPP
complete the problem by creating two binomials that represent that sides of the shape . Then multiply to get a quadratic equation . Draw a picture to help set up the problem . 6. Albert installs swimming pools . While the pools can come in different sizes, Albert only offers rectangular pools that are always twice as wide as they are long. He also puts a deck around the entire pool, and the deck is always 4ft wide on each side. Write an equation to represent the total area of the pool and deck.
The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.
Describe Binomial?In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.
Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.
Let's start by drawing a diagram to visualize the problem:
___________
| | 4 ft
| _________|_________
| | | |
| | | |
| | | | 2x
| | | |
| |_________|_________ |
| | 4 ft
|__________ |
2w
The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.
The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).
Therefore, the total area of the pool and deck can be represented as:
(2x + 8)(x + 8)
Expanding the expression, we get:
2x² + 24x + 64
So the equation that represents the total area of the pool and deck is:
A(x) = 2x² + 24x + 64
where A(x) is the area of the pool and deck, and x is the length of the pool.
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Given that New Mexico has a population of about 12 people per square miles and
an area of about 120,000 square miles, what is the population of New Mexico
Mark only one oval.
10,000
1,000,000
1,440,000
2,400,000
Answer:
1440000
Step-by-step explanation:
Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.
mira is an unmarried lady her monthly income is rs 55000 with an allowance of 3000 she gets festival expenses equivalent to monthly basic salary of a month and 10% of her salary excluding allowance and festival expenses is deducted as provident fund
Answer:
Mira's monthly income: Rs. 55,000
Allowance: Rs. 3,000
Total monthly income before festival expenses: Rs. 58,000
Festival expenses (equivalent to monthly basic salary): Rs. 55,000
Total monthly income including festival expenses: Rs. 113,000
Amount deducted for provident fund (10% of monthly income excluding allowance and festival expenses):
10% of (Rs. 55,000) = Rs. 5,500
Total monthly deduction for provident fund: Rs. 5,500
Taxable income:
Total monthly income including festival expenses - Total monthly deduction for provident fund = Rs. 107,500
To calculate the annual tax to be paid by Mira, we need to know the income tax rates and tax slabs applicable for the current financial year. Without this information, we cannot provide an accurate answer
the population of toledo, ohio, in the year 2000 was approximately 540,000. assume the population is increasing at a rate of 4.7 % per year. a. write the exponential function that relates the total population, , as a function of , the number of years since 2000.
The exponential function that relates the total population, is [tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex] and the rate at which the population is increasing in the year 2019 is 69114.53.
The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
we know that ,
the population of any city can be modeled in the form of exponential function as follows:
[tex]P(t)=P(0)(1+R)^t[/tex]
where, P(t)=population of the town at any given time t
P(0)=population of the town initially (in the year 2000 for this problem)=540,000
R=rate of increase (=5.1% in the given problem)
substituting the values in eqn(1), we get
[tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex]
as we know that
[tex]\because \frac{d}{dx}(a^x )=a^xln(a)[/tex]
so differentiating w.r.t. we get,
[tex]P'(t)=540,000\left [ 1+(5.1/100) \right ]^t*ln(1+(5.1/100) )\\\\P'(t)=540,000\left [ (105.1/100) \right ]^t*ln(105.1/100)\\\\P'(t)=540,000\left [ (1.051) \right ]^t*ln(1.051)[/tex]
so, the rate at which population is increasing in the year 2019 =
[tex]P'(19)=540,000(1.051)^{19}*ln(1.051)[/tex]
P'(19)= 69114.53.
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Complete question:
The population of Toledo, Ohio, in the year 2000 was approximately 540,000. Assume the population is increasing at a rate of 5.1 % per year.
a. Write the exponential function that relates the total population, P(t), as a function of t, the number of years since 2000. P(t) = =
b. Use part a. to determine the rate at which the population is increasing in t years. Use exact expressions. P'(t) people per year
c. Use part b. to determine the rate at which the population is increasing in the year 2019. Round to the nearest person per year. P'(19) = people per year
Find the missing dimension of the triangle.
Area = 14 ft²
6 ft
b
b = ? ft
help pls I'll mark brainlisest
Martha has read 52 pages of her book. This is
20% of the book. How many pages does the
book have?
I NEED HELP! BRAINLIEST!
Answer: 40/7 or 5.7
Step-by-step explanation:
using angle bisector theorem we get,
x/5 = 8/7
Upon substituting our given values in above equation, we will get:
x/5 X 5 = 8/7 X 5
x = 40/7 or 5.7
Answer:
3.3
Step-by-step explanation:
Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
[tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]
Cross multiply,
x *7 = 5*(8 - x)
7x = 40 - 5x
7x + 5x = 40
12x = 40
[tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]
Find the measures of each of the angles 1-7.
Answer:
1=26°
2=154°
3=26°
4=26°
5=154°
6=154°
7=26°
given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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