The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).
a) Write down the expression for the sum of the first (n − 1) terms.
b) Find the first term and common difference of the above sequence.
Answers
Answer:
(a).
\(S_{n} = \frac{n}{2} (4n + 20) \\ \\S _{n - 1} = \frac{(n - 1)}{2} (4n - 4 + 20) \\ \\ S _{n - 1} = \frac{(n - 1)}{2} (4n + 16) \\ \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2} \\ \\ { \boxed{S _{n - 1} = {2 {n}^{2} + 6n - 8}}} \\ \)
(b).
from general equation:
\(S _{n - 1} = \frac{(n - 1)}{2} (4n + 16)\)
first term is 4n
common difference:
\(16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = \frac{16}{n - 2} \)
Related Questions
how far did he walk from his starting point to his ending point
Answers
Answer:
not far enough
Step-by-step explanation:
not enough info to answer question. sorry!
In the figure, m1-m22-22 and m23-m24-123. From this, you can conclude that mZTSK-
45.
33.
35.
Answers
The measure of angle TSK is given as follows:
m < TSK = 35º.
How to obtain the measure of angle TSK?On a triangle, the sum of the measures of the internal angles is of 180º.
For triangle TSK, the internal angle measures are given as follows:
m < 1 = 22.m < 3 = 123º.m < TSK.Then the measure of angle TSK is obtained as follows:
m < TSK + 22 + 123 = 180
m < TSK = 180 - 145
m < TSK = 35º.
Meaning that the last option is correct.
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consider the continuous random variable x, which has a uniform distribution over the interval from 40 to 44. the variance of x is approximately . a. 46 b. 1.333 c. 1.155 d. 0.333
Answers
Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.
The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:
Var(x) = (b-a)^2 / 12
For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:
Var(x) = (44 - 40)^2 / 12 = 1.155
Therefore, the variance of 'x' is approximately 1.155
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plesae helpsonnnnn okkkkk
Answers
Answer:
the first one at the top left
How would you explain 0 (prime and composite wise)?
Answers
Answer: 0 = NOTHING
Step-by-step explanation:
The image point of A after a translation left 3 units and down 1 unit is the point
B(−6,3). Determine the coordinates of the pre-image point A.
Answers
Answer:
(-3, 4)
Step-by-step explanation:
First, add 3 to point B's x coordinate:
-6 + 3 = -3
Then, add 1 to the y coordinate:
3 + 1
= 4
So, the coordinates of pre image point A are (-3, 4)
Determine the nature of the solution(s) of
5w2 – 2w= -4
A- one real, rational solution
B- two real, irrational solutions
C- two imaginary solutions
D- two real, rational solutions
Answers
Answer:
Step-by-step explanation:
This is a quadratic equation. We'll find the discriminant, but must first rewrite this equation in standard form:
5w2 – 2w + 4 = -4 + 4, or 5w^2 - 2w + 4 = 0
The coefficients of the w terms are {5, -2, 4}
and so the discriminant b^2 - 4ac is 4 - 4(5)(20) = -396
Because the discriminant is negative, we know that there will be two unequal, complex solutions.
Find the STANDARD FORM equation of a line with y-intercept=2 that passes through the point (2,4) SHOW ALL WORK.
Answers
To solve this problem it's easier to first find the y-intercept form instead of the standard one, and then re-arrange it in the standard form. The y-intercept form is given below:
\(y=m\cdot x+b\)Where "m" is the slope of the line and "b" is the y-intercept. The problem already informed us of the value of "b", therefore we can use the known point to find the value of "m".
\(\begin{gathered} y=m\cdot x+2 \\ 4=m\cdot2+2 \\ m\cdot2=4-2 \\ m\cdot2=2 \\ m=\frac{2}{2}=1 \end{gathered}\)We now have the slope-intercept line as shown below:
\(y=x+2\)We need to re-arrange it in the standard form, which is shown below:
\(A\cdot x+B\cdot x=C\)Where A,B and C are constants. So we need to isolate the two variables, x and y, on the left side of the equation.
\(-x+y=2\)The volume of a rectangular prism can be computed using the formula V = lwh.
What is the width of a prism that has a volume of 1664 cubic cm a length of 16 cm and a height of 8 cm?
11 cm
13 cm
26 cm
768 cm
Answers
Answer:
13cm
Step-by-step explanation:
substitute values we have into the formula:
1664 = 16 x w x 8
rearrange:
1664/16×8 = w
which equals 13
Answer:
13
Step-by-step explanation: just took the test :)
Brady wants to purchase a skateboard that costs $245. So far, he has saved $98 and plans to save
an additional $25 per week.
What is the minimum number of weeks that Brady will be able to purchase the skateboard? Justify
your answer.
Answers
Answer:
five almost 6 weeks
Step-by-step explanation:
brady is saving up to 245 but he already has 98 which means he needs to save 147 more dollars. Brady is making 25 a week so if you divide 147 by 25 you get 5.88 so in 6 weeks he can have a new skateboard with a couple extra doll hairs.
Can someone please help?
Answers
9514 1404 393
Answer:
x > 3 : bothx < 3 : g onlyx = 3 : f onlyx ≠ 3 : g onlyStep-by-step explanation:
The attached number lines show the domains of each function.
x > 3 — both number lines are included
x < 3 — only the g(x) domain is included
x = 3 — only the f(x) domain is included
x ≠ 3 — only the g(x) domain is included in the entire region
Jug A contains 6/7 as much water as Jug B.Jug C contains 3/5 as much water as Jug A.Find the ratio of the volume of water in Jug B to the volume of water as Jug C.
Answers
The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.
Let's assume the volume of water in Jug B is x.
According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.
Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].
To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:
(x) / [(3/5) * (6/7) * x]
Simplifying the expression, we get:
x / (18/35 * x)
The x values cancel out, leaving us with:
1 / (18/35)
To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:
1 * (35/18)
The final ratio is:
35/18
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What is the slope of a line graphed below?
Answers
Answer:
Undefined
Step-by-step explanation:
The slope of a horizontal line is zero. The slope of a vertical line is undefined.
Given the following, determine the set (B n C)'.
U= {x|x EN and x < 10}
B = {x|x EN and x is even and x< 10}
C = {x|x E N and x < 10}
Answers
Answer:
Step-by-step explanation:
U={x|x∈N and x<10}
or U={1,2,3,4,5,6,7,8,9}
B={x|x∈N and x is even and x<10}
or
B={2,4,6,8}
C={x|x∈N and x<10}
or
C={1,2,3,4,5,6,7,8,9}
(B∩C)={2,4,6,8}
(B∩C)'={1,3,5,7,9}
The triangles are similar what is the value of x
Answers
Answer: 16
Step-by-step explanation:
To get from 3 to 12, you multiply by 4
To get from 5 to 20, you multiply by 4
So you just multiply 4 by 4 to get x
Answer:
x = 16
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
\(\frac{x}{4}\) = \(\frac{20}{5}\) = 4 ( multiply both sides by 4 to clear the fraction )
x = 16
The investigation phase of the SDLC involves specification of the objectives, constraints, andscope of the project. a. True b. False
Answers
It is true that the investigation phase of the SDLC involves specification of the objectives, constraints, andscope of the project
A software life cycle model, often known as a process model, is a visual and diagrammatic depiction of the software life cycle.
A life cycle model shows all the procedures needed to move a software product through each stage of its life cycle. It also records the framework in which these techniques are to be applied.
The entry and departure criteria for a stage cannot be identified without a software life cycle model. Software project managers find it challenging to track the project's development without the use of software life cycle models.
The Systems Development Life Cycle's Implementation phase is the stage that takes the longest and costs the most money (SDLC)
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Pilar has 40 shells in her collection. She goes to the beach. She collects 6 more shells in the morning and 3 more shells in the afternoon. What is the percent change in Pilar's shell collection from the beginning of the day to the end? Show your work.
Answers
The percent change in Pilar's shell collection from the beginning of the day to the end is, 22.5%
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Pilar has 40 shells in her collection.
She collects 6 more shells in the morning and 3 more shells in the afternoon.
The percent change in Pilar's shell collection from the beginning of the day to the end = ?
At the beginning of the day, Pilar has 40 shells.
In the morning, she collects 6 more shells, bringing her total to
= 40 + 6
= 46 shells.
Then, in the afternoon, she collects 3 more shells, bringing her total to
=46 + 3
= 49 shells.
To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:
percent change = (final value - initial value) / initial value * 100%
Plugging in the values we have:
percent change = (49 - 40) / 40 x 100%
percent change = 9 / 40 x 100%
percent change = 22.5%
Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.
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How many tiles are there in figure 0?
Answers
Answer:
40 is the answer
friend me
The cash register subtracts $2.00 from a $10 Coffee Cafe gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation.
Answers
The equation of the line in the slope-intercept form is: y = -2.00 x + 10.
The slope and provided point are both in the equation for the straight line.
The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.
y-y₁ = m(x-x₁)
It is the necessary equation for a line in the form of a point-slope.
That gift card to the Coffee Café has been provided. = $10
Medium coffee = $2.00
customers
The quantity of coffees a consumer can purchase can be represented using a linear equation.
Slope formula
m = (8 - 10)/(1 - 0)
m = -2
Now consider the line's point-slope shape.
y-y₁ = m(x-x₁)
( y - 10) = -2.00 ( x - 0)
y = -2.00 x + 10
The slope: m = - 2.00
The equation of the line: y = -2.00 x + 10
The y-intercept is 10
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Use calculus to find the area A of the triangle with the given vertices. (0, 6), (2, −3), (3, 4)
Answers
The area of the triangle with the given vertices is 11.5 square units.
Define the area of triangle by vertices?The area of a triangle can be calculated using the coordinates of its vertices using the following formula.
To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:
A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2
Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:
A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2
A = (0 - 4 + 27)/2
A = 23/2
A = 11.5
Therefore, the area of the triangle with the given vertices is 11.5 square units.
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A car travel 275 miles in 5 hours . At this rate how many miles will the bus travel in 8 hours?
Answers
==================================================
Explanation:
Let's find the speed or rate of the car
distance = rate*time
rate = distance/time
rate = (275 miles)/(5 hours)
rate = 55 mph
If the bus traveled this same speed, and did so for 8 hours, then...
distance = rate*time
distance = (55 mph)*(8 hours)
distance = 440 miles
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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More people leave Anytown, AL each year than move into it. The population over the past 20 years is shown in the table. Use technology to find an equation that models the exponential decline. Report the rate of decline below, rounding to the nearest hundredth.
Year Population
2000 30,000
2005 27,000
2010 25,500
2015 24,000
2020 22,400
Answers
The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
Let's suppose the equation that models the exponential decline is: y=a(bˣ).
From the data given, we can calculate the value of a and b:
a = 46348587109809610
b = 0.9861
y = 46348587109809610(0.9861)ˣ
Therefore, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
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Write 4.9 as a percentage
Answers
Answer:
490% i believe
Step-by-step explanation:
What lengths are possible for pieces cut from the 27-cm piece of string? Select all that apply. A. 2 cm B. 7 cm C. 5 cm D. 3 cm E. 9 cm F. 27 cm G. 18 cm H. 1 cm
Answers
Answer:
D, E, F, and H
Step-by-step explanation:
D. 27/3=9
E. 27/9=3
F. 27/27=1
H. 27/1=27
Answer: D,E,F, and H
Step-by-step explanation:
1, 3, 9, and 27 are the multiples of 27 itself
It can’t be 2 because it’s not an even number
It can’t be 7 because the closest number that is a multiple of 7 is 28 and it’s one over
It can’t be 5 because it doesn’t end in 5 or 0
it can’t be 18 because 18 + 18 equals 36 and that is 9 over the original number
On which number line are -6 and it’s opposite shown?
Answers
Answer:
2nd Number Line.
Step-by-step explanation:
-6 is going to be left of 0 on the number line.
The opposite of -6, or the absolute value of 6, is 6 (positive).
6 is going to be right of 0 on the number line.
Answer: number line number 2
Step-by-step explanation:
Marquis started at an elevation of 3000 feet and hiked down a mountain at a constant rate. His elevation decreased 500 feet per hour.
Graph the relationship between Marquis’ elevation and time as he hiked down the mountain.
Answers
Answer:
if u divide it then slop it u will get your answer
Step-by-step explanation:
need help asap please please please please
Answers
Answer:
What is the question actually asking for?
Step-by-step explanation:
If 12.6cm on the map is equal to 1262km in real life, determine the unit scale of the map
Answers
Answer:
1unit scale on map is equal to 100.16 km in real life
Step-by-step explanation:
since in map 12.cm =1262km in real life
1cm=(1262/12.6) km
therefore it gives us 100.158km which is approximately 100.16 km .
equations : 2x + y = -4
-3y = 2x + 12
Answers
Step-by-step explanation:
2x + y = -4
-3y = 2x + 12
convert to regular line equations, when we have only y on one side :
y = -2x - 4
y = -2/3 x - 12/3 = -2/3 x - 4
remember, the general line equation is
y = ax + b
a is the slope (y coordinate change / x coordinate change). and b is the y-intercept (the y value when x = 0).
that means, both lines have the same y-intercept : y = -4
and that means only F is the right representation of the 2 lines.