3,471,738 this is the answer
What’s 2 + 2 + 5 + 69 + 89. This will definitely help me out.
Answer:
167
Hope this helps you out
Answer:
167
Step-by-step explanation:
Break it into steps.
2+2+5 = 9
69 + 9 = 78
78 + 89 = 167
Hope this helps.
Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is assigned two riders). How many ways can you do this?
There are 120 ways in which 5 riders and 5 horses can be arranged.
We have,
5 riders and 5 horses,
Now,
We know that,
Now,
Using the arrangement formula of Permutation,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
So,
For n = 5,
And,
r = 5
As we have,
n = r,
So,
Now,
Using the above-mentioned formula of arrangement,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
Now,
Substituting values,
We get,
[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]
We get,
The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,
So,
There are 120 ways to arrange horses for riders.
Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.
Learn more about arrangements here
https://brainly.com/question/15032503
#SPJ4
URGENT!!!!!!
A researcher orders a broth of 8.8% glucose for her lab. However, she needs a stronger broth, one that is 13.8% glucose. Fortunately, she has 69.7 liters of 39.4% glucose broth in the stock room. How much 13.8% glucose broth can she make? Round your answer to the nearest tenth of a liter.
Answer:426.6
Step-by-step explanation:
.138 x =.088(x - 69.7) + .394(69.7)
.138 x - .088x = 69.7(.394 - .088)
.05x = 21.3282
/
x = 426.564
This rounds to x = 426.6
Give me brainliestWhich term describes the set of all possible input values for a function? OA. Range O B. Output O C. Domain O D. Input
Domain refers to the term which best describes the set of all possible input values for a function and is therefore denoted as option C.
What is Domain?These are all the values which go into a function which is defined and is denoted as the sign below:
dom · ( f ).
They are also among the values which form the independent variables in this type of context while on the other hand, the output is referred to as the range.
These set of values are usually inputted into the function to check its acceptability and also retrieve the output gotten from the type of operation given. It is also used to identify the independent variable which are present thereby making it the most appropriate choice.
Read more about Domain here https://brainly.com/question/26098895
#SPJ1
Gloria says the two expressions 1/4 (12x + 24) -9x and -6(x + 1) are equivalent. is she correct? Explain how you know
Answer:
No
Step-by-step explanation:
Lets simplify both expressions:
We will start with Gloria's first expression:
[tex]1/4 (12x + 24) -9x[/tex]
Apply distributive property:
[tex](3x + 6) -9x[/tex]
Combine like terms, we are then left with:
[tex]6-6x[/tex]
Now lets simplify the second expression
[tex]-6(x+1)[/tex]
Apply distributive property
[tex]-6x-6[/tex]
Rearrange:
[tex]-6-6x[/tex]
Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.
ASAAP PLEASE PLEASEPLEASE PLEASE
2b^3 -5 b^2 +b+2. R 9/ b-4
Use synthetic division
WORTH 10 POINTS PLEASE HELP!!!!!!!!!!!!!!!
Consider the functions graphed below. A curve a intersects a parabola b at (negative 1, 0 point 5) and a parabola c at (negative 2 point 4, 0 point 3). A diagonal curve d intersects the parabola b at (0 point 5, 0) and (2, 3) and parabola c at (negative 1 point 2, negative 1 point 2). Determine which function has the greatest rate of change over the interval [0, 2]. A. d B. b C. c D.
Answer:
Step-by-step explanation:
The function with the greatest rate of change over the interval [0, 2] is: D. a
Point A is at (3, -8) and point B is at (7, 3). Point M is the midpoint of point A and point B.
The midpoint of point A and point B is (5, -2.5)
How to determine the midpoint?The coordinates are given as:
A = (3, -8)
B = (7, -3)
The midpoint is calculated as:
(x, y) = 0.5 * (x1 + x2, y1 + y2)
So, we have:
(x, y) = 0.5 * (3 + 7, -8 + 3)
This gives
(x, y) = 0.5 * (10, -5)
Evaluate
(x, y) = (5, -2.5)
Hence, the midpoint of point A and point B is (5, -2.5)
Read more about midpoints at:
https://brainly.com/question/5566419
#SPJ1
Find the exact value of sin 5pi/4
The exact value of sin 5π/4 is 0. 0677
How to find the value
It is important to note that π = 3. 142
Let's find sin 5π
Substitute the value
sin 5π = sin (5 × 3. 142) = sin 15. 71
= [tex]\frac{sin 15. 71}{4}[/tex]
Find the sine of the number
= [tex]\frac{0. 27076}{4}[/tex]
= [tex]0. 0677[/tex]
Thus, the exact value of sin 5π/4 is 0. 0677
Learn more about trigonometric ratio here:
https://brainly.com/question/24349828
#SPJ1
Answer:
- sqrt2/2
Step-by-step explanation:
PLEASE HELP IM STUCK
Answer:
-3
Step-by-step explanation:
look at the hint: slope (most call it gradient) = change in y/change in x
so you take 2 x and y variables and subtract
15 - 9 = 6 ← change in y
0 - 2 = -2 ← change in x
slope (gradient) = 6/-2
slope (gradient) = -3
| 9. The distance between Town A and Town B was 108 km. A car and a van left Town A at 12 00 for Town B. On reaching Town B, the car returned to Town A by the same route. When the two vehicles met, the distance that the car and the van had travelled was in the ratio 7:5. The average speed of the van was 60 km/h. Calculate
a) the time at which the two vehicles met, and
b) the average speed of the car in km/h.
Someone please helppp
Answer:
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
Step-by-step explanation:
A -----------------------z------------B
Left Speed(km/h) Time
Car: 12PM X
Van: 12PM 60
Car/Van
DistanceCar AB + z
DistanceVan Az
Ratio: (AB+z)/Az = 7/5
Time until both meet = T (in hours)
Distance Car: xT
Distance Van: 60T
====
xT = AB + z
60T = Az
---
(xT/60T)= (7/5)
x = 60(7/5)
x = 84 km/h
=====
Time for car to reach B is: time (hr) = 108 km/(84 km/h)
time = 1.286 hours
Distance for at 1.289 hours is: distance (km) = (60 km/h)*(1.286 h)
distance = 77.14 km
At 1.286 hours, the car reverses direction. The van is (108 km - 77.14 km) or 30.86 km away.
Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours. The sum will be 30.86 km when they meet, at time of T.
Car Distance + Van Distance = 30.86 km
T(84 km/h) + t(60 km)
They meet when they are 0 km apart, which can be modeled with the following equation:
Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.
Let t be the time after 1.286 hours that both vehicles meet/collide.
t*(60 km/h) + t(84 km/h) = 30.86 km
t(60+84) = 30.86 km
t(144 km/h) = 30.86 km
t = 0.2143 hr
Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.
=================
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
==============
CHECK
Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?
Car distance is (1.5 hr)(84 km/h) = 126 km
Van distance is (1.5 hr)(60 km/h) = 90.0 km
Ratio is 126/90 or 1.4
Ratio of 7/5 is 1.4
YES
Under his cell phone plan, Liam pays a flat cost of $69.50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Liam can use while staying within his budget.
Using a linear function, the inequality is given by: 69.5 + 5x < 90.
The solution is: x < 4.1.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
The y-intercept is the flat cost of $69.50.The slope is the cost per gigabyte of $5.Hence the cost of using x gigabytes is:
C(x) = 69.5 + 5x.
The cost has to be under 90, hence the inequality is:
C(x) < 90
69.5 + 5x < 90.
Then the solution is:
5x < 90 - 69.5.
x < 20.5/5
x < 4.1.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Answer:
Inequality: 5x+35<50
Answer: x<3
Step-by-step explanation:
PLEASE HELP IM STUCK
Hello, the solution of the problem is in this photo.
If the graph of the line falls from left to right, then the slope is negative.
The stem-and-leaf plot shows the points scored by Jason in nine basketball games.
Stem Leaves
1: 0 2 9
2: 3 6 6 7
3: 4
4: 0
What is the outlier of the data set?
A - 40
B - 26
C - 23
D - 10
Considering the given stem-and-leaf plot, the outlier is given by:
A - 40
What is an stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
Outliers are usually the lowest or the highest value in the data-set. In this problem:
The lowest value is 10, but the second lowest is 12, which is close to 10.The highest value is 40, but the second lowest is 34, which is farther to 40 than 12 is to 10, hence 40 is an outlier.More can be learned about stem-and-leaf plots at https://brainly.com/question/27683035
#SPJ1
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
(x + 2y ) 2
The expansion of the expression (x + 2y)² is x² + 4xy + 4y².
How to illustrate the information?The given expression is (x + 2y)². The expansion of the expression will be:
(x + 2y)²
= (x + 2y)(x + 2y)
= x² + 2xy + 2xy + 4y².
= x² + 4xy + 4y²
The expansion is x² + 4xy + 4y².
Learn more about functions on:
brainly.com/question/723406
#SPJ1
he function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
The true statements are (b), (d) and (e)
At 2 hours, the traveler is 725 miles from home.At 3 hours, the distance is constant, at 875 miles.The total distance from home after 6 hours is 1,062.5 miles.How to determine the times and distances are represented by the function?From the function, we have the following piecewise function and the domains
D(t) = 300t + 125, 0 ≤ t < 2.5
D(t) = 875, 2.5 ≤ t ≤ 3.5
D(t) = 75t + 612.5, 3.5 < t ≤ 6
When t = 2, we use the domain 0 ≤ t < 2.5
So, we have
D(2) = 300 * 2 + 125
Evaluate the product
D(2) = 600 + 125
Evaluate the sum
D(2) = 725 --- this is true
When t = 3, we use the domain 2.5 ≤ t ≤ 3.5
So, we have
D(t) = 875
This gives
D(3) = 875 -- this is true
When t = 6, we use the domain 3.5 < t ≤ 6
So, we have
D(t) = 75t + 612.5
This gives
D(6) = 75* 6 + 612.5
Evaluate the product
D(6) = 450 + 612.5
Evaluate the sum
D(6) = 1062.5 --- this is true
Hence, the true statements are (b), (d) and (e)
Read more about piecewise functions at:
https://brainly.com/question/19030976
#SPJ1
Complete question
Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
Answer:
At 2 hours, the traveler is 725 miles from home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5 miles.
Step-by-step explanation:
Please help ASAP!! Conner and Jana are multiplying (3⁵6⁸)(3⁹6¹⁰).
Conner's Work: (3⁵6⁸)(3⁹6¹⁰) = 3⁵ + ⁹ 6⁸ + ¹⁰ = 3¹⁴6¹⁸
Jana's Work: (3⁵6⁸)(3⁹6¹⁰) = 3⁵⋅⁹ 6⁸⋅¹⁰ = 3⁴⁵6⁸⁰
Is either of them correct? Explain your reasoning. (i do think jana is incorrect but im not sure how to answer for conner)
Answer:
Step-by-step explanation:
Write it out in expanded form and you will see why Connor is correct.
3^5 means 3x3x3x3x3
6^8 means 6x6x6x6x6x6x6x6
3^9 means 3x3x3x3x3x3x3x3x3
6^10 means 6x6x6x6x6x6x6x6x6x6
These numbers are all multiplied together, so how many of each number do we have?
3x3x3x3x3x6x6x6x6x6x6x6x6x3x3x3x3x3x3x3x3x3x6x6x6x6x6x6x6x6x6x6
3^14 6^18
What is the slope of the line through (3,2) and (-3,4)?
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 3, 4 )
m = [tex]\frac{4-2}{-3-3}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
[tex]\small\mathbb\green{slope=M= \frac{y2 - y1}{x2 - x1} = \frac{4 - ( - 2)}{3 - 3} \: = \frac{6}{0} \: = ∞} [/tex]
Ivan began to prove the law of sines using the diagram and equations below.
Triangle A B C is shown. A perpendicular bisector is drawn from point C to point D on side B A to form a right angle. The length of the perpendicular bisector is h, the length of C B is a, the length of C A is b, and the length of B A is c.
sin(A) = h/b, so b sin(A) = h.
sin(B) = h/a, so a sin(B) = h.
Therefore, b sin(A) = a sin(B).
Which equation is equivalent to the equation
b sin(A) = a sin(B)?
StartFraction a Over sine (uppercase B) EndFraction = StartFraction b Over sine (uppercase A) EndFraction
StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction
StartFraction sine (uppercase A) Over sine (uppercase B) EndFraction = StartFraction b Over a EndFraction
StartFraction sine (uppercase B) Over a EndFraction = StartFraction sine (uppercase A) Over b EndFraction
An equation which is equivalent to the equation bsin(A) = asin(B) is: B. [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
In this context, we can infer and logically deduce that an equation which is equivalent to the equation bsin(A) = asin(B) is [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex].
Read more on law of sines here: https://brainly.com/question/7922954
#SPJ1
Answer: B
Explanation: sin(A)/a=sin(B)/b
v = u + at
if v=10,t=2,and u=5,find the value of a
Answer:
2.5
Step-by-step explanation:
v = u + at is one of the kinematics equations.
Given v = 10, t = 2, u = 5, we will substitute these values into the equation to find a.
[tex]v = u + at\\10=5+2a\\2a=10-5\\2a = 5\\a = \frac{5}{2} \\= 2.5[/tex]
8. The heights of female students at North Shore High School are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. About how many students in a random sample of 1000 female students could we expect to have heights less than 167.5 cm
The number of students with heights less than 163 cm should be expected is 12.
According to the statement
The mean of height is 175 cm
and the standard deviation of height is 6 cm.
We use normal distribution here with formula
Z= X - μ /σ
Here X is 167.5 and μ is 175 and σ is 6 cm.
Substitute the values in it then
Z = 167.5 - 175 / 6
Z = -1.25
-1.25 have a p value 0.012
Out of 1000 students:
0.012 x 1000 = 12.
So, The number of students with heights less than 163 cm should be expected is 12.
Learn more about DISTRIBUTION here https://brainly.com/question/1094036
#SPJ4
The image point of A after a translation right 4 units and up 2 units is the point B(1,−3). Determine the coordinates of the pre-image point A.
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The point A = (1 - 4, -3 - 2) = (-3, -5)
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
John has a few shoes. mike has 10 shoes more than john. james has 8 less than john. mike has two times of james, how many shoes does john have
Step-by-step explanation:
M=2G
M=J+10
G=J-8
2G=J+10
G=J-8
2(J-8)=J+10
2J-16=J+10
J=26
Divide 2/8 by 9/18 . Input your answer as a reduced fraction.\
Answer:
1/2
Step-by-step explanation:
There is a couple ways of thinking about this. Probably the fastest way is the rule, but the rule is not intuitive. The rule is when you divide fraction, you keep the first fraction the same and then multiple and flip the second fraction.
2/8 x 18/9 = 36/72 To reduce the fraction, could keep dividing the top and the bottom by the same number until it is no longer possible, I could use: 2, 4 3, 9, 18, or 36. If I used 36, I would only have to divide once. 36/16 is 1 and 72/36 is 2 so my answer would be 1/2.
I could have divided the top and bottom by 2 and got 18/36 and then divide by 2 again and get 9/18 and then by 9 and get 1/2. As you can, see there are a lot of option.
The second method is in the picture that I sent you, it is a little more work, but it makes sense.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{2}{8}\div\frac{9}{18} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Simplify \ \frac{2}{8} \ to \ \frac{1}{4}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\div\frac{18}{9} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: a\div \frac{b}{c}=a\times \frac{c}{b}a \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\times\frac{18}{9} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: \frac{a}{b} \times \frac{c}d{}=\frac{ac}{bd}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1\times18}{4\times9} \ \to \ \ Multiply }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ \frac{18}{36}= }}\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{2} }} \end{gathered}$}} \end{gathered}$}[/tex]
The table below shows all of the possible outcomes for rolling two six-sided number cubes. A table with 36 possible outcomes. There are 9 desired outcomes. What is the probability of rolling an even number first and an odd number second? StartFraction 1 over 9 EndFraction StartFraction 1 over 6 EndFraction One-fourth One-half Mark this and return Save and Exit
The probability of rolling an even number first and an odd number second is; One Fourth
How to find the probability of rolling a number?As two cubes are 6 sided, the total number of possibilities as seen in the attached table are;
6 * 6 = 36 possible numbers
Now in those possibilities, the first number will be even and the second number will be odd. From the the table, such possible pairs are,
(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (6,1), (6,3), (6,5)
Therefore, we can see we have a total of 9 sets with the combination of first number even and second number odd. So, the probability of rolling with this combination will be; 9/36 = 1/4
Read more about Rolling Probability at; https://brainly.com/question/14192140
#SPJ1
Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
The example on direct variation is illustrated below based on the information given.
How to illustrate the direct variation?An example will be:
When x = 2, y = 10. Find the value of y when x is 6.
In this case, this will be calculated thus:
y = kx
10 = 2k
k = 10/2
k = 5
Since y = kx.
y = 5 × 6
y = 30
The value of y is 30.
Learn more about variation on:
brainly.com/question/25215474
#SPJ1
Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button.
A) Sample size of compound event = 25
B) New Sample size = 36
What is Compound event?
A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.
An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.
Given,
Number of buttons in a container = 5
Lucas picks one button, replaces it and then picks another.
Therefore,
Sample size of the compound event
n = 5[tex]\times[/tex]5
n = 25
Now, one more button is added in the container and in total there are 6 buttons.
Lucas repeats the same process again and hence,
Sample size of the new compound event will be,
n = 6[tex]\times[/tex]6
n = 36
Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is ___ Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____
To know more about compound event
https://brainly.com/question/12314211
#SPJ4
answer the given questions please!
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ?
Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4)
A.
The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
B.
Both the reflection and dilation preserve the side lengths and angles of triangle .
C.
Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
D.
The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles.
Answer:
A. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.
ApplicationThe described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.
The appropriate description is that of choice A.
*Find the formula of the series 1+2²+3²+4²+....+n²*
The formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
What are series?
In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.
We will find the formula as shown as below:
Let [tex]S=1+2^2+3^2+4^2+................+n^2[/tex]
We know [tex](n+1)^3=n^3+3n^2+3n+1[/tex]
[tex](1+1)^3=1^3+3(1)^2+3(1)+1[/tex]
[tex](2+1)^3=2^3+3(2)^2+3(2)+1[/tex]
[tex](3+1)^3=3^3+3(3)^2+3(3)+1[/tex]
.
.
[tex](n+1)^3=n^3+3(n)^2+3(n)+1[/tex]
On adding
[tex]2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)[/tex]
[tex]2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)[/tex]
[tex](n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]2n^3+6n^2+6n=6S+3n^2+3n+2n[/tex]
[tex]6S=2n^3+3n^2+n[/tex]
[tex]6S=2n^2(n+1)+n(n+1)[/tex]
[tex]6S=(n+1)(2n^2+n)[/tex]
[tex]6S=n(n+1)(2n+1)[/tex]
[tex]S=\frac{n(n+1)(2n+1)}{6}[/tex]
Hence, the formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
Learn more about Series here:
https://brainly.com/question/24643676
#SPJ1