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3 years ago

The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series?

Mathematics

2 answers:

JulsSmile [24]3 years ago

8 0

Answer:

b. 390

Step-by-step explanation:

$a_1 =3\\a_n=75\\n=10\\\\use \ the \ arithmetic\ formula \\\\S_n=\frac{n}{2}(a_1+a_n)\\S_1_0=\frac{10}{2} (3+75)\\\\ \\S_1_0= 5 (78)\\\\S_1_0=390\\$

USPshnik [31]3 years ago

3 0

The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1 + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390

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Write an equation for each linear function described. Show your work. The graph of the function passes through the point (2,1),

svp [43]

Step-by-step explanation:

The graph of the function passes through the point (2,1), and

y increases by 4 when x increases by 1.

x y

2 1

3 5

4 9

5 13

6 17

and so on

From the table:

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-1}{3-2}$

$m=4$

As the slope-intercept form of the line is

$y=mx+b$

putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.

$1=\left(4\right)2+b$

$8+b=1$

$8+b-8=1-8$

$b=-7$

So putting $b=-7$ and $m=4$ in the slope-intercept form of the line

$y=\left(4\right)x+\left(-7\right)$

$y=4x-7$

Therefore, the equation for the linear function will be:

$y=4x-7$

8 0

3 years ago

Identify this prism and describe it using the following vocabulary terms base, edge, face, and vertex

ira [324]

Answer:

Could you show more photos of it or is that all your information?

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

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ludmilkaskok [199]

The answers are A and B

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2 years ago

How to find out the volume of a prism

slamgirl [31]

Answer:

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Step-by-step explanation:

1)Write down the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height.

2)Find the length.

3)Find the width.

4)Find the height.

5)Multiply the length, the width, and the height.

6)State your answer in cubic units.

8 0

3 years ago

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A video game store allows customers to rent games for 4.75 each. Customers can also buy a membership for $54 annually, and video

ankoles [38]

Answer:

24 video games

Step-by-step explanation:

Let x represent number of video games.
We have been given that a video game store allows customers to rent games for $4.75 each. So the cost of renting x video games would be 4.75x.

We are also told that customers can also buys a membership for $54 annually, and video games would only cost $2.50 each. The cost of renting x video games after membership would be 2.50x + 54

To find the number of video-games that will cost same for both options, we will equate both expressions as:

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Therefore, a customer would have rent 24 video games in a year in order for the two options to be equal.

3 0

3 years ago