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Allisa [31]
3 years ago
14

What is the sum of a 56-term arithmetic sequence where the first term is 6 and the last term is 391?

Mathematics
2 answers:
Sati [7]3 years ago
7 0
S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\a_1=6;\ n=56;\ a_{56}=391\\\\subtitute\\\\S_{56}=\dfrac{6+391}{2}\cdot56=\dfrac{397}{2}\cdot56=397\cdot28=11,116
klio [65]3 years ago
4 0

Answer:

The sum of 56 term is 11,116

B is correct.

Step-by-step explanation:

Given:

First term , a=6

Last term l=391

n=56

Formula: Sum of nth term of Arithmetic series.

Sum=\dfrac{n}{2}(a+l)

Substitute the value of a, l and n into formula.

Sum=\dfrac{56}{2}(6+391)

Sum=11,116

Hence, The sum of 56 term is 11,116

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Step-by-step explanation:

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3 years ago
You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane repre
natima [27]

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

ZY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

Z(0, 5) = (x_1, y_1)

Y(15, 5) = (x_2, y_2)

ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2}

AB = \sqrt{(15)^2 + (0)^2}

AB = \sqrt{225 + 0} = \sqrt{225}

AB = 15

Distance between X(15, 20) and Y(15, 5):

XY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

X(15, 20) = (x_1, y_1)

Y(15, 5) = (x_2, y_2)

XY = \sqrt{(15 - 15)^2 + (5 - 20)^2}

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3 years ago
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Step-by-step explanation:

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Solve each triangle using the information provided. If necessary, round to the<br> nearest tenth.
Goryan [66]

Answer:

1) B = 66.5° c = 10.9

Step-by-step explanation:

I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.

For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:

cos23.5 = ¹⁰⁄c

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I hope this helps you with the other 3 questions.

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