Answer:
11
Step-by-step explanation:
Distance formula is square root of (x2-x1)^2+(y2-y1)^2
square root of (6-(-5))^2+(7-7)^2
square root of (11)^2+(0)^2
square root of 121+0
square root of 121
11
distance is 11
A biker travels down the street at 15 m/s. It
takes 60 seconds to travel to the end of the
street. How long was the street?
The street was 900m long when the speed is 15m/s and, the time is 60 seconds.
What is meant by distance, speed, and time?To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.
Distance divided by time equals speed. Distance = time * speed
To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.
Given,
Speed of the biker who travels down the street=15m/s
Time taken=60seconds
Distance=?
We know that,
Distance=Speed× Time
Distance=15×60
Distance=900m
Therefore, the street was 900m long
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What is the product of (4i-5)(4i+5)
The product of (4i-5)(4i+5) is -41.
What are complex numbers?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.
Here, we have
Given function
= (4i-5) (4i+5)
After applying the product rule, we get
= 16i² + 20i - 20i - 25
= 16i² - 25
after putting i² value, we get
= 16(-1) - 25
= -41
Hence, the product of (4i-5)(4i+5) is -41.
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ind the perimeter or circumference and area of each igure. Round to the nearest tenth. 4. 6. 2.5 cm 14 yd 2 cm 3.5 cm 3 cm 5. 7. 3 cm 4 ft 5 cm 4 cm
For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.
For figure 5, The circumference is 8π ft. and the area is 16π square ft.
For figure 6, The perimeter is 56 yards and the area is 196 square yards.
For figure 7, The perimeter is 12 cm and the area is 6 square cm.
What is the perimeter?
Perimeter is the distance measured around the edge of any geometrical shape.
The perimeter of a square having side "a" is = 4 ×a.
The perimeter of a triangle having sides "a", "b", and "c" is = a+b+c.
What is the Circumference of a circle?
In geometry, the circumference is the perimeter of a circle.
To find the circumference of a circle, we can use the formula.
Circumference of a circle = 2×π×r
Where "r" is the radius of a circle.
What is the Area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
What is the Area of a triangle?
The area of a triangle is defined as the space enclosed within the three given sides of a triangle.
The formula for finding the area of a triangle for a given height "h" and base "b" is
Area of a Triangle = [tex]\frac{1}{2} *b *h[/tex]
What is the area of a square?
The area of a square is defined as the space occupied by the square.
To find the area of a square having side "a" is
Area of a Square = (a)²
For figure 4,
The sides of the given triangle are 2.5 cm, 3 cm, and 3.5 cm.
The height of the triangle is given as 2 cm.
Then, the perimeter of a triangle = 2.5 + 3 + 3.5
= 9 cm.
and the area of a triangle [tex]=\frac{1}{2}*3.5*2[/tex]
= 3.5 square cm.
For figure 5,
The radius of the given circle is 4 ft.
so, the Circumference of a circle = 2×π×r
= 2×π×4
= 8π ft.
and the area of the circle = π×r²
= π×(4)²
= 16π square ft.
For figure 6,
The side of the given square is 14 yd.
so, the perimeter of a square = 4×side
= 4×14
= 56 yards.
and the area of a square = (side)²
= (14)²
= 196 square yards.
For figure 7,
The sides are 3 cm, 5 cm, and 4 cm.
so, the perimeter of a triangle = 3+5+4
= 12 cm.
The height of a triangle is 3 cm and the base is 4 cm.
and the area of a triangle = [tex]\frac{1}{2}[/tex] × h × b
= [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 square cm.
Hence,
For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.
For figure 5, The circumference is 8π ft. and the area is 16π square ft.
For figure 6, The perimeter is 56 yards and the area is 196 square yards.
For figure 7, The perimeter is 12 cm and the area is 6 square cm.
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Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the intercepts and then
plot the intercepts to create the graph. Label the intercepts, as well as the axis on the graph.
2x+3y=6
The slope and the intercepts of the graph are determined.
Given:
the equation is :
2x+3y=6
we first find the slope of the equation:
m = -a/b
m = -2/3
now solve the intercepts:
to find x intercept, substitute in 0 for y and solve for x.
⇒ 2x+3y=6
⇒ 2x+3(0)=6
⇒ 2x+0=6
⇒ 2x=6
⇒ x=6/2
⇒ x=3
hence we get (3,0)
now, to find y intercept, substitute in 0 for x and solve for y.
⇒ 2x+3y=6
⇒ 2(0)+3y=6
⇒ 0+3y=6
⇒ 3y=6
⇒ y=6/3
⇒ y=2
hence we get (0,2) as the intercepts.
Therefore we plot the required graph.
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Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer:
360 of 10%
360 x 10/100
36
now, 360 - 36 = 324
therefore, 324 students attended haley elementry this yr.
can somebody please solve this if you send picture please send good quality
Solve each system by substitution.
4x + y = 19
6x + 7y=1
Step-by-step explanation:
that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.
finally we use one of the original equations to solve for the second variable.
4x + y = 19
so, that gives us
y = 19 - 4x
we use that now in the second equation :
6x + 7(19 - 4x) = 1
6x + 133 - 28x = 1
-22x + 133 = 1
-22x = -132
22x = 132
x = 6
now, let's use e.g.
4x + y = 19
4×6 + y = 19
24 + y = 19
y = -5
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.
The given quadratic equation is : 8x² + 16x + 3 = 0
Comparing this equation with ax² + bx + c = 0 we get :
a = 8 , b = 16 and c = 3
Now we will use the quadratic formula:
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.
[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]
The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.
Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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The length and width of a rectangle that maximises the enclosed area are 162.5 yards. The maximum area is 26,406.25 square yards.
In the given question we have to find the maximum area of the rectangular area.
A farmer with 650 meters of fencing wants to enclose a rectangle plot that border on a river.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 650
Divide by 2 on both side we get
x+y = 325................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 325-x.
Now putting the value of y
A = x(325-x)
A = 325x-x^2
On differentiating
dA/dx = 325-2x
Putting dA/dx=0
325-2x=0
Subtract 325 on both side we get
-2x= -325
Divide by -2 on both side we get
x = 162.5 yards
Now putting the value of x in the y=325-x
y=325-162.5
y=162.5 yards
So the maximum area is
A= 162.5*162.5
A= 26,406.25 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 162.5 yards. 26,406.25 square yards is the maximum area.
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Find the value of k so that the system of equation has no solution
kx + 6y = 6
y = 2/3x - 4
The value of k so that the system of equation has no solution is k = -4
How to find the value of k so that the system of equation has no solution?Since we have the system of equations
kx + 6y = 6
y = 2/3x - 4
For the system of equations to have no solution, the determinant coefficient matrix must be zero.
Re-arranging the equations, we have
kx + 6y = 6
-2/3x + y = - 4
So, the coefficient matrix is
[tex]\left[\begin{array}{ccc}k&6\\-2/3&1\end{array}\right][/tex]
So, the determinant D = k × 1 - (-2/3) × 6
= k + 2/3 × 6
= k + 2 × 2
= k + 4
Since the determinant must be zero for the system of equations to have no solution, we have that
D = 0
k + 4 = 0
k = -4
So, the value of k = -4
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1. in an experiment in which a six-sided dice is rolled twice, what is the probability that 4-dots side appears in at least one roll?
Answer:
11/36 = 0,305556 = 30,5556%
Step-by-step explanation:
5/6 * 5/6 = 25/36
36/36 - 25/36 = 11/36
The equation of the trend line is y = -0.36x + 12.6. Use the equation of the trend line to predict the wind chill for a wind speed of 58 mi/h. Round your answer to the nearest degree. The wind chill at 58 mi/h is °F.
Answer: -8
Step-by-step explanation:
Assuming that [tex]x[/tex] is the wind speed and [tex]y[/tex] is the wind chill, we can set [tex]x=58[/tex].
[tex]y=-0.36(58)+12.6 \approx -8[/tex]
Factor the polynomial by factoring out the Greatest Common Factor
The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
We are given an algebraic expression:
18y^4 + 24y^3 + 6y^2
We need to factorize by factoring out the Greatest Common Factor.
In the given algebraic expression, we can see that;
6 is the Greatest Common Factor of 18, 24, and 6.
y^2 is the Greatest Common Factor of y^4, y^3 and y^2.
So, we will take the common 6y^2 from the given expression;
18y^4 + 24y^3 + 6y^2
= 6y^2 (3y^2 + 4y + 1)
So, option A is correct.
Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
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Write the function whose graph is the graph of y = x2, but is shifted to the left 2 units.
The function whose graph is shifted 2 units to the left is y = (x + 2)² .
In the question ,
it is given that the equation is given as y = x² .
we know that when the function y = x² is shifted " a units " to the left , the shifted function becomes y = (x + a)² ,
we have to find the equation of the graph that is shifted 2 units to the left ,
So , the value of a is 2 ,
and the equation becomes
y = (x + 2)²
so , the equation is y = (x + 2)² .
the graph is shown below .
Therefore, The function whose graph is shifted 2 units to the left is y = (x + 2)² .
The given question is incomplete , the complete question is
Write the function whose graph is the graph of y = x², but is shifted to the left 2 units ?
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the product of two numbers is 432.if GCF of the numbers is 12 then the greater number is ?
.i need the steps the answer is 36, Please help
The greater factor of 432, if 12 is the greatest common factor between the two factors is 36
What is greatest common factor?The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.
The factors of 432 are 36,12, 24 ,18,4,108
But the two factors of 432 that has a multiple of 12 is 12 and 36
12× 36 = 432
The factors of 12 = 1,2,3,4,6,12
The factors of 36 = 1,2,3,4,6,9,12,18,36
the common factors are ; 1,2,3,4,6 and 12
therefore the greatest common factor = 12
since the GCF between 12 and 36 is 12, the second number will be 36
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Bobby bought 3 T-shirts at the mall
and a pair of pants for $16 at the
clothing store. All together he spent $28
for the clothes. How much was each
shirt?
Answer: $4
Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12
we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.
We can check the answer by combining the price of the shirts (12)
with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.
Answer:
Each shirt was 4 dollars.
Step-by-step explanation:
28 - 16 = 12. 12 divided by 3 = 4.
A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the dividend 3 years later? Round to the nearest cent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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Question 5 of 10
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
PLEASE PLEASE HELP NOW!!!!!
Givin: logam=x and logan=y
Prove: logamn=logam+logan
Drag the statements and reasons into the boxes to correctly complete the proof.
Answer:
2. ax=m and ay=n
4. mn=a(x+y)
6. power property of logarithms.
I took the quiz.
k12
i took the quiz this is the right answers
how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
Given that;
We need to get 3 letter passwords using a through z by two case;
(a) If repetition is allowed
(b) If repetition is not allowed
Case (a): If repetition is allowed.
The total number of letters from a through z are 26
⇒ The total number of 3 letter passwords made are;
= 26³
= 26 * 26 * 26
= 17576
If repetition is allowed then the required passwords generated are 17576.
Case (b): If repetition is not allowed.
⇒ The total number of 3 letter passwords made are;
= 26 * 25 * 24
= 15600
If repetition is not allowed then the required passwords generated are 15600.
Therefore,
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
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Zachary purchased a computer for $1200 on a payment plan.6 months after he purchased the computer, his balance was $420. 8 months after he purchased the computer, his balance was $160. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is: y = -130x + 1200.
How to find the equation?Month Balance
0 1200
6 420
8 160
Hence,
m = (y2 - y1)/(x2 - x1)
First coordinate:
m = (420 - 1200)/(6 - 0)
m = -780 /6
m = -130
Second coordinate;
m = (160 - 420)/(8 - 6)
m = -260/2
m = -130
The formula for equation in slope intercept is
y = mx + c
where;
m = slope
c = y-intercept
So, equation is;
y = -130x + 1200
Therefore the equation is y = -130x + 1200.
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Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
A probablity experiment is conducted in which the sample space of the experiment is S= (5. 6, 7, 8,9, 10, 11, 12, 13, 14, 15. 16}, event F={8,9,10,11,12,13), And event G = {12, 13, 14, 15} Assume that each outcome is equally likely. List the outcomes in F For G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G.
A. For G= {__}
(Use a comma to separate answers as needed)
Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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Hayden and Jamie completed 20 math problems together. Jamie completed 2 more than twice the number that Hayden completed. Let p represent the number of math problems Hayden completed.Write an equation that can be used to find the number of math problems that Jamie completed.
Answer:
[tex]p+p+2=20[/tex]
Step-by-step explanation:
This is what my math teacher told us, so I don't know try this.
Step-by-step explanation:
p + j = 20
j = 2p + 2 --> -2p + j = 2
[tex] \binom{1 \: 1}{ - 2 \: 1} \: \binom{20}{2} = \binom{p}{j} [/tex]
What is (-81.7)+346.2 Pls show ur work
Answer: 264.5
Step-by-step explanation:
(-81.7) + 346.2
346.2 - 81.7 = 264.5
Which equation show the relationship between the number of
hours, x, and the number of dogs groomed, y?
y = 15x
y = 5x
y = 30x
y=3x
The relation that can be formed by obersving the Cartesian Plane is y = 5x
What is Co-ordinate Geometry?
The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in a m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.
Solution:
By analysing the given Cartesian Plane
it can be observed that the rate of change of y with respect to x
is 5 times
Therefore, the relation that can be formed by obersving the Cartesian Plane is y = 5x
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greta is opening a savings account. she starts with 100$ and plans to add 50$ each week. write an equation she can use to calculate the amount of money she will have after any number of weeks. how much money will she have after 1 year?
Money she will have after 52 weeks = rs.2,700
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Unit rate of change here is =
⇒ Unit rate of change here is =
⇒ Unit rate of change here is = 50%
Part B
Equation to calculate the amount of money Greta will have after any number of weeks = ?
Money after 'x' number of weeks =
⇒ Money after 'x' number of weeks =
Part C
Money Greta will have after 1 year= ?
In a year there are 52 weeks
So, putting x = 52 in the solution of Part B
⇒ Money after 52 weeks =
⇒ Money after 52 weeks =
⇒ Money after 52 weeks = 2,700
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Write an equation for the transformation of y=x; vertical by a factor of 1/10
The equation the function after the transformation is g(x) = x/10
How to determine the transformation of the function?The equation of the function is given as
y = x
Express as a function
f(x) = x
The sequence of transformations is given as follows:
Vertically stretched by a factor of 1/10
When the above transformations are combined, we have:
Vertically stretched by a factor of 4: g(x) = 1/10f(x)
So, we have
g(x) = 1/10f(x)
Substitute x for f(x)
So, we have
g(x) = 1/10 * x
Evaluate
g(x) = x/10
Hence, the function g(x) is g(x) = x/10
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find the slope of each line
Answer:
A. 5/3
Step-by-step explanation:
The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point 3 units to the left.
We can model this using rise/run
Rise = 5
Run = 3
5/3
Write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13,
The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1
How to find nth term of arithmetic sequence?Arithmetic sequence can be represented with the formula as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..
a = 4
d = 7 - 4 = 3
Therefore,
aₙ = 4 + (n - 1)3
aₙ = 4 + 3n - 3
aₙ = 3n + 4 - 3
aₙ = 3n + 1
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