1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nostrana [21]
3 years ago
15

Use sigma notation to represent the sum of the first seven terms of the following sequence: 4, 10, 16, … the summation from n eq

uals 1 to 7 of negative 4 plus 6 times n the summation from n equals 1 to 7 of 4 plus 6 times n the summation from n equals 1 to 7 of 2 plus 6 times n the summation from n equals 1 to 7 of negative 2 plus 6 times n
Mathematics
1 answer:
Dominik [7]3 years ago
6 0

\bf 4~~,~~\stackrel{4+6}{10}~~,~~\stackrel{10+6}{16}~~,~~...~\hspace{10em}\stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=4\\ d = 6 \end{cases} \implies a_n=4+(n-1)6 \\\\\\ a_n=4-6+6n\implies a_n=6n-2~\hfill \displaystyle\boxed{\sum\limits_{n = 1}^{7}~6n-2}

You might be interested in
Nine cyclists were each asked the distance in miles they biked last week.
Ivahew [28]

Answer:

Its A or the first option

Step-by-step explanation:

good luck

4 0
3 years ago
A sound wave travels through iron at a rate of 5120\,\dfrac{\text{m}}{\text{s}}5120 s m ​ 5120, start fraction, start text, m, e
klio [65]

Answer:

18432 km/h

Step-by-step explanation:

It is given that a sound wave travels through iron at a rate of 5120 m/s.

We know that

1 km = 1000 m

1 hour = 60 minutes

1 minutes = 60 second

Using these conversions we get

1 m = 0.001 km

1 hour  = 3600 second

5120\text{ m/s }=5120\times 0.001\times 3600\text{ km/h}

5120\text{ m/s }=18432\text{ km/h}

Therefore, the sound wave travels through iron at a rate of 18432 km/h.

6 0
3 years ago
Three boxes have a total weight of 510 pounds. box a weighs twice as much as box
soldi70 [24.7K]
Work shown above! Box a is 240 lbs Box b is 120 and Box c is 150 lbs hope this helps c:

3 0
3 years ago
what is the coordinate of the vertex of the parabola y-2=1/12(x+10) a. ( 10,-2) b. (-10,2) c. (-2,10) d. (2.-10)
solniwko [45]

Answer:

y-a= c(x-b)^2

With the vertex V= (b,a)

We see that b = -10 and a = 2 and then the vertes wuld be:

V= (-10,2)

And the best option is:

b. (-10,2)

Step-by-step explanation:

For this problem we have the following function:

y-2 = \frac{1}{2} (x+10)

And if we compare this expression with the general expression for a parabola given by:

y-a= c(x-b)^2

With the vertex V= (b,a)

We see that b = -10 and a = 2 and then the vertes wuld be:

V= (-10,2)

And the best option is:

b. (-10,2)

4 0
3 years ago
The perimeter of a rectangle is 20.2 CM and it's area is 24.4 cm squared what is its length and width
erma4kov [3.2K]

Answer:

Length of Rectangle = 4 cm    And

Width of Rectangle = 1.9 cm      

Step-by-step explanation:

Given as :

The perimeter of rectangle = 20.2 cm

The area of rectangle is 24.4 cm

Let the length be L

And width be w

Now Area of rectangle = Length × width  

Or,  24.4 = L × W

And Perimeter = 2 (Length + Width ) = 2 (L + W )

Or,   20.2         = 2(L + W )

Or , L + W = 10.1 cm                   ............ 1

Now, (L - W )²  = (L + W)² -4 LW

Or,   (L - W )²  = ( 10.1)² -4 (24.4)

I.e    (L - W )² = 4.41

Or , L - W = 2.1 cm                    .............. 2

SO , From 1 and 2

( L + W) + (L - W) = 10.1 cm - 2.1 cm

Or, 2L = 8

∴  Length = 4 cm

Again , Width = 4 cm - 2.1 cm = 1.9 cm

Hence   Length of Rectangle = 4 cm    And

             Width of Rectangle = 1.9 cm       Answer

6 0
3 years ago
Other questions:
  • What is the scientific notation for 568 billion?
    9·1 answer
  • The rectangle below has an area of x^2-16 meters and the width of x+4 meters what expression represents the length of the rectan
    7·1 answer
  • Which of the transformations resulted in image Point A'?
    8·1 answer
  • 1) 9f - 2 - 8f<br> 2) -8 (-2-5z) + 7<br> 3) 8r - r<br> 4) 2-8k-6k<br> 5) (-2r-6)<br> 6) b+8b
    8·2 answers
  • Schools, peers, and co-workers are __________ because they influence or shape our self-concept, attitudes, and behaviors.
    12·2 answers
  • The sum of two mumbers is 66 and the difference is 10. What are the numbers?
    7·1 answer
  • PLEASE HELP Point P is plotted on the coordinate grid. If point Sis 10 units to the left of point P what are the coordinates of
    13·1 answer
  • Is y= 1/4x-2 parallel <br>or not?​
    5·1 answer
  • Use properties of operations to write an equivalent expression by combining like terms.
    14·2 answers
  • My little brother spent $5 on comic books and magazines. He bought 4 items. If comic books
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!